prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What types of sensors are now capable of estimating physical activity levels and physiological outcomes of older adults?

Read the following text and answer briefly.

Context 1: \section{Introduction}
Cognitive deficit of older adults is one of the biggest global public health challenges in elderly care  Approximately 5 2 million people of 65 and older are suffered with any form of cognitive impairments in United States in 2012 \cite{stat12}  Dementia is one of the major causes of the cognitive impairments which is more acute among 85 and older population (50\%) \cite{stat12}  However, the costs (financial and time) of health care and long-term care for individuals with Alzheimer's (special form of dementia) or other dementias are substantial  For example, during 2016, about 15 9 million family and friends in United States provided 18 2 billion hours of unpaid assistance to those with cognitive impairments which is a contribution to the nation valued at \$230 1 billion  One the other hand, total payments for all individuals with all form of cognitive impairments are estimated at \$259 billion  Total annual payments for health care, long-term care and hospice care for people with Alzheimer's or other dementias are projected to increase from \$259 billion in 2017 to more than \$1 1 trillion in 2050  Among the above costs, a significant amount are relevant to clinical and diagnostic tests \cite{stat17}  Although clinical and diagnostic tests have become more precise in identifying dementia, studies have shown that there is a high degree of underrecognition especially in early detection  However, there are many advantages to obtaining an early and accurate diagnosis when cognitive symptoms are first noticed as the root cause findings of impairment always lessen the progress of impairment status and sometimes symptoms can be reversible and cured 

With the proliferation of emerging ubiquitous computing technologies, many mobile and wearable devices have been available to capture continuous functional and physiological behavior of older adults  Wearable sensors are now capable of estimating number of steps being taken, physical activity levels, sleep patterns and physiological outcomes (heart rate, skin conductance) of older adults \cite{sano15}  Ambient sensors also help capture the movement patterns of objects and humans for activity and behavior recognition \cite{dawadi14,dawadi15}  Researchers also proved the existence of correlations between cognitive impairment and everyday task performance \cite{dawadi14, akl15,alam16} as well as physiological symptoms \cite{alam16,sano15}  Although current studies showed some successes in IoT-assisted cognitive health assessment in different domains individually, there are several existing challenges in developing and validating a fully automated multi-modal assessment model 

\begin{enumerate}
\item \emph{Real-time IoT System}: A real-time IoT system must include a continuous and fault tolerant data streaming capability among central hub, wearable sensors and ambient sensors regardless of network communication protocol (WiFi, Ethernet, Bluetooth etc ) which are not available in existing researches 
\item \emph{Multi-modal Context Fusion}: Though several offline clinically validated cognitive health assessment tools exist \cite{wai03, starling99, krapp07, yesavage82, zung71}, there is no universally accepted method for IoT-assisted automatic cognitive health assessment in smart home environment that can fuse multi-modal sensor contexts altogether  For example, some researchers showed ambient sensors based Activities of Daily Livigin (ADLs) sequence pattern can signify the cognitive health status of older adults \cite{akl15, dawadi15}  Researchers also showed wearable Electrodermal Activity pattern analysis may carry the significance of cognitive status \cite{sano15}  However, for validation of IoT based cognitive health assessment, self-reported surveys, clinical diagnosis and observation based tools are used individually by prior researchers \cite{akl15, dawadi15, sano15, alam16} 
\end{enumerate}

Regarding aforementioned challenges for the automation of cognitive health assessment, \emph{AutoCogniSys} considers (i) reproducibility of our model in any smart home system consists of ambient motion sensors, wearable accelerometer (ACC) sensors, wearable Electrodermal Activity (EDA) and Photoplethysmography (PPG) sensors individually or combined streams; (ii) context awareness based on ambient motion sensors and wearable ACC sensors in any types of activities such as hand gestural, postural and complex ADLs; and (iii) high accuracy, i e , a recall rate of over 90\% with less than 5\% false positive rate  More specifically, \emph{AutoCogniSys} extends our existing work \cite{alam16} in three dimensions,

\emph{(1) True Automation:} We first investigate the correlations of cognitive impairment with human activities and stress where we manually labeled activities, extract the corresponding physiological sensor (EDA and PPG) features of each activity, and use statistical method to find correlations  Then, we propose automatic complex activity recognition based on a Hierarchical Dynamic Bayesian Network (HDBN) model, fine-grained extraction of physiological sensor features and finally machine learning classification of cognitive impairment 

\emph{(2) Noises Elimination:} We define different types of noises on ACC, EDA and PPG sensors, propose extensive signal processing techniques to remove noises and show significant improvement can be achieved in cognitive impairment classification 

\emph{(3) Implementation and Evaluation:} Finally, we design and implement IoT system and analytic methods and minimize the human involvement to automate our proposed cognitive health assessment approach by considering effective smart home sensor customization and deployment, data collection, screening, cleaning and filtering, feature computation, normalization and classification, and activity  model training 

\textbf{Research Questions:} \emph{AutoCogniSys} consequently tackles the following key research questions 

$\bullet$ Can we detect simultaneously the periodic rhythms of  both hand gestures and postural activities from wrist-worn ACC sensor signal for diverse population (population with same activity but diverse ways such as walking with walker, stretcher or normally)? If so, how can we incorporate the hand gesture, posture and ambient sensor data streams to help improve the ADLs recognition models?

$\bullet$ How can we exploit and relate the micro-activity features into noise free physiological sensor signals processing to automate cognitive health assessment process? What are the critical roles of clinical survey and technology guided assessment methodologies and their inter-relationships for automating the different intermediate steps of cognitive health assessment process?

To tackle these, we make the following \textbf{key contributions}:

$\bullet$ We employ an extensive signal deconvolution technique that in conjunction with machine learning technique helps facilitate a wrist-worn ACC-based multi-label (hand gestural and postural) activity recognition for diverse population  We then leverage multi-label context sets with ambient and object sensor signals for complex activity recognition based on HDBN model 

$\bullet$ We propose a novel collaborative filter for EDA signal processing by postulating signal as a mixture of three components: \emph{tonic phase, phasic phase} and \emph{motion artifacts}, and employ convex optimization technique for filtering out the motion artifacts  We also propose a novel PPG signal processing technique to filter out the inherent motion artifacts and noises using improved Periodic Moving Average Filtering (PMAF) technique 

$\bullet$  We design and prototype an IoT system consisting of multiple devices (wearable wrist band, IP camera, object and ambient sensors) connected with central hub via WiFi, Ethernet and Bluetooth communication protocols  We collected data from 22 older adults living in a continuing care retirement community center in a very natural setting (IRB \#HP-00064387) 

$\bullet$ Finally, we employ statistical and machine learning techniques to jointly correlate the activity performance metrics and stress (EDA and PPG) features that helps achieve max  93\% of cognitive impairment status detection accuracy  We evaluate \emph{AutoCogniSys} on 5 clinically validated offline assessment tools as ground truth 
\section{Related Works}
\emph{AutoCogniSys} builds on previous works on wearable devices based low-level (postural and hand gestural) activity recognition and their integration with ambient sensors to recognize complex ADLs, the underlying signal processing and applications on cognitive health assessment automation 
\subsection{Wearable Sensor Signal Processing}
Wearable sensors can be two types: physical and physiological  Physical sensors (accelerometer, gyroscope etc ) signal values change over the movements of the sensor devices  Physiological sensors change over physiological condition of body such as EDA changes over stress and PPG changes over heart rate  However, physical movements also impose noises on physiological sensor signals which is called \emph{motion artifacts} 
\subsubsection{Physiological Signal Processing}
A continuous and descrete decomposition of EDA, and time and frequency domain analytics of PPG signal have been investigated before to extract relevant physiological features which were contaminated with noises and motion artifacts \cite{alam16}  \cite{setz10} denoised and classified EDA from cognitive load and stress with accuracy higher than 80\%  Though motion artifacts removal techniques such as exponential smoothing \cite{hern11} and low-pass filters \cite{poh10, hernandez14} provide significant improvement in filtering EDA signals, wavelet transforms offer more sophisticated refinement for any kind of physiological sensors such as electroencephalogram \cite{krish06, zikov02}, electrocardiogram \cite{erc06,alfa08}, and PPG \cite{lee03}  \cite{chen15} proposed a stationary wavelet transform (SWT) based motion artifacts removal technique  `cvxEDA' proposed  a convex optimization technique considering EDA as a mixture of white gaussian noise, tonic and phasic components where white gaussian noise includes motion artifacts and external noises \cite{greco16}  \emph{AutoCogniSys} intelligently combines SWT and `cvxEDA' together to remove noises and motion artifacts from EDA signal  On the other hand, it is more difficult to remove motion artifacts from PPG signal due to its periodicity of nature \cite{wang13}  Researchers proposed different methods such as frequency analytics \cite{garde13,wang13}, statistical analytics \cite{peng14} and digital filter \cite{lee10} to reduce noises and motion artifacts from PPG  \emph{AutoCogniSys} used Periodic Moving Average Filter (PMAF) in this regard \cite{lee07} 
\subsubsection{Physical Sensor Signal Processing}
ACC based hand gesture recognition has been explored by several researchers in past such as discrete hidden markov model \cite{liu10}, artificial neural network \cite{arce11}, weighted naive bayes and dynamic time warping \cite{mace13}  Akl et  al  proposed 18 gesture dictionary based Support Vector Machine (SVM) classifier \cite{akl11}  Wrist-worn ACC based postural activity recognition approach has been proposed using Decision Tree, Random Forest, Support Vector Machines, K-Nearest Neighbors, Naive Bayes and deep neural networks \cite{gj14, wang16}, the accuracy stagnates at 85\% using SVM method \cite{martin16}  However, neither of past works proposed any technique that can provide single body worn ACC sensor-based multiple body contexts recognition nor works efficiently for diverse posture say walking normally, with walker, with double walker or wheel chair  Our proposed 8-hand gesture recognition technique assisted sparse-deconvolution method improves classification performances on both normal and diverse postures  However, we incorporated hand gestures and postures in conjunction with ambient sensors into single-inhabitant HDBN model \cite{alam16b} that provides significant improvement in complex activity recognition 
\subsection{Cognitive Health Assessment}
Smart home environment has been used for providing automated health monitoring and assessment in the ageing population before \cite{dawadi14, gong15, akl15, dawadi15}  `SmartFABER' proposed a non-intrusive sensor network based continuous smart home environmental sensor data acquisition and a novel hybrid statistical and knowledge-based technique to analyz the data to estimate behavioral anomalies for early detection of mild-cognitively impairment \cite{riboni16}  \cite{skubic15} presented an example of unobtrusive, continuous monitoring system for the purpose of assessing early health changes to alert caregivers about the potential signs of health hazards  Though, prior researches proposed a sequence of ambient motion sensor streams as complex activity components in activity based health assessment \cite{dawadi14, gong15, akl15, dawadi15}, we consider inclusion of an wearable wrist-band with in-built ACC sensor to detect hand gesture and posture, augmenting with the ambient sensor readings to help recognize complex activities as well as cognitive health assessment of older adults  Additionally, we propose intelligent use of physiological features of skin through different physiological sensor signals (EDA, PPG) processing in daily activity tasks and incorporate context-awareness for automation of cognitive health assessment that have not been explored before 
\begin{figure}[!htb]
\begin{center}
   \epsfig{file=flowchart pdf,height=1 6in, width=3 5in}
\caption{Overall flow of \emph{AutoCogniSys} pipeline }
   \label{fig:overview}
\end{center}
\end{figure}
\section{Overall Architecture}
We first investigate existing IoT-based cognitive health care frameworks that covers every aspects of wearable (physical, physiological) and ambient (passive infrared and object) sensor signals computing  \emph{AutoCogniSys} is comprised of three component modules: (i)~sensing, (ii)~processing, and (iii)~analysis  The `sensing' module consists of clinical assessment tools (surveys, observation and clinical backgrounds) and sensing signals (ambient and wearable sensors)  `Sensor processing' module is comprised of three sub-modules: a)~clinical assessment feature extraction from assessment tools; b)~ambient sensor feature extraction; and c)~wearable sensor processing (noise removal, segmentation, feature extraction, classification etc )  `Analysis' module is comprised of machine learning and statistical analytics-based score prediction of cognitive impairment  Automation of each module's functionality and inter-intra modular transactions without human interference can be called {\it true automation} of cognitive health assessment  Fig ~\ref{fig:overview} shows the overall flow of \emph{AutoCogniSys} which is discussed in details in the following sections 
\subsection{Demographic Ground Truth Data Collection}
Currently in standard clinical practice and research, the most accurate evaluations of cognitive health assessment are one-to-one observation and supervision tasks/questionnaires for monitoring an individual's functional abilities and behavior \cite{resnick15}  In the first stage of this pilot study, we have investigated current literatures and carefully chosen the clinically proven functional and behavioral health assessment survey tools \cite{resnick15}  On the other hand, to cross check with the survey based evaluations, we have also chosen clinically justified observation based behavioral assessment methods  First, following the resident consent, our clinical research evaluator collects demographic and descriptive data (age, gender, race, ethnicity, marital status, education and medical commodities)  She has performed two types of clinical assessments: (1) \emph{Observation based} where the resident's cognition is assessed using the Saint Louis University Mental Status (SLUMS) scale \cite{wai03}  (2) \emph{Survey based} where five widely used and clinically well validated surveys are taken into account: (a) \emph{Yale Physical Activity Survey} \cite{starling99}; (b) \emph{Lawton Instrumental Activities of Daily Living}; (c) \emph{Barthel Index of Activities of Daily Living} \cite{krapp07}; (d) \emph{Geriatric Depression Rating scale} \cite{yesavage82}; and (e) \emph{Zung Self-Rating Anxiety scale} \cite{zung71} 
\subsection{Smart Environment Creation}
For an ideal IoT-based system, instrumenting and deploying it at each participant's natural living environment warrants for assembling a flexible set of hardware and software interfaces to ease the system configuration, setup, and network discovery processes  The sensor system placed in the residences of volunteers needs to meet several specific physiological signals and activity monitoring needs  However, we must confirm that the devices are reliable with potential for re-deployment as well as appear unintimidating to the participants  Inspired by the above requirements, we developed a real testbed IoT system, {\it SenseBox}, by customizing Cloud Engine PogoPlug Mobile base station firmware to integrate with WiFi (connect ambient and object sensors) and Bluetooth (connect wristband) protocol  The smart home components are as follows: (i) PogoPlug base server with a continuous power supply, (ii) 3 binary Passive Infrared sensors in three different rooms (kitchen, livingroom and bedroom) to capture room level occupancy, (iii) 7 binary object sensors attached with closet door, entry door, telephone, broom, laundry basket, trash can and trash box, (iv) three IP cameras in the appropriate positions to collect the ground truth data and (v) an Empatica E4 \cite{empatica} wrist-band (integrated sensors: PPG at 64 Hz, EDA at 4 Hz, Body temperature at 1 Hz and a triaxial ACC at 32 Hz) on the participant's dominating hand 
\section{Activity Recognition}
We aim to detect single wrist-worn ACC sensor based hand gesture and postural activities and insert these into an HDBN graphical model in conjunction with ambient and object sensor values for complex activity recognition  We consider the recognition problem asan activity tupple of $\langle gesture,posture,ambient,object \rangle$  Though, Alam et  al  provides significant performance improvement for single wrist-worn ACC sensor aided 18-hand gesture based postural activity recognition in lab environment \cite{alam17}, it faces some practical challenges in real-time smart environment with older adults due to the diversity of their postures  For example, some older adults use walker, double walking sticks or wheel chair for walking in which cases collecting 18 hand gestures and corresponding postural activities for training requires endless efforts and carefulness  To reduce the complexity of ground truth labeling and later state space explosion for graphical model (HDBN), we propose to use rotational normalization method that can merge some hand-gestures subject to directional differences and forms an 8-hand gesture model  However, our proposed Feature Weight Naive Bayes (FWNB) classifier adds significant improvement on Alam et  al  proposed sparse-deconvolution method as well as recognition in diverse postural environment 
\begin{figure}[!htb]
\begin{center}
   \epsfig{file=hand_gestures pdf,height=0 5in, width=3in}
   \vspace{- 2in}
\caption{8 hand gesture dictionary with direction}
   \label{fig:hand_gestures}
   \vspace{- 2in}
\end{center}
\end{figure}
\subsection{Hand Gesture Recognition}
\label{sec:hand_gesture}
\emph{AutoCogniSys} proposes an 8-gesture dictionary (as shown in Fig  \ref{fig:hand_gestures}) and a Feature Weighted Naive Bayesian (FWNB) framework for building, modeling and recognizing hand gestures  The method comprises of the following steps: (i) \emph{Preprocessing:} wrist-worn ACC sensor provided 3-axis data are passed through 0 4Hz low-pass filter to remove the data drift  (ii) \emph{Rotation normalization:} Normalizing the rotation of hand gestures provides greater accuracy and allows for more realistic, orientation-independent motion  At first, we find the best fit plane of the acceleration vectors thus if the motion lies in a single plane, then the acceleration vectors of a closed shape should on average lie in that main plane  Then, we take all acceleration segments between points of inflection to form one single vector called reference vector that provides us the general direction of user's motion  After that, each vector is normalized relative to the reference vector  This normalization helps remove a lot of hand gestures from prior considered 18 hand gestures resulting a reduced dictionary of 8 gestures  (iii) \emph{Feature Weighted Naive Bayesian model:} Naive Bayes classifier is light-weight and efficient technique for hand gesture recognition  We extract 12 ACC features \cite{alam17} and calculate weight for each feature type based on the similarity of feature measures of the trained gestures (0$<$weight$<$1)  While recognizing gestures, the proximity of each feature measure to the average trained feature measure of each gesture type is calculated by a normal distribution  Then, the proximity value is multiplied by the feature weight that was calculated in the training phase   All of these multiplied values are added together and the system predicts the gesture type with the greatest value as the user gesture  In the learning data points, there should be static postural activities (such as sitting, lying etc ) to avoid unexpected noises over wrist-worn ACC sensors  In the final hand gesture dictionary, we save the reference vector as our signal dictionary 
\subsection{Postural Activity Recognition}
In normal lab environment, wrist-worn ACC sensor signal is a mixture (convolution) of actual hand gesture and postural activity relevant signals \cite{alam17}  \emph{AutoCogniSys} improves the idea by reducing the number of hand gestures and postural activities to 8 (as shown in Fig \ref{fig:hand_gestures}) using rotation normalization and 4 (walking, sitting, standing and lying)  Then, we use sparse-deconvolution method (with 31\% signal reconstruction error) to get Approximately Sparse Factor  The summary of the entire process is stated bellow:

{\it Building Deconvolution Method:} We first consider the wrist-worn ACC sensor signals (3-axis values) as a convolution of hand gesture and postural activity effects and build a deconvolution framework  The deconvolution framework takes a known signal (hand gesture effects) and a equalizer parameter ($\lambda$) as input and provides an Approximately Sparse Factor signal (postural activity effects) as output  For 3-axis ACC signals, we need to learn associated 3 equalizer parameters for each hand gesture  Moreover, each equalizer parameter is involved with 4 postural activities that results a total 96 ($8\times 3\times 4$) equalizer parameters to learn  

{\it Learning Classification Model:} We use the Approximately Sparse Factor signal to extract 12 statistical features and SVM with sequential machine optimization (SMO) \cite{cao06} for postural activity recognition 

{\it Prediction Model:} After recognizing the hand gestures following the method explained in Sec ~\ref{sec:hand_gesture}, we take the corresponding reference vector as known signal and extract the Approximately Sparse Factor signals incorporating corresponding 3 equalizer parameters ($\lambda$) for the sparse-deconvolution method  Then, we apply feature extraction and prior learned SMO based SVM classifier \cite{cao06} to classify final postural activity  Fig ~\ref{fig:deconvolution} illustrates a single axis example of the deconvolution 

\begin{figure}[!htb]
\begin{center}

   \epsfig{file=deconvolution pdf,height=1 6in, width=3in}
   \vspace{- 15in}
\caption{Sample deconvolution example of X-axis  The raw x-axis of accelerometer signal, reference vector of the sample gesture and the extracted corresponding ASF signal of walking }
   \label{fig:deconvolution}
\end{center}
\vspace{- 15in}
\end{figure}

\subsection{Complex Activity Recognition}
We build a HDBN based complex activity recognition framework for single inhabitant scenario smart home environment \cite{alam16b} taking the advantage of detected hand gestural and postural activities along with the ambient and object sensor streams  At first, we obtain instant hand gestural and postural activities from our above proposed models, and additionally motion sensor and object sensor readings from our IoT-system for every time instant generating a 4-hierarchy of HDBN model  Considering the context set $\langle gestural, postural, ambient,object\rangle$ as a hierarchical activity structure (extending two 2-hierarchical HDBN \cite{alam16b}), we build complex activity recognition model for single inhabitant scenario  Finally, we infer the most-likely sequence of complex activities (and their time boundaries), utilizing the well-known Expectation Maximization (EM) algorithm \cite{dempster77} for training and the Viterbi algorithm \cite{forney73} for run-time inference 
\section{Automatic Activity Features Estimation}
The effects of cognitive ability on daily activity performance have been studied before \cite{dawadi14,akl15}  They experimentally and clinically validated that cognitive impairment highly reduces the daily activity performances and this activity performance can be computed as an indicator of cognitive ability status of older adults  The standard activity features refer to completeness of task (TC), sequential task ability (SEQ), interruption avoidance capabilities (INT) etc  In current behavioral science literature, the above activity features carry specific definition based on the sub-tasks involved with a complex activity \cite{dawadi14,akl15}  Completeness of task refers to how many sub-tasks are missed by the participants  Sequential task ability refers to how many sequences of sub-tasks are missed referring the gerontologist defined standard sequences of the sub-task for the particular complex activity  Interruption avoidance capability refers to how many times the participants stop or interleave while doing any sub-task  The final goal of activity features estimation is to provide overall task score  The task score is proportional to the functional ability of participants in performance daily activities  Our behavioral scientist team, comprises with Nursing professor, gerontologist and retirement community caregivers, carefully discus, optimize and choose 87 sub-tasks in total for 13 complex activities 

Each of the sub-task comprises with sequential occurrences of hand gesture and postural activities  However, no researchers ever considered hand gesture for activity features estimation due to complexity of multi-modal wearable and ambient sensors synchronization and multi-label activity classification \cite{dawadi14,akl15}  \emph{AutoCogniSys} exploited single wrist-worn sensor based hand gesture and postural activity recognition, and proposed an activity features (TC, SEQ and INT) estimation method including these two parameters in conjunction with object and ambient sensor features that provide significant improvement of cognitive health assessment of older adults 
\subsection{Machine Learning Based Complex Activity Features Estimation}
In current cognitive health assessment literature, complex activity features can be defined as $\langle TC,SEQ,INT,TS\rangle$  We used supervised method to estimate TC, SEQ and INT, and unsupervised method to estimate TS  We first, formulate the automated scoring as a supervised  machine learning problem in which machine learning algorithms learn a function that maps $\langle${\it hand gesture, posture, object, ambient sensor}$\rangle$ feature set to the direct observation scores  We use bagging ensemble method to learn the mapping function and SMO based SVM \cite{cao06} as base classifier  The learner averages by boostrapping individual numeric predictions to combine the base classifier predictions and generates an output for each data point that corresponds to the highest-probability label  We train three classifiers considering observation as ground truth for TC, SEQ and INT scores and test on the testing dataset  We derive unsupervised scores using dimensionality reduction technique for each feature set  First, we take all features of each activity, apply optimal discriminant analysis technique as a dimensionality reduction process \cite{zhang09} and reduce the feature sets into single dimensional value which represents the automated task completeness scores of the particular user activity  A min-max normalization is applied that provides us a uniform range of the variables using $
z_i=\frac{x_i-min(x)}{max(x)-min(x)}$ equation where $x=\{x1,\ldots,x_n\}$ and $z_i$ is $i^{th}$ normalized data  The final single dimensional score represents machine learning based TS score 
\section{Physiological Sensor Signals Processing}
The autonomic nervous system (ANS) restrains the body's physiological activities including the heart rate, skin gland secretion, blood pressure, and respiration  The ANS is divided into sympathetic (SNS) and parasympathetic (PNS) branches  While SNS actuates the body's resources for action under arousal conditions, PNS attenuates the body to help regain the steady state  Mental arousal (say stress, anxiety etc ) activates the sweat gland causing the increment and reduction of  Skin Conductance on SNS and PNS physiological conditions respectively  However, Instant Heart Rate also has similar effect on SNS and PNS physiological condtions i e , a higher value of heart rate is the effect of SNS and lower value is the outcome of PNS  EDA and PPG sensors are widely used to estimate the instant value of skin conductance and heart rate respectively \cite{alam16} 
\subsection{EDA Sensor Signal Processing}
EDA is the property of the human body that causes continuous variation in the electrical characteristics of the skin which varies with the state of sweat glands in the skin  There are three types of arousal: \emph{cognitive, affective and physical}  \emph{Cognitive} arousal occurs when a person tries to solve any problem using her cognitive ability  \emph{Affective} arousal occurs when a person is worried, frightened or angry either doing daily activities or in resting position  On the other hand, \emph{physical} arousal is related to the brain command to move bodily parts which is imposed on the total arousal as an artifact, called \emph{motion artifact}  However, there are always some noises due to the weather conditions (temperature, humidity etc ) and device motion  This \emph{motion artifact} can be the prime cause of signal contamination of physiological outcomes while performing daily activities which must be removed  \emph{AutoCogniSys} proposes an EDA sensor signal processing method consists of three steps: (i) noise and motion artifacts removal, (ii) separation of tonic component and phasic component (explained later) from contamination free EDA signal and (iii) feature extraction on the response window 
\subsubsection{Motion Artifacts Removal}
There are many types of motion artifacts but the unsual steep rise is the mostly occured ones associated with EDA signal while performing daily activities \cite{edel67}  We use well-known steep rising noises reduction technique, SWT \cite{chen15}  We first consider EDA signal as a mixture of a slow variant tonic and fast variant phasic component, i e , SWT coefficient is modeled as a mixture of two Gaussian components, phasic (close to zero valued signal) and tonic (high rising signal)  After expanding EDA signal into multiple levels of scaling and wavelet coefficients, we choose adaptively a threshold limit at each level based on the statistical estimation of the wavelet coefficients' distribution, and employ that on the wavelet coefficients of all levels  Finally, an inverse wavelet transform technique is applied to the thresholded wavelet coefficients to obtain the artifacts free EDA signal  Fig~ \ref{fig:eda_artifact_removal} shows a sample of raw and motion artifacts free EDA signal 

\begin{figure}[!htb]
\begin{center}
\vspace{- 1in}
   \epsfig{file=eda_signal_artifact pdf,height=1 6in, width=3 5in}
\caption{Dashed line represents noisy EDA signal and solid red line represents \emph{AutoCogniSys} proposed motion artifact free EDA signal}
   \label{fig:eda_artifact_removal}
\end{center}
\end{figure}
\subsubsection{Convex Optimization Technique to EDA Deconvolution}
After the motion artifact removal, we consider EDA as the sum of three components for $N$ sample: a slow tonic driver ($t$), fast (compact, bursty) non-negative sparse phasic driver ($r$) and a reminder error term ($\epsilon_r$) 
\begin{equation}
\label{eq:eda_signal}
y = t + r + \epsilon_r
\end{equation}
This additive error $\epsilon_r$ is a White Gaussian Noise  The central problem associated with the deconvolution method is to get tonic $t$ component from the above equation  \cite{greco16} showed that EDA signal deconvolution (separation of tonic, phasic and noise terms from EDA signal) is a quadratic optimization problem and defined tonic component as follows:
\begin{equation}
\label{eq:tonic}
t = Bl + Cd,
\end{equation}
where $B$ is a tall matrix whose columns are cubic $B$-spline basis functions, $l$ is the vector of spline coefficients, $C$ is a $N\times 2$ matrix, $d$ is a $2\times 1$ vector with the offset and slope coefficients for the linear trend  The above equation is subject to the following optimization problem,
\begin{eqnarray}
minimize \frac{1}{2} {||Mq + Bl + Cd- y||}^2_2 +\alpha {||Aq||}_1 + \frac{\lambda}{2} {||l||}^2_2\\
subject\;to\; Aq \geq 0\nonumber
\end{eqnarray}
where $M$ and $A$ are tridiagonal matrices and $q$ is an auxiliary variable  After solving the above equation, we can get the optimal values for $\{q,l,d\}$ that can be used to obtain tonic component from the equation~\ref{eq:tonic}  The reminder of the equation~\ref{eq:eda_signal} ($r+\epsilon_r$) is considered as a mixture of White Gaussian Noise ($\epsilon_r$) and a fast variant phasic component ($r$)  We employ butterworth low-pass filter (5Hz) and hanning smoothing with window size 4 (optimal) to remove $\epsilon_r$ from phasic component ($r$) 
\subsection{PPG Signal Processing}
PPG is used mainly for measuring the oxygen saturation in the blood and blood volume changes in skin  An ideal PPG signal processing must contain the following steps: noise and motion artifacts removal, heart rate detection, heart rate variability estimation and feature extraction 
\subsubsection{PPG Signal Noise and Motion Artifacts Removal}
Similar to EDA signal, PPG signal is also contaminated with motion artifacts and noises  However, unlike EDA signal, PPG produce quasiperiodicity in a time series spectrum \cite{mete30}  We use Periodic Moving Average Filter (PMAF) to remove motion artifacts and noises \cite{lee07}  We first segment the PPG signal on periodic boundaries and then average the $m^{th}$ samples of each period  After filtering the input PPG signal with a 5-Hz $8^{th}$-order Butterworth low-pass filter, we estimate the maximum and minimum value of each period  The mean of each period are obtained from the maximum and minimum values applying the zero crossing method  These points of the means help determine the boundaries of each period  Then, interpolation or decimation is performed to ensure that each period had the same number of samples \cite{lee07}  
\subsubsection{Heart Rate and Heart Rate Variability Estimation}
We first apply PMAF on PPG signal to remove noises and motion artifacts, refine PPG by smoothing the signal using 1-dimensional Gaussian Filter and Convolution, calculate first derivative of the convoluted signal and finally find the differences between two consecutive peak values which is called HRV \cite{sel08}  The occurrences of total peak values (R-peak or beat) in each minute is called Heart Rate (HR) with an unit of Beat Per Minute  The signal value property of HRV and HR are inversely proportional which means the mental arousal that increases HR should decrease HRV in the time segment window  Fig~\ref{fig:ppg_artifact_removal} shows a sample of the noisy and filtered PPG signal and their corresponding Instant Heart Rate 
\begin{figure}[!htb]
\vspace{- 1in}
\begin{center}
   \epsfig{file=ppg_artifact_removal pdf,height=1 4in, width=3 5in}
   \vspace{- 15in}
\caption{Top figure illustrates the noisy signal (dotted line) and filtered signal from PPG sensor based on our filtering method  Bottom figure illustrates instant heart rate calculated from noisy signal (dotted line) and filtered signal}
   \label{fig:ppg_artifact_removal}
\end{center}
\vspace{- 15in}
\end{figure}
\subsection{Physiological Sensor Signal Feature Extraction}
Using the above mentioned methods, we removed the noises and motion artifacts from EDA and PPG signals and generated two time series signal from EDA (tonic and phasic components) and one time series signal from PPG (HRV)  Then, we segment each of the time series signal based on our prior detected complex activities such that each response window starts and ends with the starting and ending points of each complex activity  We extract 7 statistical time-series features for EDA (as shown in Table~\ref{tab:eda_features}) and 8 features for HRV (Table~\ref{tab:hrv_features}) within the response window) 

\begin{table}[!t]
\begin{center}

\renewcommand{\arraystretch}{1}
\caption{EDA Features Within The Response Window}
\begin{scriptsize}


\label{tab:eda_features}
\begin{tabular}{|c|l|}
\hline
\bfseries Features& \bfseries Description\\
\hline
nSCR & Number of SCRs within response window (wrw)\\
\hline
Latency & Response latency of first significant SCR wrw\\
\hline
AmpSum & Sum of SCR-amplitudes of significant SCRs wrw\\
\hline
SCR & Average phasic driver wrw\\
\hline
ISCR & Area (i e  time integral) of phasic driver wrw\\
\hline
PhasicMax & Maximum value of phasic activity wrw\\
\hline
Tonic & Mean tonic activity wrw\\
\hline
\end{tabular}
\end{scriptsize}
\end{center}
\end{table}



\begin{table}[!t]
  \begin{center}
\renewcommand{\arraystretch}{1}
\vspace{- 3in}
\caption{Heart Rate Variability features}
\label{tab:hrv_features}
\begin{scriptsize}
\begin{tabular}{|c|l|}

\hline
\bfseries Feature& \bfseries Description\\
\hline
$\overline{RR}$&Mean RR intervals\\
\hline
SDNN&Standard deviation of RR intervals\\
\hline
SDSD&Std of successive RR interval differences\\
\hline
RMSSD&Root mean square of successive differences\\
\hline
NN50&\#successive intervals differing more than 50 ms\\
\hline
pNN50&relative amount of NN50\\
\hline
HRVTI&Total number of RR intervals/height of the histogram\\
\hline
TINN&Width of RR histogram through triangular interpolation\\
\hline
\end{tabular}
\end{scriptsize}
  \end{center}
\end{table}
\section{Experimental Evaluation}
In this section, we explain our data collection, available benchmark dataset, baseline methods and evaluation 
\subsection{Datasets and Baseline Methods}
We validate and compare \emph{AutoCogniSys} with baseline methods on both publicly available and our collected datasets 
\subsubsection{RCC Dataset: Collection and Ground Truth Annotation}
For collecting Retirement Community Center Dataset (RCC Dataset), we recruited 22 participants (19 females and 3 males) with age range from 77-93 (mean 85 5, std 3 92) in a continuing care retirement community with the appropriate institutional IRB approval and signed consent  The gender diversity in the recruited participants reflects the gender distribution (85\% female and 15\% male) in the retirement community facility  A trained gerontology graduate student evaluator completes surveys with participants to fill out the surveys  Participants are given a wrist band to wear on their dominant hand, and concurrently another trained IT graduate student have the IoT system setup in participants' own living environment (setup time 15-30 minutes)  The participants are instructed to perform 13 \emph{complex ADLs}  Another project member remotely monitors the sensor readings, videos and system failure status  The entire session lasts from 2-4 hours of time depending on participants' physical and cognitive ability 

We follow the standard protocol to annotate demographics and activities mentioned in the IRB  Two graduate students are engaged to annotate activities (postural, gestural and complex activity) whereas the observed activity performances are computed by the evaluator  Two more graduate students are engaged to validate the annotations on the videos  In overall, we are able to annotate 13 complex activities (total 291 samples) labeling for each participant; 8 hand gestures (total 43561 samples) and 4 postural activities (total 43561 samples) labeling  Annotation of postural and complex activities outcomes no difficulties from recorded videos  However, annotation of hand-gestures is extremely difficult in our scenario  We used video based hand tracker that can track and sketch wrist movements from a video episode \cite{hugo14}  This sketching can help us significantly to identify which particular hand gesture is being performed in the time segment 
\subsubsection{EES Datasets: EDA and PPG Sensor Datasets}
We used Eight-Emotion Sentics (EES) dataset to validate \emph{AutoCogniSys} proposed physiological signal processing approaches \cite{picard01}  The dataset consists of measurements of four physiological signals (PPG/Blood Volume Pulse, electromyogram, respiration and Skin Conductance/EDA) and eight affective states (neutral, anger, hate, grief, love, romantic love, joy, and reverence)  The study was taken once a day in a session lasting around 25 minutes for 20 days of recordings from an individual participant  We consider only PPG and EDA for all of the affective states in our study 
\subsubsection{Baseline Methods}
Though no frameworks ever combined all modalities together into real-time automated cognitive health assessment, we evaluate \emph{AutoCogniSys} performance by comparing the performances of its components individually with upto date relevant works  For hand gesture and postural activity recognition, we consider \cite{alam17} proposed method as baseline  For complex activity recognition, we compare our hand gesture and postural activity classifiers aided HDBN model with three-level Dynamic Bayesian Network \cite{zhu12} framework  For activity performance estimation, activity performance based cognitive health assessment; and EDA and PPG based cognitive health assessment, we have considered \cite{alam16} proposed method as baseline 
\subsection{Activity Recognition Evaluation}
The standard definition for \emph{accuracy} in any classification problem is $\frac{TP+TN}{TP+TN+FP+FN}$ where $TP,TN,FP$ and $FN$ are defined as true positive, true negative, false positive and false negative  For complex activity recognition evaluation, we additionally consider \emph{start/end duration error} as performance metric that can be explained as follows: consider that the true duration of ``cooking'' is 30 minutes (10:05 AM - 10:35 AM) and our algorithm predicts 29 minutes (10 10 - to 10 39 AM)  Then, the start/end duration error is 9 minutes ($|$5 minutes delayed start$|$ + $|$4 minutes hastened end$|$), in an overall error of e g , 30\% (9/30=0 3)  We measure cross-participant accuracy using leave-two-participants-out method for performance metrics, i e , we take out two of the participants' data points from the entire dataset, train our proposed classification models, test the model accuracy on the two left-out participants relevant data points, and continue the process for entire dataset 

\begin{figure*}[!htb]
\begin{minipage}{0 45\textwidth}
\begin{center}
   \epsfig{file=hand_gesture_accuracy pdf,height=1 6in, width=3in}
\caption{Feature Weighted Naive Bayes (FWNB) classification accuracy comparisons with baseline approaches (graphical signatures of all hand gestures are shown) }
   \label{fig:hand_gesture_accuracy}
\end{center}
\end{minipage}
\begin{minipage}{0 29\textwidth}
\begin{center}
\vspace{- 12in}
   \epsfig{file=posture_accuracy_normal pdf,height=1 6in, width=2 1in}
\caption{4-class postural level activity recognition performance and comparisons with baseline method}
   \label{fig:posture_accuracy_normal}
\end{center}
\end{minipage}
\begin{minipage}{0 25\textwidth}
 \begin{center}
 \vspace{- 12in}
   \epsfig{file=posture_accuracy_extended pdf,height=1 6in, width=2 1in}
\caption{6-class diverse postural activity recognition framework accuracy comparisons with the baseline approach }
   \label{fig:posture_accuracy_extended}
\end{center}
 \end{minipage}
\end{figure*}

Fig~\ref{fig:hand_gesture_accuracy} displays Feature Weighted Naive Bayes (FWNB) based the 8-hand gestural activity recognition accuracies comparisons with the baseline methods which clearly depicts the outperformance of our method (5\% improvement) with an overall accuracy of 92\% (FP rate 6 7\%) in RCC dataset  For postural activity recognition, dataset achieving 91\% postural activity recognition accuracy (FP rate 9 5\%) which outperforms the baseline approach significantly (8\% improvement)  Now, we expand the postural activities for RCC datasets into 3 diverse `walking' postures: `normal walking', `walking with walker', `walking with single stick' and the accuracy goes down to 88\% (FP 7 9\%)  Fig ~\ref{fig:posture_accuracy_normal} and Fig ~\ref{fig:posture_accuracy_extended} illustrate 4-class postural and extended 6-class postural classifier accuracies respectively which clearly posit that \emph{AutoCogniSys} outperforms in each case of postural activities as well as overall performances (8\% and 7\% improvement respectively) 

For complex activity classification, we choose RCC dataset to train our HDBN model  Our leave-two-participants out method results an accuracy of 85\% (FP Rate 3 6\%, precision 84 2\%, recall 84 5\%, ROC Area 98 2\%) with a start/end duration error of 9 7\%  We run the entire evaluation for baseline complex activity recognition algorithm too achieving an overall accuracy of 78\% (FP Rate 5 2\%, precision 79 6\%, recall 78 5\%, ROC Area 82 7\%) which is clearly lower performed method than our approach  Fig  \ref{fig:complex_activity_roc} and Fig~\ref{fig:complex_activity_accuracy} illustrate the ROC curve and each complex activity recognition accuracy comparisons with baseline method which depict the outperformance of our framework over baseline methods (7\% improvement)  Fig~\ref{fig:complex_activity_accuracy} also shows that inclusion of postural activity improves the final complex activity recognition (4\% improvement) 
 \begin{figure}  [!htb]
  \begin{minipage}{0 15\textwidth}
 \begin{center}
   \epsfig{file=complex_activity_roc pdf,height=1 4in, width=1 1in}
\caption{ROC curve for complex activity recognition}
   \label{fig:complex_activity_roc}
\end{center}
\end{minipage}
\begin{minipage}{0 33\textwidth}
\begin{center}

   \epsfig{file=complex_activity_accuracy pdf,height=1 4in, width=2 3in}
\caption{Complex ADLs recognition accuracy improvement and comparison with baseline \cite{zhu12} and HMM based method}
   \label{fig:complex_activity_accuracy}
\end{center}

\end{minipage}
\end{figure}

\subsection{Quantification of Performance Score}
To characterize both the qualitative and quantitative health assessment performance scores, we start with four different feature groups ranging from both functional and physiological health measures: (i) observation based activity features, (ii) automatic activity performance features, (iii) EDA features and (iv) PPG features 

In \emph{observation based activity features}, we design a complex activity set comprised of multiple subtasks which are involved with task {\it interruption, completion and sequencing}  Participants are instructed to perform the complex activities while the trained evaluator observed the aforementioned functional activity performance measures  Each incorrect attempt of performance measure will be assigned one point thus higher score reflects lower performance of functional activities \cite{dawadi14}  We first detect hand gesture and postural activities  Then, we feed the low-level activity contexts (gestural and postural) combined with ambient contexts (object and ambient motion sensor readings) into HDBN for single inhabitant model \cite{alam16b} to recognize complex activities  The complex activity recognition framework provides both activity labels and activity window (start-end points)  Then, we extract features of object sensor, ambient sensor, gestural activity and postural activity events for each activity window  The features are number of occurrences, mean number of occurrences, consecutive 1, 2, 3, $\ldots$ 20 occurrences, top 10, 20, 30, $\ldots$, 90 percentile etc (29 features in total)  In \emph{physiological features} we first detect 13 complex activities using HDBN algorithm which provides activity labels and activity window (start-end points), apply noise reduction, motion artifacts removal, extract 7 EDA features and 8 HRV features for each activity and take the mean of them over time (minutes) to get 15 (7+8) complex activity physiological features set for each participant  In summary, we extract 3 observation based activity features, 29 automatic activity performance features, 7 EDA features and 8 HRV features 
\subsection{Physiological Signal Processing Performance Evaluation}
Standard evaluation technique should use both experimental and publicly available datasets to confirm the outperformance of the novel approaches  We first evaluate our physiological signal processing techniques using a publicly available dataset (EES Dataset \cite{picard01}) to detect 8 human emotions  Then, in next section, we evaluate our methods in assessing cognitive health status of older adults using RCC dataset 

For EDA, we first apply SWT method to remove motion artifacts and noises  Then, we use cvxEDA method to separate tonic and phasic components of EDA  Then, we extract 7 EDA features on a sliding window of 4 seconds  Finally, we feed the 7 EDA features into a SMO based SVM algorithm \cite{cao06}  We use 10-fold cross validation to classify eight emotions achieving 87\% of overall accuracy (FP rate 6\%)  For PPG, we first apply our proposed PMAF based noises and motion artifacts removal technique  Then, we calculate HRV and perform time-domain feature extraction to extract 8 HRV features on a sliding window of 4 seconds  We feed these features into a SMO based SVM algorithm \cite{cao06}  Our 10-fold cross validation shows accuracy of 79\% (FP rate 11 5\%) of detecting 8 emotions on EES Dataset  Fig  \ref{fig:ees_eda} and Fig  \ref{fig:ees_ppg} clearly depict that \emph{AutoCogniSys} proposed EDA and PPG signal processing techniques significantly improve the accuracy over the baseline \cite{alam16} method (10\% and 12\% improvement) 

\begin{figure}[!htb]
\begin{minipage}{0 24\textwidth}
\begin{center}
   \epsfig{file=ees_eda pdf,height=1 2in, width=1 8in}
\caption{(EES Databaset) EDA features based Eight Emotion classification accuracy comparisons with baseline method}
   \label{fig:ees_eda}
\end{center}
\end{minipage}
\begin{minipage}{0 23\textwidth}
\begin{center}
   \epsfig{file=ees_ppg pdf,height=1 2in, width=1 7in}
\caption{(EES Dataset) PPG features based 8-Emotion classification accuracy comparisons with baseline method}
   \label{fig:ees_ppg}
\end{center}
\end{minipage}

\end{figure}
\subsection{Evaluation of Performance Scores}
The feature subsets used in the experimentation for observation and survey based clinical assessments and technology guided physiological and activity initiated health assessments are depicted in Table~\ref{tab:feature_subset}  From our 6 demographics surveys, we find significant distributions in terms of cognition only for SLUMS Score (S-Score)  Based on that, we divide our participants pool into three groups: \emph{Not Cognitively Impaired (NCI), Mild Cognitively Impaired (MCI) and Cognitively Impaired (CI)} where the number of participants are $5$, $7$ and $10$ respectively 
\begin{table}[!t]
\begin{scriptsize}


{\centering 
\renewcommand{\arraystretch}{ 6}
\caption{Feature Subsets}
\label{tab:feature_subset}
\begin{tabular}{|l|L{5 5cm}|}
\hline
\bfseries Feature& \bfseries Description\\
\hline
Observation & Task Completeness (TC), Sequencing (SEQ), Interruptions (INT)\\
\hline
Survey & SLUMS Score (S-Score), ZUNG Score (Z-Score), IADL Score (I-Score), Yale Score (YPAS), Barthel Score (B-Score), GDS Score (G-Score)\\
\hline
EDA  and HRV & 7 and 8 Features\\
\hline
Activity Performance& Supervised (TC, SEQ, INT), Unsupervised\\
\hline
Arousal& EDA and HRV features of each complex activity window\\
\hline

\end{tabular}
}
\end{scriptsize}
\end{table}


\begin{figure}[!htb]
\begin{center}
   \epsfig{file=group_correlation pdf,height=1in, width=3 3in}
\caption{\emph{AutoCogniSys} Proposed Method Based Group Correlation analysis ( $r-value$) NCI, MCI and CI represent not cognitive, mild cognitive and cognitively impaired group of population  TC, INT, SEQ, EDA and HRV represent task completeness, interruption scores, sequencing scores, electrodermal activity features and heart rate variability features}
   \label{fig:group_correlation}
\end{center}
\vspace{- 2in}
\end{figure}
\begin{figure}[!htb]
\begin{center}
   \epsfig{file=group_correlation_baseline pdf,height=1in, width=3 3in}
\caption{Baseline \cite{alam16} method based Group Correlation analysis ( $r-value$)}
   \label{fig:group_correlation_baseline}
   \vspace{- 25in}
\end{center}
\end{figure}

\subsection{Statistical Correlation Analysis of Cognitive Health}
We used Pearson correlation coefficients with significance on $p<0 05$* for individual feature and partial correlation coefficients with significance on $p<0 005$** for group of features correlation analysis  Fig  \ref{fig:group_correlation} and Fig  \ref{fig:group_correlation_baseline} show the group correlation analysis results based on \emph{AutoCogniSys} proposed framework and baseline \cite{alam16} framework respectively  It can be clearly depicted that our proposed framework improves the correlation with the ground truths 
\subsection{Machine Learning Classification of Cognitive Health}
We evaluate using machine learning classifiers to predict cognitive status of older adults using both individual modalities and combined features  We use leave-two-participants out method to train and test classification accuracy 

We first choose the individual activity features (machine learning method based interruption scores, sequencing scores, unsupervised scores) and their combined features to train and test cognitive impairment status classification for SMO based SVM algorithm \cite{cao06}  The classification accuracies are 72\%, 69\%, 76\% and 83\% respectively  Then we consider 7 EDA-activity features and 8 HRV-activity features individually in training and testing phase of SMO based SVM algorithm \cite{cao06} resulting 85\% and 80\% accuracy respectively 

\begin{figure}[!htb]
\begin{minipage}{0 24\textwidth}
\begin{center}
   \epsfig{file=combined_classification pdf,height=1 2in, width=1 7in}
   \vspace{- 15in}
\caption{Individual and combined classification accuracies comparison with baseline method for cognitive impairment status detection}
   \label{fig:combined_classification}
\end{center}
\end{minipage}
\begin{minipage}{0 23\textwidth}
\begin{center}
   \epsfig{file=each_activity_cognitive_assessment pdf,height=1 2in, width=1 7in}

\caption{Machine learning based cognitive health assessment accuracy for each complex activity in terms of activity, EDA and HRV features }
   \label{fig:each_activity_cognitive_assessment}
\end{center}
\end{minipage}
\end{figure}

For combined classifier, we first applied sequential forward feature selection to find the best combinations of 1- 3 features for cognitive impairment classification group MCI, NCI and CI in terms of combined activity features (29 features), EDA-activity features (7 features) and HRV-activity features (8) features  Our final combined classifier (SMO based SVM algorithm \cite{cao06}) provides an accuracy of {\bf 93\%} in detecting the cognitive impairment status of older adults  Fig  \ref{fig:combined_classification} shows our proposed individual and combined methods outperform the baseline \cite{alam16} significantly (13\% improvement)  Fig  \ref{fig:each_activity_cognitive_assessment} shows the cognitive impairment status prediction accuracy for each modality (activity feature, EDA and HRV) per individual complex activity 
\subsection{Discussion}
If we exclude the postural activities from automated activity performance scoring, we find reduced statistical correlation with original task completeness performance for \{NCI, MCI, CI\} participant group (INT 0 53*, SEQ 0 21' and unsupervised 0 49')  However, if we skip our proposed motion artifact removal stage, we find reduced statistical correlation with \{NCI, MCI\} and \{MCI, CI\} groups of participants (EDA and HRV correlations respectively \{0 51*, -0 51*\} and \{-0 53*,0 46\})  To test our proposed motion artifacts removal impact on EDA signals more rigorously, we choose 5 random participants, engage one expert motion artifact annotator to annotate motion artifacts segment on each participant's first 30 minutes of complex dataset using recorded video and apply both baseline and our methods to detect motion artifact segments  While baseline method achieves 75 5\% (FP rate 20 3\%) accuracy in detecting motion artifact segments, \emph{AutoCogniSys} outperforms achieving 89 9\% (FP rate 8 9\%) accuracy  In terms of experience, we have seen 100\% acceptance of wearing wrist-band,  71\% of acceptance for signing consent on using cameras and 0\% failure rate of collecting continuous data 
\section{Conclusion}
We propose, \emph{AutoCogniSys}, an IoT inspired design approach combining wearable and ambient sensors embedded smart home design, extensive signal processing, machine learning algorithms and statistical analytics to automate cognitive health assessment in terms of complex activity performances and physiological responses of daily events  Additionally, our postural activity detection approach in diverse population cum improved activity performance measurement and fundamental physiological sensor artifacts removal from physiological sensors help facilitate the automated cross-sectional cognitive health assessment of the older adults  Our efficient evaluation on each modality (physical, physiological and ambient) and each activity mode proves that any of the mode (say single activity and single sensor) also can provide significant improved cognitive health assessment measure 







ground_truth: Wearable sensors.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does the framework capture the reduced-order dynamics?

Read the following text and answer briefly.

Context 2: Paper Info

Title: Interpretable reduced-order modeling with time-scale separation Interpretable reduced-order modeling with time-scale separation
Publish Date: 7 March 2023
Author List: Sebastian Kaltenbach (from CSE-Lab, ETH Zurich, Harvard SEAS), Phaedon-Stelios Koutsourelakis (from CSE-Lab, ETH Zurich, Harvard SEAS), Petros Koumoutsakos (from CSE-Lab, ETH Zurich, Harvard SEAS), Harvard Seas (from CSE-Lab, ETH Zurich, Harvard SEAS)

Figure

FIG  5  Comparison between the phase-space of the reference solution (left) and the phase-space of the predictions
FIG  7  Comparison between predictions and reference solutions for a new initial condition fort = 1 25, 3 75, 7 5, 12 5, 20, 30  (from left to right and top to down) We note that with longer prediction time the uncertainty bounds increases Despite the chaotic nature of the KS equation, the predictive posterior mean is close to the reference solution for t ≤ 12 5

abstract

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering  However, finding solutions for these PDEs can be computationally expensive, making model-order reduction crucial  We propose such a data-driven scheme that automates the identification of the time-scales involved and, can produce stable predictions forward in time as well as under different initial conditions not included in the training data 
To this end, we combine a non-linear autoencoder architecture with a time-continuous model for the latent dynamics in the complex space  It readily allows for the inclusion of sparse and irregularly sampled training data  The learned, latent dynamics are interpretable and reveal the different temporal scales involved 
We show that this data-driven scheme can automatically learn the independent processes that decompose a system of linear ODEs along the eigenvectors of the system's matrix  Apart from this, we demonstrate the applicability of the proposed framework in a hidden Markov Model and the (discretized) Kuramoto-Shivashinsky (KS) equation 
Additionally, we propose a probabilistic version, which captures predictive uncertainties and further improves upon the results of the deterministic framework 

INTRODUCTION

High-fidelity simulations of critical phenomena such as ocean dynamics and epidemics have become essential for decision-making  They are based on physically-motivated PDEs expressing system dynamics that span multiple spatiotemporal scales and which necessitate cumbersome computations   In recent years there is increased attention to the development of data-driven models that can accelerate the solution of these PDEs as well as reveal salient, lower-dimensional features that control the long-term evolution 
In most cases, data-driven reduced-order models are not interpretable  In particular, models based on neural networks despite good predictive capabilities , they offer a black-box description of the system dynamics  A possible remedy is applying a symbolic regression to the learned neural network representation , but this adds additional computational cost due to the two-step procedure 
A number of frameworks such as SINDy allows to learn interpretable dynamics but it relies on the a-priori availability of lower-dimensional descriptors and of time-derivatives which can be very noisy for both simulation and experimental data  Other frameworks are tailored to specific problems such as molecular dynamics  
Here, we present a framework that only needs the value of the observables, and not their derivatives, as training data and is capable of identifying interpretable latent dynamics  The deployment of interpretable latent dynamics ensures that conservation of important properties of that are reflected in the reduced-order model  
The present method is related to approaches based on the Koopman-operator extended Dynamic Mode Decomposition (eDMD) but uses continuous complex-valued latent space dynamics and only requires one scalar variable per latent dimension to describe the latent space dynamics  Therefore we do not have to enforce any parametrizations on the Koopman matrix  
The time-continuous formulation moreover allows to incorporate sparse and irregularly sampled training data and fast generation of predictions after the training phase  By using a complex-valued latent space we can also incorporate harmonic effects and reduce the number of latent variables needed  Linear and non-linear autoencoders are used to map the observed, high-dimensional time-series to the lower-dimensional, latent representation and we identify simultaneously the autoencoder as well as the latent dynamics by optimizing a combined loss function 
Hence the to tasks of dimensionality reduction and discovery of the reduced dynamics are unified while other frameworks treat the two parts separately   Apart from using an architecture based on autoencoders to identify the latent space, projection-based methods could also be employed   We are also proposing a probabilistic version of our algorithm ) that makes use of probabilistic Slow Feature Analysis  
This allows for a latent representation that arart from being time-continuous, can quantify the predictive uncertainty and hierarchically decompose the dynamics into their pertinent scales while promoting the discovery of slow processes that control the system's evolution over long time horizons  The rest of the paper is structured as follows: We introduce the methodological framework as well as algorithmic details in section II 
Particular focus is paid on the interpretability of the inferred lower-dimensional dynamics  In section III we present three numerical illustrations, i e  a system of linear ODEs, a hidden Markov Model and the discretized KS-equation  We then present in section IV the probabilistic extension of the framework and apply it to the KS-equation 
We conclude with a summary and a short discussion about possible next steps  We introduce the autoencoders deployed in this work, followed by the interpretable latent space dynamic and discuss the training process  We consider data from high-dimensional time series x n ∈ R f with n = 1,    , T   We remark that the intervals between the different states do not need to be uniformly spaced 

Autoencoder

A core assumption of the method is that each high-dimensional state x n can be compressed to a lower-dimensional representation z n ∈ C c with c << f   We identify this lower-dimensional representation by an autoencoder consisiting of a parameterized encoder and decoder  The encoder maps the high-dimensional representation to the latent space as:
The latent space is complex-valued  The decoder reconstructs the high-dimensional representation based on the latent variables as: We denote the parameters of the encoder as well as the decoder by θ  As discussed later in Section II C, both set of parameters are optimized simultaneously during training and therefore there is no need for differentiating them 

Interpretable Latent Space Dynamics

We employ a propagator in the latent space to capture the reduced-order dynamics of the system  In contrast to other time-extended variational autoencoder frameworks, our representation uses complex valued latent variables  In addition the latent variables are treated independently  The latter feature enables us to have an interpretable latent dynamics as well as a model that is especially suitable for being trained in the Small Data regime due to the small number of required parameters 
This is in contrast to temporal propagators such as LSTMs   For each dimension i of the latent variable z we are using the following continuous ODE in the complex plane: By solving this ODE, we can define the operator: Interpretable reduced-order modeling with time-scale separation Here, λ is a vector containing all the individual λ's and ∆t n indicates the time-step between the latent states 
The symbol is used to indicate a component-wise multiplication  We remark that the latent variables and the parameter governing the temporal evolution are complex numbers and their role in describing the system dynamics is similar to that of an eigenvalue  The real part is associated with growth and decay whereas the imaginary part is representing the periodic component 
This approach has similarities with the Koopman-operator based methods and the extended dynamic mode decomposition   In contrast to the methods mentioned before we are using a continuous formulation in the latent space that allows us to incorporate scarce and irregularly sampled training data and directly rely on complex numbers in the latent space 

Training and Predictions

We optimize a loss function that combines both a reconstruction loss as well as a loss associated with the error of our learned propagator in the latent space: (5) We note that we could directly incorporate mini-batch training by only taking the summation over a subset of the N available training data 
For new predictions of unseen states, we use the encoder to generate a latent representations which is then advanced in time by the learned propagator  At a designated time step we are using the decoder to reconstruct the high-dimensional solution  We applied our algorithm to three systems  First, we show that the algorithm is capable of exactly reproducing the solution of a linear ODE and to identify its eigenvalues 
Afterwards we are applying the framework to a high-dimensional process generated by a complex latent dynamics, which is correctly identified  As a final test case, we are applying the algorithm to a Kuramoto Shivashinski (KS) equation  Interpretable reduced-order modeling with time-scale separation

Linear ODE

We are considering a two-dimensional ODE system for x = y 1 y 2 : Based on the obtained training data we run our algorithm using a linear encoder and decoder structure as well as two latent variables z  The loss function was optimized using the Adam algorithm   As we consider a linear ODE we can analytically compute the eigenvalues involved and compare it with the parameters λ identified by our algorithm 
We observe in Figure that the algorithm was able to recover the correct values, i e  the eigenvalues 7 and 3 of the given linear ODE  The system does not have a periodic component and the two imaginary parts correctly go to zero, whereas the real parts converge to the reference value  Moreover we are also able to identify for the linear mapping between our latent variables z and the training data a matrix consisting of a multiple of the eigenvectors (1,1) and (1,-1) and thus the correct solution 
This example was chosen to show that the algorithm is able to quickly identify the exact solution of a linear ODE in terms of its linearly independent components 

Hidden multiscale dynamics

We consider eight-dimensional synthetic time series data produced by an underlying twodimensional complex valued process  In particular, the data points x are generated by first solving for the temporal evolution for the two complex-valued processes p 1 and p 2 and than mapping to the eight-dimensional space by using a randomly sampled linear mapping W  
One of the two processes used to generate the data is chosen to be much slower than the other one and both processes have a periodic component  dp 2 dt = (−0 9 + 1 5i)p 2 (8) As training data we consider 40 time series with 150 data points each, obtained by simulating the described processes for a maximum of t = 15 s and then sampling from the obtained data points 
Hence the training data consists of: • 40 time-series • with each consisting 150 observations of the x at a uniform time-step ∆t = 0 0025 The autoencoder obtained consists of one linear layer for both the decoder as well as the encoder  The model is trained for 5000 iterations using the Adam optimizer and a learning rate of 10 −3  
The results for the convergence of the parameters λ 1 and λ 2 can be found in Figure   We note that the process which is slower decaying and thus more responsible for the long-term evolution of the system has a higher convergence rate than the faster process  With the obtained parameters λ as well as the trained autoencoder, we compute predictions based on the last time step used for training, i e  we apply the encoder to obtain our latent representation and than use the latent dynamics to advance the latent representation in time 
Afterwards, we employ the decoder to reconstruct the full high-dimensional system  The results can be found in Figure and show very good agreement between predictions and reference data  This example shows that our model is successfully able to carry out dimensionality reduction and moreover indicates that the convergence rate between latent processes can be different 
The latter is relevant when training models as for accurate predictions all latent processes and their dynamics should be converged 

Kuramoto-Sivashinsky

Finally, we applied our algorithm to the KS equation and aim to identify a reduced-order model for the solution u(y, t): We employed periodic boundary conditions, µ = 1 and a domain size y ∈ [0, 22]  For this domain-size, the KS-equation exhibits a structurally stable chaotic attractor as discussed in The black lines divides the area for which training data was given from the area without raining data 
;   The equation is discretized in space using a discretization step of 22 64 resulting in a state vector x of dimension 64 and a nonlinear system of coupled ODEs  This is solved using a stiff fourth-order solver  We employed a non-linear encoder and decoder with four fully-connected layers each and ReLU-activation functions as well as Dropout Layers between the fully-connected layers 
We trained the model for 200000 iterations using Adam and a learning rate of 5 • 10 4 and assuming a five-dimensional latent space  We obtained the λ's in Figure   Four latent variables have λ's close to zero and thus a slow temporal dynamic that is responsible for the long-term evolution whereas one latent variable is quickly decaying 
Based on the obtained parameters, we do predictions based on an unseen initial condition not contained in the training data  We are able to reconstruct the correct phase space based on our predictions despite only using a very limited amount of training data  The results for the phase space can be seen in Figure  
Although the small-scale fluctuations in the temporal dynamics are not well captured, the model identifies the correct manifold which has a good accuracy compared to the reference solution  All phase-spaces were obtained by using a finite-difference operator on the data or predictions  These results are in accordance Interpretable reduced-order modeling with time-scale separation with whose LSTM-based temporal dynamic model was also able to find the correct phase space but not to track the actual dynamics for long-term predictions 
Our model is not able to account for noise in the temporal evolution and thus dealing with chaotic, small-scale fluctuations is challenging  We believe that a probabilistic version of our algorithm could be advantageous here  This section contains a fully probabilistic formulation for the deterministic model discussed before 
We replace the Autoencoder with a Variational Autoencoder and the ODE in the latent space with a SDE  The loss function which we optimize is the Evidence-Lower Bound (ELBO) 

Model Structure

We postulate the following relations for our probabilistic model using an Ornstein-Uhlenbeck (OU) for each dimension i of the latent space and a Wiener process W t in the latent space: We again assume that the latent variables z t are complex-valued and a priori independent  Complex variables were chosen as their evolution includes a harmonic components which are observed in many physical systems 
We assume an initial conditions z 0,i ∼ CN (0, σ 2 0,i )  The total parameters associated with the latent space dynamics of our model are thus {σ 2 0,i , σ 2 i , λ i } c i=1 and will be denoted by θ together with all parameters responsible for the decoder mapping G (see next section)  These parameters along with the state variables z t have to be inferred from the data x t  
Based on probabilistic Slow Feature Analysis (SFA) , we set σ 2 i = 2; (λ j ) and σ 2 0,i = 1  As a consequence, a priori, the latent dynamics are stationary  A derivation and reasoning for this choice can be found in Appendix A  Hence the only independent parameters are the λ i , the imaginary part of which can account for periodic effects in the latent dynamics 

Variational Autoencoder

We employ a variational autoencoder to account for a probabilistic mappings from the lower-dimensional representation z n to the high-dimensional system x n   In particular we are employing a probabilistic decoder The encoder is used to infer the state variables z based on the given data and thus defined in the inference and learning section 

Inference and Learning

Given the probabilistic relations , our goal is to infer the latent variables z 0:T as well as all model parameters θ  We follow a hybrid Bayesian approach in which the posterior of the state variables is approximated using amortized Variational Inference and Maximum-A-Posteriori (MAP) point-estimates for θ are computed 
The application of Bayes' rule for each data sequence x 0:T leads to the following posterior: where p(θ) denotes the prior on the model parameters  In the context of variational inference, we use the following factorization of the approximate posterior i e  we infer only the mean µ and variance σ for each state variable based on the given data points 
This conditional density used for inference is the encoder-counterpart to the probabilistic decoder defined in the section before  It can be readily shown that the optimal parameter values are found by maximizing the Evidence Lower Bound (ELBO) F(q φ (z 0:T ), θ) which is derived in Appendix B  We compute Monte Carlo estimates of the gradient of the ELBO with respect to φ and θ with the help of the reparametrization trick and carry out stochastic optimization with the ADAM algorithm  

Results for the probabilistic extension

We applied our probabilistic version to the KS-equation  We used the same settings as for the deterministic approach but considered up to 10 complex latent variables  The obtained λ's are in Figure   The probabilistic model allows us to quantify the uncertainty in predictions  In Figure predictions for various time-steps and the respective uncertainty bounds are shown for an unseen initial condition 
Due to the chaotic nature of the KS-equation and the small amount of training data, the underlying linear dynamic of our model is only able to capture the full dynamics for a limited time horizon  Fortunately, due to the probabilistic approach the model is capable of capturing chaotic fluctuations with increasingly wide uncertainty bounds 
We also computed the phase space representation for the KS-equation based on the predictions obtained by our model and compare it with the reference solution  The probabilistic model identifies the correct manifold with a better accuracy than the deterministic model  As some of the small-scale fluctuations are accounted as noise, the resulting manifold is more concentrated at the origin and the obtained values are slightly smaller than the reference manifold although their shape is very similar 



ground_truth: By using a propagator in the latent space.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the electron correlation parameter, $\Gamma_e$?

Read the following text and answer briefly.

Context 3: \section{Introduction}

Ultracold neutral plasmas studied in the laboratory offer access to a regime of plasma physics that scales to describe thermodynamic aspects of important high-energy-density systems, including strongly coupled astrophysical plasmas \cite{VanHorn,Burrows}, as well as terrestrial sources of neutrons \cite{Hinton,Ichimaru_fusion,Atzeni,Boozer} and x-ray radiation \cite{Rousse,Esarey}   Yet, under certain conditions, low-temperature laboratory plasmas evolve with dynamics that are governed by the quantum mechanical properties of their constituent particles, and in some cases by coherence with an external electromagnetic field    

The relevance of ultracold plasmas to such a broad scope of problems in classical and quantum many-body physics has given rise to a great deal of experimental and theoretical research on these systems since their discovery in the late 90s   A series of reviews affords a good overview of progress in the last twenty years \cite{Gallagher,Killian_Science,PhysRept,Lyon}   Here, we focus on the subset of ultracold neutral plasmas that form via kinetic rate processes from state-selected Rydberg gases, and emphasize in particular the distinctive dynamics found in the evolution of molecular ultracold plasmas   

While molecular beam investigations of threshold photoionization spectroscopy had uncovered relevant effects a few years earlier \cite{Scherzer,Alt}, the field of ultracold plasma physics began in earnest with the 1999 experiment of Rolston and coworkers on metastable xenon atoms cooled in a magneto optical trap (MOT) \cite{Killian}   

This work and many subsequent efforts tuned the photoionization energy as a means to form a plasma of very low electron temperature built on a strongly coupled cloud of ultracold ions   Experiment and theory soon established that fast processes associated with disorder-induced heating and longer-time electron-ion collisional rate processes act to elevate the ion temperatures to around one degree Kelvin, and constrain the effective initial electron temperature to a range above 30 K \cite{Kuzmin,Hanson,Laha}   

This apparent limit on the thermal energy of the electrons can be more universally expressed for an expanding plasma by saying that the electron correlation parameter, $\Gamma_e$, does not exceed 0 25, where, 
\begin{equation}
\Gamma_e = \frac{e^2}{4\pi \epsilon_0 a_{ws}}\frac{1}{k_B T_e}
\label{eqn:gamma_e}
\end{equation}
defines the ratio of the average unscreened electron-electron potential energy to the electron kinetic energy   $a_{ws}$ is the Wigner-Seitz radius, related to the electron density by, $\rho_e = 1/(\frac{4}{3} \pi a_{ws}^3)$   These plasmas of weakly coupled electrons and strongly coupled ions have provided an important testing ground for ion transport theory and the study of electron-ion collision physics \cite{Strickler} 

Soon after the initial reports of ultracold plasmas formed by direct photoionization, a parallel effort began with emphasis on the plasma that forms spontaneously by Penning ionization and electron-impact avalanche in a dense ultracold Rydberg gas \cite{Mourachko}   This process affords less apparent control of the initial electron temperature   But, pulsed field-ionization measurements soon established that the photoionized plasma and that formed by the avalanche of a Rydberg gas both evolve to quasi-equilibria of electrons, ions and high-Rydberg neutrals \cite{Rolston_expand,Gallagher}   

Early efforts to understand plasmas formed by Rydberg gas avalanche paid particular attention to the process of initiation   Evolution to plasma in effusive atomic beams was long known for high-Rydberg gases of caesium and well explained by coupled rate equations \cite{Vitrant}   But, low densities and ultracold velocity distributions were thought to exclude Rydberg-Rydberg collisional mechanisms in a MOT   

In work on ultracold Rydberg gases of Rb and Cs, Gallagher, Pillet and coworkers describe the initial growth of electron signal by a model that includes ionization by blackbody radiation and collisions with a background of uncooled Rydberg atoms \cite{Mourachko,Gallagher,Li,Comparat,Tanner}  This picture was subsequently refined to include many-body excitation and autoionization, as well as attractive dipole-dipole interactions \cite{Viteau,Pillet}, later confirmed by experiments at Rice \cite{Mcquillen}   

The Orsay group also studied the effect of adding Rydberg atoms to an established ultracold plasma   They found that electron collisions in this environment completely ionize added atoms, even when selected to have deep binding energies \cite{Vanhaecke}   They concluded from estimates of electron trapping efficiency that the addition of Rydberg atoms does not significantly alter the electron temperature of the plasma   

Tuning pair distributions by varying the wavelength of the excitation laser, Weidem\"uller and coworkers confirmed the mechanical effects of van der Waals interactions on the rates of Penning ionization in ultracold $^{87}$Rb Rydberg gases \cite{Amthor_mech}   They recognized blackbody radiation as a possible means of final-state redistribution, and extended this mechanical picture to include long-range repulsive interactions \cite{Amthor_model}   This group later studied the effects of spatial correlations in the spontaneous avalanche of Rydberg gases in a regime of strong blockade, suggesting a persistence of initial spatial correlations \cite{RobertdeSaintVincent}   

Robicheaux and coworkers have recently investigated the question of prompt many-body ionization from the point of view of Monte Carlo classical trajectory calculations \cite{Goforth}   For atoms on a regular or random grid driven classically by an electromagnetic field, they find that many-body excitation enhances prompt ionization by about twenty percent for densities greater than $5 6 \times 10^{-3}/(n_0^2 a_0)^3$, where $n_0$ is the principal quantum number of the Rydberg gas and $a_0$ is the Bohr radius   They observed that density fluctuations (sampled from the distribution of nearest neighbour distances) have a greater effect, and point to the possible additional influence of secondary electron-Rydberg collisions and the Penning production of fast atoms not considered by the model, but already observed by Raithel and coworkers \cite{Knuffman}   

The Raithel group also found direct evidence for electron collisional $\ell$-mixing in a Rb MOT \cite{Dutta}, and used selective field ionization to monitor evolution to plasma on a microsecond timescale in ultracold $^{85}$Rb $65d$ Rydberg gases with densities as low as $10^8$ cm$^{-3}$ \cite{WalzFlannigan}   Research by our group at UBC has observed very much the same dynamics in the relaxation of Xe Rydberg gases of similar density prepared in a molecular beam \cite{Hung2014}   In both cases, the time evolution to avalanche is well-described by coupled rate equations (see below), assuming an initializing density of Penning electrons determined by Robicheaux's criterion \cite{Robicheaux05}, applied to an Erlang distribution of Rydberg-Rydberg nearest neighbours   

Theoretical investigations of ultracold plasma physics have focused for the most part on the long- and short-time dynamics of plasmas formed by direct photoionization \cite{PhysRept,Lyon}   In addition to studies mentioned above, key insights on the evolution dynamics of Rydberg gases have been provided by studies of Pohl and coworkers exploring the effects of ion correlations and recombination-reionization on the hydrodynamics of plasma expansion \cite{Pohl:2003,PPR}   Further research has drawn upon molecular dynamics (MD) simulations to reformulate rate coefficients for the transitions driven by electron impact between highly excited Rydberg states \cite{PVS}, and describe an effect of strong coupling as it suppresses three-body recombination \cite{Bannasch:2011}   MD simulations confirm the accuracy of coupled rate equation descriptions for systems with $\Gamma$ as large as 0 3   Newer calculations suggest a strong connection between the order created by dipole blockade in Rydberg gases and the most favourable correlated distribution of ions in a corresponding strongly coupled ultracold plasma \cite{Bannasch:2013}   

Tate and coworkers have studied ultracold plasma avalanche and expansion theoretically as well as experimentally   Modelling observed expansion rates, they recently found that $^{85}$Rb atoms in a MOT form plasmas with effective initial electron temperatures determined by initial Rydberg density and the selected initial binding energy, to the extent that these parameters determine the fraction of the excited atoms that ionize by electron impact in the avalanche to plasma \cite{Forest}   This group also returned to the question of added Rydberg atoms, and managed to identify a crossover in $n_0$, depending on the initial electron temperature, that determines whether added Rydberg atoms of a particular initial binding energy act to heat or cool the electron temperature \cite{Crockett}    

Our group has focused on the plasma that evolves from a Rydberg gas under the low-temperature conditions of a skimmed, seeded supersonic molecular beam   In work on nitric oxide starting in 2008 \cite{Morrison2008,Plasma_expan,Morrison_shock,PCCP}, we established an initial kinetics of electron impact avalanche ionization that conforms with coupled rate equation models \cite{Saquet2011,Saquet2012,Scaling,haenelCP} and agrees at early times with the properties of ultracold plasmas that evolve from ultracold atoms in a MOT   We have also observed unique properties of the NO ultracold plasma owing to the fact that its Rydberg states dissociate \cite{Haenel2017}, and identified relaxation pathways that may give rise to quantum effects \cite{SousMBL,SousNJP}   The remainder of this review focuses on the nitric oxide ultracold plasma and the unique characteristics conferred by its evolution from a Rydberg gas in a laser-crossed molecular beam   


\section{Avalanche to strong coupling in a molecular Rydberg gas}

\subsection{The molecular beam ultracold plasma compared with a MOT}

When formed with sufficient density, a Rydberg gas of principal quantum number $n_0>30$ undergoes a spontaneous avalanche to form an ultracold plasma \cite{Li,Morrison2008,RobertdeSaintVincent}   Collisional rate processes combine with ambipolar hydrodynamics to govern the properties of the evolving plasma   For a molecular Rydberg gas, neutral fragmentation, occurs in concert with electron-impact ionization, three-body recombination and electron-Rydberg inelastic scattering   Neutral dissociation combined with radial expansion in a shaped distribution of charged particles, can give rise to striking effects of self-assembly and spatial correlation \cite{Schulz-Weiling2016,Haenel2017}    

The formation of a molecular ultracold plasma requires the conditions of local temperature and density afforded by a high mach-number skimmed supersonic molecular beam   Such a beam propagates at high velocity in the laboratory, with exceedingly well-defined hydrodynamic properties, including a propagation-distance-dependent density and sub-Kelvin temperature in the moving frame \cite{MSW_tutorial}   The low-temperature gas in a supersonic molecular beam differs in three important ways from the atomic gas laser-cooled in a magneto-optical trap (MOT) 

The milli-Kelvin temperature of the gas of ground-state NO molecules entrained in a beam substantially exceeds the sub-100 micro-Kelvin temperature of laser-cooled atoms in a MOT   However, the evolution to plasma tends to erase this distinction, and the two further characteristics that distinguish a beam offer important advantages for ultracold plasma physics:  Charged-particle densities in a molecular beam can exceed those attainable in a MOT by orders of magnitude   A great many different chemical substances can be seeded in a free-jet expansion, and the possibility this affords to form other molecular ultracold plasmas, introduces interesting and potentially important new degrees of freedom governing the dynamics of their evolution 


\subsection{Supersonic molecular beam temperature and particle density}

Seeded in a skimmed supersonic molecular beam, nitric oxide forms different phase-space distributions in the longitudinal (propagation) and transverse coordinate dimensions   As it propagates in $z$, the NO molecules reach a terminal laboratory velocity, $u_{\parallel}$, of about 1400 ${\rm ms^{-1}}$, which varies with the precise seeding ratio   

The distribution of $v_{\parallel}$, narrows to define a local temperature, $T_{\parallel}$, of approximately 0 5 K   The beam forms a Gaussian spatial distribution in the transverse coordinates, $x$ and $y$   In this plane, the local velocity, $v_{\perp}(r)$ is defined for any radial distance almost entirely by the divergence velocity of the beam, $u_{\perp}(r)$   Phase-space sorting cools the temperature in the transverse coordinates, $T_{\perp}$ to a value as low as $\sim 5$ mK \cite{MSW_tutorial}   

The stagnation pressure and seeding ratio determine the local density distribution as a function of $z$   For example, expanding from a stagnation pressure of 500 kPa with a 1:10 seeding ratio, a molecular beam propagates 2 5 cm to a skimmer and then 7 5 cm to a point of laser interaction, where it contains NO at a peak density of $1 6 \times 10^{14}$ cm$^{-3}$   

Here, crossing the molecular beam with a laser beam tuned to the transition sequence, ${\rm X} ~^2 \Pi_{1/2} ~N'' = 1 \xrightarrow{\omega_1} {\rm A} ~^2\Sigma^+ ~N'=0  \xrightarrow{\omega_2} n_0 f(2)$ forms a Gaussian ellipsoidal volume of Rydberg gas in a single selected principal quantum number, $n_0$, orbital angular momentum, $\ell = 3$, NO$^+$ core rotational quantum number, $N^+ = 2$ and total angular momentum neglecting spin, $N=1$   

A typical $\omega_1$ pulse energy of 2 $\mu$J and a Gaussian width of 0 2 mm serves to drive the first step of this sequence in a regime of linear absorption   Overlapping this volume by an $\omega_2$ pulse with sufficient fluence to saturate the second step forms a Rydberg gas ellipsoid with a nominal peak density of $5 \times 10^{12}$ cm$^{-3}$  \cite{Morrison2008,MSW_tutorial}   Fluctuations in the pulse energy and longitudinal mode of $\omega_1$ cause the real density to vary   For certain experiments, we find it convenient to saturate the $\omega_1$ transition, and vary the density of Rydberg gas by delaying $\omega_2$   An $\omega_1$-$\omega_2$ delay, $\Delta t$, reduces the Rydberg gas density by a precise factor, $e^{-\Delta t/\tau}$, where $\tau$ is the 200 ns radiative lifetime of NO ${\rm A} ~^2\Sigma^+ ~N'=0$ \cite{Carter,Hancock} 


\subsection{Penning ionization}

The density distribution of a Rydberg gas defines a local mean nearest neighbour distance, or Wigner-Seitz radius of $ a_{ws} =  \left(3/4 \pi \rho \right)^{1/3} $, where $\rho$ refers to the local Rydberg gas density   For example, a Rydberg gas with a density of $ \rho_0=0 5 \times 10^{12}$ cm$^{-3} $ forms an Erlang distribution \cite{Torquato 1990} of nearest neighbour separations with a mean value of $ 2 a_{ws}=1 6$  $\mu$m   

A semi-classical model \cite{Robicheaux05} suggests that 90 percent of Rydberg molecule pairs separated by a critical distance, $ r_c = 1 8 \cdot 2 n_0^2 a_0 $ or less undergo Penning ionization within 800 Rydberg periods   We can integrate the Erlang distribution from $ r=0 $ to the critical distance $r = r_c$ for a Rydberg gas of given $n_0$, to define the local density of Penning electrons ($ \rho_e$ at $t=0$) produced by this prompt interaction, for any given initial local density, $\rho_0$ by the expression:
\begin{equation}
\rho_e(\rho_0,n_0) = \frac{0 9}{2} \cdot 4 \pi \rho_0 ^2\int_0^{r_{c}} r^2 \mathrm{e}^{-\frac{4\pi}{3}\rho_0 r^3}\mathrm{d}r \quad 
\label{eqn:Erlang}
\end{equation}

Evaluating this definite integral yields an equation in closed form that predicts the Penning electron density for any particular initial Rydberg density and principal quantum number 
\begin{equation}
\rho_e(\rho_0,n_0) =\frac{0 9 \rho_0}{2}(1-\mathrm{e}^{-\frac{4\pi}{3}\rho_0 r_c^3}) \quad 
\label{Eq:PenDens}
\end{equation}
\begin{figure}[h!]
\centering
\includegraphics[scale=0 33]{Penning_Latice pdf}
\caption{Distributions of ion-ion nearest neighbours following Penning ionization and electron-impact avalanche simulated for a predissociating molecular Rydberg gas of initial principal quantum number, $n_0$, from 30 to 80, and density of 10$^{12}$ cm$^{-3}$   Dashed lines mark corresponding values of $a_{ws}$  Calculated by counting ion distances after relaxation to plasma in 10$^6$-particle stochastic simulations  Integrated areas proportional to populations surviving neutral dissociation }
\label{fig:PL}
\end{figure}

Prompt Penning ionization acts on the portion of the initial nearest-neighbour distribution in the Rydberg gas that lies within $r_c$   When a molecule ionizes, its collision partner relaxes to a lower principal quantum number, $n'<n_0/\sqrt{2}$   This close-coupled interaction disrupts the separability of Rydberg orbital configurations in the Penning partner   This causes mixing with core penetrating states that are strongly dissociative   Penning partners are thus very likely to dissociate, leaving a spatially isolated distribution of ions   We refer to the spatial correlation that results as a Penning lattice \cite{Sadeghi:2014}   The extent of this effect varies depending on the local density and the selected initial principal quantum number   Figure \ref{fig:PL} shows the degree to which Rydberg gases with initial principal quantum numbers from 30 to 80 form a Penning lattice for an initial density of $1 \times 10^{12} ~{\rm cm}^{-3}$   

\subsection{Spontaneous electron-impact avalanche}

The electrons produced by prompt Penning ionization start an electron impact avalanche   The kinetics of this process are well described by a set of coupled rate equations that account for state-to-state electron-Rydberg inelastic scattering, electron-impact ionization and three-body ion-electron recombination \cite{PPR,Saquet2011,Saquet2012,Scaling} using detailed rate coefficients,  $k_{ij}$, $k_{i,ion}$ and $k_{i,tbr}$ validated by MD simulations \cite{PVS}   
\begin{eqnarray}
-\frac{d\rho_i}{dt}&=&\sum_{j}{k_{ij}\rho_e\rho_i}-\sum_{j}{k_{ji}\rho_e\rho_j} \nonumber\\
&& +k_{i,ion}\rho_e\rho_i-k_{i,tbr}\rho^3_e 
  \label{level_i}
\end{eqnarray}
\noindent and,
\begin{equation}
\frac{d\rho_e}{dt}=\sum_{i}{k_{i,ion}\rho_e^2}-\sum_{i}{k_{i,tbr}\rho^3_e}
  \label{electron}
\end{equation}

The relaxation of Rydberg molecules balances with collisional ionization to determine an evolving temperature of avalanche electrons to conserve total energy per unit volume  
\begin{equation}
E_{tot}=\frac{3}{2}k_BT_e(t)\rho_e(t)-R\sum_i{\frac{\rho_i(t)}{n_i^2}},
  \label{energy}
\end{equation}
Here, for simplicity, we neglect the longer-time effects of Rydberg predissociation and electron-ion dissociative recombination \cite{Saquet2012} 

Such calculations show that the conversion from Rydberg gas to plasma occurs on a timescale determined largely by the local Penning electron density, or Penning fraction, $P_f = \rho_e/\rho_0$, which depends on the local density of Rydberg molecules and their initial principal quantum number   

Avalanche times predicted by coupled rate equation calculations range widely   For example, in a model developed for experiments on xenon, simulations predict that a Rydberg gas with $n_0 = 42$ at a density of $8 8 \times 10^8 ~{\rm cm}^{-3}$ ($P_f = 6 \times 10^{-5}$) avalanches with a half time of  40 $\mu$s \cite{Hung2014}   At an opposite extreme, rate equations estimate that a Rydberg gas of NO with $n_0=60$ at a density of $1 \times 10^{12} ~{\rm cm}^{-3}$ ($P_f = 0 3$) rises to plasma in about 2 ns \cite{Saquet2012}   

\begin{figure}[h!]
\centering
\includegraphics[width=  49 \textwidth]{SFI_n=49 pdf}
   \caption{Contour plots showing SFI signal as a function the applied field for an $nf(2)$ Rydberg gas with an initial principal quantum number, $n_0=49$   Each frame represents 4,000 SFI traces, sorted by initial Rydberg gas density   Ramp field beginning at 0 and 150 ns (top, left to right), and  300 and 450 ns (bottom) after the $\omega_2$ laser pulse   The two bars of signal most evident at early ramp field delay times represent the field ionization of the $49f(2)$ Rydberg state respectively to NO$^+$ X $^1\Sigma^+$ cation rotational states, $N^+=0$ and 2   The signal waveform extracted near zero applied field represents the growing population of plasma electrons   
   }
\label{fig:SFI}
\end{figure}

Selective field ionization (SFI) probes the spectrum of binding energies in a Rydberg gas   Applied as a function of time after photoexcitation, SFI maps the evolution from a state of selected initial principal quantum number, $n_0$, to plasma \cite{Haenel2017}   Figure \ref{fig:SFI} shows SFI spectra taken at a sequence of delays after the formation of $49f(2)$ Rydberg gases of varying density     

Here, we can see that a $49f(2)$ Rydberg gas with an estimated initial density $\rho_0 = 3 \times 10^{11} ~{\rm cm}^{-3}$ relaxes to plasma on a timescale of about 500 ns   Observations such as these agree well with the predictions of coupled rate-equation calculations   We can understand this variation in relaxation dynamics with $\rho_0$ and $n_0$ quite simply in terms of the corresponding density of prompt Penning electrons these conditions afford to initiate the avalanche to plasma   

Figure \ref{fig:scaled_rise} illustrates this, showing how rise times predicted by coupled rate-equation simulations for a large range of initial densities and principal quantum number match when plotted as a function of time scaled by the ultimate plasma frequency and fraction of prompt Penning electrons   The dashed line gives an approximate account of the scaled rate of avalanche under all conditions of Rydberg gas density and initial principal quantum number in terms of the simple sigmoidal function:

\begin{equation}
\frac{\rho_e}{\rho_0} = \frac{a}{b+e^{-c\tau}},
  \label{scaledEq1}
\end{equation}
where,
\begin{equation}
\tau = t \omega_e P_f^{3/4},
  \label{scaledEq2}
\end{equation}
in which $\omega_e$ is the plasma frequency after avalanche, $P_f$ is the fraction of prompt Penning electrons, and $a = 0 00062$,  $b =   0 00082$ and $c =     0 075$ are empirical coefficients   

\begin{figure}[h!]
\centering
\includegraphics[width=  4 \textwidth]{sim_analytical_density pdf}
   \caption{Rise in fractional electron density as a function of time scaled by the plasma frequency, $\omega_e$ and fraction, $\rho_e(t=0)/\rho_0 = P_f$, of prompt Penning electrons   Simulation results shown for $n_0 = 30$, 50 and 70 with initial densities, $\rho_0 = 10^9,~10^{10},~10^{11},~{\rm and}~10^{12}~{\rm cm}^{-3}$   
   }
\label{fig:scaled_rise}
\end{figure}


\subsection{Evolution to plasma in a Rydberg gas Gaussian ellipsoid}

As outlined above, the local density and principal quantum number together determine the rate at which a Rydberg gas avalanches to plasma   Our experiment crosses a 2 mm wide cylindrically Gaussian molecular beam with a 1 mm diameter TEM$_{00}$ $\omega_1$ laser beam to produce a Gaussian ellipsoidal distribution of molecules excited to the A $^2\Sigma^+$ $v=0, ~N'=0$ intermediate state   A larger diameter $\omega_2$ pulse then drives a second step that forms a Rydberg gas in a single $n_0f(2)$ state with the spatial distribution of the intermediate state   

We model this shaped Rydberg gas as a system of 100 concentric ellipsoidal shells of varying density \cite{haenelCP}   Coupled rate equations within each shell describe the avalanche to plasma   This rate process proceeds from shell to shell with successively longer induction periods, determined by the local density as detailed above   The rising conversion of Rydberg molecules to ions plus neutral dissociation products conserves the particle number in each shell   We assume that local space charge confines electrons to shells, conserving quasi-neutrality   Electrons exchange kinetic energy at the boundaries of each shell, which determines a single plasma electron temperature   

\begin{figure}[h!]
\centering
\includegraphics[width=  5 \textwidth]{shell_model_100}
   \caption{(top frame) Cross-sectional contour diagram in the $x,y$ plane for $z=0$ describing the distribution of ion plus electron density over 100 shells of Gaussian ellipsoid with initial dimensions, $\sigma_x= 0 75$ mm and $\sigma_y= \sigma_z = 0 42$ mm and an initial $n_0 = 50$ Rydberg gas density, $\rho_0 = 2 \times 10^{11}$ cm$^{3}$ after an evolution time of 100 ns   (bottom frame) Curves describing the (dashed) ascending ion and (solid) descending Rydberg gas densities of each shell as functions of evolution time, for $t=20$, 40, 60, 80 and 100 ns   
   }
\label{fig:shell}
\end{figure}

The upper frame of Figure \ref{fig:shell} shows contours of NO$^+$ ion density after 100 ns obtained from a shell-model coupled rate-equation simulation of the avalanche of a Gaussian ellipsoidal Rydberg gas of nitric oxide with a selected initial state, $50f(2)$ and a density of $2 \times 10^{11}$ cm$^{-3}$   Here, we simulate a relaxation that includes channels of predissociation at every Rydberg level and redistributes the energy released to electrons, which determines a uniform rising electron temperature for all shells   

For comparison, the lower frame plots curves describing the ion density of each shell as a function of time from 20 to 100 ns, as determined by applying Eq \ref{scaledEq1} for the local conditions of initial Rydberg gas density   This numerical approximation contains no provision for predissociation   Coupled rate-equation simulations for uniform volumes show that predissociation depresses yield to some degree, but has less effect on the avalanche kinetics \cite{Saquet2012}   Therefore, we can expect sets of numerically estimated shell densities, scaled to agree with the simulated ion density at the elapsed time of 100 ns to provide a reasonable account of the earlier NO$^+$ density profiles as a function of time    


\begin{figure}[h!]
\centering
\includegraphics[width=  4 \textwidth]{Shell_pop}
   \caption{Global population fractions of particles as they evolve in the avalanche of a shell-model ellipsoidal Rydberg gas with the initial principal quantum number and density distribution of Figure \ref{fig:shell}
   }
\label{fig:shell_yields}
\end{figure}

For each time step, the difference, $\rho_0 - \rho_e$ defines the neutral population of each shell   We assign a fraction of this population to surviving Rydberg molecules, such that the total population of NO$^*$ as a function of time agrees with the prediction of the shell-model simulation, as shown in Figure \ref{fig:shell_yields}   We consider the balance of this neutral population to reflect NO$^*$ molecules that have dissociated to form N($^4$S) $+$ O($^3$P)   Figure \ref{fig:shell} plots these surviving Rydberg densities as a function of radial distance for each evolution time   At the initial density of this simulation, note at each time step that a higher density of Rydberg molecules encloses the tail of the ion density distribution in $x$    

\subsection{Plasma expansion and NO$^+$ - NO$^*$ charge exchange as an avenue of quench}

We regard the ions as initially stationary   The release of electrons creates a radial electric potential gradient, which gives rise to a force, $-e\nabla \phi_{k,j}(t)$, that accelerates the ions in shell $j$ in direction $k$ according to \cite{Sadeghi 2012}:

\begin{align}
\frac{-e}{m'}\nabla \phi_{k,j}(t) = & \frac{\partial u_{k,j}(t)}{\partial t} \notag  \\
= & \frac{k_BT_e(t)}{m'\rho_j(t)} \frac{\rho_{j+1}(t) - \rho_j(t)}{r_{k,j+1}(t) - r_{k,j}(t)},
  \label{dr_dt}
\end{align}

\noindent where $\rho_j(t)$ represents the density of ions in shell $j$   

The instantaneous velocity, $u_{k,j}(t)$ determines the change in the radial coordinates of each shell, $r_{k,j}(t)$, 
\begin{equation}
\frac{\partial r_{k,j}(t)}{\partial t}=u_{k,j}(t) = \gamma_{k,j}(t) r_{k,j}(t),
  \label{dr_dt}
\end{equation}
\noindent which in turn determines shell volume and thus its density, $ \rho_j(t)$    
The electron temperature supplies the thermal energy that drives this ambipolar expansion   Ions accelerate and $T_e$ falls according to: 

\begin{equation}
\frac{3k_B}{2}\frac{\partial T_e(t)}{\partial t}= -\frac{m'}{\sum_{j}{N_j}}\sum_{k,j}{N_j u_{k,j}(t)\frac{\partial u_{k,j}(t)}{\partial t}},
  \label{dr_dt}
\end{equation}
\noindent where we define an effective ion mass, $m'$, that recognizes the redistribution of the electron expansion force over all the NO$^+$ charge centres by resonant ion-Rydberg charge exchange, which occurs with a very large cross section \cite{PPR}   
\begin{equation}
m' =\left (1+ \frac{\rho^*_{j}(t)}{ \rho_j(t)}\right) m ,
  \label{dr_dt}
\end{equation}
\noindent in which $\rho^*_{j}(t)$ represents the instantaneous Rydberg density in shell $j$ 

The initial avalanche in the high-density core of the ellipsoid leaves few Rydberg molecules, so this term has little initial effect   Rydberg molecules predominate in the lower-density wings   There, momentum sharing by charge exchange assumes a greater importance   

We see this most directly in the $\omega_2$ absorption spectrum of transitions to states in the $n_0 f(2)$ Rydberg series, detected as the long-lived signal that survives a flight time of 400 $\mu$s to reach the imaging detector   The balance between the rising density of ions and the falling density of Rydberg molecules depends on the initial density of electrons produced by prompt Penning ionization   As clear from Eq \ref{Eq:PenDens}, this Penning fraction depends sensitively on the principal quantum number, and for all principal quantum numbers, on the initial Rydberg gas density   

\begin{figure}[h!]
\centering
\includegraphics[width=  4 \textwidth]{w2_spectra}
   \caption{Double-resonant spectra of nitric oxide Rydberg states in the $nf$ series converging to NO$^+$ $v=0$, $N^+=2$ (designated, $nf(2)$), derived from the late-peak signal obtained after a flight time of 400 $\mu$s by scanning $\omega_2$ for $\omega_1$ tuned to NO A $^2\Sigma^+$ $v=0$, $N'=0$ for initial $nf(2)$ densities from top to bottom of 0 07, 0 10, 0 13, 0 19, 0 27, 0 30, 0 32 and $3 \times 10^{12}$ cm$^{3}$   
  }
\label{fig:w2_spectra}
\end{figure}

Figure \ref{fig:w2_spectra} shows a series of $\omega_2$ late-signal excitation spectra for a set of initial densities   Here, we see a clear consequence of the higher-order dependence of Penning fraction - and thus the NO$^+$ ion - NO$^*$ Rydberg molecule balance - on $n_0$, the $\omega_2$-selected Rydberg gas initial principal quantum number   This Penning-regulated NO$^+$ ion - NO$^*$ Rydberg molecule balance appears necessary as a critical factor in achieving the long ultracold plasma lifetime required to produce this signal   We are progressing in theoretical work that explains the stability apparently conferred by this balance   


\subsection{Bifurcation and arrested relaxation}

Ambipolar expansion quenches electron kinetic energy as the initially formed plasma expands   Core ions follow electrons into the wings of the Rydberg gas   There, recurring charge exchange between NO$^+$ ions and NO$^*$ Rydberg molecules redistributes the ambipolar force of the expanding electron gas, equalizing ion and Rydberg velocities   This momentum matching effectively channels electron energy through ion motion into the overall $\pm x$ motion of gas volumes in the laboratory   The internal kinetic energy of the plasma, which at this point is defined almost entirely by the ion-Rydberg relative motion, falls   Spatial correlation develops, and over a period of 500 ns, the system forms the plasma/high-Rydberg quasi-equilibrium dramatically evidenced by the SFI results in Figure \ref{fig:SFI}   

\begin{figure}[h!]
\centering
\includegraphics[width=  4 \textwidth]{Bifurcation pdf}
   \caption{$x,y$ detector images of ultracold plasma volumes produced by 2:1 aspect ratio ellipsoidal Rydberg gases with selected initial state, $40f(2)$ after a flight time of 402 $\mu$s over a distance of 575 mm   Lower frame displays the distribution in $x$ of the charge integrated in $y$ and $z$   Both images represent the unadjusted raw signal acquired in each case after 250 shots   
   }
\label{fig:bifurcation}
\end{figure}

In the wings, momentum redistribution owing to cycles of ion-Rydberg charge transfer retards radial expansion \cite{Pohl2003,PPR}   By redirecting electron energy from ambipolar acceleration to $\pm x$ plasma motion, NO$^+$ to NO$^*$ charge exchange dissipates electron thermal energy   This redistribution of energy released in the avalanche of the Rydberg gas to plasma, causes the ellipsoidal Rydberg gas to bifurcate \cite{Schulz-Weiling2016,Haenel2017}, forming very long-lived, separating charged-particle distributions   We capture the electron signal from these recoiling volumes on an imaging detector as pictured in Figure \ref{fig:bifurcation}   Here, momentum matching preserves density and enables ions and Rydberg molecules to relax to positions that minimize potential energy, building spatial correlation   

The semi-classical description of avalanche and relaxation outlined above forms an important point of reference from which to interpret our experimental observations   The laser crossed molecular beam illumination geometry creates a Rydberg gas with a distinctively shaped high-density spatial distribution   This initial condition has an evident effect on the evolution dynamics   We have developed semi-classical models that explicitly consider the coupled rate and hydrodynamic processes governing the evolution from Rydberg gas to plasma using a realistic, ellipsoidal representation of the ion/electron and Rydberg densities \cite{haenelCP}   No combination of initial conditions can produce a simulation that conforms classically with the state of arrested relaxation we observe experimentally  


\subsection{A molecular ultracold plasma state of arrested relaxation}

Thus, we find that spontaneous avalanche to plasma splits the core of an ellipsoidal Rydberg gas of nitric oxide  As ambipolar expansion quenches the electron temperature of this core plasma, long-range, resonant charge transfer from ballistic ions to frozen Rydberg molecules in the wings of the ellipsoid quenches the ion-Rydberg molecule relative velocity distribution  This sequence of steps gives rise to a remarkable mechanics of self-assembly, in which the kinetic energy of initially formed hot electrons and ions drives an observed separation of plasma volumes  These dynamics redistribute ion momentum, efficiently channeling electron energy into a reservoir of mass-transport  This starts a process that evidently anneals separating volumes to a state of cold, correlated ions, electrons and Rydberg molecules  

We have devised a three-dimensional spin model to describe this arrested state of the ultracold plasma in terms of two, three and four-level dipole-dipole energy transfer interactions (spin flip-flops), together with Ising interactions that arise from the concerted pairwise coupling of resonant pairs of dipoles \cite{SousMBL,SousNJP}   

The Hamiltonian includes the effects of onsite disorder owing to the broad spectrum of states populated in the ensemble and the unique electrostatic environment of every dipole   Extending ideas developed for simpler systems \cite{Burin1,Sondhi}, one can make a case for slow dynamics, including an arrest in the relaxation of NO Rydberg molecules to predissociating states of lower principal quantum number 

Systems of higher dimension ought to thermalize by energy transfer that spreads from rare but inevitable ergodic volumes (Griffiths regions) \cite{Sarang2, Roeck_griffith, RareRegions_rev, Thermal_inclusions}   However, a feature in the self-assembly of the molecular ultracold plasma may preclude destabilization by rare thermal domains:  Whenever the quenched plasma develops a delocalizing Griffiths region, the local predissociation of relaxing NO molecules promptly proceeds to deplete that region to a void of no consequence 

In summary, the classical dynamics of avalanche and bifurcation appear to create a quenched condition of low temperature and high disorder in which dipole-dipole interactions drive self-assembly to a localized state purified by the predissociation of thermal regions   We suggest that this state of the quenched ultracold plasma offers an experimental platform for studying quantum many-body physics of disordered systems  \\

\section{Acknowledgments}
This work was supported by the US Air Force Office of Scientific Research (Grant No  FA9550-17-1-0343), together with the Natural Sciences and Engineering research Council of Canada (NSERC), the Canada Foundation for Innovation (CFI) and the British Columbia Knowledge Development Fund (BCKDF)  





ground_truth: It is the ratio of the average unscreened electron-electron potential energy to kinetic energy.