title: The number of (0,1) - Matrices with fixed row and column sums

authors: Pule, Solomone Tahamano

abstract: Let R and S be non-negative and non-increasing vectors of order m and n respectively. We consider the set A(R, S) of all m x n matrices with entries restricted to {0, 1}. We give an alternative proof of the Gale-Ryser theorem, which determines when A(R, S) is non-empty. We show conditions for R and S so that ∣A(R, S) ∣ ∈ {1, n!}. We also examine the case where ∣A(R, S) ∣ = 2 and describe the structure of those matrices. We show that for each positive integer k, there is a possible choice of R and S so that ∣A(R, S) ∣ = k. Furthermore, we explore gm,n(x; y), the generating function for the cardinality ∣A(R, S) ∣ of all possible combinations of R and S.

text: The number of (0,1) - Matrices with fixed row and column sums Let R and S be non-negative and non-increasing vectors of order m and n respectively. We consider the set A(R, S) of all m x n matrices with entries restricted to {0, 1}. We give an alternative proof of the Gale-Ryser theorem, which determines when A(R, S) is non-empty. We show conditions for R and S so that ∣A(R, S) ∣ ∈ {1, n!}. We also examine the case where ∣A(R, S) ∣ = 2 and describe the structure of those matrices. We show that for each positive integer k, there is a possible choice of R and S so that ∣A(R, S) ∣ = k. Furthermore, we explore gm,n(x; y), the generating function for the cardinality ∣A(R, S) ∣ of all possible combinations of R and S.

year: 2013

title: Towards robust and repeatable sampling methods in eDNA-based studies

authors: Dickie, Ian A.

subjects: Science & Technology

abstract: DNA‐based techniques are increasingly used for measuring the biodiversity (species presence, identity, abundance and community composition) of terrestrial and aquatic ecosystems. While there are numerous reviews of molecular methods and bioinformatic steps, there has been little consideration of the methods used to collect samples upon which these later steps are based. This represents a critical knowledge gap, as methodologically sound field sampling is the foundation for subsequent analyses. We reviewed field sampling methods used for metabarcoding studies of both terrestrial and freshwater ecosystem biodiversity over a nearly three‐year period (n = 75). We found that 95% (n = 71) of these studies used subjective sampling methods and inappropriate field methods and/or failed to provide critical methodological information. It would be possible for researchers to replicate only 5% of the metabarcoding studies in our sample, a poorer level of reproducibility than for ecological studies in general. Our findings suggest greater attention to field sampling methods, and reporting is necessary in eDNA‐based studies of biodiversity to ensure robust outcomes and future reproducibility. Methods must be fully and accurately reported, and protocols developed that minimize subjectivity. Standardization of sampling protocols would be one way to help to improve reproducibility and have additional benefits in allowing compilation and comparison of data from across studies.

text: Towards robust and repeatable sampling methods in eDNA-based studies DNA‐based techniques are increasingly used for measuring the biodiversity (species presence, identity, abundance and community composition) of terrestrial and aquatic ecosystems. While there are numerous reviews of molecular methods and bioinformatic steps, there has been little consideration of the methods used to collect samples upon which these later steps are based. This represents a critical knowledge gap, as methodologically sound field sampling is the foundation for subsequent analyses. We reviewed field sampling methods used for metabarcoding studies of both terrestrial and freshwater ecosystem biodiversity over a nearly three‐year period (n = 75). We found that 95% (n = 71) of these studies used subjective sampling methods and inappropriate field methods and/or failed to provide critical methodological information. It would be possible for researchers to replicate only 5% of the metabarcoding studies in our sample, a poorer level of reproducibility than for ecological studies in general. Our findings suggest greater attention to field sampling methods, and reporting is necessary in eDNA‐based studies of biodiversity to ensure robust outcomes and future reproducibility. Methods must be fully and accurately reported, and protocols developed that minimize subjectivity. Standardization of sampling protocols would be one way to help to improve reproducibility and have additional benefits in allowing compilation and comparison of data from across studies.

year: 2018

title: Quantification of Nitro-toxins in Karaka (Corynocarpus laevigatus) Drupes

authors: MacAskill, Jessica Jane

abstract: The karaka (Corynocarpus laevigatus) is a tree native to New Zealand (NZ), found throughout the North and South Islands. Traditionally, many parts of the karaka were used by Māori, however the parts of the karaka of most interest are the berry and nut as they were valuable food sources, in particular the nut. Karaka was known to be a toxin-bearing food, however implementation of a traditional baking and soaking process meant that the nuts were left in states fit for consumption, more often than not. The nuts also had the benefit of being able to be stored for future use when other food sources were short in supply. Karaka was readily consumed up until the 1950s, after this consumption rates decreased rapidly, after the toxic effects were associated with the incorrect preparation of the nuts.

Studies on karaka have revealed that the toxicity of the nuts primarily arises from various nitropropanoyl glucopyranoses (NPGs), twelve of which have been detected in karaka. The quantity of these NPGs has been infrequently studied and it is often only one of the NPGs-karakin which is quantified, although it is believed the toxicity in nuts arises collectively from all of the NPGs. As a result, there is the need to be able to quantify the NPGs in karaka and look at potential toxin removal techniques. If toxin removal can be accomplished, there is the potential for karaka to be a marketable ‘traditional’ or ‘Kiwi’ food item. Additionally, the toxins removed as a by-product may prove to have their own potential commercial applications, for example as insecticides or repellents. 

Since all the NPGs are assumed to be toxic, a method was developed to quantify the total toxicity in the nuts. The method involves the release of NPA via acid hydrolysis of the nitropropanoyl ester groups of the NPGs. The NPA is then able to be measured and subsequently quantified using HPLC. The method incorporates a correction factor (CF) that was determined to give the original NPA content at a time of zero (NPA0), accounting for the unavoidable loss of NPA that arises from the hydrolysis method.

The average quantity of NPA in karaka nuts was found to range from 50.25 to 138.62 g kg-1 (dry weight) which is equivalent to 5.0 to 13.9%. These are much higher percentages than any previously reported because the method used in this study measured total NPA. Earlier methods measured a limited range of NPGs (often a single NPG) unhydrolysed and could have missed NPA arising from other compounds that contribute to total toxicity. Additionally, the concentrations of NPA in karaka nuts were influenced by a number of factors including intra and inter tree variation, storage conditions and ripeness. Although quantification was focused on determining NPA content in nuts, a test conducted also showed NPA to be present in increasingly lower levels in the berry flesh, shell and pellicle respectively. 

Nuts were subjected to various potential industrial processing techniques, treatment times and conditions, in order to determine their efficacy for toxin removal. Treatments included boiling, microwave cooking, soxhlet extraction, oven roasting, autoclaving and cold-water treatments. The efficiency of each treatment varied considerably, with both heat and water proving to be beneficial in toxin removal. However, treatments involving water were found to be more effective than heat treatments alone. Out of all treatment types, times and conditions tested, none were found to leave nuts with a NPA concentration lower than the estimated safe level of daily consumption for a 70 kg adult (< 1.75 mg). Additionally, only some of the treatments resulted in nuts being left in visually appealing states. At present, toxin removal by a single process in order to render karaka nuts safe to consume appears to be an impractical activity. However, if treatment protocols were combined and modified, there is the potential for the development of an effective detoxification process. Furthermore, tests on the treatment solutions revealed that NPA can be obtained in solution as a by-product of nut treatment; with cold-water proving to be more effective than treatments that also used heat. Obtaining NPA as a by-product of toxin removal in nuts appears to be a feasible option for a natural source of NPA.

text: Quantification of Nitro-toxins in Karaka (Corynocarpus laevigatus) Drupes The karaka (Corynocarpus laevigatus) is a tree native to New Zealand (NZ), found throughout the North and South Islands. Traditionally, many parts of the karaka were used by Māori, however the parts of the karaka of most interest are the berry and nut as they were valuable food sources, in particular the nut. Karaka was known to be a toxin-bearing food, however implementation of a traditional baking and soaking process meant that the nuts were left in states fit for consumption, more often than not. The nuts also had the benefit of being able to be stored for future use when other food sources were short in supply. Karaka was readily consumed up until the 1950s, after this consumption rates decreased rapidly, after the toxic effects were associated with the incorrect preparation of the nuts.

Studies on karaka have revealed that the toxicity of the nuts primarily arises from various nitropropanoyl glucopyranoses (NPGs), twelve of which have been detected in karaka. The quantity of these NPGs has been infrequently studied and it is often only one of the NPGs-karakin which is quantified, although it is believed the toxicity in nuts arises collectively from all of the NPGs. As a result, there is the need to be able to quantify the NPGs in karaka and look at potential toxin removal techniques. If toxin removal can be accomplished, there is the potential for karaka to be a marketable ‘traditional’ or ‘Kiwi’ food item. Additionally, the toxins removed as a by-product may prove to have their own potential commercial applications, for example as insecticides or repellents. 

Since all the NPGs are assumed to be toxic, a method was developed to quantify the total toxicity in the nuts. The method involves the release of NPA via acid hydrolysis of the nitropropanoyl ester groups of the NPGs. The NPA is then able to be measured and subsequently quantified using HPLC. The method incorporates a correction factor (CF) that was determined to give the original NPA content at a time of zero (NPA0), accounting for the unavoidable loss of NPA that arises from the hydrolysis method.

The average quantity of NPA in karaka nuts was found to range from 50.25 to 138.62 g kg-1 (dry weight) which is equivalent to 5.0 to 13.9%. These are much higher percentages than any previously reported because the method used in this study measured total NPA. Earlier methods measured a limited range of NPGs (often a single NPG) unhydrolysed and could have missed NPA arising from other compounds that contribute to total toxicity. Additionally, the concentrations of NPA in karaka nuts were influenced by a number of factors including intra and inter tree variation, storage conditions and ripeness. Although quantification was focused on determining NPA content in nuts, a test conducted also showed NPA to be present in increasingly lower levels in the berry flesh, shell and pellicle respectively. 

Nuts were subjected to various potential industrial processing techniques, treatment times and conditions, in order to determine their efficacy for toxin removal. Treatments included boiling, microwave cooking, soxhlet extraction, oven roasting, autoclaving and cold-water treatments. The efficiency of each treatment varied considerably, with both heat and water proving to be beneficial in toxin removal. However, treatments involving water were found to be more effective than heat treatments alone. Out of all treatment types, times and conditions tested, none were found to leave nuts with a NPA concentration lower than the estimated safe level of daily consumption for a 70 kg adult (< 1.75 mg). Additionally, only some of the treatments resulted in nuts being left in visually appealing states. At present, toxin removal by a single process in order to render karaka nuts safe to consume appears to be an impractical activity. However, if treatment protocols were combined and modified, there is the potential for the development of an effective detoxification process. Furthermore, tests on the treatment solutions revealed that NPA can be obtained in solution as a by-product of nut treatment; with cold-water proving to be more effective than treatments that also used heat. Obtaining NPA as a by-product of toxin removal in nuts appears to be a feasible option for a natural source of NPA.

year: 2013