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Channel equalization is fundamental for mitigating distortions such as frequency-selective fading and inter-symbol interference. Unlike standard supervised learning approaches that require costly retraining or fine-tuning for each new task,…
Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…
Accurate curve forecasting is of vital importance for policy planning, decision making and resource allocation in many engineering and industrial applications. In this paper we establish a theoretical foundation for the optimal short-term…
This work proposes a new a framework for determining robust periodic invariant sets and their associated control laws for constrained uncertain linear systems. Necessary and sufficient conditions for stabilizability by periodic controllers…
We study statistical models for one-dimensional diffusions which are recurrent null. A first parameter in the drift is the principal one, and determines regular varying rates of convergence for the score and the information process. A…
The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient…
An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The…
We prove the existence of periodic tessellations of $\mathbb{R}^N$ minimizing a general nonlocal perimeter functional, defined as the interaction between a set and its complement through a nonnegative kernel, which we assume to be either…
Integrated sensing and communication (ISAC) emerges as an essential technique for overcoming spectrum congestion. However, the performance of traditional ISAC systems with fixed-position-antennas (FPA) is limited due to insufficient spatial…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
We describe a nonlinear kagome lattice with nonlinear dynamics described by Klein-Gordon interactions with a scalar unknown at each node, such as might occur in a nonlinear electrical lattice. We show that the dispersion relation has three…
In recent years, traditional zero-correlation zone (ZCZ) sequences are being studied due to support interference-free quasi-synchronous code division multiple access (QS-CDMA) systems. However, in cognitive radio (CR) network, it is…
Integrated sensing and communication (ISAC) through Zak-transform-based orthogonal time frequency space (Zak-OTFS) modulation is a promising solution for high-mobility scenarios. Realizing accurate bistatic sensing and robust communication…
We consider the problem of finding feasible systems with respect to stochastic constraints when system performance is evaluated through simulation. Our objective is to solve this problem with high computational efficiency and statistical…
We study piecewise-smooth systems with three zones, $\dot{z} = f_i(z)$, $i = 1,2,3,$ whose discontinuity set $\Sigma$ consists either of a pair of parallel lines or a pair of circles tangent to each other internally or externally. Each…
Motivated by a growing list of nontraditional statistical estimation problems of the piecewise kind, this paper provides a survey of known results supplemented with new results for the class of piecewise linear-quadratic programs. These are…
Despite the recent success of large language models (LLMs) in time-series forecasting, most existing methods still adopt a Deep Synchronous Fusion strategy, where dense interactions between textual and temporal features are enforced at…
Linear-threshold networks (LTNs) capture the mesoscale behavior of interacting populations of neurons and are of particular interest to control theorists due to their dynamical richness and relative ease of analysis. The aim of this paper…
Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, e.g., identifiability and asymptotic properties of statistical estimation are still obscure. This paper…
In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…