arXiv research

Mobile technologies offer opportunities for higher resolution monitoring of health conditions. This opportunity seems of particular promise in psychiatry where diagnoses often rely on retrospective and subjective recall of mood states. However, getting actionable information from these rather complex time series is cha…

Study uses interviews to automatically detect BD and BPD with good accuracy.

Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. Recent technological advances allow the prospective reporting of mood in real time enabl…

Autoencoders identify brain networks linked to stress and genotype.

Key features of mental illnesses are reflected in speech. Our research focuses on designing a multimodal deep learning structure that automatically extracts salient features from recorded speech samples for predicting various mental disorders including depression, bipolar, and schizophrenia. We adopt a variety of pre-t…

Accurate diagnosis of psychiatric disorders plays a critical role in improving the quality of life for patients and potentially supports the development of new treatments. Many studies have been conducted on machine learning techniques that seek brain imaging data for specific biomarkers of disorders. These studies hav…

The classification procedure of streaming data usually requires various ad hoc methods or particular heuristic models. We explore a novel non-parametric and systematic approach to analysis of heterogeneous sequential data. We demonstrate an application of this method to classification of the delays in responding to the…

Activity and motion analysis has the potential to be used as a diagnostic tool for mental disorders. However, to-date, little work has been performed in turning stratification measures of activity into useful symptom markers. The research presented in this thesis has focused on the identification of objective activity …

The bipolar filtration introduced by T. Cochran, S. Harvey, and P. Horn is a framework for the study of smooth concordance of topologically slice knots and links. It is known that there are topologically slice 1-bipolar knots which are not 2-bipolar. For knots, this is the highest known level at which the filtration do…

Let T denote the group of smooth concordance classes of topologically sice knots. We show that the first quotient in the bipolar filtration of T (i.e. 0-bipolar knots modulo 1-bipolar knots) has infinite rank, even modulo Alexander polynomial one knots. Any 0-bipolar knot has vanishing tau-, epsilon-, and s-invariants.…

Paper generalizes bipolar theorems for non-negative random variables.

We show that if a Riemannian manifold satisfies (3,3)-bipolar comparisons and has an open flat subset then it is flat. The same holds for a version of MTW where the perpendicularity is dropped. In particular we get that the (3,3)-bipolar comparison is strictly stronger than the Alexandrov comparison.

Topology classifies bipolar surfaces; they are not embedded.

The paper bounds the Morse index and nullity of bipolar surfaces related to Otsuki tori.

The bipolar filtration of Cochran, Harvey and Horn presents a framework of the study of deeper structures in the smooth concordance group of topologically slice knots. We show that the graded quotient of the bipolar filtration of topologically slice knots has infinite rank at each stage greater than one. To detect nont…

For every integer g, we construct a 2-solvable and 2-bipolar knot whose topological 4-genus is greater than g. Note that 2-solvable knots are in particular algebraically slice and have vanishing Casson-Gordon obstructions. Similarly all known smooth 4-genus bounds from gauge theory and Floer homology vanish for 2-bipol…

In many machine learning scenarios, supervision by gold labels is not available and consequently neural models cannot be trained directly by maximum likelihood estimation (MLE). In a weak supervision scenario, metric-augmented objectives can be employed to assign feedback to model outputs, which can be used to extract …

Recurrent correlation neural networks (RCNNs), introduced by Chiueh and Goodman as an improved version of the bipolar correlation-based Hopfield neural network, can be used to implement high-capacity associative memories. In this paper, we extend the bipolar RCNNs for processing hypercomplex-valued data. Precisely, we …

We propose a simple extension to the ReLU-family of activation functions that allows them to shift the mean activation across a layer towards zero. Combined with proper weight initialization, this alleviates the need for normalization layers. We explore the training of deep vanilla recurrent neural networks (RNNs) with…

The i-th eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of fixed area. Extremal points of these functionals correspond to surfaces admitting minimal isometric immersions into spheres. Recently, critical metrics for the first eigenvalue were classified on tori a…

Network analysis of human brain connectivity is critically important for understanding brain function and disease states. Embedding a brain network as a whole graph instance into a meaningful low-dimensional representation can be used to investigate disease mechanisms and inform therapeutic interventions. Moreover, by …

Bipolar disorder (BPD) is a chronic mental illness characterized by extreme mood and energy changes from mania to depression. These changes drive behaviors that often lead to devastating personal or social consequences. BPD is managed clinically with regular interactions with care providers, who assess mood, energy lev…

Recently Penskoi [J. Geom. Anal. 25 (2015), 2645-2666, arXiv:1308.1628] generalized the well known two-parametric family of Lawson tau-surfaces $τ_{r,m}$ minimally immersed in spheres to a three-parametric family $T_{a,b,c}$ of tori and Klein bottles minimally immersed in spheres. It was remarked that this family inclu…

Let $\mathcal{T}$ be the group of smooth concordance classes of topologically slice knots, and $\{0\}\subset\cdots\subset \mathcal{T}_{n+1}\subset\mathcal{T}_{n}\subset \cdots\subset \mathcal{T}_{0}\subset \mathcal{T}$ be the bipolar filtration. In this paper, we show that a proper collection of the knots employed by H…

Established a Hardy inequality on Finsler manifolds.

ED-Filter improves eating disorder classification on Twitter.

Study on a pinning model with random walk increments, showing convergence to a critical disordered pinning measure.

In this paper, we propose a classification based glottal closure instants (GCI) detection from pathological acoustic speech signal, which finds many applications in vocal disorder analysis. Till date, GCI for pathological disorder is extracted from laryngeal (glottal source) signal recorded from Electroglottograph, a d…

New algorithm balances personalization and statistical validity in MRTs.

We define a new type of metric comparison similar to the comparison of Alexandrov. We show that it has strong connections to continuity of optimal transport between regular measures on a Riemannian manifold, in particular to the so called MTW condition introduced by Xi-Nan Ma, Neil Trudinger and Xu-Jia Wang.

Automated detection of voice disorders with computational methods is a recent research area in the medical domain since it requires a rigorous endoscopy for the accurate diagnosis. Efficient screening methods are required for the diagnosis of voice disorders so as to provide timely medical facilities in minimal resourc…

As a mental disorder progresses, it may affect brain structure, but brain function expressed in brain dynamics is affected much earlier. Capturing the moment when brain dynamics express the disorder is crucial for early diagnosis. The traditional approach to this problem via training classifiers either proceeds from ha…

Whole MILC learns brain disorder dynamics from unlabeled data.

The study predicts how discussions in mental disorder Reddit communities affect users' emotional states.

The opioid epidemic in the United States claims over 40,000 lives per year, and it is estimated that well over two million Americans have an opioid use disorder. Over-prescription and misuse of prescription opioids play an important role in the epidemic. Individuals who are prescribed opioids, and who are diagnosed wit…

New algorithm optimizes matrix reordering for noisy disordered matrices.

Vocal disorders have affected several patients all over the world. Due to the inherent difficulty of diagnosing vocal disorders without sophisticated equipment and trained personnel, a number of patients remain undiagnosed. To alleviate the monetary cost of diagnosis, there has been a recent growth in the use of data a…

Neuronal circuits formed in the brain are complex with intricate connection patterns. Such complexity is also observed in the retina as a relatively simple neuronal circuit. A retinal ganglion cell receives excitatory inputs from neurons in previous layers as driving forces to fire spikes. Analytical methods are requir…

We show that Lawson's bipolar surface $\tildeτ_{3,1}$ is after stereographic projection the unique minimizer among immersed Klein bottles in its conformal class. We conjecture that it actually is the unique minimizer among immersed Klein bottles into $\mathbb{R}^n$, $n\geq 4$, whose existence the authors and P. Breunin…

The $i$-th eigenvalue $λ_i$ of the Laplace-Beltrami operator on a surface can be considered as a functional on the space of all Riemannian metrics of unit volume on this surface. Surprisingly only few examples of extremal metrics for these functionals are known. In the present paper a new countable family of extremal m…

Model predicts cannabis use disorder risk for adolescents and young adults.

We construct 1-parameter families of non-periodic embedded minimal surfaces of infinite genus in $T \times \mathbb{R}$, where $T$ denotes a flat 2-tori. Each of our families converges to a foliation of $T \times \mathbb{R}$ by $T$. These surfaces then lift to minimal surfaces in $\mathbb{R}^3$ that are periodic in hori…

Deep learning predicts opioid use disorder risk in patients.

Diagnosing Autism Spectrum Disorder (ASD) is a challenging problem, and is based purely on behavioral descriptions of symptomology (DSM-5/ICD-10), and requires informants to observe children with disorder across different settings (e.g. home, school). Numerous limitations (e.g., informant discrepancies, lack of adheren…

We define two transforms between minimal surfaces with non-circular ellipse of curvature in the 5-sphere, and show how this enables us to construct, from one such surface, a sequence of such surfaces. We also use the transforms to show how to associate to such a surface a corresponding ruled minimal Lagrangian submanif…

Let {T_n} be the bipolar filtration of the smooth concordance group of topologically slice knots, which was introduced by Cochran, Harvey, and Horn. It is known that for each n not equal to 1 the quotient group T_n/T_{n+1} has infinite rank and T_1/T_2 has positive rank. In this paper, we show that T_1/T_2 also has inf…

This thesis explores emergent intelligence in disordered systems like spin glasses and neural networks.

Transfer entropy shows abnormal brain connectivity in depression.