Patent Publication Number: US-2022236236-A1

Title: Systems and methods for diagnostics for biological disorders associated with periodic variations in metal metabolism

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims priority to U.S. Provisional Patent Application No. 62/858,260, entitled “Systems and Methods for Hair Based Diagnostics for Autism Spectrum Disorders,” filed Jun. 6, 2019, which is hereby incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure generally relates to diagnostics for biological conditions associated with metal metabolism through the analysis of biological samples from subjects tested for such biological conditions. 
     BACKGROUND 
     Metal ions have an important role in many biological processes having structural and functional significance for humans. An imbalanced gain of certain metal ions, either due to the amount of certain metals in nutrition or metabolic dysregulation of certain metals, is associated with many biological conditions. The imbalance includes either an excessive gain of certain metal ions or a lack of certain metal ions. Examples of biological conditions associated with metal metabolism include neurological conditions (e.g., autism spectrum disorder, schizophrenia, or attention-deficit/hyperactivity disorder (ADHD)), neurodegenerative conditions (e.g., amyotrophic lateral sclerosis (ALS), Alzheimer&#39;s disease, Parkinson&#39;s disease, and Huntington&#39;s disease), and some cancers (e.g., pediatric cancer). 
     Recent studies have indicated a connection between autism spectrum disorder and metabolic dysfunctions, in particular metal dysregulation (see, for example, Cheng et al. in “Metabolic Dysfunction Underlying Autism Spectrum Disorder and Potential Treatment Approaches,” Front Mol Neurosci. 10, p. 34, February 2017 and Arora et al. in “Fetal and postnatal metal dysregulation in Autism,” Nat. Commun. 8, p. 15493, June 2017). As another example, recent studies have indicated a connection between neuronal degenerations and biologic rhythms of metal detectable from a hair and/or a tooth of a subject (see, for example, Appenzeller et al. in “Stable Isotope Ratios in Hair and Teeth Reflect Biologic Rhythms,” PLoS ONE 2(7): e636. https://doi.org/10.1371/journal.pone.0000636, April 2017). However, there 
     Given the above background, what is needed in the art are improved systems and methods for accurate diagnosis of biological conditions associated with metal metabolism. In particular, there is a need for biomarkers detectable with non-invasive methods for diagnosis of the biological conditions associated with metal metabolism. 
     SUMMARY 
     Accordingly, there is a demand for accurate methods and systems for the diagnosis of biological conditions associated with metal metabolism, and especially for non-invasive diagnosis. The present disclosure addresses these needs, for example, by providing a biological sample biomarker for diagnosis of biological conditions associated with metal metabolism. The biological sample includes a human biological specimen that includes deposits of certain metals and is associated with growth. Such a biological sample could be a hair shaft, a tooth, and a nail. The non-invasive biomarker of the present disclosure can be used for the diagnosis of young children, even infants younger than one year old. 
     In accordance with some embodiments, a method for evaluating a subject for a first biological condition associated with metal metabolism includes sampling each respective position in a plurality of positions along a reference line on a biological sample associated with metal metabolism of the subject, thereby obtaining a plurality of ion samples. Each ion sample in the plurality of ion samples corresponds to a different position in the plurality of positions, and each position in the plurality of positions represents a different period of growth of the biological sample associated with metal metabolism. The method includes analyzing each ion sample in the plurality of ion samples (e.g., with a mass spectrometer or other spectroscopic methods) thereby obtaining a first dataset that includes a plurality of traces. Each trace in the plurality of traces is a concentration of a corresponding elemental isotope, in a plurality of elemental isotopes, over time collectively determined from the plurality of ion samples. The method includes deriving a second dataset from the plurality of traces that includes a set of features. Each respective feature in the set of features is determined by a variation of a single isotope or a combination of isotopes in the plurality of traces. The method includes inputting the set of features into a trained classifier thereby obtaining a probability from the trained classifier that the subject has the first biological condition associated with metal metabolism. 
     In some embodiments, the plurality of elemental isotopes is selected from the elemental isotopes listed in Table 1. In some embodiments, the plurality of elemental isotopes includes at least 22 elemental isotopes of the elemental isotopes listed in Table 1. 
     In accordance with some embodiments, each feature in the set of features is associated with a single respective trace of the plurality of traces or with two respective traces of the plurality of traces. In some embodiments, the set of features is selected from the features listed in Table 2, and, optionally, the set of features further includes one or more features listed in Table 3. In some embodiments, the set of features includes at least 23 features listed in Table 2. 
     In some embodiments, the first biological condition associated with metal metabolism is selected from the group consisting of autism spectrum disorder (ADS), attention-deficit/hyperactivity disorder (ADHD), amyotrophic lateral sclerosis (ALS), schizophrenia, irritable bowel disease (IBD), pediatric kidney transplant rejection, and pediatric cancer. 
     In some embodiments, evaluating the subject for a first biological condition associated with metal metabolism further includes discriminating between the first biological condition associated with metal metabolism and a second biological condition associated with metal metabolism distinct from the first biological condition associated with metal metabolism. In some embodiments, the first biological condition is autism spectrum disorder and the second biological condition is attention-deficit/hyperactivity disorder. 
     In some embodiments, the subject is a human. In some embodiments, the subject is less than 1 year old, less than 2 years old, less than 3 years old, less than 4 years old or less than 5 years old. 
     In some embodiments, the biological sample associated with metal metabolism of the subject is selected from the group consisting of a hair shaft, a tooth, and a nail. 
     In some embodiments, the method further includes, prior to sampling the hair shaft of the subject, pretreating the hair shaft with a solvent and/or irradiating the hair shaft with a low powered laser to remove any debris from the hair shaft. In some embodiments, the biological sample associated with metal metabolism of the subject is the hair shaft and the reference line corresponds to a longitudinal direction of the hair shaft. In some embodiments, the biological sample associated with metal metabolism of the subject is the tooth and the reference line corresponds to a neonatal line of the tooth on an enamel surface of the tooth. 
     In some embodiments, the method further includes pretreating the biological sample associated with metal metabolism of the subject with a solvent or a surfactant prior to the sampling. In some embodiments, the method further includes irradiating, with a laser, the biological sample associated with metal metabolism of the subject with a low powered laser to remove any debris from the biological sample associated with metal metabolism of the subject prior to the sampling. 
     In some embodiments, the sampling includes irradiating, with a laser, the biological sample associated with metal metabolism of the subject with the laser thereby extracting a plurality of particles from the biological sample associated with metal metabolism of the subject and ionizing the plurality of particles with an inductively coupled plasma mass spectrometer, thereby obtaining the plurality of ion samples. 
     In some embodiments, the plurality of positions is sequenced such that a first position in the plurality of positions along the biological sample associated with metal metabolism of the subject corresponds to a position closest to a tip of the biological sample associated with metal metabolism of the subject. In some embodiments, the plurality of positions includes at least 100, 150, 200, 250, 300, 350, 400, 450, or 500 positions. 
     In some embodiments, each trace in the plurality of traces includes a plurality of data points. Each data point is an instance of the respective position in the plurality of position. 
     In some embodiments, the deriving the second dataset includes removing from the plurality of data points such data points that do not meet a first criteria. The first criteria includes a mean absolute difference between adjacent data points in the plurality of data points being three times a standard deviation of the mean absolute difference between adjacent points. 
     In some embodiments, the concentration of the corresponding elemental isotope corresponds to a relative abundance of the corresponding elemental isotope to a control elemental isotope, the control elemental isotope included in the plurality of ion samples. In some embodiments, the control elemental isotope is sulfur. 
     In some embodiments, the set of features is selected from a mean diagonal length, a determinism, a recurrence time, an entropy, a trapping time, and a laminarity. 
     In some embodiments, the trained classifier computes: 
     
       
         
           
             
               p 
               ⁡ 
               
                 ( 
                 subject 
                 ) 
               
             
             = 
             
               1 
               
                 1 
                 + 
                 
                   e 
                   
                     - 
                     
                       ( 
                       
                         α 
                         + 
                         
                           
                             β 
                             1 
                           
                           ⁢ 
                           
                             x 
                             1 
                           
                         
                         + 
                         … 
                         + 
                         
                           
                             β 
                             k 
                           
                           ⁢ 
                           
                             x 
                             k 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     where p(subject) is the probability that the subject has the first biological condition associated with metal metabolism, e is Euler&#39;s number, α is a calculated parameter associated with the probability that the subject has the biological condition associated with metal metabolism when β 1 x 1 + . . . +β k x k  equals to zero, x 1, . . . , k  corresponds to a value derived for each feature in the set of features, the set of features including features from 1 through k, and β 1, . . . , k  corresponds to a weight parameter associated with each feature in the set of features including features from 1 through k. 
     In some embodiments, the method further includes, in accordance with determining that p(subject) is above a predetermined threshold, deeming the subject to have the first biological condition associated with metal metabolism. 
     In some embodiments, the biological condition associated with metal metabolism is related to a periodic dysregulation of metabolism of a plurality of metals, the plurality of metals corresponding to the plurality of elemental isotopes. 
     In accordance with some embodiments, a device for evaluating a subject for a biological condition associated with metal metabolism comprising one or more processors, and memory storing one or more programs for execution by the one or more processors. The one or more programs include instructions for sampling each respective position in a plurality of positions along a reference line on a biological sample associated with metal metabolism of the subject, thereby obtaining a plurality of ion samples. Each ion sample in the plurality of ion samples corresponds to a different position in the plurality of positions. Each position in the plurality of positions represents a different period of growth of the biological sample associated with metal metabolism. The one or more programs include instructions for analyzing each ion sample in the plurality of ion samples with a mass spectrometer thereby obtaining a first dataset that includes a plurality of traces. Each trace in the plurality of traces being a concentration of a corresponding elemental isotope, in a plurality of elemental isotopes, over time collectively determined from the plurality of ion samples. The one or more programs include instructions for deriving a second dataset from the plurality of traces that includes a set of features, each respective feature in the set of features being determined by a variation of a single isotope or a combination of isotopes in the plurality of traces. The one or more programs include instructions for inputting the set of features into a trained classifier thereby obtaining a probability from the trained classifier that the subject has the biological condition associated with metal metabolism. 
     In accordance with some embodiments, a non-transitory computer readable storage medium embeds one or more computer programs for classification. The one or more computer programs include instructions which, when executed by a computer system, cause the computer system to perform a method for evaluating a subject for a biological condition associated with metal metabolism. The method includes sampling each respective position in a plurality of positions along a reference line on a biological sample associated with metal metabolism of the subject, thereby obtaining a plurality of ion samples. Each ion sample in the plurality of ion samples corresponds to a different position in the plurality of positions, and each position in the plurality of positions represents a different period of growth of the biological sample associated with metal metabolism. The method includes analyzing each ion sample in the plurality of ion samples with a mass spectrometer thereby obtaining a first dataset that includes a plurality of traces. Each trace in the plurality of traces is a concentration of a corresponding elemental isotope, in a plurality of elemental isotopes, over time collectively determined from the plurality of ion samples. The method includes deriving a second dataset from the plurality of traces that includes a set of features. Each respective feature in the set of features is determined by a variation of a single isotope or a combination of isotopes in the plurality of traces. The method includes inputting the set of features into a trained classifier thereby obtaining a probability from the trained classifier that the subject has the first biological condition associated with metal metabolism. 
     In accordance with some embodiments, a classification method is performed at a computer system having one or more processors and memory storing one or more programs for execution by the one or more processors. The classification method is performed for each respective training subject in a plurality of training subjects. A first subset of training subjects in the plurality of training subjects have a first diagnostic status corresponding to having a first biological condition associated with metal metabolism and a second subset of training subjects in the plurality of training subjects have a second diagnostic status corresponding to not having the first biological condition associated with metal metabolism. The classification method includes sampling each respective position in a corresponding plurality of positions of a corresponding reference line on a corresponding biological sample associated with metal metabolism of the respective training subject, thereby obtaining a corresponding plurality of ion samples. Each ion sample in the corresponding plurality of ion samples for a different position in the corresponding plurality of positions. Each position in the corresponding plurality of positions represents a different period of growth of the corresponding biological sample associated with metal metabolism. The classification method includes analyzing each respective ion sample in the corresponding plurality of ion samples with a mass spectrometer thereby obtaining a respective first dataset that includes a corresponding plurality of traces. Each trace in the corresponding plurality of traces is a concentration of a corresponding elemental isotope, in a plurality of elemental isotopes, over time collectively determined from the corresponding plurality of ion samples. The classification method includes deriving a respective second dataset from the corresponding plurality of traces that includes a corresponding set of features. Each respective feature in the corresponding set of features is determined by a variation of a single isotope or a combination of isotopes in the corresponding plurality of traces. The classification method includes training an untrained or partially untrained classifier with (i) the corresponding set of features of each respective second dataset of each training subject in the plurality of training subjects and (ii) the corresponding diagnostic status of each training subject in the plurality of training subjects, selected from among the first diagnostic status and the second diagnostic status, thereby obtaining a trained classifier. The classifier provides an indication as to whether a test subject has the first biological condition associated with metal metabolism based on values for features in a set of features acquired from a biological sample associated with metal metabolism of the test subject. 
     In some embodiments, the trained classifier is a neural network algorithm, a support vector machine algorithm, a decision tree algorithm, an unsupervised clustering model algorithm, a supervised clustering model algorithm, or a regression model. 
     In some embodiments, the trained classifier is multinomial or binomial. In some embodiments, the plurality of elemental isotopes is selected from the elemental isotopes listed in Table 1. 
     In some embodiments, each feature in the set of features is associated with a single respective trace of the plurality of traces or with two respective traces of the plurality of traces. In some embodiments, the set of features is selected from the features listed in Table 2, and, optionally, the set of features further includes one or more features listed in Table 3. 
     In some embodiments, the first biological condition associated with metal metabolism is selected from the group consisting of autism spectrum disorder (ADS), attention-deficit/hyperactivity disorder (ADHD), amyotrophic lateral sclerosis (ALS), schizophrenia, irritable bowel disease (IBD), pediatric kidney transplant rejection, and pediatric cancer. 
     In some embodiments, evaluating the subject for a first biological condition associated with metal metabolism further includes discriminating between the first biological condition associated with metal metabolism and a second biological condition associated with metal metabolism distinct from the first biological condition associated with metal metabolism. In some embodiments, the first biological condition is autism spectrum disorder and the second biological condition is attention-deficit/hyperactivity disorder. 
     In some embodiments, the subject is a human. In some embodiments, the subject is less than 1 year old, less than 2 years old, less than 3 years old, less than 4 years old or less than 5 years old. 
     In some embodiments, the biological sample associated with metal metabolism of the subject is selected from the group consisting of a hair shaft, a tooth, and a nail. 
     In some embodiments, the method further includes, prior to sampling the hair shaft of the subject, pretreating the hair shaft with a solvent and/or irradiating the hair shaft with a low powered laser to remove any debris from the hair shaft. In some embodiments, the biological sample associated with metal metabolism of the subject is the hair shaft and the reference line corresponds to a longitudinal direction of the hair shaft. In some embodiments, the biological sample associated with metal metabolism of the subject is the tooth and the reference line corresponds to a neonatal line of the tooth on an enamel surface of the tooth. 
     In some embodiments, the method further includes pretreating the biological sample associated with metal metabolism of the subject with a solvent or a surfactant prior to the sampling. In some embodiments, the method further includes irradiating the biological sample associated with metal metabolism of the subject with a low powered laser to remove any debris from the biological sample associated with metal metabolism of the subject prior to the sampling. 
     In some embodiments, the sampling includes irradiating, with a laser, the biological sample associated with metal metabolism of the subject with the laser thereby extracting a plurality of particles from the biological sample associated with metal metabolism of the subject and ionizing the plurality of particles with an inductively coupled plasma mass spectrometer, thereby obtaining the plurality of ion samples. 
     In some embodiments, the plurality of positions is sequenced such that a first position in the plurality of positions along the biological sample associated with metal metabolism of the subject corresponds to a position closest to a tip of the biological sample associated with metal metabolism of the subject. In some embodiments, the plurality of positions includes at least 100, 150, 200, 250, 300, 350, 400, 450, or 500 positions. 
     In some embodiments, each trace in the plurality of traces includes a plurality of data points. Each data point is an instance of the respective position in the plurality of position. 
     In some embodiments, the deriving the second dataset includes removing from the plurality of data points such data points that do not meet a first criteria. The first criteria includes a mean absolute difference between adjacent data points in the plurality of data points being three times a standard deviation of the mean absolute difference between adjacent points. 
     In some embodiments, the concentration of the corresponding elemental isotope corresponds to a relative abundance of the corresponding elemental isotope to a control elemental isotope, the control elemental isotope included in the plurality of ion samples. In some embodiments, the control elemental isotope is sulfur. 
     In some embodiments, the set of features is selected from a mean diagonal length, a determinism, a recurrence time, an entropy, a trapping time, and a laminarity. 
     In some embodiments, the trained classifier computes: 
     
       
         
           
             
               p 
               ⁡ 
               
                 ( 
                 subject 
                 ) 
               
             
             = 
             
               1 
               
                 1 
                 + 
                 
                   e 
                   
                     - 
                     
                       ( 
                       
                         α 
                         + 
                         
                           
                             β 
                             1 
                           
                           ⁢ 
                           
                             x 
                             1 
                           
                         
                         + 
                         … 
                         + 
                         
                           
                             β 
                             k 
                           
                           ⁢ 
                           
                             x 
                             k 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     where p(subject) is the probability that the subject has the first biological condition associated with metal metabolism, e is Euler&#39;s number, α is a calculated parameter associated with the probability that the subject has the biological condition associated with metal metabolism when β 1 x 1 + . . . +β k x k  equals to zero, x 1, . . . , k  corresponds to a value derived for each feature in the set of features, the set of features including features from 1 through k, and β 1, . . . , k  corresponds to a weight parameter associated with each feature in the set of features including features from 1 through k. 
     In some embodiments, the method further includes, in accordance with determining that p(subject) is above a predetermined threshold, deeming the subject to have the first biological condition associated with metal metabolism. 
     In some embodiments, the biological condition associated with metal metabolism is related to a periodic dysregulation of metabolism of a plurality of metals, the plurality of metals corresponding to the plurality of elemental isotopes. 
     In accordance with some embodiments, a classification device includes one or more processors and memory storing one or more programs for execution by the one or more processors. The one or more programs includes instructions for performing a classification method. The classification method is performed for each respective training subject in a plurality of training subjects. A first subset of training subjects in the plurality of training subjects have a first diagnostic status corresponding to having a first biological condition associated with metal metabolism and a second subset of training subjects in the plurality of training subjects have a second diagnostic status corresponding to not having the first biological condition associated with metal metabolism. The classification method includes sampling each respective position in a corresponding plurality of positions of a corresponding reference line on a corresponding biological sample associated with metal metabolism of the respective training subject, thereby obtaining a corresponding plurality of ion samples. Each ion sample in the corresponding plurality of ion samples for a different position in the corresponding plurality of positions. Each position in the corresponding plurality of positions represents a different period of growth of the corresponding biological sample associated with metal metabolism. The classification method includes analyzing each respective ion sample in the corresponding plurality of ion samples with a mass spectrometer thereby obtaining a respective first dataset that includes a corresponding plurality of traces. Each trace in the corresponding plurality of traces is a concentration of a corresponding elemental isotope, in a plurality of elemental isotopes, over time collectively determined from the corresponding plurality of ion samples. The classification method includes deriving a respective second dataset from the corresponding plurality of traces that includes a corresponding set of features. Each respective feature in the corresponding set of features is determined by a variation of a single isotope or a combination of isotopes in the corresponding plurality of traces. The classification method includes training an untrained or partially untrained classifier with (i) the corresponding set of features of each respective second dataset of each training subject in the plurality of training subjects and (ii) the corresponding diagnostic status of each training subject in the plurality of training subjects, selected from among the first diagnostic status and the second diagnostic status, thereby obtaining a trained classifier. The classifier provides an indication as to whether a test subject has the first biological condition associated with metal metabolism based on values for features in a set of features acquired from a biological sample associated with metal metabolism of the test subject. 
     In accordance with some embodiments, a non-transitory computer readable storage medium embeds one or more computer programs for classification. The one or more computer programs include instructions which, when executed by a computer system, cause the computer system to perform a classification method. The classification method is performed for each respective training subject in a plurality of training subjects. A first subset of training subjects in the plurality of training subjects have a first diagnostic status corresponding to having a first biological condition associated with metal metabolism and a second subset of training subjects in the plurality of training subjects have a second diagnostic status corresponding to not having the first biological condition associated with metal metabolism. The classification method includes sampling each respective position in a corresponding plurality of positions of a corresponding reference line on a corresponding biological sample associated with metal metabolism of the respective training subject, thereby obtaining a corresponding plurality of ion samples. Each ion sample in the corresponding plurality of ion samples for a different position in the corresponding plurality of positions. Each position in the corresponding plurality of positions represents a different period of growth of the corresponding biological sample associated with metal metabolism. The classification method includes analyzing each respective ion sample in the corresponding plurality of ion samples with a mass spectrometer thereby obtaining a respective first dataset that includes a corresponding plurality of traces. Each trace in the corresponding plurality of traces is a concentration of a corresponding elemental isotope, in a plurality of elemental isotopes, over time collectively determined from the corresponding plurality of ion samples. The classification method includes deriving a respective second dataset from the corresponding plurality of traces that includes a corresponding set of features. Each respective feature in the corresponding set of features is determined by a variation of a single isotope or a combination of isotopes in the corresponding plurality of traces. The classification method includes training an untrained or partially untrained classifier with (i) the corresponding set of features of each respective second dataset of each training subject in the plurality of training subjects and (ii) the corresponding diagnostic status of each training subject in the plurality of training subjects, selected from among the first diagnostic status and the second diagnostic status, thereby obtaining a trained classifier. The classifier provides an indication as to whether a test subject has the first biological condition associated with metal metabolism based on values for features in a set of features acquired from a biological sample associated with metal metabolism of the test subject. 
     As disclosed herein, any embodiment disclosed herein when applicable can be applied to any aspect. 
     Additional aspects and advantages of the present disclosure will become readily apparent to those skilled in this art from the following detailed description, wherein only illustrative embodiments of the present disclosure are shown and described. As will be realized, the present disclosure is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the disclosure. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  illustrates a block diagram of an example computing device, in accordance with some embodiments of the present disclosure. 
         FIG. 2A  provides a flow chart of a method for evaluating a subject for a biological condition, in accordance with some embodiments of the present disclosure. 
         FIG. 2B  provides exemplary illustrations of a hair, a tooth, and a nail sample of a subject, in accordance with some embodiments of the present disclosure. 
         FIG. 2C  provides an exemplary schematic illustration of laser sampling a hair shaft of a subject, in accordance with some embodiments of the present disclosure. 
         FIG. 2D  provides an exemplary illustration of a trace describing a concentration of an elemental isotope over time, in accordance with some embodiments of the present disclosure. 
         FIG. 2E  provides exemplary illustrations of features corresponding to a variation of a single isotope derived from a trace, in accordance with some embodiments of the present disclosure. 
         FIG. 2F  provides an illustration of experimental data for discriminating between an autism spectrum disorder and other neurodevelopmental disorders, in accordance with some embodiments of the present disclosure. In  FIG. 2F , autism spectrum disorder (labeled ASD) cases are contrasted with attention-deficit/hyperactivity disorder (labeled ADHD) cases, subjects diagnosed with comorbid ASD and ADHD diagnoses (labeled CM), and neurotypical subjects (labeled NT) who have received no neurodevelopmental disorder diagnosis. 
         FIGS. 3A-3E  collectively provide a flow chart of processes and features for evaluating a subject for a biological condition, in which optional blocks are indicated with dashed boxes, in accordance with some embodiments of the present disclosure. 
         FIG. 4  provides a flow chart of processes and features for training a classifier to evaluate a subject for a biological condition, in which optional blocks are indicated with dashed boxes, in accordance with some embodiments of the present disclosure. 
         FIGS. 5A, 5B, 5C, and 5D  illustrate experimental Receiver Operating Characteristic (ROC) curves for evaluating autism spectrum disorder, in accordance with some embodiments. 
         FIG. 6  illustrates an ROC curve for evaluating accuracy of the disclosed method for evaluating amyotrophic lateral sclerosis, in accordance with some embodiments. 
         FIG. 7  illustrates an ROC curve for evaluating accuracy of the disclosed method for evaluating schizophrenia, in accordance with some embodiments. 
         FIG. 8  illustrates an ROC curve for evaluating accuracy of the disclosed method for evaluating irritable bowel disorder, in accordance with some embodiments. 
         FIG. 9  illustrates an ROC curve for evaluating accuracy of the disclosed method for evaluating kidney transplant rejection, in accordance with some embodiments. 
         FIG. 10  illustrates an ROC curve for evaluating accuracy of the disclosed method for evaluating pediatric cancer, in accordance with some embodiments. 
     
    
    
     Like reference numerals refer to corresponding parts throughout the several views of the drawings. The drawings are not drawn to scale. 
     DETAILED DESCRIPTION 
     The present disclosure provides systems and methods for evaluating a subject for a biological condition associated with metal metabolism from a biological sample associated with metal metabolism of the subject. In particular, the disclosed methods provide for a biological sample biomarker for that can be obtained from a subject non-invasively. The method can be applied to evaluate subjects of any age, and is especially useful in diagnosis of small children, even infants under 1 year of age, to enable early treatment and intervention. 
     Definitions 
     The terminology used in the present disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the description of the invention and the appended claims, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and/or” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     As used herein, the term “if” may be construed to mean “when” or “upon” or “in response to determining” or “in response to detecting,” depending on the context. Similarly, the phrase “if it is determined” or “if [a stated condition or event] is detected” may be construed to mean “upon determining” or “in response to determining” or “upon detecting [the stated condition or event]” or “in response to detecting [the stated condition or event],” depending on the context. 
     As used herein, a biological condition associated with metal metabolism (also called a metal metabolism disorder) herein refers to a biological condition that is related to, or caused by, a periodic dysregulation of metabolism of certain metals. The periodic dysregulation may be manifested as periodic decrease in an uptake (e.g., deficiency) of one or more metals, as periodic increase in the uptake of one or more metals, or as a combination of periodic decrease and periodic increase in the uptake of the one or more metals. Non-limiting examples of biological conditions associated with metal metabolism include autism spectrum disorder (ADS), attention-deficit/hyperactivity disorder (ADHD), amyotrophic lateral sclerosis (ALS), schizophrenia, kidney transplant rejection, some types of cancer, Alzheimer&#39;s disease, Parkinson&#39;s disease, Huntington&#39;s disease, metabolic disorders (obesity and irritable bowel disease (IBD)), and/or any conditions or disorders associated with metal metabolism. 
     As used herein, a biological sample associated with metal metabolism refers herein to a human biological specimen that includes deposits of certain metals and is associated with growth (e.g., hair, nails, and teeth). The biological samples associated with metal metabolism of the present disclosure have a requirement of expressing growth along a reference line such that abundance of the deposits of certain metals are detectable with respect to time. These biological samples associated with metal metabolism thereby facilitate detection of periodic variations in abundance of the certain metals. In some embodiments, the biological sample associated with metal metabolism includes a hair shaft where a reference line corresponds to a line along the longitudinal direction of the hair shaft. In some embodiments, the biological sample associated with metal metabolism includes a tooth where a reference line corresponds to a neonatal line of the tooth on an enamel surface of the tooth. In some embodiments, the biological sample associated with metal metabolism includes a nail where a reference line corresponds to a line in direction of growth of the nail. For example, the reference line extends from the nail root toward the tip of the nail. 
     As used herein, the term “trained classifier” refers to a model (e.g., a machine learning algorithm, such as logistic regression, neural network, regression, support vector machine, clustering algorithm, decision tree etc.) with specific parameters (weights) and thresholds, ready to be applied to previously unseen samples. 
     As used herein, the term “untrained classifier or partially trained classifier” refers to a model (e.g., a machine learning algorithm, such as logistic regression, neural network, regression, support vector machine, clustering algorithm, decision tree etc.) with at least some unfixed parameters (weights) and thresholds, ready to be trained on a training set in order to optimize and fix the parameters and thresholds. 
     It will also be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first subject could be termed a second subject, and, similarly, a second subject could be termed a first subject, without departing from the scope of the present disclosure. The first subject and the second subject are both subjects, but they are not the same subject. Furthermore, the terms “subject,” “user,” and “patient” are used interchangeably herein. 
     As used herein, the term “subject” refers to a human (e.g., a male human, female human, fetus, pregnant female, child, or the like). In some embodiments, a subject is a male or female of any stage (e.g., a man, a women or a child). 
     As used herein, the term “autism spectrum disorder” refers to a range of neurodevelopmental conditions associated with impairments in social interactions, developmental language and communication skills and repetitive behaviors. For example, standardized criteria for diagnosis of autism spectrum disorder by Centers of Disease Control and Prevention (CDC) includes 1) persistent deficits in social communication and social interaction and 2) restricted, repetitive patterns of behavior, interests, or activities. Autism spectrum disorder includes, for example, autistic disorder (a.k.a. “classic autism”), Asperger&#39;s Syndrome, and Pervasive Developmental Disorder (a.k.a. “atypical” autism). 
     As used herein, the term “recurrence quantification analysis” (“RQA”) refers to a non-linear data analysis that quantifies a number and duration of recurrences in dynamical systems. RQA is used for characterizing a dynamic system&#39;s behavior in a phase space. 
     As used herein, the term “recurrence plot” refers to a graphical visualization of time-dependent periodical structures in an experimental data. 
     As used herein, the term “trace” refers to a time-dependent abundance (or concentration) of an elemental isotope. The trace includes a plurality of data points, where each data point is associated with a temporal measure and an abundance measure. 
     As used herein, the term “feature,” refers to a dynamical periodical feature extracted from a time-dependent abundance trace of an elemental isotope, or a combination of two or more time-dependent abundance traces of elemental isotopes, e.g., by using RQA. 
     As used herein, the term “mean diagonal length” (“MDL”) refers to a critical measure derived from RQA, reflecting a straightforward measurement of an average length of diagonal lines present in a two-dimensional recurrence plot. This measure can be taken as an absolute indicator of the duration of periodic components in a given signal. 
     As used herein, the term “determinism,” which is related to the mean diagonal length, refers to a relative ratio of periodic components to non-periodic components in a recurrence analysis. The determinism indicates an overall periodic content of a given signal. 
     As used herein, the term “recurrence time” (“RT 2 ”) refers to a mean time interval between diagonal elements, i.e. the interval between periodicities. 
     As used herein, the term “entropy” refers to a variability in the distribution of mean diagonal lengths, with low entropy signals exhibiting little complexity in a distribution of periodic components, and high entropy signals exhibiting diversity in short- and long-duration periodicities. 
     As used herein, the term “trapping time” (“TT”) refers to a mean length of laminar (vertical or horizontal) structures in a two-dimensional recurrence plot, which indicate stable states, analogous to how mean diagonal length captures the duration of periodic processes. 
     As used herein, the term “laminarity” refers to an overall measure of signal stability. Laminarity quantifies a ratio of recurrence points belonging to laminar structures against the total frequency of recurrence points. 
     The terminology used herein is for the purpose of describing particular cases only and is not intended to be limiting. As used herein, the singular forms “a,” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. Furthermore, to the extent that the terms “including,” “includes,” “having,” “has,” “with,” or variants thereof are used in either the detailed description and/or the claims, such terms are intended to be inclusive in a manner similar to the term “comprising.” 
     Several aspects are described below with reference to example applications for illustration. It should be understood that numerous specific details, relationships, and methods are set forth to provide a full understanding of the features described herein. One having ordinary skill in the relevant art, however, will readily recognize that the features described herein can be practiced without one or more of the specific details or with other methods. The features described herein are not limited by the illustrated ordering of acts or events, as some acts can occur in different orders and/or concurrently with other acts or events. Furthermore, not all illustrated acts or events are required to implement a methodology in accordance with the features described herein. 
     Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be apparent to one of ordinary skill in the art that the present disclosure may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments. 
     Example System Embodiments. 
     Now that an overview of some aspects of the present disclosure has been provided, details of an exemplary system are now described in conjunction with  FIG. 1   FIG. 1A  illustrates a block diagram of an example computing device  100 , in accordance with some embodiments of the present disclosure. The device  100  in some implementations includes one or more processing units CPU(s)  102  (also referred to as processors), one or more network interfaces  104 , a user interface  106 , a non-persistent memory  111 , a persistent memory  112 , and one or more communication buses  114  for interconnecting these components. The one or more communication buses  114  optionally include circuitry (sometimes called a chipset) that interconnects and controls communications between system components. The non-persistent memory  111  typically includes high-speed random access memory, such as DRAM, SRAM, DDR RAM, ROM, EEPROM, flash memory, whereas the persistent memory  112  typically includes CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, magnetic disk storage devices, optical disk storage devices, flash memory devices, or other non-volatile solid state storage devices. The persistent memory  112  optionally includes one or more storage devices remotely located from the CPU(s)  102 . The persistent memory  112 , and the non-volatile memory device(s) within the non-persistent memory  112 , comprise non-transitory computer readable storage medium. In some implementations, the non-persistent memory  111  or alternatively the non-transitory computer readable storage medium stores the following programs, modules and data structures, or a subset thereof, sometimes in conjunction with the persistent memory  112 :
         an optional operating system  116 , which includes procedures for handling various basic system services and for performing hardware dependent tasks;   an optional network communication module (or instructions)  118  for connecting the system  100  with other devices and/or a communication network  104 ;   an optional classifier training module  120  for training classifiers for evaluating a subject for a biological condition associated with metal metabolism;   an optional data store for datasets for biological samples from training subjects  122  including feature data for one or more training subjects  124 , where the feature data includes a parameter associated with each of features  126 , and diagnostic status  128  (e.g., an indication that a respective training subject has been diagnosed with a biological condition associated with metal metabolism or has not been diagnosed with a biological condition associated with metal metabolism);   an optional classifier validation module  130  for validating classifiers that distinguish the a biological condition associated with metal metabolism;   an optional data store for datasets for biological samples from validation subjects  132 ; and   an optional patient classification module  134  for classifying a subject as having a biological condition associated with metal metabolism, e.g., as trained using classifier training module  120 .       

     In various implementations, one or more of the above identified elements are stored in one or more of the previously mentioned memory devices, and correspond to a set of instructions for performing a function described above. The above identified modules, data, or programs (e.g., sets of instructions) need not be implemented as separate software programs, procedures, datasets, or modules, and thus various subsets of these modules and data may be combined or otherwise re-arranged in various implementations. In some implementations, the non-persistent memory  111  optionally stores a subset of the modules and data structures identified above. Furthermore, in some embodiments, the memory stores additional modules and data structures not described above. In some embodiments, one or more of the above identified elements is stored in a computer system, other than that of visualization system  100 , that is addressable by visualization system  100  so that visualization system  100  may retrieve all or a portion of such data when needed. 
     In some embodiments, the system  100  is connected to, or includes, one or more analytical devices for performing chemical analyzes. For example, the optional network communication module (or instructions)  118  is configured to connect the system  100  with the one or more analytical devices, e.g., via the communication network  104 . In some embodiments, the one or more analytical devices include a laser ablation-inductively coupled-plasma mass spectrometer (LA-ICP-MS). 
     Although  FIG. 1  depicts a “system  100 ,” the figure is intended more as functional description of the various features which may be present in computer systems than as a structural schematic of the implementations described herein. In practice, and as recognized by those of ordinary skill in the art, items shown separately could be combined and some items could be separated. Moreover, although  FIG. 1  depicts certain data and modules in non-persistent memory  111 , some or all of these data and modules may be in persistent memory  112 . 
     Classification Methods. 
     While a system in accordance with the present disclosure has been disclosed with reference to  FIG. 1 , detailed processes and features of a method  200  for evaluating a subject for a biological condition associated with metal metabolism from a biological sample in accordance with the present disclosure is provided in conjunction with  FIGS. 2A-2F . 
     As defined above, a biological sample associated with metal metabolism (also called here “a biological sample”) includes a human biological specimen that with deposits of certain metals and is associated with growth (e.g., hair, nails, and teeth). The biological samples associated with metal metabolism of the present disclosure have a requirement of expressing growth along a reference line such that abundance of the deposits of certain metals are detectable with respect to time. In some embodiments, the biological sample associated with metal metabolism includes a hair shaft where a reference line corresponds to a line along the longitudinal direction of the hair shaft. In some embodiments, the biological sample associated with metal metabolism includes a tooth where a reference line corresponds to a neonatal line of the tooth on an enamel surface of the tooth. In some embodiments, the biological sample associated with metal metabolism includes a nail where a reference line corresponds to a line in direction of growth of the nail. For example, the reference line extends from the nail root toward the tip of the nail. 
     In some embodiments, the method  200  includes obtaining ( 202 ) a biological sample (e.g., a strand of hair including a hair shaft). The subject is a human. In some embodiments, the subject is a child aged equal to or below 5 years (e.g., the child is aged equal to or below 5 years, 4 years, 3 years, 2 years, 1 year, 9 months, 6 months, 3 months, or 1 month). In some embodiments, the subject is an adult.  FIG. 2B  section I provides an exemplary image of a hair sample of a subject including a hair shaft, in accordance with some embodiments of the present disclosure. The hair sample may be simply cut from the subject (e.g., with help of scissors). The method of obtaining the hair sample is therefore non-invasive. The obtained hair sample has a minimum length of 1 cm (e.g., the hair sample is 1 cm, 2 cm, 3 cm, 4 cm, or 5 cm long). The hair sample may include any portion of a hair (e.g., a tip or a portion between the tip and a follicle). In particular, there is no special requirement for the hair sample to include the hair follicle.  FIG. 2B  section II provides an exemplary image of a tooth sample of a subject, in accordance with some embodiments of the present disclosure.  FIG. 2B  section III provides an exemplary image of a nail sample of a subject, in accordance with some embodiments of the present disclosure. In instances of a tooth or a hair, obtaining a biological sample refers to positioning the subject such that the tooth or the nail could be sampled. 
     In some embodiments, the obtained biological sample is pretreated ( 204 ) by washing the biological sample with one or more solvents and/or surfactants and drying. In an instance that the biological sample is a hair, the hair sample is washed in TRITON X-100® and ultrapure metal free water (e.g., MILLI-Q® water) and dried overnight in an oven (e.g., at 60 degrees Celsius). The pretreatment further includes preparing the hair shaft for a measurement by placing the hair shaft on a glass slide (e.g., a microscopic glass slide) with an adhesive film (e.g., a double sided tape). The hair shaft is positioned such that the hair shaft is substantially straight. The glass slide with the hair shaft is then placed into a laser ablation-inductively coupled-plasma mass spectrometer (LA-ICP-MS) for performing analysis ( 206 ). In an instance that the biological sample is a tooth or a nail, a surface of the biological sample is cleaned (e.g., by surfactant, water, or one or more solvents). The subject is positioned in vicinity of a LA-ICP-MS for performing the analysis. 
     In some embodiments, the LA-ICP-MS analyses includes pre-ablating the biological sample to remove surface debris and/or impurities from the biological sample. The pre-ablation is performed using such a low laser energy that it only releases particles on the surface of the biological sample but does not release particles from below the surface of the biological sample. For example, the pre-ablation is performed using a laser wavelength of 193 nm and laser energy below 0.4 J/cm 2  (e.g., the laser energy is 0.4 J/cm 2 , 0.3 J/cm 2 , 0.2 J/cm 2  or 0.1 J/cm 2 ). In some embodiments, the laser energy ranges from 0.2 J/cm 2  to 0.4 J/cm 2 . 
     After pre-ablation, method  200  includes sampling the biological sample with a laser to obtain ion samples ( 208 ) from respective positions along a reference line of the biological sample. As explained above, in an instance of a hair shaft the reference line corresponds to a line along the longitudinal direction of the hair shaft. For example,  FIG. 2B  section A illustrates a hair shaft with reference line  201  along the longitudinal direction of the hair shaft. In an instance of a tooth, the reference line corresponds to a neonatal line of the tooth on an enamel surface of the tooth. For example,  FIG. 2B  section II illustrates tooth  220  including portions of enamel  226  and primary dentine  224 . Reference line  222  corresponds to a neonatal line of tooth  220 . A neonatal line herein refers to a particular band of incremental growth lines on an enamel portion of a tooth. In an instance of a nail, the reference line corresponds to a line in direction of growth of the nail. For example,  FIG. 2B  section II illustrates nail  230  with reference line  232  extending from the nail root toward the tip of the nail. The sampling includes irradiating the biological sample with a laser beam (e.g., laser ablating the hair shaft) and ionizing the plurality of particles with an inductively coupled plasma mass spectrometer. For example, areas  200 A and  200 B in  FIG. 2B  section I correspond to exemplary positions along the hair shaft that are irradiated with a laser during the laser ablation. The mass spectrometer analyzes ( 210 ) the obtained ion samples from each respective position.  FIG. 2C  provides an exemplary schematic illustration of laser sampling a hair shaft of a subject, in accordance with some embodiments of the present disclosure. Laser  202  in  FIG. 2C  irradiates an area  200 C on the hair shaft thereby releasing particles  204 . The particles  204  are ionized by an inductively-coupled-plasma (ICP), and further analyzed by a mass spectrometer (MS). 
     In some embodiments, the laser irradiation is performed using a laser having wavelength 193 nm and laser energy ranging from 0.6 to 1.5 J/cm 2  (e.g., the laser energy is 0.6 J/cm 2 , 0.7 J/cm 2 , 0.8 J/cm 2 , 0.9 J/cm 2 , 1.0 J/cm 2 , 1.1 J/cm 2 , 1.2 J/cm 2 , 1.3 J/cm 2 , 1.4 J/cm 2 , or 1.5 J/cm 2 ). In some embodiments, the laser energy ranges from 0.9 to 1.3 J/cm 2 . In some embodiments, the laser has a beam diameter ranging from 25 micrometers to 35 micrometers (e.g., 25, 27.5, 30, 32.5, or 35 micrometers). In some embodiments, the laser has a beam diameter of 30 micrometers. In an instance of sampling a hair shaft, the laser beam size, wavelength and/or laser energy are adjusted such that the laser sampling ablates most of the hair shaft without releasing any particles from the adhesive film and/or the glass slide holding the hair shaft. 
     The laser irradiation is repeated, and elemental isotope data is collected, sequentially at a plurality of positions along the biological sample (e.g., the areas  200 A and  200 B of the hair shaft in  FIG. 2B  section I). In some embodiments, the plurality of positions along the reference line of the biological sample includes at least 100 positions (e.g., 100, 150, 200, 250, 300, 350, 400, 450, or 500 positions). In some embodiments, the respective positions (e.g., areas  200 A and  200 B in  FIG. 2B  section I) are adjacent to each other. By this method, each area corresponding to a distinct position on the biological sample (e.g., areas  200 A and  200 B) is thereby associated with an abundance of elemental isotopes (e.g., metal isotopes Zn, Fe, Pb, and Mn shown in  FIG. 2C ). In some embodiments, the respective positions are separated by a predefined distance. In some embodiments, the sampling is performed along the reference line of the biological sample starting from a respective position nearest to the tip of the hair (e.g., at a position that corresponds to the youngest age of the subject). In general, the sampling can be performed starting from a respective position nearest to the tip or the root, as long as the direction of the sampling is known and an appropriate trained classifier is used for the analyses. 
     The laser sampling thereby produces sets of data points. Each set of data points corresponds to an abundance (e.g., a concentration) of a respective elemental isotope measured at a plurality of positions along the biological sample. Each position on the reference line of the biological sample corresponds to a specific time of growth of the biological sample. In some embodiments, in an instance of the hair shaft, each position corresponds to approximately 130 min period of hair growth (e.g., the period of hair growth calculated using a 30 micrometer laser beam size and an average rate of hair growth 1 cm per month). By correlating the plurality of positions along the reference line of the biological sample to corresponding time periods of the growth, a first dataset including a plurality of traces is obtained. Each trace includes a time-dependent abundance of a respective elemental isotope measured from the biological sample. 
       FIG. 2D  provides an exemplary illustration of a trace  208 , in accordance with some embodiments of the present disclosure. Each data point in  FIG. 2D  corresponds to an abundance (i.e., count ratio on the y-axis) of a particular elemental isotope measured at a plurality of positions along a biological sample (i.e., laser distance on the bottom x-axis). The distance moved by the laser along the biological sample corresponds to an estimated growth of the biological sample (i.e., biological time), as is illustrated on the top x-axis. For example,  FIG. 2D  illustrates the abundance of a particular elemental isotope measured for a hair along a 1.2 cm (12 000 micrometers) distance. Such distance corresponds to a biological time of approximately 35 days. The biological time is estimated by using an average rate of hair growth (e.g., 1 cm per month). 
     In some embodiments, the plurality of elemental isotopes is selected from the elemental isotopes listed in Table 1. In some embodiments, the plurality of elemental isotopes includes at least 50%, 60%, 70%, 80% or 90% of the isotopes included in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 List of Elemental Isotopes 
               
            
           
           
               
               
               
            
               
                   
                 Elemental Isotope 
                 Element Name 
               
               
                   
                   
               
               
                   
                 Li-7 (Li) 
                 lithium 
               
               
                   
                 Mg-24 (Mg) 
                 magnesium 
               
               
                   
                 Mg-25 (Mg25) 
                 magnesium 
               
               
                   
                 Al-27 (Al) 
                 aluminum 
               
               
                   
                 P-31 (P) 
                 phosphorus 
               
               
                   
                 S-34 (S) 
                 sulfur 
               
               
                   
                 Ca-44 (Ca) 
                 calcium 
               
               
                   
                 Ca-43 (Ca43) 
                 calcium 
               
               
                   
                 Cr-52 (Cr) 
                 chromium 
               
               
                   
                 Mn-55 (Mn) 
                 manganese 
               
               
                   
                 Fe-56 (Fe) 
                 iron 
               
               
                   
                 Co-59 (Co) 
                 cobalt 
               
               
                   
                 Ni-60 (Ni) 
                 nickel 
               
               
                   
                 Cu-63 (Cu) 
                 copper 
               
               
                   
                 Zn-66 (Zn) 
                 zinc 
               
               
                   
                 As-75 (As) 
                 arsenic 
               
               
                   
                 Sr-88 (Sr) 
                 strontium 
               
               
                   
                 Cd-111 (Cd) 
                 cadmium 
               
               
                   
                 Sn-118 (Sn) 
                 tin 
               
               
                   
                 I-127 (I) 
                 iodine 
               
               
                   
                 Ba-138 (Ba) 
                 barium 
               
               
                   
                 Hg-201 (Hg) 
                 mercury 
               
               
                   
                 Pb-208 (Pb) 
                 lead 
               
               
                   
                 Bi-209 (Bi) 
                 bismuth 
               
               
                   
                 Mo-95(Mo) 
                 molybdenum 
               
               
                   
                   
               
            
           
         
       
     
     In some embodiments, the method  200  includes analyzing ( 212 ) the first dataset including the obtained plurality of traces where each trace corresponds to a time-dependent abundance (e.g., a time-dependent concentration) of a respective elemental isotope. In some embodiments, the analyzing the data includes performing customized operations to clean the data ( 214 ). In some embodiments, cleaning the data includes smoothening the data over a time span, and/or removing data points that are higher or lower than a predetermined threshold. In some embodiments, the data analyzing includes removing, from the traces, data points that have a mean absolute difference between adjacent data points that is three times a standard deviation of the mean absolute difference between adjacent points.  FIG. 2D  illustrates an operation to remove data points that are higher than a predetermined threshold. Peaks  210  correspond to data points that have a mean absolute difference between adjacent data points that is more than three times the standard deviation of the mean absolute difference between adjacent points. The peaks  210  are therefore removed from the trace  208 . 
     In some embodiments, the analyzing the data set further includes normalizing each trace against an internal standard. In some embodiments, in an instance where the sample is a hair shaft, the internal standard is sulfur which is the most abundant of the elemental isotopes in hair and therefore can be used as a measure of hair density and/or hardness. However, in practice, any element detected in the samples that is evenly incorporated during the development/growth of a biological sample that does not fluctuate with environmental exposures (e.g., diet) can serve as an internal standard including any of the elements disclosed in the table of the present disclosure. For example, in the case where the sample is a tooth, Bismuth-209 can be used an in internal standard. 
     The method  200  includes performing recurrence quantification analysis (RQA) to analyze the first data set which includes time-dependent traces of elemental isotopes to obtain a set of features that describe dynamical periodical characteristics of the traces. RQA measures variability in the time-dependent traces of elemental isotopes. RQA involves the estimation of features that describe periodic properties in a given waveform, which include the determinism, mean diagonal length, and entropy. Methods and features of RQA are described, for example, by Webber et al. in “ Simpler Methods Do It Better: Success of Recurrence Quantification Analysis as a General Purpose Data Analysis Tool ,” Physics Letters A 373, 3753-3756 (2009) and by Marwan et al. in “ Recurrence Plots for the Analysis of Complex Systems ,” Physics Reports 438, 237-239 (2007), the contents of each of which are herein incorporated by reference in their entirety. In some embodiments, the time-dependent traces of elemental isotopes are analyzed by using other analytical methods known in the art, such as Fourier Transformations, Wavelet Analysis, and Cosinor analysis. Such method can be applied to derive similar metrics, including spectral analysis of frequency components and their associated power. These metrics and associated derivative measures may be used in place of the features derived from RQA to analyze the time-dependent traces of elemental isotopes obtained from biological samples for purposes of predictive classification. 
     The RQA includes construction of recurrence plots ( 216 ) that visualize and analyze dynamical temporal structures in respective obtained traces.  FIG. 2E  provides exemplary illustrations of a variation of an abundance of a single isotope derived from a respective trace, in accordance with some embodiments of the present disclosure. Section I of  FIG. 2E  illustrates a trace corresponding to a time-dependent abundance (or concentration) of copper (Cu) as measured from the hair shaft of the subject. The y-axis illustrates measured abundance of copper, and the x-axis illustrates sequential measurements along a hair shaft, which reflect longitudinal increments of time. Section II of  FIG. 2E  is a phase portrait derived from the trace of Section I. From the one dimensional trace measured from the hair shaft, additional dimensions are computationally derived to embed the trace in a higher dimensional space referred to as a phase portrait, where t refers to the values of the original trace, and dimensions (t+τ) and (t+2τ) are derived from lagging the original time series by interval T. Subsequent analyses are then undertaken on the embedded phase portrait to construct recurrence plots and recurrence quantification analysis. Section III illustrates a recurrence quantification plot of the copper isotope derived from the phase portrait illustrated in Section II. The RQA method examines the interval of delay between states in a given system, with a black point reflecting the temporal interval when a system revisits the same state. Periodic processes, where a system successively reiterates a given pattern of states, will manifest in a recurrence plot as diagonal black lines, whereas periods of stability will manifest as square structures, spurious repetitions as black dots, and, unique events as white space. 
     In some embodiment, the recurrence plots are constructed for traces of a single elemental isotope or a combination of two elemental isotopes (e.g., for elemental isotopes selected from Table 1.) For example,  FIG. 2E  illustrates a recurrence plot of copper isotope. Alternatively, a recurrence plot is constructed to visualize an interactive periodic pattern of two elemental isotopes. In some embodiments, the recurrence plots are constructed for a combination of three or more elemental isotopes. 
     The method  200  further includes analyzing the recurrence plots to obtain ( 218 ) a set of features associated with the recurrence plots. The features, which interchangeably can be termed “rhythmicity features,” or “dynamic features,” provide a quantitative measure describing the periodicity present in the plurality of traces. The features are selected from a mean diagonal length (MDL), determinism (or predictability), recurrence time (RT), entropy, trapping time (TT), and laminarity. Definitions of each of these feature types are provided above in the Definitions section. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Table 2. 
     In some embodiments, the set of features includes all the features listed in Table 2. 
     In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 2. In some embodiments, the features drawn from Table 2 in this manner, are considered to be the “core” features for evaluating a subject for a first biological condition (e.g., autism spectrum disorder, etc.), in accordance with the present disclosure. In some embodiments, the set of features further includes one or more features listed in Table 3 (in addition to the core features). 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 List of features associated with their respective elemental 
               
               
                 isotopes or respective combination of two elemental isotopes. 
               
            
           
           
               
               
               
            
               
                   
                 Feature 
                 Elemental Isotope name 
               
               
                   
                   
               
               
                   
                 Determinism (Determinism_Cd) 
                 Cd 
               
               
                   
                 Determinism (Determinism_Cr) 
                 Cr 
               
               
                   
                 Determinism (Determinism_ZnHg) 
                 ZnHg 
               
               
                   
                 Determinism (Determinism_Cu) 
                 Cu 
               
               
                   
                 Determinism (Determinism_ZnMn) 
                 ZnMn 
               
               
                   
                 Determinism (Determinism_Sr) 
                 Sr 
               
               
                   
                 Entropy (Entropy_As) 
                 As 
               
               
                   
                 Determinism (Determinism_Mg) 
                 Mg 
               
               
                   
                 Entropy (Entropy_Li) 
                 Li 
               
               
                   
                 Determinism (Determinism_ZnCu) 
                 ZnCu 
               
               
                   
                 Entropy (Entropy_ZnCu) 
                 ZnCu 
               
               
                   
                 Mean Diagonal length (MDL_ZnCu) 
                 ZnCu 
               
               
                   
                 Determinism (Determinism_Ca) 
                 Ca 
               
               
                   
                 Determinism (Determinism_Mn) 
                 Mn 
               
               
                   
                 Determinism (Determinism_Ni) 
                 Ni 
               
               
                   
                 Determinism (Determinism_ZnMg) 
                 ZnMg 
               
               
                   
                 Determinism (Determinism_ZnCr) 
                 ZnCr 
               
               
                   
                 Determinism (Determinism_Pb) 
                 Pb 
               
               
                   
                 Determinism (Determinism_ZnNi) 
                 ZnNi 
               
               
                   
                 Determinism (Determinism_ZnSn) 
                 ZnSn 
               
               
                   
                 Determinism (Determinism_Li) 
                 Li 
               
               
                   
                 Determinism (Determinism_Hg) 
                 Hg 
               
               
                   
                 Determinism (Determinism_Fe) 
                 Fe 
               
               
                   
                 Determinism (Determinism_As) 
                 As 
               
               
                   
                 Determinism (Determinism_ZnI) 
                 ZnI 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 List of additional features associated with their respective elemental 
               
               
                 isotopes or respective combination of two elemental isotopes. 
               
            
           
           
               
               
               
            
               
                   
                 Feature 
                 Elemental Isotope name 
               
               
                   
                   
               
               
                   
                 Entropy (Entropy_Ni) 
                 Ni 
               
               
                   
                 Determinism (Determinism_Bi) 
                 Bi 
               
               
                   
                 Laminarity (Laminarity_Li) 
                 Li 
               
               
                   
                 Determinism (Determinism_ZnSr) 
                 ZnSr 
               
               
                   
                 MDL (MDL_As) 
                 As 
               
               
                   
                 Determinism (Determinism_ZnAs) 
                 ZnAs 
               
               
                   
                 Determinism (Determinism_ZnCd) 
                 ZnCd 
               
               
                   
                 Determinism (Determinism_ZnS) 
                 ZnS 
               
               
                   
                 Determinism (Determinism_ZnCa) 
                 ZnCa 
               
               
                   
                 Determinism (Determinism_ZnPb) 
                 ZnPb 
               
               
                   
                 Determinism (Determinism_ZnFe) 
                 ZnFe 
               
               
                   
                 Determinism (Determinism_S) 
                 S 
               
               
                   
                 Entropy (Entropy_Cu) 
                 Cu 
               
               
                   
                 Entropy (Entropy_Sr) 
                 Sr 
               
               
                   
                 Entropy (Entropy_Pb) 
                 Pb 
               
               
                   
                 Entropy (Entropy_Ca) 
                 Ca 
               
               
                   
                 MDL (MDL_Ni) 
                 Ni 
               
               
                   
                 MDL (MDL_Li) 
                 Li 
               
               
                   
                 Entropy (Entropy_P) 
                 P 
               
               
                   
                 Laminarity (Laminarity_As) 
                 As 
               
               
                   
                 Entropy (Entropy_Cr) 
                 Cr 
               
               
                   
                 Laminarity (Laminarity_Mn) 
                 Mn 
               
               
                   
                 Laminarity (Laminarity_Cd) 
                 Cd 
               
               
                   
                 Entropy (Entropy_Co) 
                 Co 
               
               
                   
                 Laminarity (Laminarity_Mg) 
                 Mg 
               
               
                   
                 Entropy (Entropy_Cd) 
                 Cd 
               
               
                   
                 Entropy (Entropy_Mg) 
                 Mg 
               
               
                   
                 TT (TT_Pb) 
                 Pb 
               
               
                   
                 Entropy (Entropy_Sn) 
                 Sn 
               
               
                   
                 Entropy (Entropy_ZnCd) 
                 ZnCd 
               
               
                   
                 TT (TT_P) 
                 P 
               
               
                   
                 Laminarity (Laminarity_Cu) 
                 Cu 
               
               
                   
                 TT (TT_Zn) 
                 Zn 
               
               
                   
                 Laminarity (Laminarity_Sn) 
                 Sn 
               
               
                   
                 MDL (MDL_P) 
                 P 
               
               
                   
                 MDL (MDL_ZnCd) 
                 ZnCd 
               
               
                   
                 Laminarity (Laminarity_Fe) 
                 Fe 
               
               
                   
                 Laminarity (Laminarity_Co) 
                 Co 
               
               
                   
                 MDL (MDL_Pb) 
                 Pb 
               
               
                   
                 TT (TT_As) 
                 As 
               
               
                   
                 MDL (MDL_Sr) 
                 Sr 
               
               
                   
                 MDL (MDL_Cd) 
                 Cd 
               
               
                   
                 MDL (MDL_Ca) 
                 Ca 
               
               
                   
                 Determinism (Determinism_ZnLi) 
                 ZnLi 
               
               
                   
                 MDL (MDL_Cu) 
                 Cu 
               
               
                   
                 Laminarity (Laminarity_Pb) 
                 Pb 
               
               
                   
                 Laminarity (Laminarity_Bi) 
                 Bi 
               
               
                   
                 Entropy (Entropy_Mn) 
                 Mn 
               
               
                   
                 MDL (MDL_Cr) 
                 Cr 
               
               
                   
                 MDL (MDL_Mg) 
                 Mg 
               
               
                   
                 TT (TT_Mn) 
                 Mn 
               
               
                   
                 TT (TT_S) 
                 S 
               
               
                   
                 MDL (MDL_Sn) 
                 Sn 
               
               
                   
                 Determinism (Determinism_ZnAl) 
                 ZnAl 
               
               
                   
                 TT (TT_Mg) 
                 Mg 
               
               
                   
                 MDL (MDL_ZnAs) 
                 ZnAs 
               
               
                   
                 RT2 (RT2_Mn) 
                 Mn 
               
               
                   
                 TT (TT_Li) 
                 Li 
               
               
                   
                 TT (TT_Sr) 
                 Sr 
               
               
                   
                 Entropy (Entropy_ZnMn) 
                 ZnMn 
               
               
                   
                 MDL (MDL_Co) 
                 Co 
               
               
                   
                 Determinism (Determinism_Co) 
                 Co 
               
               
                   
                 TT (TT_Ca) 
                 Ca 
               
               
                   
                 TT (TT_Cd) 
                 Cd 
               
               
                   
                 RT2 (RT2_Ni) 
                 Ni 
               
               
                   
                 TT (TT_Fe) 
                 Fe 
               
               
                   
                 RT (RT Fe) 
                 Fe 
               
               
                   
                 MDL (MDL_ZnBi) 
                 ZnBi 
               
               
                   
                 RT2 (RT2_ZnAl) 
                 ZnAl 
               
               
                   
                 RT2 (RT2_Zn) 
                 Zn 
               
               
                   
                 RT2 (RT2_Al) 
                 Al 
               
               
                   
                 MDL (MDL_ZnMn) 
                 ZnMn 
               
               
                   
                 Laminarity (Laminarity_Zn) 
                 Zn 
               
               
                   
                 TT (TT_Cu) 
                 Cu 
               
               
                   
                 MDL (MDL_ZnBa) 
                 ZnBa 
               
               
                   
                 RT2 (RT2_P) 
                 P 
               
               
                   
                 RT2 (RT2_ZnFe) 
                 ZnFe 
               
               
                   
                 MDL (MDL_Mn) 
                 Mn 
               
               
                   
                 RT2 (RT2_Cr) 
                 Cr 
               
               
                   
                 Entropy (Entropy_ZnBa) 
                 ZnBa 
               
               
                   
                 RT2 (RT2_Cd) 
                 Cd 
               
               
                   
                 RT2 (RT2_ZnS) 
                 ZnS 
               
               
                   
                 RT2 (RT2_S) 
                 S 
               
               
                   
                 RT2 (RT2_Pb) 
                 Pb 
               
               
                   
                 RT2 (RT2_ZnMn) 
                 ZnMn 
               
               
                   
                 MDL (MDL_ZnLi) 
                 ZnLi 
               
               
                   
                 RT2 (RT2_ZnAs) 
                 ZnAs 
               
               
                   
                 Entropy (Entropy_ZnAs) 
                 ZnAs 
               
               
                   
                 RT2 (RT2_Sr) 
                 Sr 
               
               
                   
                 RT2 (RT2_ZnSr) 
                 ZnSr 
               
               
                   
                 MDL (MDL_Zn) 
                 Zn 
               
               
                   
                 Laminarity (Laminarity_Ca) 
                 Ca 
               
               
                   
                 RT2 (RT2_ZnCd) 
                 ZnCd 
               
               
                   
                 RT2 (RT2_ZnLi) 
                 ZnLi 
               
               
                   
                 RT2 (RT2_ZnSn) 
                 ZnSn 
               
               
                   
                 MDL (MDL_ZnMg) 
                 ZnMg 
               
               
                   
                 RT2 (RT2_Sn) 
                 Sn 
               
               
                   
                 RT2 (RT2_ZnMg) 
                 ZnMg 
               
               
                   
                 Entropy (Entropy_ZnBi) 
                 ZnBi 
               
               
                   
                 RT2 (RT2_ZnNi) 
                 ZnNi 
               
               
                   
                 MDL (MDL_ZnNi) 
                 ZnNi 
               
               
                   
                 RT2 (RT2_ZnBi) 
                 ZnBi 
               
               
                   
                 RT2 (RT2_Mg) 
                 Mg 
               
               
                   
                 RT2 (RT2_Ba) 
                 Ba 
               
               
                   
                 RT2 (RT2_ZnCu) 
                 ZnCu 
               
               
                   
                 RT2 (RT2_ZnBa) 
                 ZnBa 
               
               
                   
                 RT2 (RT2_ZnP) 
                 ZnP 
               
               
                   
                 RT2 (RT2_Co) 
                 Co 
               
               
                   
                 RT2 (RT2_ZnHg) 
                 ZnHg 
               
               
                   
                 RT2 (RT2_Cu) 
                 Cu 
               
               
                   
                 RT2 (RT2_ZnCo) 
                 ZnCo 
               
               
                   
                 Laminarity (Laminarity_Sr) 
                 Sr 
               
               
                   
                 RT2 (RT2_Ca) 
                 Ca 
               
               
                   
                 RT2 (RT2_ZnCa) 
                 ZnCa 
               
               
                   
                 MDL (MDL_ZnCa) 
                 ZnCa 
               
               
                   
                 RT2 (RT2_ZnPb) 
                 ZnPb 
               
               
                   
                 Entropy (Entropy_Zn) 
                 Zn 
               
               
                   
                 RT2 (RT2_Bi) 
                 Bi 
               
               
                   
                 MDL (MDL_I) 
                 I 
               
               
                   
                 Entropy (Entropy_I) 
                 I 
               
               
                   
                 Laminarity (Laminarity_Ni) 
                 Ni 
               
               
                   
                 MDL (MDL_ZnSr) 
                 ZnSr 
               
               
                   
                 MDL (MDL_ZnP) 
                 ZnP 
               
               
                   
                 RT2 (RT2_ZnCr) 
                 ZnCr 
               
               
                   
                 RT2 (RT2_ZnI) 
                 ZnI 
               
               
                   
                 MDL (MDL_ZnFe) 
                 ZnFe 
               
               
                   
                 RT2 (RT2_As) 
                 As 
               
               
                   
                 Entropy (Entropy_ZnMg) 
                 ZnMg 
               
               
                   
                 MDL (MDL_ZnSn) 
                 ZnSn 
               
               
                   
                 TT (TT_Al) 
                 Al 
               
               
                   
                 MDL (MDL_ZnHg) 
                 ZnHg 
               
               
                   
                 Entropy (Entropy_ZnSn) 
                 ZnSn 
               
               
                   
                 MDL (MDL_ZnCr) 
                 ZnCr 
               
               
                   
                 MDL (MDL_Ba) 
                 Ba 
               
               
                   
                 TT (TT_Bi) 
                 Bi 
               
               
                   
                 RT2 (RT2_Hg) 
                 Hg 
               
               
                   
                 Entropy (Entropy_ZnP) 
                 ZnP 
               
               
                   
                 MDL (MDL_ZnPb) 
                 ZnPb 
               
               
                   
                 TT (TT_Sn) 
                 Sn 
               
               
                   
                 RT2 (RT2 I) 
                 I 
               
               
                   
                 TT (TT_Ba) 
                 Ba 
               
               
                   
                 TT (TT_I) 
                 I 
               
               
                   
                 TT (TT_Ni) 
                 Ni 
               
               
                   
                 MDL (MDL_ZnAl) 
                 ZnAl 
               
               
                   
                 MDL (MDL-Bi) 
                 Bi 
               
               
                   
                 RT2 (RT2_Li) 
                 Li 
               
               
                   
                 Entropy (Entropy_ZnCo) 
                 ZnCo 
               
               
                   
                 Entropy (Entropy_ZnLi) 
                 ZnLi 
               
               
                   
                 Entropy (Entropy_ZnNi) 
                 ZnNi 
               
               
                   
                 Entropy (Entropy_ZnCa) 
                 ZnCa 
               
               
                   
                 MDL (MDL_Fe) 
                 Fe 
               
               
                   
                 MDL (MDL_S) 
                 S 
               
               
                   
                 MDL (MDL_ZnCo) 
                 ZnCo 
               
               
                   
                 Entropy (Entropy_ZnHg) 
                 ZnHg 
               
               
                   
                 TT (TT_Co) 
                 Co 
               
               
                   
                 MDL (MDL_ZnI) 
                 ZnI 
               
               
                   
                 Entropy (Entropy_ZnPb) 
                 ZnPb 
               
               
                   
                 MDL (MDL_Al) 
                 Al 
               
               
                   
                 Entropy (Entropy_ZnCr) 
                 ZnCr 
               
               
                   
                 Entropy (Entropy_Ba) 
                 Ba 
               
               
                   
                 Entropy (Entropy_ZnFe) 
                 ZnFe 
               
               
                   
                 MDL (MDL_ZnS) 
                 ZnS 
               
               
                   
                 MDL (MDL_Hg) 
                 Hg 
               
               
                   
                 Entropy (Entropy_ZnSr) 
                 ZnSr 
               
               
                   
                 Entropy (Entropy_S) 
                 S 
               
               
                   
                 TT (TT_Hg) 
                 Hg 
               
               
                   
                 Laminarity (Laminarity_Al) 
                 Al 
               
               
                   
                 Entropy (Entropy_ZnAl) 
                 ZnAl 
               
               
                   
                 Entropy (Entropy_Bi) 
                 Bi 
               
               
                   
                 Determinism (Determinism_ZnP) 
                 ZnP 
               
               
                   
                 Entropy (Entropy_Fe) 
                 Fe 
               
               
                   
                 Determinism (Determinism_ZnBi) 
                 ZnBi 
               
               
                   
                 Entropy (Entropy_ZnI) 
                 ZnI 
               
               
                   
                 Laminarity (Laminarity_Ba) 
                 Ba 
               
               
                   
                 Determinism (Determinism_I) 
                 I 
               
               
                   
                 TT (TT_Cr) 
                 Cr 
               
               
                   
                 Determinism (Determinism_Ba) 
                 Ba 
               
               
                   
                 Laminarity (Laminarity_I) 
                 I 
               
               
                   
                 Determinism (Determinism_Sn) 
                 Sn 
               
               
                   
                 Determinism (Determinism_ZnBa) 
                 ZnBa 
               
               
                   
                 Entropy (Entropy_Al) 
                 Al 
               
               
                   
                 Determinism (Determinism_ZnCo) 
                 ZnCo 
               
               
                   
                 Entropy (Entropy_Hg) 
                 Hg 
               
               
                   
                 Laminarity (Laminarity_Cr) 
                 Cr 
               
               
                   
                 Laminarity (Laminarity_P) 
                 P 
               
               
                   
                 Laminarity (Laminarity_S) 
                 S 
               
               
                   
                 Determinism (Determinism_Zn) 
                 Zn 
               
               
                   
                 Entropy (Entropy_ZnS) 
                 ZnS 
               
               
                   
                 Determinism (Determinism_Al) 
                 Al 
               
               
                   
                 Determinism (Determinism_P) 
                 P 
               
               
                   
                 Laminarity (Laminarity_Hg) 
                 Hg 
               
               
                   
                   
               
            
           
         
       
     
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Table 3. In some embodiments, the set of features includes all the features listed in Table 3. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 3. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Tables 2 and 3. In some embodiments, the set of features includes all the features listed in Tables 2 and 3. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Tables 2 and 3. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Table 4. In some embodiments, the set of features includes all the features listed in Table 4. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 4. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Table 5. In some embodiments, the set of features includes all the features listed in Table 5. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 5. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Table 6. In some embodiments, the set of features includes all the features listed in Table 6. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 6. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Table 7. In some embodiments, the set of features includes all the features listed in Table 7. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 7. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Table 8. In some embodiments, the set of features includes all the features listed in Table 8. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 8. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Table 9. In some embodiments, the set of features includes all the features listed in Table 9. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 9. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in Table 10. In some embodiments, the set of features includes all the features listed in Table 10. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 10. 
     In some embodiments, the set of features, where each feature is associated with a respective elemental isotope or a combination of elemental isotopes (e.g., a combination of two elemental isotopes, or a combination of more than two element isotopes), is selected from the features listed in any combination of Tables 2, 3, 4, 5, 6, 7, 8, 9 and 10. In some embodiments, the set of features includes all the features listed in Tables 2, 3, 4, 5, 6, 7, 8, 9 and 10. In some embodiments, the set of features includes at least 5%, 10%, 15%, 20% or 25% of the features listed in Tables 2, 3, 4, 5, 6, 7, 8, 9 and 10. 
     Method  200  further includes inputting the obtained set of features ( 220 ) to a trained classifier. In some embodiments, the trained classifier includes a predictive computational algorithm to obtain a probability ( 222 ) for the subject having a biological condition associated with metal metabolism. In some embodiments, the predictive computational algorithm computes 
     
       
         
           
             
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     p 
                     ⁡ 
                     
                       ( 
                       subject 
                       ) 
                     
                   
                   = 
                   
                     1 
                     
                       1 
                       + 
                       
                         e 
                         
                           - 
                           
                             ( 
                             
                               α 
                               + 
                               
                                 
                                   β 
                                   1 
                                 
                                 ⁢ 
                                 
                                   x 
                                   1 
                                 
                               
                               + 
                               … 
                               + 
                               
                                 
                                   β 
                                   k 
                                 
                                 ⁢ 
                                 
                                   x 
                                   k 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where, 
     p(subject) is the probability that the subject has the biological condition associated with metal metabolism, 
     e is Euler&#39;s number, 
     α is a calculated parameter associated with a probability that the subject has the biological condition associated with metal metabolism when β 1 x 1 + . . . +β k x k  equals to zero, β 1, . . . , k  corresponds to a weight parameter associated with each feature in the set of features including features from 1 through k, k, and 
     x 1, . . . , k  corresponds to a value derived for each feature in the set of features, the set of features including features from 1 through k. 
     The features from 1 through k are selected from the features listed in Table 2, and optionally, additionally, from Table 3. The weight parameters β 1, . . . , k  are defined based on classifier training. The probability p(subject) is provided as a number ranging from 0 to 1, where 1 corresponds to a 100% probability that the subject has a biological condition associated with metal metabolism. 
     In some embodiments, the method  200  also includes applying a predetermined threshold ( 224 ) to the obtained probability p(subject). If the obtained probability p(subject) is above the predetermined threshold, the subject is evaluated as having a biological condition associated with metal metabolism. If the obtained probability is below the predetermined threshold, the subject is evaluated as not having a biological condition associated with metal metabolism. In some embodiments, the predetermined threshold is between 0.3-0.6 (e.g., the predetermined threshold is 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, or 0.6). In some embodiments, the predetermined threshold is 0.45. In some embodiments, the obtained probability is expressed in terms of associated odds (e.g., odds ratio (OR), which may be derived from a probability such that OR=p/(1−p)). For example, the evaluation includes evaluating odds that the subject has the biological condition associated with metal metabolism. 
     In some embodiments, the method  200  further includes discriminating a first biological condition associated with metal metabolism from an alternative condition, e.g., a second, biological condition associated with metal metabolism. In some embodiments, the alternative condition is associated with no known condition (e.g., a neurotypical condition (NT)). In some embodiments, the first biological condition associated with metal metabolism is associated with autism spectrum disorder (ASD) and the alternative condition is associated with an attention-deficit/hyperactivity disorder (ADHD). In some embodiments, the alternative condition is any other neurodevelopmental condition, or a comorbid diagnosis for two neurodevelopmental conditions.  FIG. 2F  provides an illustration of experimental data describing discriminating between an autism spectrum disorder (ASD) and other neurodevelopmental disorders, in accordance with some embodiments of the present disclosure. It is noted that, based on the experimental data shown in  FIG. 2F , the method  200  of the present disclosure is capable of discriminating between autism spectrum disorder and ADHD. As shown, the present disclosure is also capable of distinguishing autism spectrum disorder from comorbid (CM) cases diagnosed for both autism spectrum disorder and ADHD. 
     Now that the details of processes and features of the method  200  for evaluating a subject for a biological condition associated with metal metabolism from a biological sample has been disclosed with reference to  FIG. 2 ,  FIGS. 3A-3E  collectively provide a flow chart of fundamental processes and features of a method  3000  for evaluating a subject for a biological sample associated with metal metabolism, in which optional blocks are indicated with dashed boxes, in accordance with some embodiments of the present disclosure. In some embodiments, the method  3000  corresponds to the method  200 . 
     Block  3100  of  FIG. 3A . The method  3000  includes sampling, e.g., with a laser (e.g., with a LA-ICP-MS), each respective position in a plurality of positions along a reference line on a biological sample associated with metal metabolism of the subject, thereby obtaining a plurality of ion samples (e.g., the areas  200 A and  200 B of a hair shaft in  FIG. 2B  section I). Each ion sample in the plurality of ion samples corresponds to a different position in the plurality of positions, and each position in the plurality of positions representing a different period of growth of the biological sample associated with metal metabolism. 
     Block  3200  of  FIG. 3A . The method  3000  includes analyzing each ion sample in the plurality of ion samples with a mass spectrometer, thereby obtaining a first dataset. The first dataset includes a plurality of traces (e.g., the trace  208  in  FIG. 2D ). Each trace in the plurality of traces is a concentration of a corresponding elemental isotope, in a plurality of elemental isotopes, over time collectively determined from the plurality of ion samples. 
     Block  3300  of  FIG. 3A . The method  3000  includes deriving a second dataset from the plurality of traces that includes a set of features (e.g., a set of features selected from features listed in Table 2). Each respective feature in the set of features is determined by a variation of a single isotope or a combination of isotopes in the plurality of traces. For example, Section III of  FIG. 2E  illustrates a recurrence plot of copper isotope derived from the trace of Section II of  FIG. 2E . The variation of the copper isotope abundance is observed as diagonal patterns in the recurrence plot. 
     Block  3400  of  FIG. 3A . In some embodiments, the method  3000  also includes inputting the set of features into a trained classifier thereby obtaining a probability from the trained classifier that the subject has the first biological condition associated with metal metabolism. In some embodiments, is the trained classifier is a neural network algorithm, a support vector machine algorithm, a decision tree algorithm, an unsupervised clustering model algorithm, a supervised clustering model algorithm, or a regression model. 
     Block  3110  of  FIG. 3B . In some embodiments, the sampling the hair shaft includes irradiating, with a laser, the biological sample associated with metal metabolism of the subject with the laser thereby extracting a plurality of particles from the biological sample associated with metal metabolism of the subject and ionizing the plurality of particles with an inductively coupled plasma mass spectrometer, thereby obtaining the plurality of ion samples (e.g.,  FIG. 2C ). 
     Block  3120  of  FIG. 3B . In some embodiments, the plurality of positions (e.g., the areas  200 A and  200 B of a hair shaft in  FIG. 2B  section I) along the hair shaft is sequenced a first position in the plurality of positions along the biological sample associated with metal metabolism of the subject corresponds to a position closest to a tip of the biological sample associated with metal metabolism of the subject. 
     Block  3130  of  FIG. 3B . The method  3000  also includes, prior to sampling the hair shaft of the subject, the biological sample associated with metal metabolism of the subject with a solvent or a surfactant. For example, the hair shaft is washed with TRITON X-100® and ultrapure metal free water (e.g., MILLI-Q® water) and dried overnight in an oven (e.g., at 60 degrees Celsius). 
     Block  3140  of  FIG. 3B . The method  3000  also includes, prior to sampling the hair shaft of the subject, irradiating the biological sample associated with metal metabolism of the subject with a low powered laser to remove any debris from the biological sample associated with metal metabolism of the subject (e.g., pre-ablating a hair shaft, a tooth, or a nail). For example, the pre-ablation is performed using a laser wavelength of 193 nm and laser energy below 0.4 J/cm 2  (e.g., the laser energy is 0.4 J/cm 2 , 0.3 J/cm 2 , 0.2 J/cm 2  or 0.1 J/cm 2 ). In some embodiments, the laser energy ranges from 0.2 J/cm 2  to 0.4 J/cm 2 . 
     Block  3141  of  FIG. 3B . The biological sample associated with metal metabolism of the subject is selected from the group consisting of a hair shaft, a tooth, and a nail (e.g., a hair shaft, a tooth, and a nail illustrated in sections I, II, and III of  FIG. 2B , respectively. 
     Block  3141 - 1  of  FIG. 3B . The biological sample associated with metal metabolism of the subject is the hair shaft and the reference line corresponds to a longitudinal direction of the hair shaft (e.g., reference line  201  in  FIG. 2B  section I). 
     Block  3141 - 1  of  FIG. 3B . The biological sample associated with metal metabolism of the subject is the tooth and the reference line corresponds to a neonatal line of the tooth on an enamel surface of the tooth (e.g., reference line  222  along a neonatal line of tooth  220  in  FIG. 2B  section II). In some embodiments, the biological sample associated with metal metabolism of the subject is the nail and the reference line corresponds to a line extending from a root of the nail to the tip of the nail (e.g., reference line  232  of nail  230  in  FIG. 2B  section III). 
     Block  3210  of  FIG. 3C . The plurality of elemental isotopes is selected from the elemental isotopes listed in Table 1. In some embodiments, the plurality of elemental isotopes includes at least 50%, 60%, 70%, 80% or 90% of the isotopes included in Table 1.} 
     Block  3220  of  FIG. 3C . Each trace in the plurality of traces includes a plurality of data points. Each data point is an instance of the respective position in the plurality of position. In some embodiments, each trace includes at least 100 positions (e.g., 100, 150, 200, 250, 300, 350, 400, 450, or 500 positions). In some embodiments, each data point corresponds to approximately 130 min period of hair growth (e.g., the period of hair growth being calculated using a 30 micrometer laser beam size and an average rate of hair growth 1 cm per month. 
     Block  3230  of  FIG. 3C . The concentration of the corresponding elemental isotope corresponds to a relative abundance of the corresponding elemental isotope to a control elemental isotope. The control elemental isotope is included in the plurality of ion samples. In some embodiments, the control elemental isotope is sulfur. 
     Block  3310  of  FIG. 3D . The set of features is selected from the features listed in Table 2. In some embodiments, the set of features includes the features listed in Table 2. In some embodiments, the set of features includes at least 50%, 60%, 70%, 80% or 90% of the features listed in Table 2. Each feature in the set of features is associated with a single respective trace of the plurality of traces or with two respective traces of the plurality of traces. 
     Block  3320  of  FIG. 3D . The set of features further includes, in addition to the features selected from the features listed in Table 2, one or more features listed in Table 3. 
     Block  3330  of  FIG. 3D . The deriving of the second dataset includes removing from the plurality of data points such data points that do not meet a first criteria. In some embodiments, the first criteria includes a mean absolute difference between adjacent data points in the plurality of data points being three times a standard deviation of the mean absolute difference between adjacent points (e.g., the peaks  210  are removed from the trace  208  in  FIG. 2D ). 
     Block  3340  of  FIG. 3D . The set of features is selected from a mean diagonal length, a determinism, a recurrence time, an entropy, a trapping time, and a laminarity. 
     Block  3410  of  FIG. 3E . In some embodiments, the trained classifier computes: 
     
       
         
           
             
               
                 
                   
                     p 
                     ⁡ 
                     
                       ( 
                       subject 
                       ) 
                     
                   
                   = 
                   
                     1 
                     
                       1 
                       + 
                       
                         e 
                         
                           - 
                           
                             ( 
                             
                               α 
                               + 
                               
                                 
                                   β 
                                   1 
                                 
                                 ⁢ 
                                 
                                   x 
                                   1 
                                 
                               
                               + 
                               … 
                               + 
                               
                                 
                                   β 
                                   k 
                                 
                                 ⁢ 
                                 
                                   x 
                                   k 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where, p(subject) is the probability that the subject has the biological condition associated with metal metabolism, e is Euler&#39;s number, α is a calculated parameter associated with a probability that the subject has the biological condition associated with metal metabolism when β 1 x 1 + . . . +β k x k  equals to zero, β 1, . . . , k  corresponds to a weight parameter associated with each feature in the set of features including features from 1 through k, and x 1, . . . , k  value derived for each feature in the set of features, the set of features including features  1  through k. 
     Block  3420  of  FIG. 3E . In accordance with determining that p(subject) is above a predetermined threshold, determine that the subject has the biological condition associated with metal metabolism. 
     Block  3500  of  FIG. 3E . In some embodiments, evaluating the subject for the biological condition associated with metal metabolism further includes discriminating between the first biological condition associated with metal metabolism and a second biological condition associated with metal metabolism distinct from the first biological condition associated with metal metabolism. 
     Block  3510  of  FIG. 3E . In some embodiments, the first biological condition is autism spectrum disorder and the second biological condition is attention-deficit/hyperactivity disorder. 
     Block  3510  of  FIG. 3E . In some embodiments, the first biological condition associated with metal metabolism is selected from the group consisting of autism spectrum disorder (ADS), attention-deficit/hyperactivity disorder (ADHD), amyotrophic lateral sclerosis (ALS), schizophrenia, irritable bowel disease (IBD), pediatric kidney transplant rejection, and pediatric cancer. 
     In some embodiments, the method  3000  described with respect to  FIGS. 3A-3E  is performed by a device executing one or more programs (e.g., one or more programs stored in the Non-Persistent Memory  111  or in the Persistent Memory  112  in  FIG. 1 ) including instructions to perform the method  3000 . In some embodiments, the method  3000  is performed by a system comprising at least one processor (e.g., the processing core  102 ) and memory (e.g., one or more programs stored in the Non-Persistent Memory  111  or in the Persistent Memory  112 ) comprising instructions to perform the method  3000 . 
     Classifier Training. 
     Now that the methods and features of the method  3000  have been disclosed with reference to  FIGS. 3A-3E ,  FIG. 4  provides a flow chart of processes and features of a method  4000  for training a classifier for evaluating a subject for a biological condition associated with metal metabolism, in which optional blocks are indicated with dashed boxes, in accordance with some embodiments of the present disclosure. The method of training a classifier includes collecting biological sample associated with metal metabolism of a respective training subject from a plurality of training subjects and training the classifier using the collected biological samples. The training subjects are humans. Each training has a diagnostic status indicating that they have either been diagnosed with the biological condition associated with metal metabolism, or have not been diagnosed with the biological condition associated with metal metabolism. In some embodiments, the training subjects are children aged equal to, or below, 5 years (e.g., equal to or below 5 years, 4 years, 3 years, 2 years, 1 year, 9 months, 6 months, 3 months or 1 month). Steps of the method  4000  described below with respect to Blocks  4100 - 4300  are performed for each training subject in a plurality of training subjects. 
     Block  4100  of  FIG. 4 . The method  4000  includes sampling, with a laser, each respective position in a corresponding plurality of positions of a corresponding reference line on a corresponding biological sample associated with metal metabolism of the respective training subject, thereby obtaining a corresponding plurality of ion samples. Each ion sample in the corresponding plurality of ion samples for a different position in the corresponding plurality of positions, and each position in the corresponding plurality of positions representing a different period of growth of the corresponding biological sample associated with metal metabolism. 
     Block  4200  of  FIG. 4 . The method  4000  includes each respective ion sample in the corresponding plurality of ion samples with a mass spectrometer thereby obtaining a respective first dataset that includes a corresponding plurality of traces. Each trace in the corresponding plurality of traces being a concentration of a corresponding elemental isotope, in a plurality of elemental isotopes, over time collectively determined from the corresponding plurality of ion samples. 
     Block  4300  of  FIG. 4 . The method  4000  includes deriving a respective second dataset from the corresponding plurality of traces that includes a corresponding set of features, each respective feature in the corresponding set of features being determined by a variation of a single isotope or a combination of isotopes in the corresponding plurality of traces. 
     Block  4400  of  FIG. 4 . The method  4000  further includes training an untrained or partially untrained classifier with (i) the corresponding set of features of each respective second dataset of each training subject in the plurality of training subjects and (ii) the corresponding diagnostic status of each training subject in the plurality of training subjects, selected from among the first diagnostic status and the second diagnostic status, thereby obtaining a trained classifier. The trained classifier provides an indication as to whether a test subject has the first biological condition associated with metal metabolism based on values for features in a set of features acquired from a biological sample associated with metal metabolism of the test subject. In some embodiments, (Block  4410 ) the trained classifier is a neural network algorithm, a convolutional neural network algorithm, a support vector machine algorithm, a decision tree algorithm, an unsupervised clustering model algorithm, a supervised clustering model algorithm, or a regression model. In some embodiments, (Block  4420 ) the trained classifier is multinomial or binomial. In some embodiments, the trained classifier can be used to make a binary prediction as to whether a sample was derived from a subject with the first biological condition associated with metal metabolism or not; or, may be multinomial, distinguishing subjects with no diagnosis from those with the first biological condition associated with metal metabolism or a second biological condition associated with metal metabolism, where the second biological condition is distinct from the first biological condition. 
     In some embodiments, the classifier is a neural network or a convolutional neural network. See, Vincent et al., 2010, “Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion,” J Mach Learn Res 11, pp. 3371-3408; Larochelle et al., 2009, “Exploring strategies for training deep neural networks,” J Mach Learn Res 10, pp. 1-40; and Hassoun, 1995, Fundamentals of Artificial Neural Networks, Massachusetts Institute of Technology, each of which is hereby incorporated by reference. 
     SVMs are described in Cristianini and Shawe-Taylor, 2000, “An Introduction to Support Vector Machines,” Cambridge University Press, Cambridge; Boser et al., 1992, “A training algorithm for optimal margin classifiers,” in Proceedings of the 5 th  Annual ACM Workshop on Computational Learning Theory, ACM Press, Pittsburgh, Pa., pp. 142-152; Vapnik, 1998 , Statistical Learning Theory , Wiley, New York; Mount, 2001 , Bioinformatics: sequence and genome analysis , Cold Spring Harbor Laboratory Press, Cold Spring Harbor, N.Y.; Duda,  Pattern Classification , Second Edition, 2001, John Wiley &amp; Sons, Inc., pp. 259, 262-265; and Hastie, 2001 , The Elements of Statistical Learning , Springer, New York; and Furey et al., 2000 , Bioinformatics  16, 906-914, each of which is hereby incorporated by reference in its entirety. When used for classification, SVMs separate a given set of binary labeled data with a hyper-plane that is maximally distant from the labeled data. For cases in which no linear separation is possible, SVMs can work in combination with the technique of ‘kernels’, which automatically realizes a non-linear mapping to a feature space. The hyper-plane found by the SVM in feature space corresponds to a non-linear decision boundary in the input space. 
     Decision trees are described generally by Duda, 2001 , Pattern Classification , John Wiley &amp; Sons, Inc., New York, pp. 395-396, which is hereby incorporated by reference. Tree-based methods partition the feature space into a set of rectangles, and then fit a model (like a constant) in each one. In some embodiments, the decision tree is random forest regression. One specific algorithm that can be used is a classification and regression tree (CART). Other specific decision tree algorithms include, but are not limited to, ID3, C4.5, MART, and Random Forests. CART, ID3, and C4.5 are described in Duda, 2001 , Pattern Classification , John Wiley &amp; Sons, Inc., New York. pp. 396-408 and pp. 411-412, which is hereby incorporated by reference. CART, MART, and C4.5 are described in Hastie et al., 2001 , The Elements of Statistical Learning , Springer-Verlag, New York, Chapter 9, which is hereby incorporated by reference in its entirety. Random Forests are described in Breiman, 1999, “Random Forests—Random Features,” Technical Report 567, Statistics Department, U.C. Berkeley, September 1999, which is hereby incorporated by reference in its entirety. 
     Clustering (e.g., unsupervised clustering model algorithms and supervised clustering model algorithms) is described at pages 211-256 of Duda and Hart,  Pattern Classification  and Scene Analysis, 1973, John Wiley &amp; Sons, Inc., New York, (hereinafter “Duda 1973”) which is hereby incorporated by reference in its entirety. As described in Section 6.7 of Duda 1973, the clustering problem is described as one of finding natural groupings in a dataset. To identify natural groupings, two issues are addressed. First, a way to measure similarity (or dissimilarity) between two samples is determined. This metric (similarity measure) is used to ensure that the samples in one cluster are more like one another than they are to samples in other clusters. Second, a mechanism for partitioning the data into clusters using the similarity measure is determined. Similarity measures are discussed in Section 6.7 of Duda 1973, where it is stated that one way to begin a clustering investigation is to define a distance function and to compute the matrix of distances between all pairs of samples in the training set. If distance is a good measure of similarity, then the distance between reference entities in the same cluster will be significantly less than the distance between the reference entities in different clusters. However, as stated on page 215 of Duda 1973, clustering does not require the use of a distance metric. For example, a nonmetric similarity function s(x, x′) can be used to compare two vectors x and x′. Conventionally, s(x, x′) is a symmetric function whose value is large when x and x′ are somehow “similar.” An example of a nonmetric similarity function s(x, x′) is provided on page 218 of Duda 1973. Once a method for measuring “similarity” or “dissimilarity” between points in a dataset has been selected, clustering requires a criterion function that measures the clustering quality of any partition of the data. Partitions of the data set that extremize the criterion function are used to cluster the data. See page 217 of Duda 1973. Criterion functions are discussed in Section 6.8 of Duda 1973. More recently, Duda et al., Pattern Classification, 2 nd  edition, John Wiley &amp; Sons, Inc. New York, has been published. Pages 537-563 describe clustering in detail. More information on clustering techniques can be found in Kaufman and Rousseeuw, 1990 , Finding Groups in Data: An Introduction to Cluster Analysis , Wiley, New York, N.Y.; Everitt, 1993, Cluster analysis (3d ed.), Wiley, New York, N.Y.; and Backer, 1995, Computer-Assisted Reasoning in Cluster Analysis, Prentice Hall, Upper Saddle River, N.J., each of which is hereby incorporated by reference. Particular exemplary clustering techniques that can be used in the present disclosure include, but are not limited to, hierarchical clustering (agglomerative clustering using nearest-neighbor algorithm, farthest-neighbor algorithm, the average linkage algorithm, the centroid algorithm, or the sum-of-squares algorithm), k-means clustering, fuzzy k-means clustering algorithm, and Jarvis-Patrick clustering. In some embodiments, the clustering comprises unsupervised clustering, where no preconceived notion of what clusters should form when the training set is clustered, are imposed. 
     Regression models, such as the of the multi-category logit models, are described in Agresti,  An Introduction to Categorical Data Analysis,  1996, John Wiley &amp; Sons, Inc., New York, Chapter 8, which is hereby incorporated by reference in its entirety. In some embodiments, the classifier makes use of a regression model disclosed in Hastie et al., 2001 , The Elements of Statistical Learning , Springer-Verlag, New York. 
     In some embodiments, the method  4000  described with respect to  FIG. 4  is performed by a device executing one or more programs (e.g., one or more programs stored in the Non-Persistent Memory  111  or in the Persistent Memory  112  in  FIG. 1 ) including instructions to perform the method  4000 . In some embodiments, the method  4000  is performed by a system comprising at least one processor (e.g., the processing core  102 ) and memory (e.g., one or more programs stored in the Non-Persistent Memory  111  or in the Persistent Memory  112 ) comprising instructions to perform the method  4000 . 
     EXAMPLES 
     Example 1—Evaluation of a Subject for Autism Spectrum Disorder 
     Two subjects (Subject 1 and Subject 2) were evaluated for autism spectrum disorder using the method  200  described with respect to  FIGS. 2A-2F . Table 4 illustrates the results including the features from Table 2 (e.g., column “Features”) associated with respective parameter estimate β values obtained from a training set and empirical results (e.g., x values) for Subject 1 and Subject 2. The β values are obtained by estimating each feature in the training data set that describes a change in log odds of autism spectrum disorder status associated with a 1-unit change for a respective feature. The estimated parameters β and the x values for each respective subject are input to the algorithm computing p(subject) for each respective subject (see, Equation 1 above) given a calculated α parameter of 36.31. For Subject 1, the estimated parameters β and empirical results x yielded an estimated probability p(subject 1 ) of 2.28% that Subject 1 has autism spectrum disorder. For Subject 2, the estimated parameters β and empirical results x yielded an estimated probability p(subject) of 96.9 that Subject 2 has autism spectrum disorder. With a predetermined threshold of 50%, Subject 1 was therefore evaluated as not having autism spectrum disorder and Subject 2 is evaluated has having autism spectrum disorder. Furthermore, odds for Subject 1 having autism spectrum disorder equal to 0.023 and odds for Subject 2 having autism spectrum disorder equal to 31.2. Odds are calculated from probability using Equation 2. 
     
       
         
           
             
               
                 
                   Odds 
                   = 
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           subject 
                           i 
                         
                         ) 
                       
                     
                     
                       1 
                       - 
                       
                         p 
                         ⁡ 
                         
                           ( 
                           
                             subject 
                             i 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Features with associated parameter estimates obtained from a training 
               
               
                 set and empirical x values for Subject 1 and Subject 2. 
               
            
           
           
               
               
               
               
               
            
               
                   
                 β value 
                   
                   
                 Feature 
               
               
                   
                 obtained 
                 x value 
                 x value 
                 present in 
               
               
                   
                 from a 
                 for 
                 for 
                 Table 
               
               
                 Feature 
                 training set 
                 Subject 1 
                 Subject 2 
                 2 or 3? 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Determinism_Cd 
                 0.429 
                 0.903 
                 0.932 
                 Yes 
               
               
                 Determinism_Cr 
                 −36.579 
                 0.904 
                 0.893 
                 Yes 
               
               
                 Determinism_ZnHg 
                 −68.008 
                 0.863 
                 0.903 
                 Yes 
               
               
                 Determinism_Cu 
                 −1.834 
                 0.901 
                 0.901 
                 Yes 
               
               
                 Determinism_ZnMn 
                 −2.447 
                 0.909 
                 0.933 
                 Yes 
               
               
                 Determinism_Sr 
                 −3.453 
                 0.951 
                 0.929 
                 Yes 
               
               
                 Entropy_As 
                 −12.823 
                 1.972 
                 1.778 
                 Yes 
               
               
                 Determinism_Mg 
                 −3.018 
                 0.969 
                 0.932 
                 Yes 
               
               
                 Entropy_Li 
                 −9.800 
                 2.096 
                 1.758 
                 Yes 
               
               
                 Determinism_ZnCu 
                 −7.356 
                 0.911 
                 0.866 
                 Yes 
               
               
                 Entropy_ZnCu 
                 −0.255 
                 1.962 
                 1.856 
                 Yes 
               
               
                 MDL_ZnCu 
                 −0.006 
                 4.325 
                 3.883 
                 Yes 
               
               
                 Determinism_Ca 
                 −37.419 
                 0.947 
                 0.909 
                 Yes 
               
               
                 Determinism_Mn 
                 1.600 
                 0.919 
                 0.900 
                 Yes 
               
               
                 Determinism_Ni 
                 −5.041 
                 0.893 
                 0.888 
                 Yes 
               
               
                 Determinism_ZnMg 
                 14.018 
                 0.941 
                 0.921 
                 Yes 
               
               
                 Determinism_ZnCr 
                 −5.769 
                 0.899 
                 0.930 
                 Yes 
               
               
                 Determinism_Pb 
                 −8.253 
                 0.918 
                 0.914 
                 Yes 
               
               
                 Determinism_ZnNi 
                 7.175 
                 0.905 
                 0.935 
                 Yes 
               
               
                 Determinism_ZnSn 
                 15.285 
                 0.931 
                 0.935 
                 Yes 
               
               
                 Determinism_Li 
                 21.384 
                 0.917 
                 0.864 
                 Yes 
               
               
                 Determinism_Hg 
                 12.154 
                 0.888 
                 0.883 
                 Yes 
               
               
                 Determinism_Fe 
                 26.657 
                 0.895 
                 0.941 
                 Yes 
               
               
                 Determinism_As 
                 33.235 
                 0.892 
                 0.873 
                 Yes 
               
               
                 Determinism_ZnI 
                 55.574 
                 0.861 
                 0.907 
                 Yes 
               
               
                   
               
            
           
         
       
     
     Example 2—Receiver Operating Characteristics (ROC) Curve 
       FIG. 5A  illustrates an experimental Receiver Operating Characteristics (ROC) curve for evaluating accuracy of the disclosed method of evaluating a subject for autism spectrum disorder, in accordance with some embodiments. In the experiment described with respect to  FIG. 5A , the evaluation is performed by measuring hair shaft of the subject. A ROC curve can be used for evaluating a performance of a binary classifier. A ROC curve is plotted as sensitivity (also called as a true positive rate) against specificity (also called as a true negative rate). A perfect classifier would have a 100% sensitivity and 100% specificity and an area under the curve (AUC) corresponding to 1. As shown in  FIG. 5A , the ROC curve derived from experimental data to evaluate the performance of the disclosed classification method has an AUC corresponding to 0.947, indicating that the disclosed method has above 90% accuracy for evaluating that a subject has autism spectrum disorder. 
     Example 3—Evaluation of a Subject for Autism Spectrum Disorder from a Hair Sample of One or Two Parents 
     To develop a classifier that could determine whether a subject has autism spectrum disorder or not, hair was collected from parents (biological mother and father) of twins in a study based in Sweden (Roots of Autism and ADHD Study in Sweden—RATSS; Marwan et al., 2007, “Recurrence plots for the analysis of complex systems,” Phys. Rep. 438, 237-329.). The aim of the study was to predict the autism spectrum disorder (ASD) diagnosis of the children from only the parents&#39; hair. The children have undergone clinical testing for autism. In this analysis, no data on the child is used other than the diagnosis. Three classifiers were developed: a) classifier using only mother&#39;s hair to predict child autism (n=29; 14 ASD cases, 15 controls); b) classifier using only father&#39;s hair (n=23; 9 ASD cases and 14 controls); and c) classifier using both mother&#39;s and father&#39;s hair (n=52; 23 ASD cases, 29 controls. 
     Table 5 illustrates the features used and their β values for the mother&#39;s hair cohort, father&#39;s hair cohort, and the combination of mother&#39;s and father&#39;s hair coort. The β values are obtained by estimating each feature in the respective cohort that describes a change in log odds of autism spectrum disorder status associated with a 1-unit change for a respective feature. 
       FIGS. 5B, 5C, and 5D  respectively illustrate the experimental ROC curves for evaluating accuracy of the trained classifier for autism spectrum disorder based on mother&#39;s hair, father&#39;s hair, and the combination of the mother&#39;s and the father&#39;s hair, in accordance with some embodiments. As shown in  FIG. 5B , the ROC curve derived from experimental data to evaluate the performance of the disclosed classification method has an AUC corresponding to 0.886, indicating that the disclosed method has above 85% accuracy for evaluating that a subject has autism spectrum disorder based on a sample of the subject&#39;s mother&#39;s hair. As shown in  FIG. 5C , the ROC curve derived from experimental data to evaluate the performance of the disclosed classification method has an AUC corresponding to 0.800, indicating that the disclosed method has 80% accuracy for evaluating that a subject has autism spectrum disorder based on a sample of the subject&#39;s father&#39;s hair. As shown in  FIG. 5D , the ROC curve derived from experimental data to evaluate the performance of the disclosed classification method has an AUC corresponding to 0.859, indicating that the disclosed method has above 85% accuracy for evaluating that a subject has autism spectrum disorder based on a combination of a sample of the subject&#39;s mother&#39;s hair and the subject&#39;s father&#39;s hair. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Features with empirical x values for a subject based on a sample taken from the subject&#39;s 
               
               
                 mother, subject&#39;s farther and a combination of the subject&#39;s mother and father. 
               
            
           
           
               
               
               
               
               
            
               
                   
                 β value 
                 β value 
                 β value 
                   
               
               
                   
                 obtained from 
                 obtained from 
                 obtained from 
                 Feature in 
               
               
                 Feature 
                 mother cohort 
                 father cohort 
                 combined cohort 
                 Table 2 or 3? 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Determinism_Ba 
                 0.26995224 
                 −0.099215 
                 −0.018623 
                 Yes 
               
               
                 Determinism_Ca 
                 0.30179438 
                 −0.582311 
                 0.8019875 
                 Yes 
               
               
                 Determinism_Cr 
                 1.41987747 
                 1.22403 
                 1.066073 
                 Yes 
               
               
                 Determinism_Cu 
                 −0.8056872 
                 0.390644 
                 −0.127668 
                 Yes 
               
               
                 Determinism_Fe 
                 0.61809714 
                 −0.337452 
                 0.8514657 
                 Yes 
               
               
                 Determinism_I 
                 −1.6204623 
                 −1.000588 
                 −3.012296 
                 Yes 
               
               
                 Determinism_Mg 
                 0.49033131 
                 −0.895876 
                 −0.032059 
                 Yes 
               
               
                 Determinism_Mn 
                 2.13899536 
                 0.6433259 
                 2.1328616 
                 Yes 
               
               
                 Determinism_P 
                 0.18257282 
                 0.4688593 
                 −1.905231 
                 Yes 
               
               
                 Determinism_Pb 
                 −0.89968 
                 −1.816234 
                 0.3425074 
                 Yes 
               
               
                 Determinism_S 
                 1.53986487 
                 −5.893958 
                 −0.507446 
                 Yes 
               
               
                 Determinism_Sn 
                 0.22557473 
                 −0.961602 
                 0.0582074 
                 Yes 
               
               
                 Determinism_Sr 
                 −0.5469032 
                 1.0391182 
                 0.8212948 
                 Yes 
               
               
                 Determinism_Zn 
                 0.17079778 
                 0.2256547 
                 −0.235289 
                 No 
               
               
                 Determinism_ZnBa 
                 0.20471351 
                 0.5033085 
                 0.3960209 
                 Yes 
               
               
                 Determinism_ZnCa 
                 0.21490655 
                 −0.038427 
                 0.1804033 
                 Yes 
               
               
                 Determinism_ZnCr 
                 0.57026275 
                 −0.047577 
                 −0.080889 
                 Yes 
               
               
                 Determinism_ZnCu 
                 0.30597749 
                 0.5666415 
                 0.0273199 
                 Yes 
               
               
                 Determinism_ZnFe 
                 −0.1061911 
                 0.3103529 
                 0.2348702 
                 Yes 
               
               
                 Determinism_ZnI 
                 0.06927202 
                 0.3023726 
                 −0.772397 
                 Yes 
               
               
                 Determinism_ZnMg 
                 0.31475826 
                 0.3667723 
                 0.3215559 
                 Yes 
               
               
                 Determinism_ZnMn 
                 0.06897562 
                 −0.375193 
                 −0.566958 
                 Yes 
               
               
                 Determinism_ZnP 
                 −0.1060363 
                 0.976308 
                 −0.566118 
                 Yes 
               
               
                 Determinism_ZnPb 
                 0.16626519 
                 1.0407674 
                 0.1548639 
                 Yes 
               
               
                 Determinism_ZnS 
                 0.58909549 
                 −0.042635 
                 −0.586531 
                 Yes 
               
               
                 Determinism_ZnSn 
                 0.21543319 
                 0.2843955 
                 0.1103138 
                 Yes 
               
               
                 Determinism_ZnSr 
                 0.12936851 
                 0.2932143 
                 0.2832403 
                 Yes 
               
               
                 MDL_Ba 
                 −0.0175887 
                 0.0168481 
                 0.0280754 
                 Yes 
               
               
                 MDL_Ca 
                 0.012664 
                 −0.023574 
                 0.0268955 
                 Yes 
               
               
                 MDL_Cr 
                 0.13840947 
                 0.1117677 
                 0.1047073 
                 Yes 
               
               
                 MDL_Cu 
                 −0.0195811 
                 0.016205 
                 0.0122942 
                 Yes 
               
               
                 MDL_Fe 
                 0.0533853 
                 −0.020462 
                 −0.00092 
                 Yes 
               
               
                 MDL_I 
                 −0.1399248 
                 −0.159781 
                 −0.244053 
                 Yes 
               
               
                 MDL_Mg 
                 0.01089451 
                 0.009199 
                 0.0078554 
                 Yes 
               
               
                 MDL_Mn 
                 0.10680868 
                 −0.000665 
                 0.0578152 
                 Yes 
               
               
                 MDL_P 
                 0.06724766 
                 −0.005505 
                 −0.137642 
                 Yes 
               
               
                 MDL_Pb 
                 −0.0472965 
                 0.0006465 
                 0.0219535 
                 Yes 
               
               
                 MDL_S 
                 0.09097365 
                 −0.024026 
                 −0.030172 
                 Yes 
               
               
                 MDL_Sn 
                 0.01869144 
                 0.0166052 
                 0.0320733 
                 Yes 
               
               
                 MDL_Sr 
                 −0.0224024 
                 0.0440478 
                 0.0236678 
                 Yes 
               
               
                 MDL_Zn 
                 −0.0122259 
                 −0.020605 
                 −0.038804 
                 Yes 
               
               
                 MDL_ZnBa 
                 −0.0101652 
                 0.0025333 
                 0.0119736 
                 Yes 
               
               
                 MDL_ZnCa 
                 −0.0042781 
                 −0.015974 
                 −0.011638 
                 Yes 
               
               
                 MDL_ZnCr 
                 0.03220882 
                 −0.001205 
                 −0.023751 
                 Yes 
               
               
                 MDL_ZnCu 
                 −0.0151274 
                 −0.003606 
                 −0.019749 
                 Yes 
               
               
                 MDL_ZnFe 
                 −0.0109976 
                 −0.057743 
                 −0.004976 
                 Yes 
               
               
                 MDL_ZnI 
                 −0.0259466 
                 0.0044879 
                 −0.060072 
                 Yes 
               
               
                 MDL_ZnMg 
                 −0.005591 
                 0.0015727 
                 −0.002783 
                 Yes 
               
               
                 MDL_ZnMn 
                 0.01023798 
                 −0.042947 
                 −0.040765 
                 Yes 
               
               
                 MDL_ZnP 
                 −0.0110143 
                 0.0628644 
                 0.0339964 
                 Yes 
               
               
                 MDL_ZnPb 
                 −0.0175028 
                 −0.013542 
                 −0.020343 
                 Yes 
               
               
                 MDL_ZnS 
                 0.03383046 
                 −0.033119 
                 −0.067766 
                 Yes 
               
               
                 MDL_ZnSn 
                 0.02019903 
                 0.0107794 
                 0.0243532 
                 Yes 
               
               
                 MDL_ZnSr 
                 −0.0046591 
                 −0.011486 
                 −0.005694 
                 Yes 
               
               
                 Entropy_Ba 
                 −0.028773 
                 0.0610208 
                 0.0982191 
                 Yes 
               
               
                 Entropy_Ca 
                 0.05788363 
                 −0.093436 
                 0.1229156 
                 Yes 
               
               
                 Entropy_Cr 
                 0.37859451 
                 0.3216797 
                 0.2793699 
                 Yes 
               
               
                 Entropy_Cu 
                 −0.0516145 
                 0.0699055 
                 0.0539494 
                 Yes 
               
               
                 Entropy_Fe 
                 0.14061759 
                 −0.045755 
                 0.0528002 
                 Yes 
               
               
                 Entropy_I 
                 −0.3312469 
                 −0.416349 
                 −0.597241 
                 Yes 
               
               
                 Entropy_Mg 
                 0.05500931 
                 0.0072411 
                 0.0322303 
                 Yes 
               
               
                 Entropy_Mn 
                 0.27564835 
                 0.0167556 
                 0.2061444 
                 Yes 
               
               
                 Entropy_P 
                 0.16962518 
                 −0.010326 
                 −0.350157 
                 Yes 
               
               
                 Entropy_Pb 
                 −0.110991 
                 0.0140247 
                 0.092294 
                 Yes 
               
               
                 Entropy_S 
                 0.27532791 
                 −0.122115 
                 −0.100868 
                 Yes 
               
               
                 Entropy_Sn 
                 0.0546037 
                 0.0211283 
                 0.0877334 
                 Yes 
               
               
                 Entropy_Sr 
                 −0.0635242 
                 0.1687305 
                 0.1053903 
                 Yes 
               
               
                 Entropy_Zn 
                 −0.0099921 
                 −0.052325 
                 −0.082714 
                 Yes 
               
               
                 Entropy_ZnBa 
                 −0.0034346 
                 0.0311443 
                 0.0666616 
                 Yes 
               
               
                 Entropy_ZnCa 
                 0.0157374 
                 −0.009689 
                 0.012736 
                 Yes 
               
               
                 Entropy_ZnCr 
                 0.10055577 
                 0.0126058 
                 −0.043222 
                 Yes 
               
               
                 Entropy_ZnCu 
                 −0.0126217 
                 0.018627 
                 −0.03692 
                 Yes 
               
               
                 Entropy_ZnFe 
                 0.0380713 
                 −0.155539 
                 0.0069564 
                 Yes 
               
               
                 Entropy_ZnI 
                 −0.0033752 
                 0.0344947 
                 −0.103396 
                 Yes 
               
               
                 Entropy_ZnMg 
                 0.01394646 
                 0.0315456 
                 0.0418649 
                 Yes 
               
               
                 Entropy_ZnMn 
                 0.09446064 
                 −0.124788 
                 −0.019134 
                 Yes 
               
               
                 Entropy_ZnP 
                 −8.00E−05 
                 0.1807677 
                 0.0826718 
                 Yes 
               
               
                 Entropy_ZnPb 
                 −0.0235718 
                 −0.027717 
                 −0.045725 
                 Yes 
               
               
                 Entropy_ZnS 
                 0.1063242 
                 −0.097799 
                 −0.179409 
                 Yes 
               
               
                 Entropy_ZnSn 
                 0.06490719 
                 0.0156185 
                 0.065172 
                 Yes 
               
               
                 Entropy_ZnSr 
                 0.04530203 
                 0.0014764 
                 0.0352422 
                 Yes 
               
               
                 Laminarity_Ba 
                 0.12745187 
                 0.1155964 
                 0.2371277 
                 Yes 
               
               
                 Laminarity_Ca 
                 −0.0180744 
                 0.013396 
                 0.0142638 
                 Yes 
               
               
                 Laminarity_Cr 
                 −0.1043894 
                 0.0172006 
                 0.4130502 
                 Yes 
               
               
                 Laminarity_Cu 
                 0.07412039 
                 0.042768 
                 0.2020793 
                 Yes 
               
               
                 Laminarity_Fe 
                 0.70827704 
                 −0.638965 
                 −0.06603 
                 Yes 
               
               
                 Laminarity_I 
                 −0.1197673 
                 −0.013497 
                 −0.222448 
                 Yes 
               
               
                 Laminarity_Mg 
                 0.14505143 
                 0.0176582 
                 0.1166678 
                 Yes 
               
               
                 Laminarity_Mn 
                 −0.000969 
                 −0.341907 
                 −0.112651 
                 Yes 
               
               
                 Laminarity_P 
                 −0.6526684 
                 −0.156536 
                 −0.613885 
                 Yes 
               
               
                 Laminarity_Pb 
                 −0.4757098 
                 0.0270424 
                 −0.02499 
                 Yes 
               
               
                 Laminarity_S 
                 0.74634502 
                 0.0656507 
                 −0.174632 
                 Yes 
               
               
                 Laminarity_Sn 
                 −0.0258771 
                 −0.059034 
                 −0.211966 
                 Yes 
               
               
                 Laminarity_Sr 
                 −0.0391883 
                 0.1600092 
                 0.1981753 
                 Yes 
               
               
                 Laminarity_Zn 
                 −0.1632985 
                 −0.218497 
                 −0.342863 
                 Yes 
               
               
                 Laminarity_ZnBa 
                 −0.1445399 
                 −0.026258 
                 −0.013961 
                 No 
               
               
                 Laminarity_ZnCa 
                 −0.0237264 
                 −0.192702 
                 −0.074107 
                 No 
               
               
                 Laminarity_ZnCr 
                 −0.1550697 
                 −0.233279 
                 0.1056167 
                 No 
               
               
                 Laminarity_ZnCu 
                 −0.0559319 
                 0.0193648 
                 0.0287148 
                 No 
               
               
                 Laminarity_ZnFe 
                 −0.1135849 
                 −0.465737 
                 −0.076332 
                 No 
               
               
                 Laminarity_ZnI 
                 −0.2049815 
                 −0.278001 
                 −0.426026 
                 No 
               
               
                 Laminarity_ZnMg 
                 0.01570192 
                 −0.166143 
                 −0.067021 
                 No 
               
               
                 Laminarity_ZnMn 
                 −0.2066339 
                 −0.437386 
                 −0.449783 
                 No 
               
               
                 Laminarity_ZnP 
                 −0.3425974 
                 −0.188652 
                 −0.194951 
                 No 
               
               
                 Laminarity_ZnPb 
                 −0.2914047 
                 0.057845 
                 −0.111126 
                 No 
               
               
                 Laminarity_ZnS 
                 0.24119318 
                 0.2077668 
                 −0.395565 
                 No 
               
               
                 Laminarity_ZnSn 
                 −0.1111781 
                 −0.097204 
                 −0.229503 
                 No 
               
               
                 Laminarity_ZnSr 
                 −0.1221951 
                 −0.137035 
                 −0.116571 
                 No 
               
               
                 TT_Ba 
                 0.02051527 
                 0.0235494 
                 0.0713402 
                 Yes 
               
               
                 TT_Ca 
                 0.00141797 
                 −0.019106 
                 0.020209 
                 Yes 
               
               
                 TT_Cr 
                 −0.0517325 
                 −0.049081 
                 −0.00155 
                 Yes 
               
               
                 TT_Cu 
                 −0.0481607 
                 0.0075708 
                 −1.95E−05 
                 Yes 
               
               
                 TT_Fe 
                 0.19242796 
                 −0.110022 
                 −0.01397 
                 Yes 
               
               
                 TT_I 
                 −0.095872 
                 0.0490718 
                 −0.149766 
                 Yes 
               
               
                 TT_Mg 
                 0.02247774 
                 0.0086803 
                 0.0083814 
                 Yes 
               
               
                 TT_Mn 
                 −0.0306581 
                 −0.178184 
                 −0.193638 
                 Yes 
               
               
                 TT_P 
                 −0.2443903 
                 0.0237726 
                 −0.217035 
                 Yes 
               
               
                 TT_Pb 
                 −0.124633 
                 −0.015009 
                 0.0165998 
                 Yes 
               
               
                 TT_S 
                 0.14002116 
                 0.0316466 
                 −0.033064 
                 Yes 
               
               
                 TT_Sn 
                 0.08078177 
                 0.014262 
                 −8.82E−05 
                 Yes 
               
               
                 TT_Sr 
                 −0.0329912 
                 0.0347752 
                 0.0433465 
                 Yes 
               
               
                 TT_Zn 
                 −0.0330303 
                 −0.035842 
                 −0.100424 
                 Yes 
               
               
                 TT_ZnBa 
                 −0.0259845 
                 −0.000934 
                 0.0254744 
                 Yes 
               
               
                 TT_ZnCa 
                 −0.008845 
                 −0.022942 
                 −0.00739 
                 No 
               
               
                 TT_ZnCr 
                 −0.0031782 
                 −0.072472 
                 0.0274496 
                 No 
               
               
                 TT_ZnCu 
                 −0.0629332 
                 0.0155481 
                 0.0080091 
                 No 
               
               
                 TT_ZnFe 
                 −0.0025839 
                 −0.04601 
                 −0.002762 
                 No 
               
               
                 TT_ZnI 
                 −0.0386104 
                 −0.029132 
                 −0.06475 
                 No 
               
               
                 TT_ZnMg 
                 −0.0045818 
                 −0.018092 
                 −0.010328 
                 No 
               
               
                 TT_ZnMn 
                 −0.0104633 
                 −0.205922 
                 −0.02292 
                 No 
               
               
                 TT_ZnP 
                 −0.1875745 
                 0.0690681 
                 0.0053797 
                 No 
               
               
                 TT_ZnPb 
                 −0.0955299 
                 −0.014054 
                 −0.009815 
                 No 
               
               
                 TT_ZnS 
                 0.13780415 
                 0.1133418 
                 −0.037847 
                 No 
               
               
                 TT_ZnSn 
                 0.02869677 
                 0.018639 
                 0.0222917 
                 No 
               
               
                 TT_ZnSr 
                 −0.006393 
                 −0.024858 
                 −0.009046 
                 No 
               
               
                 RT2_Ba 
                 0.01753878 
                 −0.005345 
                 0.0096051 
                 Yes 
               
               
                 RT2_Ca 
                 0.0057303 
                 0.0147895 
                 0.0100111 
                 Yes 
               
               
                 RT2_Cr 
                 −0.0109448 
                 0.035535 
                 0.0976647 
                 Yes 
               
               
                 RT2_Cu 
                 −0.0054492 
                 −0.019742 
                 −0.005034 
                 Yes 
               
               
                 RT2_Fe 
                 0.01192527 
                 0.0086596 
                 −0.005167 
                 No 
               
               
                 RT2_I 
                 0.10029701 
                 −0.002962 
                 0.0345432 
                 Yes 
               
               
                 RT2_Mg 
                 0.00441249 
                 −0.003118 
                 −0.001238 
                 Yes 
               
               
                 RT2_Mn 
                 0.01166653 
                 0.0282244 
                 0.0445817 
                 Yes 
               
               
                 RT2_P 
                 −0.0467173 
                 −0.014714 
                 −0.030091 
                 Yes 
               
               
                 RT2_Pb 
                 −0.0356385 
                 0.0121896 
                 −0.005266 
                 Yes 
               
               
                 RT2_S 
                 −0.0126324 
                 0.0037994 
                 0.0116706 
                 Yes 
               
               
                 RT2_Sn 
                 0.01129278 
                 −0.051285 
                 −0.021345 
                 Yes 
               
               
                 RT2_Sr 
                 0.0080479 
                 0.012611 
                 0.0044624 
                 Yes 
               
               
                 RT2_Zn 
                 0.00181413 
                 0.0131742 
                 0.0078403 
                 Yes 
               
               
                 RT2_ZnBa 
                 0.01226505 
                 −0.007477 
                 −0.001362 
                 Yes 
               
               
                 RT2_ZnCa 
                 0.00551711 
                 0.0145315 
                 0.0114526 
                 Yes 
               
               
                 RT2_ZnCr 
                 −0.0162167 
                 0.0371156 
                 0.0076685 
                 Yes 
               
               
                 RT2_ZnCu 
                 −0.0044728 
                 0.0003192 
                 −6.73E−05 
                 Yes 
               
               
                 RT2_ZnFe 
                 0.02795988 
                 0.0166935 
                 0.0145322 
                 Yes 
               
               
                 RT2_ZnI 
                 0.02424935 
                 0.0020863 
                 0.0189538 
                 Yes 
               
               
                 RT2_ZnMg 
                 0.0031477 
                 −5.67E−05 
                 −0.008444 
                 Yes 
               
               
                 RT2_ZnMn 
                 0.00746097 
                 0.0225867 
                 0.0065851 
                 Yes 
               
               
                 RT2_ZnP 
                 −0.0250943 
                 −0.001581 
                 −0.024449 
                 Yes 
               
               
                 RT2_ZnPb 
                 −0.0041028 
                 0.0130104 
                 −0.0014 
                 Yes 
               
               
                 RT2_ZnS 
                 −0.0076205 
                 0.0106253 
                 0.0129481 
                 Yes 
               
               
                 RT2_ZnSn 
                 −0.0038046 
                 −0.012371 
                 −0.017383 
                 Yes 
               
               
                 RT2_ZnSr 
                 0.00105254 
                 0.008575 
                 −0.00386 
                 Yes 
               
               
                   
               
            
           
         
       
     
     Example 4—Amyotrophic Lateral Sclerosis (ALS) 
     ALS participants, meeting revised EI Escorial Word Federation of Neurology criteria (N=36) were recruited at an ALS clinic. Clinical and family history data were obtained. Age- and sex-matched control participants were recruited at the Oral Surgery Clinic. Control subjects (N=31) were excluded if they or a first- or second-degree family member had a neurodegenerative disease. Participants or next of kin provided informed consent. 
     For ALS, the evaluation was performed from tooth samples. Table 6 illustrates the features used and their corresponding β values. The β values are obtained by estimating each feature in the respective cohort that describes a change in log odds of ALS status associated with a 1-unit change for a respective feature.  FIG. 6  illustrates the experimental ROC curve for evaluating accuracy of the disclosed method of evaluating ALS across the cohort. As shown in  FIG. 6 , the ROC curve derived from experimental data to evaluate the performance of the disclosed classification method has an AUC corresponding to 0.869, indicating that the disclosed method has 85% accuracy across the cohort for evaluation of ALS based on tooth samples. 
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Features with empirical x values for a subject based on a tooth 
               
               
                 sample of the subject for evaluating the subject for ALS. 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Feature in 
               
               
                   
                 Feature 
                 β value 
                 Table 2 or 3? 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 (Intercept) 
                 83.96232 
                 No 
               
               
                   
                 result.Cu.MaxFreq 
                 −1.27115 
                 No 
               
               
                   
                 result.Li.MaxFreq 
                 −0.0579 
                 No 
               
               
                   
                 result.Mg.MaxFreq 
                 −267.415 
                 No 
               
               
                   
                 result.Mn.MaxFreq 
                 23.69603 
                 No 
               
               
                   
                 result.Zn.MaxFreq 
                 −35.6081 
                 No 
               
               
                   
                 Determinism_Cu 
                 48.30136 
                 Yes 
               
               
                   
                 Determinism_Li 
                 −96.9188 
                 Yes 
               
               
                   
                 Determinism_Mg 
                 43.43997 
                 Yes 
               
               
                   
                 Determinism_Mn 
                 63.09591 
                 Yes 
               
               
                   
                 Determinism_Zn 
                 123.8952 
                 No 
               
               
                   
                 Entropy_Cu 
                 −68.1936 
                 Yes 
               
               
                   
                 Entropy_Li 
                 61.47467 
                 Yes 
               
               
                   
                 Entropy_Mg 
                 −3.63648 
                 Yes 
               
               
                   
                 Entropy_Mn 
                 −17.6021 
                 Yes 
               
               
                   
                 Entropy_Zn 
                 −28.8004 
                 Yes 
               
               
                   
                 MDL_Cu 
                 8.374507 
                 Yes 
               
               
                   
                 MDL_Li 
                 −11.6838 
                 Yes 
               
               
                   
                 MDL_Mg 
                 83.96232 
                 Yes 
               
               
                   
                 MDL_Mn 
                 −1.27115 
                 Yes 
               
               
                   
                 MDL_Zn 
                 −0.0579 
                 Yes 
               
               
                   
                   
               
            
           
         
       
     
     Example 5—Schizophrenia 
     Participants with a DSM-IV diagnosis of schizophrenia were selected from the Genetic Risk and OUtcome of Psychosis (GROUP) study (n=20) and unaffected siblings were used as controls (n=7). Severity of positive symptoms, negative symptoms, and general psychopathology were assessed by the Positive and Negative Symptom Scale (PANSS). In addition, participants with a DSM-IV diagnosis of schizophrenia (n=25) and controls (n=24) were selected from the Avon Longitudinal Study of Parents and Children (ALSPAC), a prospective longitudinal cohort study based in the UK. Presence of DSM-IV schizophrenia in ALSAPC was determined at age 18 and 24 using a semi-structured interview based on the Schedules for Clinical Assessment in Neuropsychiatry psychosis section (SCAN version 2.0). 
     For schizophrenia, the evaluation was performed from tooth samples. Table 7 illustrates the features used and their corresponding β values. The β values are obtained by estimating each feature in the respective cohort that describes a change in log odds of schizophrenia status associated with a 1-unit change for a respective feature.  FIG. 7  illustrates the experimental ROC curve for evaluating schizophrenia across the cohort. As shown in  FIG. 7 , the ROC curve has an AUC corresponding to 1.000, indicating that the disclosed method has 100% accuracy in determining schizophrenia based on tooth samples across the cohort. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Features with empirical x values for a subject based on a tooth sample 
               
               
                 of the subject for evaluating the subject for schizophrenia. 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Feature in 
               
               
                   
                 Feature 
                 β value 
                 Table 2 or 3? 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Determinism_Sr 
                 −0.457644394 
                 Yes 
               
               
                   
                 Determinism_Mn 
                 −0.442460904 
                 Yes 
               
               
                   
                 Determinism_Mg 
                 −0.402732595 
                 Yes 
               
               
                   
                 Determinism_Zn 
                 −0.384259825 
                 No 
               
               
                   
                 Determinism_Ca 
                 −0.382835469 
                 Yes 
               
               
                   
                 Determinism_Li 
                 −0.335344646 
                 Yes 
               
               
                   
                 Determinism_As 
                 −0.320110102 
                 Yes 
               
               
                   
                 Determinism_Al 
                 −0.318766205 
                 Yes 
               
               
                   
                 Determinism_Ba 
                 −0.277937215 
                 Yes 
               
               
                   
                 Determinism_Cu 
                 −0.259516956 
                 Yes 
               
               
                   
                 Determinism_Se 
                 −0.245987898 
                 No 
               
               
                   
                 Determinism_Cr 
                 −0.244131668 
                 Yes 
               
               
                   
                 Determinism_Pb 
                 −0.236575919 
                 Yes 
               
               
                   
                 Determinism_Ni 
                 −0.230505691 
                 Yes 
               
               
                   
                 Determinism_Sn 
                 −0.225723456 
                 Yes 
               
               
                   
                 Determinism_Co 
                 −0.198677773 
                 Yes 
               
               
                   
                 Entropy_Li 
                 −0.129943086 
                 Yes 
               
               
                   
                 Entropy_Al 
                 −0.120001216 
                 Yes 
               
               
                   
                 Entropy_Zn 
                 −0.116505828 
                 Yes 
               
               
                   
                 Entropy_Mg 
                 −0.110037638 
                 Yes 
               
               
                   
                 Entropy_As 
                 −0.109300067 
                 Yes 
               
               
                   
                 Entropy_Ca 
                 −0.105637312 
                 Yes 
               
               
                   
                 Entropy_Mn 
                 −0.101053528 
                 Yes 
               
               
                   
                 MDL_Li 
                 −0.095287157 
                 Yes 
               
               
                   
                 Entropy_Se 
                 −0.090043146 
                 No 
               
               
                   
                 MDL_Al 
                 −0.086620564 
                 Yes 
               
               
                   
                 Entropy_Pb 
                 −0.084836256 
                 Yes 
               
               
                   
                 Entropy_Sr 
                 −0.084833755 
                 Yes 
               
               
                   
                 Entropy_Cu 
                 −0.084363276 
                 Yes 
               
               
                   
                 Entropy_Sn 
                 −0.083399856 
                 Yes 
               
               
                   
                 Entropy_Cr 
                 −0.081410354 
                 Yes 
               
               
                   
                 Entropy_Ni 
                 −0.080268765 
                 Yes 
               
               
                   
                 Entropy_Co 
                 −0.072165671 
                 Yes 
               
               
                   
                 MDL_As 
                 −0.069228208 
                 Yes 
               
               
                   
                 MDL_Se 
                 −0.058812871 
                 No 
               
               
                   
                 MDL_Zn 
                 −0.058073407 
                 Yes 
               
               
                   
                 Entropy_Ba 
                 −0.053496347 
                 Yes 
               
               
                   
                 MDL_Mg 
                 −0.050907767 
                 Yes 
               
               
                   
                 MDL_Ca 
                 −0.048437027 
                 Yes 
               
               
                   
                 MDL_Sn 
                 −0.045623074 
                 Yes 
               
               
                   
                 MDL_Pb 
                 −0.04510374 
                 Yes 
               
               
                   
                 MDL_Cr 
                 −0.041331302 
                 Yes 
               
               
                   
                 MDL_Cu 
                 −0.040429247 
                 Yes 
               
               
                   
                 MDL_Co 
                 −0.039999687 
                 Yes 
               
               
                   
                 MDL_Ni 
                 −0.03813012 
                 Yes 
               
               
                   
                 MDL_Mn 
                 −0.034183415 
                 Yes 
               
               
                   
                 MDL_Sr 
                 −0.024060458 
                 Yes 
               
               
                   
                 MDL_Ba 
                 −0.012524148 
                 Yes 
               
               
                   
                 MDL_Bi 
                 0.052480638 
                 No 
               
               
                   
                 Entropy_Bi 
                 0.118716291 
                 Yes 
               
               
                   
                 Determinism_Bi 
                 0.336109649 
                 Yes 
               
               
                   
                   
               
            
           
         
       
     
     Example 6—Irritable Bowel Disease (IBD) 
     Subjects were recruited from a study based in Portugal. Tooth samples were obtained from 11 patients diagnosed with TBD (Chron&#39;s Disease=6, ulcerative colitis/indeterminate colitis=5) and 16 unaffected controls. All participants were born and grew up in the same Portuguese Province. Each subject was evaluated for TDB using a similar method as described above with respect to Examples 2 and 3. For IDB the evaluation was performed from a tooth sample. Table 8 illustrates the features used and their corresponding β values. The β values are obtained by estimating each feature in the respective cohort that describes a change in log odds of IBD status associated with a 1-unit change for a respective feature. 
       FIG. 8  illustrates experimental ROC curves for evaluating accuracy of the disclosed method of evaluating a subject for schizophrenia. As shown in  FIG. 8 , the ROC curve derived from experimental data to evaluate the performance of the disclosed classification method has an AUC corresponding to 0.915, indicating that the disclosed method has above 90% accuracy for IBD determination based on tooth samples. 
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Features with empirical x values for IBD. 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Feature in 
               
               
                   
                 Feature 
                 β value 
                 Table 2 or 3? 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Determinism_Pb 
                 0.837721661 
                 Yes 
               
               
                   
                 Determinism_CoCd 
                 0.608033699 
                 No 
               
               
                   
                 Determinism_NiCd 
                 0.583651036 
                 No 
               
               
                   
                 Determinism_Mn 
                 0.580065903 
                 Yes 
               
               
                   
                 Determinism_ZnSn 
                 0.579284697 
                 Yes 
               
               
                   
                 Determinism_AlPb 
                 0.577467897 
                 No 
               
               
                   
                 Determinism_Bi 
                 0.537065232 
                 Yes 
               
               
                   
                 Determinism_SrPb 
                 0.493960945 
                 No 
               
               
                   
                 Determinism_CoCu 
                 0.463814561 
                 No 
               
               
                   
                 Determinism_CoAs 
                 0.456605412 
                 No 
               
               
                   
                 Determinism_SrSn 
                 0.447913275 
                 No 
               
               
                   
                 Determinism_NiMo 
                 0.446153665 
                 No 
               
               
                   
                 Determinism_NiSn 
                 0.442477131 
                 No 
               
               
                   
                 Determinism_CoSn 
                 0.440085861 
                 No 
               
               
                   
                 Determinism_MnCu 
                 0.420156241 
                 No 
               
               
                   
                 Determinism_AlAs 
                 0.394030337 
                 No 
               
               
                   
                 Determinism_AlCa43 
                 0.393499257 
                 No 
               
               
                   
                 Determinism_AlMn 
                 0.388228381 
                 No 
               
               
                   
                 Determinism_CoNi 
                 0.369794172 
                 No 
               
               
                   
                 Determinism_Ca43Cu 
                 0.367746635 
                 No 
               
               
                   
                 Determinism_AlCu 
                 0.367706871 
                 No 
               
               
                   
                 Determinism_NiPb 
                 0.366479003 
                 No 
               
               
                   
                 Determinism_CuPb 
                 0.365132868 
                 No 
               
               
                   
                 Determinism_CoZn 
                 0.358897573 
                 No 
               
               
                   
                 Determinism_SnBa 
                 0.348806193 
                 No 
               
               
                   
                 Determinism_NiBi 
                 0.347509524 
                 No 
               
               
                   
                 Determinism_Ca43Ba 
                 0.338250186 
                 No 
               
               
                   
                 Determinism_CoSr 
                 0.335913385 
                 No 
               
               
                   
                 Determinism_CoPb 
                 0.330166861 
                 No 
               
               
                   
                 Determinism_AlSr 
                 0.327066202 
                 No 
               
               
                   
                 Determinism_CrCu 
                 0.323166738 
                 No 
               
               
                   
                 Determinism_NiAs 
                 0.319802598 
                 No 
               
               
                   
                 Determinism_MnAs 
                 0.303183281 
                 No 
               
               
                   
                 Determinism_AlBa 
                 0.283176281 
                 No 
               
               
                   
                 Determinism_MnSn 
                 0.277834073 
                 No 
               
               
                   
                 Determinism_Cu 
                 0.272437834 
                 No 
               
               
                   
                 Determinism_NiZn 
                 0.271167365 
                 No 
               
               
                   
                 Determinism_AlSn 
                 0.266885502 
                 No 
               
               
                   
                 Determinism_CdSn 
                 0.264283744 
                 No 
               
               
                   
                 Determinism_SrMo 
                 0.258823829 
                 No 
               
               
                   
                 Determinism_SnPb 
                 0.258076389 
                 No 
               
               
                   
                 Determinism_Co 
                 0.251749701 
                 Yes 
               
               
                   
                 Determinism_AlZn 
                 0.251072583 
                 No 
               
               
                   
                 Determinism_Ni 
                 0.243471714 
                 Yes 
               
               
                   
                 Determinism_MnNi 
                 0.236046191 
                 No 
               
               
                   
                 Determinism_CuBa 
                 0.225800693 
                 No 
               
               
                   
                 Determinism_Ca43Pb 
                 0.221077979 
                 No 
               
               
                   
                 Determinism_AsSr 
                 0.21986349 
                 No 
               
               
                   
                 Determinism_AlNi 
                 0.208256778 
                 No 
               
               
                   
                 Determinism_Mg25Pb 
                 0.204110935 
                 No 
               
               
                   
                 Determinism_CoBi 
                 0.192229974 
                 No 
               
               
                   
                 Determinism_AlBi 
                 0.19174288 
                 No 
               
               
                   
                 Determinism_NiCu 
                 0.189023023 
                 No 
               
               
                   
                 Determinism_Al 
                 0.188772179 
                 Yes 
               
               
                   
                 Determinism_MnBi 
                 0.181404932 
                 No 
               
               
                   
                 Determinism_SrBi 
                 0.179589562 
                 No 
               
               
                   
                 Determinism_CoMo 
                 0.178920834 
                 No 
               
               
                   
                 Determinism_CuSr 
                 0.173849996 
                 No 
               
               
                   
                 Determinism_AlCr 
                 0.169620126 
                 No 
               
               
                   
                 Determinism_Sn 
                 0.157158501 
                 Yes 
               
               
                   
                 Entropy_MnCu 
                 0.150045454 
                 No 
               
               
                   
                 Determinism_CoBa 
                 0.14806543 
                 No 
               
               
                   
                 Determinism_SnBi 
                 0.146080673 
                 No 
               
               
                   
                 Determinism_MnCo 
                 0.13689247 
                 No 
               
               
                   
                 Determinism_AlMo 
                 0.135095212 
                 No 
               
               
                   
                 Entropy_SrBi 
                 0.133631105 
                 No 
               
               
                   
                 Determinism_MnBa 
                 0.131543875 
                 No 
               
               
                   
                 Determinism_BaPb 
                 0.129043442 
                 No 
               
               
                   
                 Determinism_NiSr 
                 0.118585723 
                 No 
               
               
                   
                 Entropy_NiMo 
                 0.117468751 
                 No 
               
               
                   
                 Determinism_SrBa 
                 0.110628434 
                 No 
               
               
                   
                 Determinism_CdBa 
                 0.105904929 
                 No 
               
               
                   
                 Entropy_Pb 
                 0.096701332 
                 Yes 
               
               
                   
                 Entropy_LiNi 
                 0.096600763 
                 No 
               
               
                   
                 Entropy_AlNi 
                 0.096261656 
                 No 
               
               
                   
                 Entropy_LiCr 
                 0.095557786 
                 No 
               
               
                   
                 Determinism_AlCd 
                 0.093269413 
                 No 
               
               
                   
                 Entropy_NiCd 
                 0.090526996 
                 No 
               
               
                   
                 Entropy_Mn 
                 0.088216945 
                 Yes 
               
               
                   
                 Entropy_AsSr 
                 0.086331274 
                 No 
               
               
                   
                 Determinism_Mg25Cu 
                 0.085901097 
                 No 
               
               
                   
                 Entropy_LiCa43 
                 0.085357299 
                 No 
               
               
                   
                 Entropy_MnNi 
                 0.085231831 
                 No 
               
               
                   
                 Entropy_MoCd 
                 0.084513633 
                 No 
               
               
                   
                 Entropy_AlCr 
                 0.083519607 
                 No 
               
               
                   
                 Entropy_AlSn 
                 0.081448169 
                 No 
               
               
                   
                 Entropy_LiAl 
                 0.078847087 
                 No 
               
               
                   
                 Entropy_Sn 
                 0.07782499 
                 Yes 
               
               
                   
                 Determinism_Mg25Ni 
                 0.077455521 
                 No 
               
               
                   
                 Determinism_MoSn 
                 0.074550109 
                 No 
               
               
                   
                 Entropy_NiAs 
                 0.073763013 
                 No 
               
               
                   
                 Determinism_AsBa 
                 0.073113685 
                 No 
               
               
                   
                 Determinism_Mg25Mo 
                 0.072837473 
                 No 
               
               
                   
                 Determinism_Mg25Ca43 
                 0.066896429 
                 No 
               
               
                   
                 Entropy_CuSr 
                 0.066616184 
                 No 
               
               
                   
                 Entropy_MnBi 
                 0.065186033 
                 No 
               
               
                   
                 Entropy_SrSn 
                 0.064276558 
                 No 
               
               
                   
                 Determinism_ZnBi 
                 0.063181991 
                 No 
               
               
                   
                 Entropy_LiZn 
                 0.06274205 
                 No 
               
               
                   
                 Entropy_NiSn 
                 0.062065578 
                 No 
               
               
                   
                 Entropy_AlCd 
                 0.061932776 
                 No 
               
               
                   
                 Entropy_MnSn 
                 0.061917389 
                 No 
               
               
                   
                 Entropy_AlAs 
                 0.060589179 
                 No 
               
               
                   
                 Entropy_LiAs 
                 0.059907306 
                 No 
               
               
                   
                 Entropy_AlCu 
                 0.059570784 
                 No 
               
               
                   
                 MDL_NiPb 
                 0.059356348 
                 No 
               
               
                   
                 Determinism_CuSn 
                 0.057883324 
                 No 
               
               
                   
                 Entropy_CoAs 
                 0.056975722 
                 No 
               
               
                   
                 Entropy_CoCd 
                 0.056619699 
                 No 
               
               
                   
                 Entropy_AlBi 
                 0.056592751 
                 No 
               
               
                   
                 Entropy_LiSn 
                 0.055407714 
                 No 
               
               
                   
                 MDL_NiCu 
                 0.05462465 
                 No 
               
               
                   
                 Determinism_Sr 
                 0.052769123 
                 Yes 
               
               
                   
                 MDL_SrBi 
                 0.052757632 
                 No 
               
               
                   
                 Entropy_MnCd 
                 0.051491996 
                 No 
               
               
                   
                 MDL_AlCu 
                 0.051084234 
                 No 
               
               
                   
                 Entropy_MnZn 
                 0.05095569 
                 No 
               
               
                   
                 MDL_NiCd 
                 0.050821168 
                 No 
               
               
                   
                 MDL_NiAs 
                 0.049999502 
                 No 
               
               
                   
                 MDL_NiMo 
                 0.049942464 
                 No 
               
               
                   
                 MDL_LiPb 
                 0.049236366 
                 No 
               
               
                   
                 Entropy_BaBi 
                 0.04888417 
                 No 
               
               
                   
                 Entropy_AlSr 
                 0.048461583 
                 No 
               
               
                   
                 Entropy_NiZn 
                 0.04818889 
                 No 
               
               
                   
                 MDL_MnNi 
                 0.045506307 
                 No 
               
               
                   
                 Entropy_ZnBa 
                 0.045366615 
                 Yes 
               
               
                   
                 MDL_CoAs 
                 0.045133938 
                 No 
               
               
                   
                 MDL_AlNi 
                 0.044994651 
                 No 
               
               
                   
                 Entropy_Cu 
                 0.044750116 
                 Yes 
               
               
                   
                 MDL_AlPb 
                 0.044651067 
                 No 
               
               
                   
                 MDL_NiSn 
                 0.04447437 
                 No 
               
               
                   
                 Determinism_CuZn 
                 0.04346297 
                 No 
               
               
                   
                 MDL_MnBi 
                 0.04293887 
                 No 
               
               
                   
                 Entropy_SrCd 
                 0.041911866 
                 No 
               
               
                   
                 Entropy_CoNi 
                 0.040717095 
                 No 
               
               
                   
                 Entropy_SnBa 
                 0.040439261 
                 No 
               
               
                   
                 MDL_LiCu 
                 0.040400882 
                 No 
               
               
                   
                 MDL_CoNi 
                 0.039722706 
                 No 
               
               
                   
                 MDL_CrCu 
                 0.039141039 
                 No 
               
               
                   
                 MDL_Sn 
                 0.039030533 
                 Yes 
               
               
                   
                 Determinism_LiCu 
                 0.03819333 
                 No 
               
               
                   
                 Entropy_MnAs 
                 0.037845825 
                 No 
               
               
                   
                 Entropy_LiMo 
                 0.037836232 
                 No 
               
               
                   
                 Entropy_Mg25Cu 
                 0.037830094 
                 No 
               
               
                   
                 MDL_CoSn 
                 0.037703149 
                 No 
               
               
                   
                 MDL_AlCr 
                 0.036913043 
                 No 
               
               
                   
                 MDL_ZnPb 
                 0.036670246 
                 Yes 
               
               
                   
                 Entropy_LiCu 
                 0.035253147 
                 No 
               
               
                   
                 MDL_MoCd 
                 0.034863673 
                 No 
               
               
                   
                 MDL_AlSn 
                 0.033729785 
                 No 
               
               
                   
                 MDL_AlCd 
                 0.033444913 
                 No 
               
               
                   
                 Entropy_Mg25Ca43 
                 0.033104137 
                 No 
               
               
                   
                 MDL_MnCd 
                 0.032959444 
                 No 
               
               
                   
                 Entropy_LiBi 
                 0.032933544 
                 No 
               
               
                   
                 MDL_BaBi 
                 0.032773839 
                 No 
               
               
                   
                 Determinism_CrBa 
                 0.03267654 
                 No 
               
               
                   
                 Entropy_CuBa 
                 0.032551901 
                 No 
               
               
                   
                 Entropy_LiPb 
                 0.03241727 
                 No 
               
               
                   
                 Entropy_AlPb 
                 0.031942708 
                 No 
               
               
                   
                 Determinism_MnMo 
                 0.03151546 
                 No 
               
               
                   
                 MDL_AsSr 
                 0.030340482 
                 No 
               
               
                   
                 MDL_Pb 
                 0.030277868 
                 Yes 
               
               
                   
                 MDL_CoCd 
                 0.030102262 
                 No 
               
               
                   
                 Entropy_AsPb 
                 0.029893974 
                 No 
               
               
                   
                 Entropy_SrMo 
                 0.028854133 
                 No 
               
               
                   
                 MDL_MnAs 
                 0.028558981 
                 No 
               
               
                   
                 MDL_Bi 
                 0.028474966 
                 No 
               
               
                   
                 MDL_AlBi 
                 0.028265509 
                 No 
               
               
                   
                 Entropy_CrSr 
                 0.028254263 
                 No 
               
               
                   
                 MDL_Mn 
                 0.02754259 
                 Yes 
               
               
                   
                 Entropy_LiMg25 
                 0.02719571 
                 No 
               
               
                   
                 MDL_CuSn 
                 0.026802102 
                 No 
               
               
                   
                 Entropy_Al 
                 0.026660621 
                 Yes 
               
               
                   
                 MDL_SrSn 
                 0.026417738 
                 No 
               
               
                   
                 Determinism_BaBi 
                 0.026118071 
                 No 
               
               
                   
                 MDL_CuMo 
                 0.025833509 
                 No 
               
               
                   
                 MDL_Ca43Cu 
                 0.025021625 
                 No 
               
               
                   
                 Entropy_CrBa 
                 0.024590968 
                 No 
               
               
                   
                 Entropy_CuSn 
                 0.023936374 
                 No 
               
               
                   
                 Entropy_SnBi 
                 0.023796602 
                 No 
               
               
                   
                 Entropy_NiBi 
                 0.023666703 
                 No 
               
               
                   
                 Entropy_BaPb 
                 0.02316239 
                 No 
               
               
                   
                 MDL_SnBi 
                 0.022967977 
                 No 
               
               
                   
                 MDL_MnZn 
                 0.022794853 
                 No 
               
               
                   
                 Entropy_AsBa 
                 0.022724576 
                 No 
               
               
                   
                 Entropy_AlBa 
                 0.022251972 
                 No 
               
               
                   
                 MDL_MnSn 
                 0.022230802 
                 No 
               
               
                   
                 MDL_ZnAs 
                 0.022102064 
                 Yes 
               
               
                   
                 Entropy_ZnAs 
                 0.021389434 
                 Yes 
               
               
                   
                 MDL_BaPb 
                 0.021250278 
                 No 
               
               
                   
                 MDL_NiZn 
                 0.020720792 
                 No 
               
               
                   
                 Entropy_Ba 
                 0.020553585 
                 Yes 
               
               
                   
                 Entropy_Co 
                 0.019950137 
                 Yes 
               
               
                   
                 Entropy_NiPb 
                 0.019835982 
                 No 
               
               
                   
                 MDL_AlAs 
                 0.019594507 
                 No 
               
               
                   
                 MDL_CuSr 
                 0.019428846 
                 No 
               
               
                   
                 Determinism_CdPb 
                 0.019354351 
                 No 
               
               
                   
                 MDL_Cr 
                 0.019090509 
                 Yes 
               
               
                   
                 Entropy_NiCu 
                 0.018579507 
                 No 
               
               
                   
                 MDL_MnPb 
                 0.018264661 
                 No 
               
               
                   
                 Entropy_Cr 
                 0.017852524 
                 Yes 
               
               
                   
                 MDL_AsPb 
                 0.017053517 
                 No 
               
               
                   
                 MDL_Al 
                 0.016864812 
                 Yes 
               
               
                   
                 Entropy_ZnPb 
                 0.016837243 
                 Yes 
               
               
                   
                 MDL_NiBi 
                 0.015778181 
                 No 
               
               
                   
                 MDL_AlBa 
                 0.015732134 
                 No 
               
               
                   
                 Determinism_Ba 
                 0.015387888 
                 Yes 
               
               
                   
                 Entropy_CoSn 
                 0.015061341 
                 No 
               
               
                   
                 MDL_CuBi 
                 0.014143895 
                 No 
               
               
                   
                 Entropy_AlZn 
                 0.014101886 
                 No 
               
               
                   
                 Entropy_CoMo 
                 0.014040446 
                 No 
               
               
                   
                 Entropy_CuMo 
                 0.013876978 
                 No 
               
               
                   
                 MDL_CrBa 
                 0.013871868 
                 No 
               
               
                   
                 MDL_Ba 
                 0.013657256 
                 Yes 
               
               
                   
                 MDL_MnCu 
                 0.013536051 
                 No 
               
               
                   
                 Entropy_Bi 
                 0.013378595 
                 Yes 
               
               
                   
                 MDL_CrNi 
                 0.013115327 
                 No 
               
               
                   
                 MDL_CuBa 
                 0.012143264 
                 No 
               
               
                   
                 MDL_SrCd 
                 0.011897196 
                 No 
               
               
                   
                 Entropy_Ca43Sr 
                 0.011668152 
                 No 
               
               
                   
                 Entropy_ZnSn 
                 0.010322362 
                 Yes 
               
               
                   
                 Entropy_Mg25Cr 
                 0.010258145 
                 No 
               
               
                   
                 Entropy_CuBi 
                 0.009857028 
                 No 
               
               
                   
                 MDL_SnBa 
                 0.009355043 
                 No 
               
               
                   
                 MDL_CoPb 
                 0.009250621 
                 No 
               
               
                   
                 MDL_ZnSn 
                 0.009214463 
                 Yes 
               
               
                   
                 MDL_CdPb 
                 0.008436296 
                 No 
               
               
                   
                 MDL_ZnBa 
                 0.008373169 
                 Yes 
               
               
                   
                 MDL_CrSn 
                 0.00831045 
                 No 
               
               
                   
                 MDL_CoMo 
                 0.008195326 
                 No 
               
               
                   
                 MDL_CrPb 
                 0.008157123 
                 No 
               
               
                   
                 MDL_Mg25Ca43 
                 0.00808495 
                 No 
               
               
                   
                 MDL_CoZn 
                 0.008064695 
                 No 
               
               
                   
                 Entropy_MnBa 
                 0.00798082 
                 No 
               
               
                   
                 Entropy_NiSr 
                 0.007615698 
                 No 
               
               
                   
                 MDL_Mg25Cu 
                 0.007513622 
                 No 
               
               
                   
                 MDL_CrZn 
                 0.007458255 
                 No 
               
               
                   
                 MDL_Cu 
                 0.007404707 
                 Yes 
               
               
                   
                 MDL_AlSr 
                 0.006611509 
                 No 
               
               
                   
                 Entropy_Ni 
                 0.006471257 
                 No 
               
               
                   
                 MDL_AsBa 
                 0.006254217 
                 No 
               
               
                   
                 MDL_MnBa 
                 0.00598819 
                 No 
               
               
                   
                 Entropy_Ca43Cu 
                 0.005658041 
                 No 
               
               
                   
                 MDL_Mg25Pb 
                 0.00559757 
                 No 
               
               
                   
                 Determinism_LiNi 
                 0.004788003 
                 No 
               
               
                   
                 MDL_AlZn 
                 0.004786941 
                 No 
               
               
                   
                 MDL_CuZn 
                 0.004075936 
                 No 
               
               
                   
                 MDL_Mg25Sn 
                 0.003699523 
                 No 
               
               
                   
                 MDL_MnMo 
                 0.003341513 
                 No 
               
               
                   
                 Entropy_CoPb 
                 0.002872541 
                 No 
               
               
                   
                 MDL_SrPb 
                 0.0026864 
                 No 
               
               
                   
                 MDL_LiCa43 
                 0.002653581 
                 No 
               
               
                   
                 MDL_SnPb 
                 0.002566204 
                 No 
               
               
                   
                 MDL_CrSr 
                 0.002467427 
                 No 
               
               
                   
                 MDL_CoSr 
                 0.002339729 
                 No 
               
               
                   
                 MDL_Sr 
                 0.002243815 
                 Yes 
               
               
                   
                 Entropy_Mg25Pb 
                 0.002122864 
                 No 
               
               
                   
                 MDL_LiNi 
                 0.001696513 
                 No 
               
               
                   
                 Entropy_CrCu 
                 0.001582979 
                 No 
               
               
                   
                 MDL_SrBa 
                 0.001162027 
                 No 
               
               
                   
                 Entropy_SnPb 
                 0.000916207 
                 No 
               
               
                   
                 Determinism_Mg25 
                 0.000803475 
                 No 
               
               
                   
                 MDL_Co 
                 0.00025716 
                 Yes 
               
               
                   
                 Entropy_AlCa43 
                 −1.38E−05 
                 No 
               
               
                   
                 MDL_NiBa 
                 −0.000244236 
                 No 
               
               
                   
                 MDL_Ca43Sn 
                 −0.001253881 
                 No 
               
               
                   
                 MDL_SrMo 
                 −0.001497868 
                 No 
               
               
                   
                 Entropy_Mg25Sn 
                 −0.001842896 
                 No 
               
               
                   
                 MDL_CrAs 
                 −0.002029876 
                 No 
               
               
                   
                 MDL_Ni 
                 −0.002069796 
                 Yes 
               
               
                   
                 Entropy_MnPb 
                 −0.00291857 
                 No 
               
               
                   
                 MDL_AsCd 
                 −0.002927082 
                 No 
               
               
                   
                 MDL_LiBi 
                 −0.003023387 
                 No 
               
               
                   
                 MDL_CuAs 
                 −0.003515146 
                 No 
               
               
                   
                 Entropy_LiBa 
                 −0.003785078 
                 No 
               
               
                   
                 MDL_AlCa43 
                 −0.003900959 
                 No 
               
               
                   
                 Entropy_CrZn 
                 −0.005150422 
                 No 
               
               
                   
                 Determinism_Ca43 
                 −0.005493317 
                 No 
               
               
                   
                 Entropy_Ca43 
                 −0.005523451 
                 No 
               
               
                   
                 MDL_AlMn 
                 −0.005635517 
                 No 
               
               
                   
                 MDL_Zn 
                 −0.006177405 
                 Yes 
               
               
                   
                 Entropy_CoSr 
                 −0.006810491 
                 No 
               
               
                   
                 Entropy_AsCd 
                 −0.007060322 
                 No 
               
               
                   
                 Determinism_CrSr 
                 −0.007322712 
                 No 
               
               
                   
                 Determinism_SrCd 
                 −0.007335886 
                 No 
               
               
                   
                 MDL_Mg25Ba 
                 −0.007450877 
                 No 
               
               
                   
                 Entropy_Sr 
                 −0.007681616 
                 Yes 
               
               
                   
                 MDL_AlMo 
                 −0.007777482 
                 No 
               
               
                   
                 MDL_MoSn 
                 −0.007813266 
                 No 
               
               
                   
                 MDL_MnSr 
                 −0.0078902 
                 No 
               
               
                   
                 MDL_CoBa 
                 −0.007987333 
                 No 
               
               
                   
                 MDL_Mg25Cr 
                 −0.008021723 
                 No 
               
               
                   
                 MDL_CoBi 
                 −0.008026512 
                 No 
               
               
                   
                 MDL_LiBa 
                 −0.008125012 
                 No 
               
               
                   
                 MDL_Ca43Pb 
                 −0.00876952 
                 No 
               
               
                   
                 MDL_CuCd 
                 −0.009012709 
                 No 
               
               
                   
                 MDL_CrBi 
                 −0.009417947 
                 No 
               
               
                   
                 MDL_Ca43Sr 
                 −0.009530661 
                 No 
               
               
                   
                 MDL_LiSr 
                 −0.00958387 
                 No 
               
               
                   
                 MDL_CoCu 
                 −0.010617794 
                 No 
               
               
                   
                 MDL_LiZn 
                 −0.010869207 
                 No 
               
               
                   
                 Determinism_Mg25Cd 
                 −0.011141724 
                 No 
               
               
                   
                 MDL_NiSr 
                 −0.01145434 
                 No 
               
               
                   
                 MDL_Ca43 
                 −0.011517201 
                 No 
               
               
                   
                 Entropy_LiMn 
                 −0.01154657 
                 No 
               
               
                   
                 MDL_Mg25 
                 −0.011778792 
                 No 
               
               
                   
                 MDL_LiMn 
                 −0.012781052 
                 No 
               
               
                   
                 Entropy_CrPb 
                 −0.012946148 
                 No 
               
               
                   
                 MDL_Mg25Zn 
                 −0.013235864 
                 No 
               
               
                   
                 Determinism_AlCo 
                 −0.013262931 
                 No 
               
               
                   
                 Entropy_Ca43Sn 
                 −0.013327267 
                 No 
               
               
                   
                 Entropy_AlMo 
                 −0.013771315 
                 No 
               
               
                   
                 Entropy_MnMo 
                 −0.014437184 
                 No 
               
               
                   
                 MDL_LiMg25 
                 −0.01450352 
                 No 
               
               
                   
                 MDL_MoBi 
                 −0.014867918 
                 No 
               
               
                   
                 Entropy_SrPb 
                 −0.015029508 
                 No 
               
               
                   
                 MDL_CrMo 
                 −0.015069864 
                 No 
               
               
                   
                 MDL_CrMn 
                 −0.015081756 
                 No 
               
               
                   
                 MDL_CuPb 
                 −0.015290387 
                 No 
               
               
                   
                 MDL_CrCd 
                 −0.01558969 
                 No 
               
               
                   
                 MDL_Mo 
                 −0.016203811 
                 No 
               
               
                   
                 MDL_Ca43As 
                 −0.016903291 
                 No 
               
               
                   
                 MDL_LiCr 
                 −0.016947259 
                 No 
               
               
                   
                 MDL_PbBi 
                 −0.017265814 
                 No 
               
               
                   
                 Entropy_AlMn 
                 −0.017868533 
                 No 
               
               
                   
                 Entropy_SrBa 
                 −0.017897945 
                 No 
               
               
                   
                 Entropy_LiCd 
                 −0.018744594 
                 No 
               
               
                   
                 MDL_Ca43Cr 
                 −0.019023403 
                 No 
               
               
                   
                 MDL_AlCo 
                 −0.019624384 
                 No 
               
               
                   
                 Entropy_Zn 
                 −0.019976226 
                 Yes 
               
               
                   
                 MDL_Mg25Sr 
                 −0.02039631 
                 No 
               
               
                   
                 Entropy_CrAs 
                 −0.020718782 
                 No 
               
               
                   
                 MDL_ZnBi 
                 −0.020858078 
                 Yes 
               
               
                   
                 MDL_Ca43Ba 
                 −0.021093231 
                 No 
               
               
                   
                 MDL_LiAl 
                 −0.021601851 
                 No 
               
               
                   
                 MDL_LiAs 
                 −0.021825883 
                 No 
               
               
                   
                 MDL_Mg25Ni 
                 −0.021988545 
                 No 
               
               
                   
                 Entropy_CoBi 
                 −0.022110929 
                 No 
               
               
                   
                 MDL_Mg25Al 
                 −0.023379235 
                 No 
               
               
                   
                 Entropy_LiSr 
                 −0.023993698 
                 No 
               
               
                   
                 Entropy_CrNi 
                 −0.024059903 
                 No 
               
               
                   
                 MDL_Ca43Bi 
                 −0.025026622 
                 No 
               
               
                   
                 MDL_AsBi 
                 −0.025351338 
                 No 
               
               
                   
                 Determinism_CrMn 
                 −0.025693548 
                 No 
               
               
                   
                 Entropy_NiBa 
                 −0.025877792 
                 No 
               
               
                   
                 MDL_Mg25As 
                 −0.027214955 
                 No 
               
               
                   
                 Entropy_CrSn 
                 −0.027976947 
                 No 
               
               
                   
                 Determinism_LiAs 
                 −0.028028835 
                 No 
               
               
                   
                 Entropy_MoSn 
                 −0.028055204 
                 No 
               
               
                   
                 MDL_LiCo 
                 −0.028277584 
                 No 
               
               
                   
                 MDL_LiSn 
                 −0.029087385 
                 No 
               
               
                   
                 MDL_Mg25Bi 
                 −0.029221437 
                 No 
               
               
                   
                 Determinism_ZnPb 
                 −0.029334441 
                 Yes 
               
               
                   
                 MDL_Li 
                 −0.030323494 
                 No 
               
               
                   
                 Determinism_MoCd 
                 −0.03175983 
                 No 
               
               
                   
                 Entropy_Ca43Cr 
                 −0.032616587 
                 No 
               
               
                   
                 Entropy_Mg25 
                 −0.032844403 
                 No 
               
               
                   
                 MDL_CrCo 
                 −0.033010033 
                 No 
               
               
                   
                 Determinism_Mg25Mn 
                 −0.033143092 
                 No 
               
               
                   
                 Entropy_CuZn 
                 −0.033520671 
                 No 
               
               
                   
                 Entropy_Mg25Al 
                 −0.034991785 
                 No 
               
               
                   
                 MDL_Ca43Mn 
                 −0.035057 
                 No 
               
               
                   
                 MDL_Ca43Zn 
                 −0.035089518 
                 No 
               
               
                   
                 Determinism_Mg25As 
                 −0.035099283 
                 No 
               
               
                   
                 Entropy_Mg25Ba 
                 −0.03522107 
                 No 
               
               
                   
                 MDL_LiCd 
                 −0.035288476 
                 No 
               
               
                   
                 Entropy_Ca43As 
                 −0.03555932 
                 No 
               
               
                   
                 MDL_Mg25Mn 
                 −0.036626043 
                 No 
               
               
                   
                 Entropy_MnSr 
                 −0.036794479 
                 No 
               
               
                   
                 MDL_MoPb 
                 −0.036998779 
                 No 
               
               
                   
                 Determinism_Mg25Ba 
                 −0.037297617 
                 No 
               
               
                   
                 MDL_Mg25Cd 
                 −0.037841873 
                 No 
               
               
                   
                 Entropy_CoZn 
                 −0.038888092 
                 No 
               
               
                   
                 MDL_Ca43Cd 
                 −0.0398772 
                 No 
               
               
                   
                 MDL_ZnSr 
                 −0.039929996 
                 Yes 
               
               
                   
                 Entropy_CrBi 
                 −0.040063787 
                 No 
               
               
                   
                 MDL_MoBa 
                 −0.040294352 
                 No 
               
               
                   
                 Entropy_PbBi 
                 −0.040644702 
                 No 
               
               
                   
                 Entropy_Mg25Zn 
                 −0.040674759 
                 No 
               
               
                   
                 Entropy_CoBa 
                 −0.041682071 
                 No 
               
               
                   
                 MDL_AsSn 
                 −0.042482389 
                 No 
               
               
                   
                 Determinism_AsCd 
                 −0.042590229 
                 No 
               
               
                   
                 MDL_As 
                 −0.042816404 
                 Yes 
               
               
                   
                 MDL_LiMo 
                 −0.042942789 
                 No 
               
               
                   
                 Entropy_Mo 
                 −0.04356696 
                 No 
               
               
                   
                 MDL_Ca43Ni 
                 −0.044126031 
                 No 
               
               
                   
                 Entropy_LiCo 
                 −0.044596271 
                 No 
               
               
                   
                 Entropy_Ca43Ba 
                 −0.045718289 
                 No 
               
               
                   
                 MDL_Mg25Mo 
                 −0.046804847 
                 No 
               
               
                   
                 Entropy_Mg25As 
                 −0.046981031 
                 No 
               
               
                   
                 MDL_Mg25Co 
                 −0.04714293 
                 No 
               
               
                   
                 Entropy_CrMn 
                 −0.047468897 
                 No 
               
               
                   
                 Entropy_AsBi 
                 −0.049035215 
                 No 
               
               
                   
                 Entropy_ZnBi 
                 −0.049648752 
                 Yes 
               
               
                   
                 Entropy_Mg25Ni 
                 −0.049731513 
                 No 
               
               
                   
                 Entropy_CrMo 
                 −0.049796621 
                 No 
               
               
                   
                 Determinism_Mg25Sn 
                 −0.049818644 
                 No 
               
               
                   
                 Determinism_CrAs 
                 −0.051814773 
                 No 
               
               
                   
                 MDL_Ca43Mo 
                 −0.051841513 
                 No 
               
               
                   
                 Entropy_CuCd 
                 −0.051964319 
                 No 
               
               
                   
                 Entropy_MoBi 
                 −0.05278141 
                 No 
               
               
                   
                 MDL_MnCo 
                 −0.053184893 
                 No 
               
               
                   
                 Entropy_Mg25Sr 
                 −0.053816077 
                 No 
               
               
                   
                 MDL_ZnMo 
                 −0.054941163 
                 No 
               
               
                   
                 Determinism_CrSn 
                 −0.056475746 
                 No 
               
               
                   
                 MDL_ZnCd 
                 −0.056742477 
                 Yes 
               
               
                   
                 Entropy_CrCd 
                 −0.057661784 
                 No 
               
               
                   
                 Entropy_Ca43Bi 
                 −0.057689103 
                 No 
               
               
                   
                 Entropy_Mg25Bi 
                 −0.058660945 
                 No 
               
               
                   
                 MDL_CdBa 
                 −0.060345967 
                 No 
               
               
                   
                 Determinism_AsPb 
                 −0.062519923 
                 No 
               
               
                   
                 Entropy_CuPb 
                 −0.062639141 
                 No 
               
               
                   
                 Entropy_CoCu 
                 −0.063222545 
                 No 
               
               
                   
                 MDL_Ca43Co 
                 −0.063449824 
                 No 
               
               
                   
                 MDL_AsMo 
                 −0.063500069 
                 No 
               
               
                   
                 Determinism_CuAs 
                 −0.06375552 
                 No 
               
               
                   
                 Entropy_CrCo 
                 −0.066089162 
                 No 
               
               
                   
                 Determinism_NiBa 
                 −0.066485204 
                 No 
               
               
                   
                 Determinism_MnZn 
                 −0.066897861 
                 No 
               
               
                   
                 Determinism_Mg25Cr 
                 −0.067032328 
                 No 
               
               
                   
                 Determinism_LiPb 
                 −0.068610383 
                 No 
               
               
                   
                 MDL_Cd 
                 −0.070338308 
                 Yes 
               
               
                   
                 Entropy_Ca43Cd 
                 −0.070640761 
                 No 
               
               
                   
                 Determinism_CrZn 
                 −0.070982816 
                 No 
               
               
                   
                 MDL_CdBi 
                 −0.071508472 
                 No 
               
               
                   
                 Entropy_CuAs 
                 −0.071694453 
                 No 
               
               
                   
                 Entropy_As 
                 −0.073888148 
                 No 
               
               
                   
                 Determinism_MnPb 
                 −0.075416383 
                 No 
               
               
                   
                 Determinism_AsSn 
                 −0.076106607 
                 No 
               
               
                   
                 Entropy_AsSn 
                 −0.077219424 
                 No 
               
               
                   
                 Entropy_Li 
                 −0.079541735 
                 Yes 
               
               
                   
                 Entropy_Mg25Cd 
                 −0.081355567 
                 No 
               
               
                   
                 MDL_CdSn 
                 −0.085397153 
                 No 
               
               
                   
                 Determinism_CrCd 
                 −0.086603414 
                 No 
               
               
                   
                 Entropy_Ca43Mn 
                 −0.087840267 
                 No 
               
               
                   
                 Entropy_MoPb 
                 −0.088690854 
                 No 
               
               
                   
                 Determinism_CrNi 
                 −0.08955169 
                 No 
               
               
                   
                 Entropy_Ca43Pb 
                 −0.091069981 
                 No 
               
               
                   
                 Entropy_ZnMo 
                 −0.092435832 
                 No 
               
               
                   
                 Entropy_Mg25Co 
                 −0.094448688 
                 No 
               
               
                   
                 Entropy_ZnSr 
                 −0.095115262 
                 Yes 
               
               
                   
                 Determinism_Ca43Mn 
                 −0.095454483 
                 No 
               
               
                   
                 Entropy_MoBa 
                 −0.096175158 
                 No 
               
               
                   
                 Entropy_AlCo 
                 −0.09643681 
                 No 
               
               
                   
                 Determinism_AsBi 
                 −0.098945245 
                 No 
               
               
                   
                 Determinism_CuMo 
                 −0.100397016 
                 No 
               
               
                   
                 Determinism_CrPb 
                 −0.100511882 
                 No 
               
               
                   
                 Determinism_CuBi 
                 −0.104531163 
                 No 
               
               
                   
                 Determinism_ZnAs 
                 −0.106361378 
                 Yes 
               
               
                   
                 Entropy_Ca43Zn 
                 −0.110030137 
                 No 
               
               
                   
                 Entropy_MnCo 
                 −0.112253585 
                 No 
               
               
                   
                 Determinism_Ca43Bi 
                 −0.116845644 
                 No 
               
               
                   
                 Entropy_Mg25Mo 
                 −0.119482329 
                 No 
               
               
                   
                 Entropy_Mg25Mn 
                 −0.120712767 
                 No 
               
               
                   
                 Entropy_AsMo 
                 −0.125823549 
                 No 
               
               
                   
                 Entropy_Ca43Mo 
                 −0.126525635 
                 No 
               
               
                   
                 Determinism_Ca43Sr 
                 −0.129139365 
                 No 
               
               
                   
                 Determinism_Mg25Al 
                 −0.129310933 
                 No 
               
               
                   
                 Determinism_Mg25Co 
                 −0.132447668 
                 No 
               
               
                   
                 Entropy_Ca43Ni 
                 −0.135349623 
                 No 
               
               
                   
                 Entropy_ZnCd 
                 −0.140786669 
                 Yes 
               
               
                   
                 Determinism_MoBi 
                 −0.142377275 
                 No 
               
               
                   
                 Entropy_Ca43Co 
                 −0.142669153 
                 No 
               
               
                   
                 Determinism_Ca43As 
                 −0.143199433 
                 No 
               
               
                   
                 Determinism_Mg25Zn 
                 −0.156576846 
                 No 
               
               
                   
                 Determinism_Cr 
                 −0.158077761 
                 Yes 
               
               
                   
                 Entropy_CdBa 
                 −0.163994048 
                 No 
               
               
                   
                 Determinism_Ca43Sn 
                 −0.164777802 
                 No 
               
               
                   
                 Determinism_ZnSr 
                 −0.175344304 
                 Yes 
               
               
                   
                 Determinism_CrBi 
                 −0.177702068 
                 No 
               
               
                   
                 Entropy_CdPb 
                 −0.177794228 
                 No 
               
               
                   
                 Determinism_MoPb 
                 −0.183135158 
                 No 
               
               
                   
                 Entropy_CdSn 
                 −0.185633704 
                 No 
               
               
                   
                 Entropy_Cd 
                 −0.187420522 
                 Yes 
               
               
                   
                 Determinism_ZnBa 
                 −0.191891102 
                 Yes 
               
               
                   
                 Determinism_ZnCd 
                 −0.195471091 
                 Yes 
               
               
                   
                 Entropy_CdBi 
                 −0.208651743 
                 No 
               
               
                   
                 Determinism_MnCd 
                 −0.20928994 
                 No 
               
               
                   
                 Determinism_Mg25Sr 
                 −0.212734283 
                 No 
               
               
                   
                 Determinism_Ca43Zn 
                 −0.219269022 
                 No 
               
               
                   
                 Determinism_LiZn 
                 −0.228405173 
                 No 
               
               
                   
                 Determinism_AsMo 
                 −0.229631149 
                 No 
               
               
                   
                 Determinism_Ca43Ni 
                 −0.240518024 
                 No 
               
               
                   
                 Determinism_As 
                 −0.253072839 
                 Yes 
               
               
                   
                 Determinism_Ca43Mo 
                 −0.265534336 
                 No 
               
               
                   
                 Determinism_ZnMo 
                 −0.272024886 
                 No 
               
               
                   
                 Determinism_MoBa 
                 −0.274507417 
                 No 
               
               
                   
                 Determinism_PbBi 
                 −0.274576625 
                 No 
               
               
                   
                 Determinism_Ca43Cd 
                 −0.277001258 
                 No 
               
               
                   
                 Determinism_Mg25Bi 
                 −0.280768606 
                 No 
               
               
                   
                 Determinism_Zn 
                 −0.285103674 
                 No 
               
               
                   
                 Determinism_LiCa43 
                 −0.30617652 
                 No 
               
               
                   
                 Determinism_CrMo 
                 −0.308477976 
                 No 
               
               
                   
                 Determinism_Ca43Co 
                 −0.30955258 
                 No 
               
               
                   
                 Determinism_LiSn 
                 −0.329271649 
                 No 
               
               
                   
                 Determinism_MnSr 
                 −0.337554128 
                 No 
               
               
                   
                 Determinism_CuCd 
                 −0.34833967 
                 No 
               
               
                   
                 Determinism_CrCo 
                 −0.348342147 
                 No 
               
               
                   
                 Determinism_LiCd 
                 −0.381890549 
                 No 
               
               
                   
                 Determinism_Ca43Cr 
                 −0.437649851 
                 No 
               
               
                   
                 Determinism_LiMo 
                 −0.466404292 
                 No 
               
               
                   
                 Determinism_LiSr 
                 −0.486704206 
                 No 
               
               
                   
                 (Intercept) 
                 −0.535887209 
                 No 
               
               
                   
                 Determinism_LiMn 
                 −0.564746942 
                 No 
               
               
                   
                 Determinism_LiAl 
                 −0.583409959 
                 No 
               
               
                   
                 Determinism_LiMg25 
                 −0.610883387 
                 No 
               
               
                   
                 Determinism_LiBa 
                 −0.620245549 
                 No 
               
               
                   
                 Determinism_LiCr 
                 −0.640710424 
                 No 
               
               
                   
                 Determinism_Li 
                 −0.669879537 
                 Yes 
               
               
                   
                 Determinism_LiCo 
                 −0.689653181 
                 No 
               
               
                   
                 Determinism_CdBi 
                 −0.690031813 
                 No 
               
               
                   
                 Determinism_Mo 
                 −0.697738514 
                 No 
               
               
                   
                 Determinism_LiBi 
                 −0.823539112 
                 No 
               
               
                   
                 Determinism_Cd 
                 −1.116088768 
                 Yes 
               
               
                   
                   
               
            
           
         
       
     
     Example 7—Kidney Transplant Rejection Prediction 
     Hair samples were collected from kidney transplant recipients at the time of biopsy-proven acute rejection (n=6) and age- and sex-matched control kidney transplant recipients with no acute rejection at surveillance biopsy at the same time after transplant (n=5). All participants were recruited from the Mount Sinai Hospital. Table 9 illustrates the features used and their corresponding β values. The β values are obtained by estimating each respective feature in the respective cohort that describes a change in log odds of kidney transplate status associated with a 1-unit change for the respective feature. 
       FIG. 9  illustrates the ROC curve for evaluating accuracy of the disclosed method of evaluating subjects for kidney transplant rejection. As shown in  FIG. 9 , the ROC curve derived from experimental data to evaluate the performance of the disclosed classification method has an AUC corresponding to 0.900, indicating that the disclosed method has 9000 accuracy for evaluating kidney transplant rejection based on a hair sample. 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 Features with empirical x values for kidney 
               
               
                 transplant rejection prediction. 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Feature in 
               
               
                   
                 Feature 
                 β value 
                 Table 2 or 3? 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Determinism_Bi 
                 2.937600551 
                 Yes 
               
               
                   
                 Determinism_Al 
                 2.276918409 
                 Yes 
               
               
                   
                 Determinism_P 
                 1.593375022 
                 Yes 
               
               
                   
                 Determinism_I 
                 1.576526144 
                 Yes 
               
               
                   
                 Determinism_Hg 
                 1.352609521 
                 Yes 
               
               
                   
                 Determinism_Mn 
                 1.324694388 
                 Yes 
               
               
                   
                 Determinism_S 
                 1.251337611 
                 Yes 
               
               
                   
                 Entropy_Bi 
                 1.057509572 
                 Yes 
               
               
                   
                 Determinism_Sn 
                 0.910193817 
                 Yes 
               
               
                   
                 Determinism_Ba 
                 0.882379546 
                 Yes 
               
               
                   
                 Determinism_As 
                 0.612241143 
                 Yes 
               
               
                   
                 Determinism_Pb 
                 0.410747 
                 Yes 
               
               
                   
                 Determinism_Sr 
                 0.378952574 
                 Yes 
               
               
                   
                 MDL_Bi 
                 0.335770724 
                 No 
               
               
                   
                 Entropy_Hg 
                 0.259591313 
                 Yes 
               
               
                   
                 Entropy_Mn 
                 0.220488734 
                 Yes 
               
               
                   
                 Entropy_Zn 
                 0.170166112 
                 Yes 
               
               
                   
                 Entropy_P 
                 0.169228029 
                 Yes 
               
               
                   
                 Entropy_S 
                 0.165291088 
                 Yes 
               
               
                   
                 Entropy_Sn 
                 0.140767004 
                 Yes 
               
               
                   
                 Entropy_I 
                 0.131182754 
                 Yes 
               
               
                   
                 Entropy_Ba 
                 0.123782562 
                 Yes 
               
               
                   
                 Entropy_Ni 
                 0.119190841 
                 Yes 
               
               
                   
                 Entropy_Pb 
                 0.095014851 
                 Yes 
               
               
                   
                 Entropy_Cu 
                 0.093029191 
                 Yes 
               
               
                   
                 MDL_Hg 
                 0.090579868 
                 Yes 
               
               
                   
                 MDL_Mn 
                 0.070363291 
                 Yes 
               
               
                   
                 MDL_Zn 
                 0.069119728 
                 Yes 
               
               
                   
                 MDL_Ni 
                 0.065047882 
                 Yes 
               
               
                   
                 Entropy_Mg 
                 0.060600108 
                 Yes 
               
               
                   
                 MDL_S 
                 0.055566047 
                 Yes 
               
               
                   
                 MDL_P 
                 0.054680842 
                 Yes 
               
               
                   
                 MDL_Sn 
                 0.037235088 
                 Yes 
               
               
                   
                 MDL_I 
                 0.037166283 
                 Yes 
               
               
                   
                 MDL_Pb 
                 0.027730044 
                 Yes 
               
               
                   
                 MDL_Cu 
                 0.019758971 
                 Yes 
               
               
                   
                 MDL_Ba 
                 0.017861445 
                 Yes 
               
               
                   
                 MDL_Mg 
                 0.013919756 
                 Yes 
               
               
                   
                 Entropy_Sr 
                 0.012056904 
                 Yes 
               
               
                   
                 MDL_Sr 
                 0.011186722 
                 Yes 
               
               
                   
                 Determinism_Mg 
                 −0.00081932 
                 Yes 
               
               
                   
                 MDL_Ca 
                 −0.006427457 
                 Yes 
               
               
                   
                 MDL_Li 
                 −0.020601779 
                 Yes 
               
               
                   
                 MDL_Al 
                 −0.028804713 
                 Yes 
               
               
                   
                 Determinism_Ca 
                 −0.031452338 
                 Yes 
               
               
                   
                 MDL_Co 
                 −0.033385007 
                 Yes 
               
               
                   
                 Entropy_Li 
                 −0.044124857 
                 Yes 
               
               
                   
                 Determinism_Ni 
                 −0.048105079 
                 Yes 
               
               
                   
                 Entropy_Ca 
                 −0.068325786 
                 Yes 
               
               
                   
                 MDL_Cr 
                 −0.078030836 
                 Yes 
               
               
                   
                 Entropy_Al 
                 −0.09122596 
                 Yes 
               
               
                   
                 Entropy_Co 
                 −0.105659709 
                 Yes 
               
               
                   
                 MDL_Fe 
                 −0.128893502 
                 Yes 
               
               
                   
                 Entropy_Cr 
                 −0.167258915 
                 Yes 
               
               
                   
                 MDL_As 
                 −0.171607981 
                 Yes 
               
               
                   
                 MDL_Cd 
                 −0.199946789 
                 Yes 
               
               
                   
                 Entropy_As 
                 −0.379551271 
                 Yes 
               
               
                   
                 Entropy_Fe 
                 −0.404300467 
                 Yes 
               
               
                   
                 Entropy_Cd 
                 −0.613573066 
                 Yes 
               
               
                   
                 Determinism_Cu 
                 −0.700031087 
                 Yes 
               
               
                   
                 Determinism_Co 
                 −0.7229317 
                 Yes 
               
               
                   
                 Determinism_Li 
                 −0.927509995 
                 Yes 
               
               
                   
                 Determinism_Fe 
                 −1.693252621 
                 Yes 
               
               
                   
                 Determinism_Zn 
                 −1.826370946 
                 No 
               
               
                   
                 Determinism_Cd 
                 −2.069910206 
                 Yes 
               
               
                   
                 Determinism_Cr 
                 −2.585054024 
                 Yes 
               
               
                   
                 Intercept 
                 −7.703959822 
                 No 
               
               
                   
                   
               
            
           
         
       
     
     Example 8—Pediatric Cancer 
     Subjects were evaluated for pediatric cancer using a similar method as described above with respect to Examples 2 and 3. A total of 28 children were recruited from a hospital cancer center. Twenty-two were pediatric cancer cases and 6 were controls. Diagnoses were made using standard clinical protocols-blood testing and histopathology and confirmed by an oncologist. Table 10 illustrates the features used and their corresponding β values. The β values are obtained by estimating each respective feature in the respective cohort that describes a change in log odds of pediatric cancer status associated with a 1-unit change for the respective feature. 
       FIG. 10  illustrates the ROC curve for evaluating accuracy of the disclosed method of evaluating a subject for pediatric cancer. As shown in  FIG. 10 , the ROC curve derived from experimental data to evaluate the performance of the disclosed classification method has an AUC corresponding to 0.962, indicating that the disclosed method has above 95% accuracy across the cohort of 28 children for pediatric cancer based on tooth sampling. 
     
       
         
           
               
             
               
                 TABLE 10 
               
             
            
               
                   
               
               
                 Features with empirical x values for pediatric cancer determination. 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Feature in 
               
               
                   
                 Feature 
                 β value 
                 Table 2 or 3? 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Determinism_CrAs 
                 0.83118208 
                 No 
               
               
                   
                 Determinism_CrPb 
                 0.8064229 
                 No 
               
               
                   
                 Determinism_AsMo 
                 0.75871856 
                 No 
               
               
                   
                 Determinism_AsSn 
                 0.67313952 
                 No 
               
               
                   
                 Determinism_Mg25Cu 
                 0.66743556 
                 No 
               
               
                   
                 Determinism_AlSr 
                 0.65730066 
                 No 
               
               
                   
                 Determinism_CrNi 
                 0.61364904 
                 No 
               
               
                   
                 Determinism_MnNi 
                 0.59432577 
                 No 
               
               
                   
                 Determinism_CrSn 
                 0.58804872 
                 No 
               
               
                   
                 Determinism_Al 
                 0.58617909 
                 Yes 
               
               
                   
                 Determinism_CrMo 
                 0.58520657 
                 No 
               
               
                   
                 Determinism_AsPb 
                 0.58326161 
                 No 
               
               
                   
                 Determinism_CrZn 
                 0.56050935 
                 No 
               
               
                   
                 Determinism_CrSr 
                 0.54090339 
                 No 
               
               
                   
                 Determinism_AlCr 
                 0.53743572 
                 No 
               
               
                   
                 Determinism_Mg25Al 
                 0.48446496 
                 No 
               
               
                   
                 Determinism_Cr 
                 0.4817402 
                 Yes 
               
               
                   
                 Determinism_AlPb 
                 0.45549817 
                 No 
               
               
                   
                 Determinism_CrMn 
                 0.45130031 
                 No 
               
               
                   
                 Determinism_AsSr 
                 0.44475806 
                 No 
               
               
                   
                 Determinism_AlBa 
                 0.42164038 
                 No 
               
               
                   
                 Determinism_AlZn 
                 0.37990421 
                 No 
               
               
                   
                 Determinism_AlMn 
                 0.37500187 
                 No 
               
               
                   
                 Determinism_Mg25 
                 0.3683976 
                 No 
               
               
                   
                 Determinism_AlSn 
                 0.35158099 
                 No 
               
               
                   
                 Determinism_AlCa43 
                 0.34405451 
                 No 
               
               
                   
                 Determinism_CrCu 
                 0.3360983 
                 No 
               
               
                   
                 Determinism_MnBa 
                 0.33540969 
                 No 
               
               
                   
                 Determinism_MoSn 
                 0.33192421 
                 No 
               
               
                   
                 Determinism_Mn 
                 0.31460247 
                 Yes 
               
               
                   
                 Determinism_MnSr 
                 0.31368106 
                 No 
               
               
                   
                 Determinism_AsBa 
                 0.30838099 
                 No 
               
               
                   
                 Determinism_Ca43Sn 
                 0.29984189 
                 No 
               
               
                   
                 Determinism_AlMo 
                 0.28857433 
                 No 
               
               
                   
                 Determinism_AlNi 
                 0.2837695 
                 No 
               
               
                   
                 Determinism_Mg25Cr 
                 0.28189452 
                 No 
               
               
                   
                 Determinism_As 
                 0.28036618 
                 Yes 
               
               
                   
                 Determinism_MnMo 
                 0.26611626 
                 No 
               
               
                   
                 Determinism_MnZn 
                 0.25921097 
                 No 
               
               
                   
                 Determinism_Mg25Ni 
                 0.2517347 
                 No 
               
               
                   
                 Determinism_Mg25Ca43 
                 0.24790031 
                 No 
               
               
                   
                 Determinism_Ca43Cu 
                 0.23667494 
                 No 
               
               
                   
                 Determinism_Mg25As 
                 0.2302827 
                 No 
               
               
                   
                 Determinism_AlAs 
                 0.22992372 
                 No 
               
               
                   
                 Determinism_Mg25Sr 
                 0.21738528 
                 No 
               
               
                   
                 Determinism_Mo 
                 0.21074891 
                 No 
               
               
                   
                 Determinism_Ca43Pb 
                 0.19990923 
                 No 
               
               
                   
                 Determinism_MnCu 
                 0.19801204 
                 No 
               
               
                   
                 Determinism_AlCu 
                 0.19386486 
                 No 
               
               
                   
                 Entropy_AsMo 
                 0.19141784 
                 No 
               
               
                   
                 Determinism_Mg25Sn 
                 0.18876961 
                 No 
               
               
                   
                 Determinism_Ca43As 
                 0.18366859 
                 No 
               
               
                   
                 Determinism_Mg25Zn 
                 0.18155086 
                 No 
               
               
                   
                 Determinism_MnAs 
                 0.16882166 
                 No 
               
               
                   
                 Determinism_Mg25Pb 
                 0.16563132 
                 No 
               
               
                   
                 Determinism_Mg25Mo 
                 0.16249869 
                 No 
               
               
                   
                 Entropy_Mg25Al 
                 0.15440345 
                 No 
               
               
                   
                 Entropy_CrMo 
                 0.15286797 
                 No 
               
               
                   
                 Entropy_AlSr 
                 0.15164735 
                 No 
               
               
                   
                 Determinism_Ca43Zn 
                 0.14229664 
                 No 
               
               
                   
                 Entropy_AlCu 
                 0.14029367 
                 No 
               
               
                   
                 Entropy_Mg25Ca43 
                 0.13724276 
                 No 
               
               
                   
                 Entropy_Cr 
                 0.13724044 
                 Yes 
               
               
                   
                 Determinism_LiCu 
                 0.13655695 
                 No 
               
               
                   
                 Entropy_AlMo 
                 0.13573654 
                 No 
               
               
                   
                 Entropy_CrZn 
                 0.13488609 
                 No 
               
               
                   
                 Determinism_Ca43 
                 0.1342346 
                 No 
               
               
                   
                 Entropy_AlZn 
                 0.13367488 
                 No 
               
               
                   
                 Entropy_AsSn 
                 0.13157993 
                 No 
               
               
                   
                 Entropy_CrSr 
                 0.13155615 
                 No 
               
               
                   
                 Entropy_As 
                 0.12753161 
                 No 
               
               
                   
                 Determinism_CuAs 
                 0.12740537 
                 No 
               
               
                   
                 Entropy_CrSn 
                 0.12636765 
                 No 
               
               
                   
                 Entropy_CrNi 
                 0.12602336 
                 No 
               
               
                   
                 Determinism_MnSn 
                 0.12491913 
                 No 
               
               
                   
                 Entropy_CrCu 
                 0.11837983 
                 No 
               
               
                   
                 Entropy_AlBa 
                 0.11789151 
                 No 
               
               
                   
                 Entropy_Al 
                 0.11758586 
                 Yes 
               
               
                   
                 Entropy_CrAs 
                 0.11754868 
                 No 
               
               
                   
                 Entropy_CrBa 
                 0.1097003 
                 No 
               
               
                   
                 Entropy_Ca43Sn 
                 0.10626234 
                 No 
               
               
                   
                 Entropy_AlCa43 
                 0.10583429 
                 No 
               
               
                   
                 Entropy_CuMo 
                 0.10061917 
                 No 
               
               
                   
                 Entropy_SnBa 
                 0.09721063 
                 No 
               
               
                   
                 Determinism_LiSn 
                 0.09101129 
                 No 
               
               
                   
                 Entropy_MnNi 
                 0.09012707 
                 No 
               
               
                   
                 Entropy_Mg25Cu 
                 0.08972304 
                 No 
               
               
                   
                 Entropy_CrMn 
                 0.08918573 
                 No 
               
               
                   
                 Entropy_CuSn 
                 0.08872076 
                 No 
               
               
                   
                 Entropy_Ca43 
                 0.08599791 
                 No 
               
               
                   
                 Entropy_AlSn 
                 0.08431399 
                 No 
               
               
                   
                 MDL_AsMo 
                 0.08345802 
                 No 
               
               
                   
                 Entropy_CrPb 
                 0.08287164 
                 No 
               
               
                   
                 Entropy_Ca43Cu 
                 0.08059603 
                 No 
               
               
                   
                 MDL_CrPb 
                 0.07907872 
                 No 
               
               
                   
                 Determinism_Mg25Mn 
                 0.07527645 
                 No 
               
               
                   
                 MDL_CrMo 
                 0.07412785 
                 No 
               
               
                   
                 Determinism_Ca43Mn 
                 0.071783 
                 No 
               
               
                   
                 Entropy_MnSr 
                 0.07124762 
                 No 
               
               
                   
                 Entropy_AlMn 
                 0.07101429 
                 No 
               
               
                   
                 Determinism_MnPb 
                 0.07067955 
                 No 
               
               
                   
                 MDL_AlMo 
                 0.0695314 
                 No 
               
               
                   
                 Entropy_Mg25Mo 
                 0.06869675 
                 No 
               
               
                   
                 MDL_CrSn 
                 0.06663217 
                 No 
               
               
                   
                 MDL_AsSn 
                 0.0656736 
                 No 
               
               
                   
                 Entropy_Ca43Sr 
                 0.06557269 
                 No 
               
               
                   
                 Determinism_LiCa43 
                 0.06345066 
                 No 
               
               
                   
                 MDL_Cr 
                 0.06302333 
                 Yes 
               
               
                   
                 Entropy_Mg25Sn 
                 0.06282819 
                 No 
               
               
                   
                 Entropy_MnAs 
                 0.06200469 
                 No 
               
               
                   
                 Determinism_CuSr 
                 0.06199107 
                 No 
               
               
                   
                 Entropy_MoBa 
                 0.06028466 
                 No 
               
               
                   
                 Entropy_Ca43Ni 
                 0.06008138 
                 No 
               
               
                   
                 Entropy_Mg25As 
                 0.0581392 
                 No 
               
               
                   
                 MDL_CrAs 
                 0.0579383 
                 No 
               
               
                   
                 Determinism_Ca43Mo 
                 0.05760132 
                 No 
               
               
                   
                 MDL_Mg25Al 
                 0.05743773 
                 No 
               
               
                   
                 Determinism_Cu 
                 0.05482349 
                 No 
               
               
                   
                 MDL_CrNi 
                 0.05476749 
                 No 
               
               
                   
                 Entropy_AsPb 
                 0.05328563 
                 No 
               
               
                   
                 Determinism_CrBa 
                 0.05265275 
                 No 
               
               
                   
                 Entropy_Sn 
                 0.05221241 
                 Yes 
               
               
                   
                 Entropy_AsSr 
                 0.05198491 
                 No 
               
               
                   
                 Entropy_AsBa 
                 0.05172377 
                 No 
               
               
                   
                 Determinism_Ca43Sr 
                 0.0514286 
                 No 
               
               
                   
                 Entropy_MnCu 
                 0.05120313 
                 No 
               
               
                   
                 Entropy_Mo 
                 0.0507179 
                 No 
               
               
                   
                 Entropy_MnSn 
                 0.05033457 
                 No 
               
               
                   
                 Entropy_MnZn 
                 0.05032908 
                 No 
               
               
                   
                 MDL_AlSn 
                 0.0492198 
                 No 
               
               
                   
                 Entropy_Ca43Mo 
                 0.04889074 
                 No 
               
               
                   
                 MDL_As 
                 0.04884107 
                 Yes 
               
               
                   
                 Entropy_MnMo 
                 0.04873734 
                 No 
               
               
                   
                 MDL_CrZn 
                 0.04864297 
                 No 
               
               
                   
                 MDL_AlZn 
                 0.04828068 
                 No 
               
               
                   
                 Entropy_SrSn 
                 0.04789085 
                 No 
               
               
                   
                 Entropy_AlAs 
                 0.04671146 
                 No 
               
               
                   
                 Entropy_Mg25Pb 
                 0.04592187 
                 No 
               
               
                   
                 Determinism_Ca43Ba 
                 0.04530086 
                 No 
               
               
                   
                 Entropy_CuSr 
                 0.04508388 
                 No 
               
               
                   
                 Entropy_AlCr 
                 0.04458986 
                 No 
               
               
                   
                 MDL_AlCa43 
                 0.04451255 
                 No 
               
               
                   
                 MDL_AlBa 
                 0.04436354 
                 No 
               
               
                   
                 Entropy_Ca43Ba 
                 0.04403844 
                 No 
               
               
                   
                 MDL_Ca43Sn 
                 0.04378155 
                 No 
               
               
                   
                 MDL_AlSr 
                 0.04372138 
                 No 
               
               
                   
                 Entropy_Mg25Ni 
                 0.04350715 
                 No 
               
               
                   
                 MDL_CuSn 
                 0.04335379 
                 No 
               
               
                   
                 MDL_Mg25Ca43 
                 0.04214704 
                 No 
               
               
                   
                 Entropy_Mg25Sr 
                 0.04175057 
                 No 
               
               
                   
                 Entropy_Mg25 
                 0.04174833 
                 No 
               
               
                   
                 Entropy_MnBa 
                 0.04106751 
                 No 
               
               
                   
                 Entropy_AlNi 
                 0.04059491 
                 No 
               
               
                   
                 MDL_Al 
                 0.0404738 
                 Yes 
               
               
                   
                 Entropy_CuAs 
                 0.039935 
                 No 
               
               
                   
                 Entropy_MoSn 
                 0.03948098 
                 No 
               
               
                   
                 MDL_MnNi 
                 0.03774724 
                 No 
               
               
                   
                 Entropy_Mg25Cr 
                 0.03757149 
                 No 
               
               
                   
                 MDL_AlAs 
                 0.03692396 
                 No 
               
               
                   
                 MDL_AlCu 
                 0.03685177 
                 No 
               
               
                   
                 MDL_CrCu 
                 0.03670764 
                 No 
               
               
                   
                 MDL_CrSr 
                 0.03568829 
                 No 
               
               
                   
                 MDL_CuMo 
                 0.03207434 
                 No 
               
               
                   
                 MDL_Ca43Cu 
                 0.03182457 
                 No 
               
               
                   
                 MDL_Mg25Cu 
                 0.0317094 
                 No 
               
               
                   
                 MDL_SnPb 
                 0.0313948 
                 No 
               
               
                   
                 Determinism_CuMo 
                 0.03131308 
                 No 
               
               
                   
                 Determinism_LiPb 
                 0.03108278 
                 No 
               
               
                   
                 MDL_MnAs 
                 0.0307727 
                 No 
               
               
                   
                 MDL_AsPb 
                 0.03076553 
                 No 
               
               
                   
                 Entropy_AlPb 
                 0.03053911 
                 No 
               
               
                   
                 Entropy_Mn 
                 0.02955969 
                 Yes 
               
               
                   
                 Entropy_LiAl 
                 0.02955272 
                 No 
               
               
                   
                 Entropy_Ca43Pb 
                 0.02952587 
                 No 
               
               
                   
                 Entropy_Ca43As 
                 0.02947391 
                 No 
               
               
                   
                 Entropy_Mg25Zn 
                 0.02932978 
                 No 
               
               
                   
                 Entropy_Cu 
                 0.02928631 
                 Yes 
               
               
                   
                 MDL_Mg25Mo 
                 0.02897986 
                 No 
               
               
                   
                 MDL_AlNi 
                 0.02876477 
                 No 
               
               
                   
                 MDL_AlCr 
                 0.0284849 
                 No 
               
               
                   
                 MDL_MnMo 
                 0.02803741 
                 No 
               
               
                   
                 MDL_Ca43 
                 0.02724049 
                 No 
               
               
                   
                 MDL_Ca43Ni 
                 0.02631872 
                 No 
               
               
                   
                 MDL_Ca43Mo 
                 0.02598735 
                 No 
               
               
                   
                 MDL_AlMn 
                 0.02590792 
                 No 
               
               
                   
                 MDL_CrBa 
                 0.025747 
                 No 
               
               
                   
                 MDL_CrMn 
                 0.02478309 
                 No 
               
               
                   
                 Entropy_Ca43Zn 
                 0.02464592 
                 No 
               
               
                   
                 Entropy_MnPb 
                 0.02456997 
                 No 
               
               
                   
                 MDL_AlPb 
                 0.02445773 
                 No 
               
               
                   
                 MDL_AsSr 
                 0.02432544 
                 No 
               
               
                   
                 MDL_Sn 
                 0.02333864 
                 Yes 
               
               
                   
                 MDL_LiAl 
                 0.02157883 
                 No 
               
               
                   
                 MDL_Mo 
                 0.02078952 
                 No 
               
               
                   
                 MDL_MnSr 
                 0.02077614 
                 No 
               
               
                   
                 MDL_Mg25Sn 
                 0.02036126 
                 No 
               
               
                   
                 MDL_Cu 
                 0.02027604 
                 Yes 
               
               
                   
                 MDL_SnBa 
                 0.01998098 
                 No 
               
               
                   
                 Determinism_CuZn 
                 0.01880794 
                 No 
               
               
                   
                 MDL_Ca43Sr 
                 0.01840131 
                 No 
               
               
                   
                 Entropy_LiMo 
                 0.018315 
                 No 
               
               
                   
                 MDL_MoSn 
                 0.01762092 
                 No 
               
               
                   
                 MDL_Mg25As 
                 0.01753597 
                 No 
               
               
                   
                 Entropy_LiNi 
                 0.01735916 
                 No 
               
               
                   
                 MDL_MnCu 
                 0.01697323 
                 No 
               
               
                   
                 MDL_MoBa 
                 0.01628387 
                 No 
               
               
                   
                 Entropy_SnPb 
                 0.01604937 
                 No 
               
               
                   
                 Entropy_Ca43Cr 
                 0.01592327 
                 No 
               
               
                   
                 MDL_MnSn 
                 0.0158718 
                 No 
               
               
                   
                 MDL_CuAs 
                 0.01565716 
                 No 
               
               
                   
                 MDL_Ca43As 
                 0.01552682 
                 No 
               
               
                   
                 MDL_MnZn 
                 0.01520005 
                 No 
               
               
                   
                 MDL_LiMo 
                 0.01378473 
                 No 
               
               
                   
                 MDL_Mg25Cr 
                 0.01369645 
                 No 
               
               
                   
                 MDL_Mg25Ni 
                 0.01356079 
                 No 
               
               
                   
                 MDL_MnBa 
                 0.01260993 
                 No 
               
               
                   
                 Entropy_CuZn 
                 0.01254063 
                 No 
               
               
                   
                 Entropy_Ca43Mn 
                 0.01229527 
                 No 
               
               
                   
                 Entropy_Sr 
                 0.01194537 
                 Yes 
               
               
                   
                 MDL_Ca43Ba 
                 0.01133665 
                 No 
               
               
                   
                 MDL_Ca43Pb 
                 0.01119663 
                 No 
               
               
                   
                 MDL_Ca43Zn 
                 0.01097782 
                 No 
               
               
                   
                 MDL_LiNi 
                 0.01062496 
                 No 
               
               
                   
                 MDL_AsBa 
                 0.01055529 
                 No 
               
               
                   
                 Entropy_LiCr 
                 0.0102781 
                 No 
               
               
                   
                 MDL_CuSr 
                 0.00967959 
                 No 
               
               
                   
                 MDL_Mg25Pb 
                 0.0079405 
                 No 
               
               
                   
                 MDL_Ca43Cr 
                 0.00697082 
                 No 
               
               
                   
                 MDL_MnPb 
                 0.00669827 
                 No 
               
               
                   
                 MDL_Mg25 
                 0.00653391 
                 No 
               
               
                   
                 MDL_LiCr 
                 0.00552944 
                 No 
               
               
                   
                 MDL_Mg25Zn 
                 0.00522171 
                 No 
               
               
                   
                 MDL_Mn 
                 0.00505689 
                 Yes 
               
               
                   
                 MDL_LiPb 
                 0.00501943 
                 No 
               
               
                   
                 MDL_Sr 
                 0.00334692 
                 Yes 
               
               
                   
                 MDL_Ca43Mn 
                 0.00260287 
                 No 
               
               
                   
                 MDL_MoPb 
                 0.0021107 
                 No 
               
               
                   
                 Entropy_Mg25Mn 
                 0.00210428 
                 No 
               
               
                   
                 MDL_CuZn 
                 0.00172756 
                 No 
               
               
                   
                 MDL_SrSn 
                 0.00152638 
                 No 
               
               
                   
                 MDL_Zn 
                 0.00140798 
                 Yes 
               
               
                   
                 Entropy_LiPb 
                 0.00134958 
                 No 
               
               
                   
                 MDL_Mg25Sr 
                 0.00075164 
                 No 
               
               
                   
                 Determinism_LiZn 
                 8.93E−05 
                 No 
               
               
                   
                 MDL_LiCa43 
                 −0.0022607 
                 No 
               
               
                   
                 MDL_SrBa 
                 −0.0031041 
                 No 
               
               
                   
                 MDL_ZnMo 
                 −0.0044459 
                 No 
               
               
                   
                 MDL_ZnSr 
                 −0.0044924 
                 Yes 
               
               
                   
                 MDL_LiMn 
                 −0.0045107 
                 No 
               
               
                   
                 Determinism_Ca43Cr 
                 −0.0045376 
                 No 
               
               
                   
                 MDL_LiSn 
                 −0.0069244 
                 No 
               
               
                   
                 MDL_Mg25Mn 
                 −0.0074759 
                 No 
               
               
                   
                 Entropy_MoPb 
                 −0.0075005 
                 No 
               
               
                   
                 Entropy_Zn 
                 −0.0079352 
                 Yes 
               
               
                   
                 Entropy_SrBa 
                 −0.0082067 
                 No 
               
               
                   
                 MDL_SrPb 
                 −0.0082519 
                 No 
               
               
                   
                 MDL_LiSr 
                 −0.0094466 
                 No 
               
               
                   
                 Entropy_LiMn 
                 −0.0120857 
                 No 
               
               
                   
                 Entropy_ZnSr 
                 −0.0123194 
                 Yes 
               
               
                   
                 MDL_ZnSn 
                 −0.0157546 
                 Yes 
               
               
                   
                 MDL_LiZn 
                 −0.0167321 
                 No 
               
               
                   
                 MDL_Pb 
                 −0.0168931 
                 Yes 
               
               
                   
                 Entropy_LiCa43 
                 −0.0183219 
                 No 
               
               
                   
                 Determinism_LiAs 
                 −0.0195469 
                 No 
               
               
                   
                 MDL_CuBa 
                 −0.0217746 
                 No 
               
               
                   
                 MDL_Ba 
                 −0.0222979 
                 Yes 
               
               
                   
                 MDL_NiZn 
                 −0.0225005 
                 No 
               
               
                   
                 MDL_ZnBa 
                 −0.0225495 
                 Yes 
               
               
                   
                 Entropy_Mg25Ba 
                 −0.0226595 
                 No 
               
               
                   
                 MDL_ZnAs 
                 −0.0227291 
                 Yes 
               
               
                   
                 MDL_CuPb 
                 −0.0229478 
                 No 
               
               
                   
                 Entropy_BaPb 
                 −0.0241505 
                 No 
               
               
                   
                 Determinism_LiNi 
                 −0.0242261 
                 No 
               
               
                   
                 MDL_BaPb 
                 −0.0243734 
                 No 
               
               
                   
                 Entropy_ZnMo 
                 −0.0251275 
                 No 
               
               
                   
                 Entropy_LiSr 
                 −0.0253481 
                 No 
               
               
                   
                 Entropy_CuBa 
                 −0.0261639 
                 No 
               
               
                   
                 Entropy_CuPb 
                 −0.0269427 
                 No 
               
               
                   
                 Entropy_Pb 
                 −0.0280515 
                 Yes 
               
               
                   
                 MDL_LiBa 
                 −0.0281562 
                 No 
               
               
                   
                 MDL_LiAs 
                 −0.0294673 
                 No 
               
               
                   
                 Entropy_LiBa 
                 −0.0304657 
                 No 
               
               
                   
                 MDL_NiPb 
                 −0.0305375 
                 No 
               
               
                   
                 MDL_Mg25Ba 
                 −0.0309118 
                 No 
               
               
                   
                 Determinism_CuPb 
                 −0.031625 
                 No 
               
               
                   
                 MDL_NiSr 
                 −0.031904 
                 No 
               
               
                   
                 Entropy_SrPb 
                 −0.0334324 
                 No 
               
               
                   
                 MDL_ZnPb 
                 −0.0335973 
                 Yes 
               
               
                   
                 MDL_LiMg25 
                 −0.0337371 
                 No 
               
               
                   
                 MDL_Ni 
                 −0.0343914 
                 Yes 
               
               
                   
                 MDL_LiCu 
                 −0.0344311 
                 No 
               
               
                   
                 Entropy_LiZn 
                 −0.0356069 
                 No 
               
               
                   
                 MDL_Li 
                 −0.0364019 
                 Yes 
               
               
                   
                 MDL_NiBa 
                 −0.0369198 
                 No 
               
               
                   
                 Determinism_LiAl 
                 −0.0396184 
                 No 
               
               
                   
                 MDL_SrMo 
                 −0.0412142 
                 No 
               
               
                   
                 MDL_NiSn 
                 −0.0433706 
                 No 
               
               
                   
                 Entropy_ZnBa 
                 −0.0437905 
                 Yes 
               
               
                   
                 Entropy_NiZn 
                 −0.0441552 
                 No 
               
               
                   
                 Entropy_NiPb 
                 −0.0441841 
                 No 
               
               
                   
                 Entropy_ZnSn 
                 −0.0479249 
                 Yes 
               
               
                   
                 Entropy_LiCu 
                 −0.0506353 
                 No 
               
               
                   
                 Entropy_LiSn 
                 −0.0520773 
                 No 
               
               
                   
                 MDL_NiAs 
                 −0.0529876 
                 No 
               
               
                   
                 Entropy_LiAs 
                 −0.056885 
                 No 
               
               
                   
                 Entropy_NiBa 
                 −0.0578575 
                 No 
               
               
                   
                 Entropy_Li 
                 −0.0584355 
                 Yes 
               
               
                   
                 Determinism_LiMg25 
                 −0.0615968 
                 No 
               
               
                   
                 MDL_NiMo 
                 −0.0637464 
                 No 
               
               
                   
                 MDL_NiCu 
                 −0.0657485 
                 No 
               
               
                   
                 Entropy_ZnPb 
                 −0.066002 
                 Yes 
               
               
                   
                 Entropy_ZnAs 
                 −0.0703648 
                 Yes 
               
               
                   
                 Entropy_Ni 
                 −0.0708359 
                 Yes 
               
               
                   
                 Entropy_LiMg25 
                 −0.071669 
                 No 
               
               
                   
                 Determinism_Ca43Ni 
                 −0.0761811 
                 No 
               
               
                   
                 Entropy_NiCu 
                 −0.0779726 
                 No 
               
               
                   
                 Entropy_Ba 
                 −0.0820585 
                 Yes 
               
               
                   
                 Determinism_ZnSr 
                 −0.0900876 
                 Yes 
               
               
                   
                 Determinism_SrPb 
                 −0.0916928 
                 No 
               
               
                   
                 Entropy_NiAs 
                 −0.0950552 
                 No 
               
               
                   
                 Determinism_ZnBa 
                 −0.0959118 
                 Yes 
               
               
                   
                 Determinism_LiMn 
                 −0.0978331 
                 No 
               
               
                   
                 Entropy_NiSn 
                 −0.1060182 
                 No 
               
               
                   
                 Determinism_SrSn 
                 −0.1094853 
                 No 
               
               
                   
                 Determinism_CuBa 
                 −0.1107066 
                 No 
               
               
                   
                 Entropy_SrMo 
                 −0.1111222 
                 No 
               
               
                   
                 Determinism_SrBa 
                 −0.1138937 
                 No 
               
               
                   
                 Entropy_NiSr 
                 −0.1199173 
                 No 
               
               
                   
                 Determinism_LiMo 
                 −0.1247136 
                 No 
               
               
                   
                 Determinism_Pb 
                 −0.1284508 
                 Yes 
               
               
                   
                 Entropy_NiMo 
                 −0.129908 
                 No 
               
               
                   
                 Determinism_Sr 
                 −0.1328462 
                 Yes 
               
               
                   
                 Determinism_LiBa 
                 −0.1403608 
                 No 
               
               
                   
                 Determinism_LiCr 
                 −0.1514256 
                 No 
               
               
                   
                 Determinism_MoPb 
                 −0.1527844 
                 No 
               
               
                   
                 Determinism_Mg25Ba 
                 −0.1566375 
                 No 
               
               
                   
                 Determinism_SnPb 
                 −0.1656892 
                 No 
               
               
                   
                 Determinism_LiSr 
                 −0.1711748 
                 No 
               
               
                   
                 Determinism_CuSn 
                 −0.1742272 
                 No 
               
               
                   
                 Determinism_Sn 
                 −0.1751359 
                 Yes 
               
               
                   
                 Determinism_MoBa 
                 −0.183775 
                 No 
               
               
                   
                 Determinism_ZnAs 
                 −0.184485 
                 Yes 
               
               
                   
                 Determinism_ZnSn 
                 −0.1924023 
                 Yes 
               
               
                   
                 Determinism_ZnMo 
                 −0.2001491 
                 No 
               
               
                   
                 Determinism_SnBa 
                 −0.207863 
                 No 
               
               
                   
                 Determinism_NiPb 
                 −0.2160932 
                 No 
               
               
                   
                 Determinism_Li 
                 −0.2579859 
                 Yes 
               
               
                   
                 Determinism_ZnPb 
                 −0.2617748 
                 Yes 
               
               
                   
                 Determinism_NiMo 
                 −0.3166897 
                 No 
               
               
                   
                 Determinism_Ba 
                 −0.3180302 
                 Yes 
               
               
                   
                 Determinism_Zn 
                 −0.3387266 
                 No 
               
               
                   
                 Determinism_BaPb 
                 −0.3854676 
                 No 
               
               
                   
                 Determinism_NiCu 
                 −0.3949591 
                 No 
               
               
                   
                 Determinism_SrMo 
                 −0.4133329 
                 No 
               
               
                   
                 Determinism_NiSr 
                 −0.4561735 
                 No 
               
               
                   
                 Determinism_NiZn 
                 −0.5695511 
                 No 
               
               
                   
                 Determinism_NiAs 
                 −0.5844446 
                 No 
               
               
                   
                 Determinism_NiBa 
                 −0.5948487 
                 No 
               
               
                   
                 Determinism_Ni 
                 −0.5994648 
                 Yes 
               
               
                   
                 Determinism_NiSn 
                 −0.7561256 
                 No 
               
               
                   
                 Intercept 
                 −21.741388 
                 No 
               
               
                   
                   
               
            
           
         
       
     
     REFERENCES CITED AND ALTERNATIVE EMBODIMENTS 
     All references cited herein are incorporated herein by reference in their entirety and for all purposes to the same extent as if each individual publication or patent or patent application was specifically and individually indicated to be incorporated by reference in its entirety for all purposes. 
     Many modifications and variations of this invention can be made without departing from its spirit and scope, as will be apparent to those skilled in the art. The specific embodiments described herein are offered by way of example only. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. The invention is to be limited only by the terms of the appended claims, along with the full scope of equivalents to which such claims are entitled.