This study examined the effectiveness of a v ision-based framework for m ultiple s clerosis (MS) and Parkinson's disease (PD) gait dysfunction prediction. We collected gait video data from multi-view digital cameras during self-paced walking from MS, PD patients and age, weight, height and gender-matched healthy older adults (HOA). We then extracted characteristic 3D joint keypoints from the collected videos. In this work, we proposed a data-driven methodology to classify strides in persons with MS (PwMS), persons with PD (PwPD) and HOA that may generalize across different walking tasks and subjects. We presented a comprehensive quantitative comparison of 16 diverse traditional machine and deep learning (DL) algorithms. When generalizing from comfortable walking (W) to walking-while-talking (WT), multi-scale residual neural network achieved perfect accuracy and AUC for classifying individuals with a given gait disorder; for subject generalization in W trials, residual neural network resulted in the highest accuracy and AUC of $\mathbf {78.1\%}$ and 0.87 (resp.), and 1D convolutional neural network (CNN) had highest accuracy of $\mathbf {75\%}$ in WT trials. Finally, when generalizing over new subjects in different tasks, again 1D CNN had the top classification accuracy and AUC of $\mathbf {79.3\%}$ and 0.93 (resp.). This work is the first attempt to apply and demonstrate the potential of DL with a multi-view digital camera-based gait analysis framework for neurological gait dysfunction prediction. This study suggests the viability of inexpensive vision-based systems for diagnosing certain neurological disorders.

Objective: Multiple Sclerosis (MS) is a neurological condition which widely affects people 50-60 years of age. While clinical presentations of MS are highly heterogeneous, mobility limitations are one of the most frequent symptoms. This study examines a machine learning (ML) framework for identifying MS through spatiotemporal and kinetic gait features. Methods: In this study, gait data during self-paced walking on an instrumented treadmill from 20 persons with MS and 20 age, weight, height, and gender-matched healthy older adults (HOA) were obtained. We explored two strategies to normalize data and minimize dependence on subject demographics; size-normalization (standard body size-based normalization) and regress-normalization (regression-based normalization using scaling factors derived by regressing gait features on multiple subject demographics); and proposed an ML based methodology to classify individual strides of older persons with MS (PwMS) from healthy controls. We generalized both across different walking tasks and subjects. Results: We observed that regress-normalization improved the accuracy of identifying pathological gait using ML when compared to size-normalization. When generalizing from comfortable walking to walking while talking, gradient boosting machine achieved the optimal subject classification accuracy and AUC of 94.3 and 1.0, respectively and for subject generalization, a multilayer perceptron resulted in the best accuracy and AUC of 80 % and 0.86, respectively, both with regression-normalized data. Conclusion: The integration of gait data and ML may provide a viable patient-centric approach to aid clinicians in monitoring MS. Significance: The results of this study have future implications for the way regression normalized gait features may be clinically used to design ML-based disease prediction strategies and monitor disease progression in PwMS.

The theory of nonlinear filtering forms the framework of many data assimilation problems. When the rates of change of different variables differ by orders of magnitude, efficient data assimilation can be accomplished by constructing nonlinear filtering equations for the coarse-grained signal. We consider the conditional law of a signal given the observations in a multi-scale context. In particular, we study how scaling interacts with filtering via stochastic averaging. This is an extension of our previous work (Park et al 2008 Stoch. Dyn. 8 543–60) where the observation process depended only on the fast variable, so the filter became independent of the observation in the limit. Here, we investigate a more realistic setting in which the observation depends on both the slow and the fast variables.

We propose and study a stylization of high frequency trading (HFT). Our interest is an order book which consists of orders from slow liquidity traders and orders from high-frequency traders. We would like to frame a model which is amenable to the (seemingly natural) mathematical toolkit of separation of scales and which can be used to address some of the larger issues involved in HFT. The main issue to which we address our model is volatility. An important question is how volatility is affected by HFT. In our stylized model, we show how HFT increases volatility, and can quantify this effect as a function of the parameters in our model and the separation of scales.

Objective: Multiple sclerosis (MS) is a chronic neurological condition of the central nervous system leading to various physical, mental and psychiatric complexities. Mobility limitations are amongst the most frequent and early markers of MS. We evaluated the effectiveness of a DeepMS2G ( deep learning (DL) for MS differentiation using m ulti- s tride dynamics in g ait) framework, which is a DL-based methodology to classify multi-stride sequences of persons with MS (PwMS) from healthy controls (HC), in order to generalize over newer walking tasks and subjects. Methods: We collected single-task Walking and dual-task Walking-while-Talking gait data using an instrumented treadmill from a balanced collection of 20 HC and 20 PwMS. We utilized domain knowledge-based spatiotemporal and kinetic gait features along with two normalization schemes, namely standard size-based and multiple regression normalization strategies. To differentiate between multi-stride sequences of HC and PwMS, we compared 16 traditional machine learning and DL algorithms. Further, we studied the interpretability of our highest-performing models; and discussed the association between the lower extremity function of participants and our model predictions. Results: We observed that residual neural network (ResNet) based models with regression-based normalization were the top performers across both task and subject generalization classification designs. Considering regression-based normalization, a multi-scale ResNet attained a subject classification accuracy and F $_{1}$ -score of 1.0 when generalizing from single-task Walking to dual-task Walking-while-Talking ; and a ResNet resulted in the top subject-wise accuracy and F $_{1}$ of 0.83 and 0.81 (resp.), when generalizing over unseen participants. Conclusion: We used advanced DL and dynamics across domain knowledge-based spatiotemporal and kinetic gait parameters to successfully classify MS gait across distinct walking trials and unseen participants. Significance: Our proposed DL algorithms might contribute to efforts to automate MS diagnoses.