All posts under category "Research"
Many problems in Computer Vision can be reduced to either working around a known transform, or given a model for the transform computing the inverse problem of the transform itself. We will look at two ways of working with the matrix A and see how
In this paper, we study large-time asymptotics for heat and fractional heat equations in two discrete settings: the full lattice (mathbb Z^d) and finite connected subgraphs with Dirichlet boundary condition. These results provide a unified discrete t
Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While existing approa
Estimating consumer preferences is central to many problems in economics and marketing. This paper develops a flexible framework for learning individual preferences from partial ranking information by interpreting observed rankings as collections of
The acoustic cues used by humans and other animals to localise sounds are subtle, and change during and after development. This means that we need to constantly relearn or recalibrate the auditory spatial map throughout our lifetimes. This is often t
Nonlinear system identificationhas proven to be effective in obtaining accurate models from data for complex real-world systems. In particular, recent encoder-based methods with artificial neural network state-space (ANN-SS) models have achieved stat
Probabilistic modeling is an effective tool for evaluating team performance and predicting outcomes in sports. However, an important question that hasn't been fully explored is whether these models can reliably reflect actual performance while assign
Offline safe reinforcement learning (RL) is increasingly important for cyber-physical systems (CPS), where safety violations during training are unacceptable and only pre-collected data are available. Existing offline safe RL methods typically balanc
Feedback delays are inevitable in real-world multi-agent learning. They are known to severely degrade performance, and the convergence rate under delayed feedback is still unclear, even for bilinear games. This paper derives the rate of linear conver
We consider a tagged particle in mean field interaction with a free gas of density N at equilibrium. In dimensions dgeq4 , we prove the convergence of its trajectory, as N goes to infinity, to the one of a diffusion process associated with the linea
We consider the general problem of learning a predictor that satisfies multiple objectives of interest simultaneously, a broad framework that captures a range of specific learning goals including calibration, regret, and multiaccuracy. We work in an
For a broad family of discriminative models that includes autoregressive language models, identifiability results imply that if two models induce the same conditional distributions, then their internal representations agree up to an invertible linear
This research was to design a 2.4 GHz class E Power Amplifier (PA) for health care, with 0.18um Semiconductor Manufacturing International Corporation CMOS technology by using Cadence software. And also RF switch was designed at cadence software with
In two-phase multiwave sampling, inexpensive measurements are collected on a large sample and expensive, more informative measurements are adaptively obtained on subsets of units across multiple waves. Adaptively collecting the expensive measurements
Dubé introduced cone decompositions and their Macaulay constants and used them to obtain an upper bound on the degrees of the generators in a Gröbner basis of an ideal. Liang extended the theory to submodules of a free module. In this paper, Macaulay
In the age of digital epidemiology, epidemiologists are faced by an increasing amount of data of growing complexity and dimensionality. Machine learning is a set of powerful tools that can help to analyze such enormous amounts of data. This chapter l
This paper introduces a novel, open-source MARL simulation framework for studying implicit cooperation in LEMs, modeled as a decentralized partially observable Markov decision process and implemented as a Gymnasium environment for MARL. Our framework
On exposure to 1,2-propanediol (1,2-PD), Salmonella enterica serovar Typhimurium LT2 produces 1,2-PD utilization (Pdu) microcompartments (MCPs), nanoscale protein-bound shells that encapsulate metabolic enzymes. MCPs serve as a bioengineering platfor
Direction-sensitive direct dark matter search experiments have been conducted using gaseous detectors. In spite of the long history of the study on the energy deposition of charged particles in materials, a full agreement between the measured results
Epidemic and pandemic preparedness with rapid outbreak response rely on timely, trustworthy evidence. Mathematical models are crucial for supporting timely and reliable evidence generation for public health decision-making with models spanning approa
Large language models (LLMs) face inherent limitations in memory, including restricted context windows, long-term knowledge forgetting, redundant information accumulation, and hallucination generation. These issues severely constrain sustained dialog
Computation in biological systems is fundamentally energy-constrained, yet standard theories of computation treat energy as freely available. Here, we argue that variational free energy minimization under a Poisson assumption offers a principled path
Free-space optical communications with moving targets, such as satellite terminals, demand ultrafast wavefront sensing and correction. This is typically addressed using a Shack-Hartmann sensor, which pairs a high-speed camera with a lenslet array, bu
In this paper, we analyze a specific class of missing not at random (MNAR) assumptions called tree graphs, extending upon the work of pattern graphs. We build off previous work by introducing the idea of a conjugate odds family in which certain param
Generative models derived from large protein sequence alignments define complex fitness landscapes, but their utility for accurately modeling non-equilibrium evolutionary dynamics remains unclear. In this work, we perform a rigorous comparative analy
This paper deals with temporal and archive object-oriented data warehouse modelling and querying. In a first step, we define a data model describing warehouses as central repositories of complex and temporal data extracted from one information source
Deep generative modeling to stochastically design small molecules is an emerging technology for accelerating drug discovery and development. However, one major issue in molecular generative models is their lower frequency of drug-like compounds. To r
In this paper, we investigate synchronization in a small-world network of coupled nonlinear oscillators. This network is constructed by introducing random shortcuts in a nearest-neighbors ring. The local stability of the synchronous state is closely
We study nonlinear reactive transport in a layered porous medium separated by an varepsilon -thin, highly heterogeneous fracture whose aperture and obstacle pattern vary periodically. Species transport in the bulk is governed by parabolic reaction--
Synthetic aperture radar (SAR) is a tomographic sensor that measures 2D slices of the 3D spatial Fourier transform of the scene. In many operational scenarios, the measured set of 2D slices does not fill the 3D space in the Fourier domain, resulting
In this paper, a new approach is presented to determine common eigenvalues of two matrices. It is based on Gerschgorin theorem and Bisection method. The proposed approach is simple and can be useful in image processing and noise estimation.
Radially symmetric non-BPS 't Hooft-Polyakov monopoles and dyons are constructed as resurgent transseries: infinite sums of exponentially decaying terms, each multiplied by a factorially divergent fluctuation factor. All higher exponential terms are
Functional inequalities such as the Poincaré and log-Sobolev inequalities quantify convergence to equilibrium in continuous-time Markov chains by linking generator properties to variance and entropy decay. However, many applications, including multis
A curve C defined over mathbb Q is modular of level N if there exists a non-constant morphism from X_1(N) onto C defined over mathbb Q for some positive integer N . We provide a sufficient and necessary condition for the existence of a m
Herd immunity is shaped not only by the infection capacity of a spreading epidemic or the contact structure of the hosting population, but also by how and under what circumstances individuals acquire immunity. Immunization strategies may interact wit
We study the spectrum of high frequency radiation emerging from mildly dissipative photospheres of long-duration gamma-ray burst outflows. Building on the results of recent numerical investigations, we assume that electrons are heated impulsively to
Decentralized air traffic management requires coordination among self-interested stakeholders operating under shared safety and capacity constraints, where conventional centralized or implicitly cooperative models do not adequately capture this setti
We propose nonparametric identification and semiparametric estimation of joint potential outcome distributions in the presence of confounding. First, in settings with observed confounding, we derive tighter, covariate-informed bounds on the joint dis
This paper proposes a nonplanar model predictive control (MPC) framework for autonomous vehicles operating on nonplanar terrain. To approximate complex vehicle dynamics in such environments, we develop a geometry-aware modeling approach that learns a
Block-chain world is very dynamic and there is need for strong governance and underlying technology architecture to be robust to face challenges. This paper considers Ethereum, a leading block chain. We deep dive into the nature of this block chain,
We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by the Schrödi
Integrating artificial intelligence (AI) into wireless channel modeling requires large, accurate, and physically consistent datasets derived from real measurements. Such datasets are essential for training and validating models that learn spatio-temp
Epilepsy affects over 50 million people worldwide, and one-third of patients suffer drug-resistant seizures where surgery offers the best chance of seizure freedom. Accurate localization of the epileptogenic zone (EZ) relies on intracranial EEG (iEEG
This paper establishes a categorical equivalence between the category mathbb{COL} of complete orthomodular lattices and the category mathscr{T}mathbb{ODA} of mathscr{T} -based orthomodular dynamic algebras. Complete orthomodular lattices serve a
Let {ρ_λ:G_Krightarrow GL_n(overline E_λ)} be a semisimple E-rational compatible system of a number field K. In a first step, building upon the theory of pseudocharacters [Ro96],[Ch14], we attach to each ρ_λ an algebraic monodromy group G_λ def
Let mathcal{E} be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class mathcal{E} is closed under taking idempotent quotients, idempotent
We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to the minimi
Let P be a set of n points in the plane, not all on a line, each colored emph{red} or emph{blue}. The classical Motzkin--Rabin theorem guarantees the existence of a emph{monochromatic} line. Motivated by the seminal work of Green and Tao (2013) o
Generalized Sliced Inverse Regression (GSIR) is one of the most important methods for nonlinear sufficient dimension reduction. As shown in Li and Song (2017), it enjoys a convergence rate that is independent of the dimension of the predictor, thus a
We derive the approximate pressure profiles, density profiles, and temperature profiles of an atmosphere, also called barometric formulas. Our variant of a derivation goes beyond the common standard exercise of a thermodynamics lecture, where commonl
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