arXiv subjects

Jonathan Rubin

Publications and source records attributed to Jonathan Rubin.

27 records · Page 2Linked to original sources

arXiv2017

Densely Connected Convolutional Networks and Signal Quality Analysis to Detect Atrial Fibrillation Using Short Single-Lead ECG Recordings

The development of new technology such as wearables that record high-quality single channel ECG, provides an opportunity for ECG screening in a larger population, especially for atrial fibrillation screening. The main goal of this study is to develop an automatic classification algorithm for normal sinus rhythm (NSR), atrial fibrillation (AF), other rhythms (O), and noise from a single channel short ECG segment (9-60 seconds). For this purpose, signal quality index (SQI) along with dense convolutional neural networks was used. Two convolutional neural network (CNN) models (main model that accepts 15 seconds ECG and secondary model that processes 9 seconds shorter ECG) were trained using the training data set. If the recording is determined to be of low quality by SQI, it is immediately classified as noisy. Otherwise, it is transformed to a time-frequency representation and classified with the CNN as NSR, AF, O, or noise. At the final step, a feature-based post-processing algorithm classifies the rhythm as either NSR or O in case the CNN model's discrimination between the two is indeterminate. The best result achieved at the official phase of the PhysioNet/CinC challenge on the blind test set was 0.80 (F1 for NSR, AF, and O were 0.90, 0.80, and 0.70, respectively).

eess.SP↗

arXiv2017

Enriched model categories in equivariant contexts

We give a general framework of equivariant model category theory. Our groups G, called Hopf groups, are suitably defined group objects in any well-behaved symmetric monoidal category V. For any V, a discrete group G gives a Hopf group, denoted I[G]. When V is cartesian monoidal, the Hopf groups are just the group objects in V. When V is the category of modules over a commutative ring R, I[G] is the group ring R[G] and the general Hopf groups are the cocommutative Hopf algebras over R. We show how all of the usual constructs of equivariant homotopy theory, both categorical and model theoretic, generalize to Hopf groups for any V. This opens up some quite elementary unexplored mathematical territory, while systematizing more familiar terrain.

math.AT↗

arXiv2017

An Ensemble Boosting Model for Predicting Transfer to the Pediatric Intensive Care Unit

Our work focuses on the problem of predicting the transfer of pediatric patients from the general ward of a hospital to the pediatric intensive care unit. Using data collected over 5.5 years from the electronic health records of two medical facilities, we develop classifiers based on adaptive boosting and gradient tree boosting. We further combine these learned classifiers into an ensemble model and compare its performance to a modified pediatric early warning score (PEWS) baseline that relies on expert defined guidelines. To gauge model generalizability, we perform an inter-facility evaluation where we train our algorithm on data from one facility and perform evaluation on a hidden test dataset from a separate facility. We show that improvements are witnessed over the PEWS baseline in accuracy (0.77 vs. 0.69), sensitivity (0.80 vs. 0.68), specificity (0.74 vs. 0.70) and AUROC (0.85 vs. 0.73).

cs.LG↗

arXiv2016

Sufficient Conditions for Graphicality of Bidegree Sequences

There are a variety of existing conditions for a degree sequence to be graphic. When a degree sequence satisfies any of these conditions, there exists a graph that realizes the sequence. We formulate several novel sufficient graphicality criteria that depend on the number of elements in the sequence, corresponding to the number of nodes in an associated graph, and the mean degree of the sequence. These conditions, which are stated in terms of bidegree sequences for directed graphs, are easier to apply than classic necessary and sufficient graphicality conditions involving multiple inequalities. They are also more flexible than more recent graphicality conditions, in that they imply graphicality of some degree sequences not covered by those conditions. The form of our results will allow them to be easily used for the generation of graphs with particular degree sequences for applications.

math.CO↗

arXiv2016

Degree switching and partitioning for enumerating graphs to arbitrary orders of accuracy

We provide a novel method for constructing asymptotics (to arbitrary accuracy) for the number of directed graphs that realize a fixed bidegree sequence $d = a \times b$ with maximum degree $d_{max}=O(S^{\frac{1}{2}-τ})$ for an arbitrarily small positive number $τ$, where $S$ is the number edges specified by $d$. Our approach is based on two key steps, graph partitioning and degree preserving switches. The former idea allows us to relate enumeration results for given sequences to those for sequences that are especially easy to handle, while the latter facilitates expansions based on numbers of shared neighbors of pairs of nodes. While we focus primarily on directed graphs allowing loops, our results can be extended to other cases, including bipartite graphs, as well as directed and undirected graphs without loops. In addition, we can relax the constraint that $d_{max} = O(S^{\frac{1}{2}-τ})$ and replace it with $a_{max} b_{max} = O(S^{1-τ})$. where $a_{max}$ and $b_{max}$ are the maximum values for $a$ and $b$ respectively. The previous best results, from Greenhill et al., only allow for $d_{max} = o(S^{\frac{1}{3}})$ or alternatively $a_{max} b_{max} = o(S^{\frac{2}{3}})$. Since in many real world networks, $d_{max}$ scales larger than $o(S^{\frac{1}{3}})$, we expect that this work will be helpful for various applications.

math.CO↗

arXiv2015

Traveling Wave Solutions in a Chain of periodically Forced Couple Nonlinear Oscillators

Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts and annihilation of radial ones. Finally, we show that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.

nlin.PS↗

arXiv2008

Competition between transients in the rate of approach to a fixed point

Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the use of Poincare maps and phase resetting curves, have been developed for the study of periodic orbits. However, the analysis of transient dynamics associated with solutions on their way to an attracting fixed point has not received much rigorous attention. This paper introduces methods for the study of such transient dynamics. In particular, we focus on the analysis of whether one component of a solution to a system of differential equations can overtake the corresponding component of a reference solution, given that both solutions approach the same stable node. We call this phenomenon tolerance, which derives from a certain biological effect. Here, we establish certain general conditions, based on the initial conditions associated with the two solutions and the properties of the vector field, that guarantee that tolerance does or does not occur in two-dimensional systems. We illustrate these conditions in particular examples, and we derive and demonstrate additional techniques that can be used on a case by case basis to check for tolerance. Finally, we give a full rigorous analysis of tolerance in two-dimensional linear systems.

math.DS↗

arXiv2000

Equilibrium Properties of Temporally Asymmetric Hebbian Plasticity

A theory of temporally asymmetric Hebb (TAH) rules which depress or potentiate synapses depending upon whether the postsynaptic cell fires before or after the presynaptic one is presented. Using the Fokker-Planck formalism, we show that the equilibrium synaptic distribution induced by such rules is highly sensitive to the manner in which bounds on the allowed range of synaptic values are imposed. In a biologically plausible multiplicative model, we find that the synapses in asynchronous networks reach a distribution that is invariant to the firing rates of either the pre- or post-synaptic cells. When these cells are temporally correlated, the synaptic strength varies smoothly with the degree and phase of synchrony between the cells.

cond-mat.dis-nn↗

arXiv1999

Existence and stability of hole solutions to complex Ginzburg-Landau equations

We consider the existence and stability of the hole, or dark soliton, solution to a Ginzburg-Landau perturbation of the defocusing nonlinear Schroedinger equation (NLS), and to the nearly real complex Ginzburg-Landau equation (CGL). By using dynamical systems techniques, it is shown that the dark soliton can persist as either a regular perturbation or a singular perturbation of that which exists for the NLS. When considering the stability of the soliton, a major difficulty which must be overcome is that eigenvalues may bifurcate out of the continuous spectrum, i.e., an edge bifurcation may occur. Since the continuous spectrum for the NLS covers the imaginary axis, and since for the CGL it touches the origin, such a bifurcation may lead to an unstable wave. An additional important consideration is that an edge bifurcation can happen even if there are no eigenvalues embedded in the continuous spectrum. Building on and refining ideas first presented in Kapitula and Sandstede (Physica D, 1998) and Kapitula (SIAM J. Math. Anal., 1999), we show that when the wave persists as a regular perturbation, at most three eigenvalues will bifurcate out of the continuous spectrum. Furthermore, we precisely track these bifurcating eigenvalues, and thus are able to give conditions for which the perturbed wave will be stable. For the NLS the results are an improvement and refinement of previous work, while the results for the CGL are new. The techniques presented are very general and are therefore applicable to a much larger class of problems than those considered here.

patt-sol↗