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We establish two structural majorization relations, which we call precursors, underlying the properties of supermodularity and subadditivity on the lattice induced by majorization. These are precursors in that they immediately imply that all sums of concave fu

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their statistical efficiency

We prove a list recovery guarantee for random low-rate linear codes over sufficiently large prime fields. For fixed dimension $d$, error fraction $α$, and accuracy parameter $\varepsilon$, a random $d$-dimensional linear code $C \subseteq \mathbb{F}_p^n$ is, w

We study estimation in the low signal-to-noise ratio (SNR) regime for a broad class of Gaussian latent-variable models, including Gaussian mixtures and orbit recovery problems. We show that, in this regime, the generalized method-of-moments (GMoM) matches the

Superimposed pilot (SIP) transmission improves spectral efficiency by eliminating the dedicated pilot overhead required in orthogonal pilot (OP)-based schemes. However, SIP suffers from severe pilot-data coupling, which leads to a critical performance-complexi

Integrated sensing, communication, and computation (ISCC) provides a promising framework for indoor human-centric applications. In these applications, short-term human pose prediction facilitates continuous human tracking and resource allocation in advance. In

This paper investigates a multi-user indoor integrated sensing and communication (ISAC) system operating in the terahertz (THz) band, designed for adaptive communication based on gesture recognition. Leveraging gesture tracking through an extended Kalman filte

Contrastive learning is effective for aligning paired views or modalities, but alignment beyond two modalities remains non-trivial and comparatively underexplored. Pairwise CLIP-style losses decompose multi-modal alignment into independent two-way comparisons

We introduce the \emph{Topological Stability Index} (TSI), a variance-based scalar measure for persistence barcodes that quantifies the dispersion of persistence lifetimes. Unlike persistent entropy, which depends only on normalized weights, the TSI captures a

In radar sensing, the self-ambiguity function of the probing waveform plays a crucial role in the resolvability and detection of multiple targets. In the recent Zak-OTFS based radar literature, Gaussian pulse shaping filter has been considered, and it has been

High Altitude Platform Stations (HAPS) have emerged as a promising enabler for next-generation wireless networks, offering ubiquitous connectivity to ground users. Operating either in standalone mode or in integration with terrestrial networks, HAPS can signif

Algebraic representations of time series are symbolic representations whose symbols belong to a finite group. Precisely, the framework of the present paper is the analysis of coupled time series in algebraic representations and, more generally, group-valued ti