pwc-archive/papers-with-abstracts huggingface dataset:
On Recursive State Estimation for Linear State-Space Models Having Quantized Output Data
Authors: Angel L. Cedeño, Ricardo Albornoz, Boris I. Godoy, Rodrigo Carvajal, Juan C. Agüero
Date: 2021-12-15 00:00:00
Tasks: Quantization, State Estimation, State Space Models

In this paper, we study the problem of estimating the state of a dynamic state-space system where the output is subject to quantization. We compare some classical approaches and a new development in the literature to obtain the filtering and smoothing distributions of the state conditioned to quantized data. The classical approaches include the Extended Kalman filter/smoother in which we consider an approximation of the quantizer non-linearity based on the arctan function, the quantized Kalman filter/smoother, the Unscented Kalman filter/smoother, and the Sequential Monte Carlo sampling method also called particle filter/smoother. We consider a new approach based on the Gaussian sum filter/smoother where the probability mass function of the quantized data given the state is modeled as an integral equation and approximated using Gauss-Legendre quadrature. The Particle filter is addressed considering some resampling methods used to deal with the degeneracy problem. Also, the sample impoverishment caused by the resampling method is addressed by introducing diversity in the samples set using the Markov Chain Monte Carlo method. In this paper, we discuss the implementation of the aforementioned algorithms and the Particle filter/smoother implementation is studied by using different resampling methods combined with two Markov Chain algorithms. A numerical simulation is presented to analyze the accuracy of the estimation and the computational cost.
Active RIS Versus Passive RIS: Which Is Superior with the Same Power Budget?
Authors: Kangda Zhi, Cunhua Pan, Hong Ren, Kok Keong Chai, Maged Elkashlan
Date: 2021-12-14 00:00:00

This letter theoretically compares the active reconfigurable intelligent surface (RIS)-aided system with the passive RIS-aided system. For fair comparison, we consider that these two systems have the same overall power budget that can be used at both the base station (BS) and the RIS. For active RIS, we first derive the optimal power allocation between the BS's transmit signal power and RIS's output signal power. We also analyze the impact of various system parameters on the optimal power allocation ratio. Then, we compare the performance between the active RIS and the passive RIS, which demonstrates that the active RIS would be superior if the power budget is not very small and the number of RIS elements is not very large.
Adaptive Beamwidth Configuration for Millimeter Wave V2X Scheduling
Authors: Baldomero Coll-Perales, Javier Gozalvez, Esteban Egea-Lopez
Date: 2021-12-14 00:00:00
Tasks: Management, Scheduling

Millimeter wave (mmWave) technologies will support the high bandwidth and data rate requirements of V2X services demanded by connected and automated vehicles (CAVs). MmWave V2X technologies will leverage directional antennas that challenge the management of the communications in dynamic scenarios including the identification of available links, beams alignment, and scheduling. Previous studies have shown that these challenges can be reduced when mmWave communications are supported by side information like the one transmitted in sub-6GHz V2X technologies. In this context, this paper proposes a beamwidth-aware mmWave scheduling scheme for V2V communications supported by sub-6GHz V2X technologies. The proposal enables mmWave transmitters to schedule a mmWave transmission to several neighboring vehicles at the same time by adapting the beamwidth configuration. In addition, the proposal derives the minimum beamwidth that mmWave transmitters should use to contact their neighboring vehicles in a limited number of scheduling intervals. The obtained results demonstrate that the proposal helps increasing the amount of mmWave data that can be transmitted to neighboring vehicles.
Relative Kinematics Estimation Using Accelerometer Measurements
Authors: Anurodh Mishra, Raj Thilak Rajan
Date: 2021-12-14 00:00:00

Given a network of $N$ static nodes in $D$-dimensional space and the pairwise distances between them, the challenge of estimating the coordinates of the nodes is a well-studied problem. However, for numerous application domains, the nodes are mobile and the estimation of relative kinematics (e.g., position, velocity and acceleration) is a challenge, which has received limited attention in literature. In this paper, we propose a time-varying Grammian-based data model for estimating the relative kinematics of mobile nodes with polynomial trajectories, given the time-varying pairwise distance measurements between the nodes. Furthermore, we consider a scenario where the nodes have on-board accelerometers, and extend the proposed data model to include these accelerometer measurements. We propose closed-form solutions to estimate the relative kinematics, based on the proposed data models. We conduct simulations to showcase the performance of the proposed estimators, which show improvement against state-of-the-art methods.
Estimation of Physical Activity Level and Ambient Condition Thresholds for Respiratory Health using Smartphone Sensors
Authors: Chinazunwa Uwaoma
Date: 2021-12-11 00:00:00

While physical activity has been described as a primary prevention against chronic diseases, strenuous physical exertion under adverse ambient conditions has also been reported as a major contributor to exacerbation of chronic respiratory conditions. Maintaining a balance by monitoring the type and the level of physical activities of affected individuals, could help in reducing the cost and burden of managing respiratory ailments. This paper explores the potentiality of motion sensors in Smartphones to estimate physical activity thresholds that could trigger symptoms of exercise induced respiratory conditions (EiRCs). The focus is on the extraction of measurements from the embedded motion sensors to determine the activity level and the type of activity that is tolerable to individuals respiratory health. The calculations are based on the correlation between Signal Magnitude Area (SMA) and Energy Expenditure (EE). We also consider the effect of changes in the ambient conditions like temperature and humidity, as contributing factors to respiratory distress during physical exercise. Real time data collected from healthy individuals were used to demonstrate the potentiality of a mobile phone as tool to regulate the level of physical activities of individuals with EiRCs. We describe a practical situation where the experimental outcomes can be applied to promote good respiratory health.
Stability analysis of an eight parameter SIR-type model including loss of immunity, and disease and vaccination fatalities
Authors: Florin Avram, Rim Adenane, Gianluca Bianchin, Andrei Halanay
Date: 2021-12-16 00:00:00
Tasks: All

We revisit here a landmark five parameter SIR-type model of [DvdD93, Sec. 4], which is maybe the simplest example where a complete picture of all cases, including non-trivial bistability behavior, may be obtained using simple tools. We also generalize it by adding essential vaccination and vaccination-induced death parameters, with the aim of revealing the role of vaccination and its possible failure. The main result is Theorem 5, which describes the stability behavior of our model in all possible cases.
A polynomial invariant for a new class of phylogenetic networks
Authors: Joan Carles Pons, Tomás M. Coronado, Michael Hendriksen, Andrew Francis
Date: 2021-12-30 00:00:00

Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this paper, we generalize a complete polynomial invariant on trees to a class of phylogenetic networks called separable networks, which will include orchard networks. Networks are becoming increasingly important for their ability to represent reticulation events, such as hybridization, in evolutionary history. We provide a function from the space of internally multi-labelled phylogenetic networks, a more generic graph structure than phylogenetic networks where the reticulations are also labelled, to a polynomial ring. We prove that the separability condition allows us to characterize, via the polynomial, the phylogenetic networks with the same number of leaves and same number of reticulations by considering their internally labelled versions. While the invariant for trees is a polynomial in Z[x_1,..., x_n,y] where n is the number of leaves, the invariant for internally multi-labelled phylogenetic networks is an element of Z[x_1,..., x_n,lambda_1,...,lambda_r,y], where r is the number of reticulations in the network. When the networks are considered without leaf labels the number of variables reduces to r+2.
SIS/R model on Bi-Uniform Hypergraph
Authors: Rohan Nuckchady
Date: 2021-12-26 00:00:00
Tasks: model

This report is based on the work in (1). We first review definitions and notation developped there and provide derivations for the exact mathematical description of an SIS epidemic on a hypergraph. We then generalise the work in (1) to a new class of models that encompass SIS and SIR models. The exact differential equations are derived for the expected values of the population of each state. Focusing on Bi-uniform hypergraphs, we make suitable approximations obtain numerical solutions to those equations. These are compared with stochastic simulations of the model for various systems.
Interplay between risk perception, behaviour, and COVID-19 spread
Authors: Philipp Dönges, Joel Wagner, Sebastian Contreras, Emil Iftekhar, Simon Bauer, Sebastian B. Mohr, Jonas Dehning, André Calero Valdez, Mirjam Kretzschmar, Michael Mäs, Kai Nagel, Viola Priesemann
Date: 2021-12-22 00:00:00

Pharmaceutical and non-pharmaceutical interventions (NPIs) have been crucial for controlling COVID-19. They are complemented by voluntary health-protective behaviour, building a complex interplay between risk perception, behaviour, and disease spread. We studied how voluntary health-protective behaviour and vaccination willingness impact the long-term dynamics. We analysed how different levels of mandatory NPIs determine how individuals use their leeway for voluntary actions. If mandatory NPIs are too weak, COVID-19 incidence will surge, implying high morbidity and mortality before individuals react; if they are too strong, one expects a rebound wave once restrictions are lifted, challenging the transition to endemicity. Conversely, moderate mandatory NPIs give individuals time and room to adapt their level of caution, mitigating disease spread effectively. When complemented with high vaccination rates, this also offers a robust way to limit the impacts of the Omicron variant of concern. Altogether, our work highlights the importance of appropriate mandatory NPIs to maximise the impact of individual voluntary actions in pandemic control.
Nonlocal Models in the Analysis of Brain Neurodegenerative Protein Dynamics with Application to Alzheimer's Disease
Authors: Swadesh Pal, Roderick Melnik
Date: 2021-12-22 00:00:00

It is well known that today nearly one in six of the world's population has to deal with neurodegenerative disorders. While a number of medical devices have been developed for the detection, prevention, and treatments of such disorders, some fundamentals of the progression of associated diseases are in urgent need of further clarification. In this paper, we focus on Alzheimer's disease, where it is believed that the concentration changes in amyloid-beta and tau proteins play a central role in its onset and development. A multiscale model is proposed to analyze the propagation of these concentrations in the brain connectome. In particular, we consider a modified heterodimer model for the protein-protein interactions. Higher toxic concentrations of amyloid-beta and tau proteins destroy the brain cell. We have studied these propagations for the primary and secondary and their mixed tauopathy. We model the damage of a brain cell by the nonlocal contributions of these toxic loads present in the brain cells. With the help of rigorous analysis, we check the stability behaviour of the stationary points corresponding to the homogeneous system. After integrating the brain connectome data into the developed model, we see that the spreading patterns of the toxic concentrations for the whole brain are the same, but their concentrations are different in different regions. Also, the time to propagate the damage in each region of the brain connectome is different.
GOPHER: Categorical probabilistic forecasting with graph structure via local continuous-time dynamics
Authors: Ke Alexander Wang, Danielle Maddix, Yuyang Wang
Date: 2021-12-18 00:00:00
Tasks: Inductive Bias

We consider the problem of probabilistic forecasting over categories with graph structure, where the dynamics at a vertex depends on its local connectivity structure. We present GOPHER, a method that combines the inductive bias of graph neural networks with neural ODEs to capture the intrinsic local continuous-time dynamics of our probabilistic forecasts. We study the benefits of these two inductive biases by comparing against baseline models that help disentangle the benefits of each. We find that capturing the graph structure is crucial for accurate in-domain probabilistic predictions and more sample efficient models. Surprisingly, our experiments demonstrate that the continuous time evolution inductive bias brings little to no benefit despite reflecting the true probability dynamics.
A Dynamical Model for the Origin of Anisogamy
Authors: Joseph D. Johnson, Nathan L. White, Alain Kangabire, Daniel M. Abrams
Date: 2021-12-16 00:00:00
Tasks: model, Open-Ended Question Answering

The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Using theoretical analysis and numerical simulation, we demonstrate that competition between individuals that is linked to the mean gamete size will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.
Analyzing population dynamics models via Sumudu transform
Authors: M. O. Aibinu, S. C. Moyo, S. Moyo
Date: 2021-12-14 00:00:00
Tasks: Form

This study demonstrates how to construct the solutions of a more general form of population dynamics models via a blend of variational iterative method with Sumudu transform. In this paper, population growth models are formulated in the form of delay differential equations of pantograph type which is a general form for the existing models. Innovative ways are presented for obtaining the solutions of population growth models where other analytic methods fail. Stimulating procedures for finding patterns and regularities in seemingly chaotic processes have been elucidated in this paper. How, when and why the changes in population sizes occur can be deduced through this study.
The entropic barrier is $n$-self-concordant
Authors: Sinho Chewi
Date: 2021-12-21 00:00:00

For any convex body $K \subseteq \mathbb R^n$, S. Bubeck and R. Eldan introduced the entropic barrier on $K$ and showed that it is a $(1+o(1)) \, n$-self-concordant barrier. In this note, we observe that the optimal bound of $n$ on the self-concordance parameter holds as a consequence of the dimensional Brascamp-Lieb inequality.
On Asymptotic Linear Convergence of Projected Gradient Descent for Constrained Least Squares
Authors: Trung Vu, Raviv Raich
Date: 2021-12-22 00:00:00
Tasks: compressed sensing, Image Restoration, Matrix Completion

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent is a simple yet efficient method for solving such constrained optimization problems. Local convergence analysis furthers our understanding of its asymptotic behavior near the solution, offering sharper bounds on the convergence rate compared to global convergence analysis. However, local guarantees often appear scattered in problem-specific areas of machine learning and signal processing. This manuscript presents a unified framework for the local convergence analysis of projected gradient descent in the context of constrained least squares. The proposed analysis offers insights into pivotal local convergence properties such as the conditions for linear convergence, the region of convergence, the exact asymptotic rate of convergence, and the bound on the number of iterations needed to reach a certain level of accuracy. To demonstrate the applicability of the proposed approach, we present a recipe for the convergence analysis of projected gradient descent and demonstrate it via a beginning-to-end application of the recipe on four fundamental problems, namely, linear equality-constrained least squares, sparse recovery, least squares with the unit norm constraint, and matrix completion.
Mean-Covariance Robust Risk Measurement
Authors: Viet Anh Nguyen, Soroosh Shafiee, Damir Filipović, Daniel Kuhn
Date: 2021-12-18 00:00:00
Tasks: Portfolio Optimization

We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. We find that, for a large class of risk measures, mean-covariance robust portfolio optimization boils down to the Markowitz model, subject to a regularization term given in closed form. This includes the finance standards, value-at-risk and conditional value-at-risk, and can be solved highly efficiently.
Nonlinear Discrete-time System Identification without Persistence of Excitation: Finite-time Concurrent Learning Methods
Authors: Farzaneh Tatari, Christos Panayiotou, Marios Polycarpou
Date: 2021-12-14 00:00:00

This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to approximate the uncertainties of the discrete-time nonlinear systems in an online fashion by employing current data along with recorded experienced data satisfying an easy-to-check rank condition on the richness of the recorded data which is less restrictive in comparison with persistence of excitation condition. For the proposed finite-time concurrent learning methods, rigorous proofs guarantee the finite-time convergence of the estimated parameters to their optimal values based on the discrete-time Lyapunov analysis. Compared with the existing work in the literature, simulation results illustrate that the proposed methods can timely and precisely approximate the uncertainties.
Non-linear shrinkage of the price return covariance matrix is far from optimal for portfolio optimisation
Authors: Christian Bongiorno, Damien Challet
Date: 2021-12-14 00:00:00
Tasks: Portfolio Optimization

Portfolio optimization requires sophisticated covariance estimators that are able to filter out estimation noise. Non-linear shrinkage is a popular estimator based on how the Oracle eigenvalues can be computed using only data from the calibration window. Contrary to common belief, NLS is not optimal for portfolio optimization because it does not minimize the right cost function when the asset dependence structure is non-stationary. We instead derive the optimal target. Using historical data, we quantify by how much NLS can be improved. Our findings reopen the question of how to build the covariance matrix estimator for portfolio optimization in realistic conditions.
Compensatory model for quantile estimation and application to VaR
Authors: Shuzhen Yang
Date: 2021-12-14 00:00:00
Tasks: Time Series, Time Series Analysis

In contrast to the usual procedure of estimating the distribution of a time series and then obtaining the quantile from the distribution, we develop a compensatory model to improve the quantile estimation under a given distribution estimation. A novel penalty term is introduced in the compensatory model. We prove that the penalty term can control the convergence error of the quantile estimation of a given time series, and obtain an adaptive adjusted quantile estimation. Simulation and empirical analysis indicate that the compensatory model can significantly improve the performance of the value at risk (VaR) under a given distribution estimation.
Wasserstein Generative Learning of Conditional Distribution
Authors: Shiao Liu, Xingyu Zhou, Yuling Jiao, Jian Huang
Date: 2021-12-19 00:00:00
Tasks: Density Estimation, Image Generation, Image Reconstruction, Uncertainty Quantification

Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a conditional generator to transform a known distribution to the target conditional distribution. The conditional generator is estimated by matching a joint distribution involving the conditional generator and the target joint distribution, using the Wasserstein distance as the discrepancy measure for these joint distributions. We establish non-asymptotic error bound of the conditional sampling distribution generated by the proposed method and show that it is able to mitigate the curse of dimensionality, assuming that the data distribution is supported on a lower-dimensional set. We conduct numerical experiments to validate proposed method and illustrate its applications to conditional sample generation, nonparametric conditional density estimation, prediction uncertainty quantification, bivariate response data, image reconstruction and image generation.
Folding molecular dynamics simulation of T-peptide, a HIV viral entry inhibitor : Structure, dynamics, and comparison with the experimental data
Authors: Ioanna Gkogka, Nicholas M. Glykos
Date: 2021-12-28 00:00:00

Peptide T is a synthetic octapeptide fragment, which corresponds to the region 185-192 of the gp120 HIV coat protein and functions as a viral entry inhibitor. In this work, a folding molecular dynamics simulation of peptide T in a membrane-mimicking (DMSO) solution was performed with the aim of characterizing the peptide's structural and dynamical properties. We show that peptide T is highly flexible and dynamic. The main structural characteristics observed were rapidly interconverting short helical stretches and turns, with a notable preference for the formation of $\beta$-turns. The simulation also indicated that the C-terminal part appears to be more stable than the rest of the peptide, with the most preferred conformation for residues 5-8 being a $\beta$-turn. In order to validate the accuracy of the simulations, we compared our results with the experimental NMR data obtained for the T-peptide in the same solvent. In agreement with the simulation, the NMR data indicated the presence of a preferred structure in solution that was consistent with a $\beta$-turn comprising the four C-terminal residues. An additional comparison between the experimental and simulation-derived chemical shifts also showed a reasonable agreement between experiment and simulation, further validating the simulation-derived structural characterization of the T-peptide.