arXiv preprints from January 1, 2026 through September 22, 2026 — 10:37:28 EST
Recent progress in large language models and multimodal interaction has made it possible to develop AI companions that can have fluent and emotionally expressive conversations. However, many of these systems have problems keeping users satisfied and engaged over long periods. This paper argues that these problems do not come mainly...
Purpose: Myocardium segmentation in echocardiography videos is a challenging task due to low contrast, noise, and anatomical variability. Traditional deep learning models either process frames independently, ignoring temporal information, or rely on memory-based feature propagation, which accumulates error over time. Methods: We...
In this paper we develop a data-driven approach for marking nonblocking supervisory control of discrete-event systems (DES). We consider a setup in which models of DES to be controlled are unknown, but a set of data concerning the behaviors of DES is available. We ask the question: Under what conditions of the available data set can a...
In this paper the Mikhailov model is discretized by means of the Cauchy matrix approach. A pair of discrete Miura transformations are constructed. The discrete Mikhailov model is a coupled system, in which one equation comes from the compatibility of the two Miura transformations, the other is transformed from the discrete negative...
This paper proposes a novel paradigm centered on Artificial Intelligence (AI)-empowered propagation channel prediction to address the limitations of traditional channel modeling. We present a comprehensive framework that deeply integrates heterogeneous environmental data and physical propagation knowledge into AI models for...
This paper provides a quantitative analysis of the rightmost eigenvalue for a chiral non-Hermitian random Dirac matrix in the maximally non-Hermitian regime ($τ=0$). Let $(σ_i)_{1\le i\le n}$ be the eigenvalues with positive real part. We define the normalization constants \[ s_n = \frac{4n(n+v)}{2n+v}, \qquad γ_n = \frac{1}{2}\log...
Nonlocality is a peculiar nature of quanta and it stands as an important quantum resource in application. Yet mere linear property of it, viz. the first order in moment, has been explored through various inequalities. Noticing the vast higher-order regime unexplored, in this study we investigate the higher-order quantum correlations...
Let $M$ be a $d$-dimensional complete Riemannian manifold and let $π: SM \to M$ denote the canonical projection from the unit tangent bundle. We prove that if $E \subset SM$ is a set that invariant under the geodesic flow with Hausdorff dimension $\dim_{\mathcal{H}} E \ge 2(k-1)+1 +β$ for some integer $1 \le k \le d-1$ and some $β\in...
Polynomials and elements over finite fields exhibit closely related algebraic structures, and many properties defined for elements extend naturally to polynomials. The concepts of order and $\mathbb{F}_q$-Order for elements have been extensively studied. In this paper, we investigate several properties of $r$-primitive and $k$-normal...
We introduce A.X K1, a 519B-parameter Mixture-of-Experts (MoE) language model trained from scratch. Our design leverages scaling laws to optimize training configurations and vocabulary size under fixed computational budgets. A.X K1 is pre-trained on a corpus of approximately 10T tokens, curated by a multi-stage data processing...
Ultracompact dwarf galaxies (UCDs) are thought to be remnants of stripped galactic nuclei, among which a handful are known to host a central supermassive black hole (SMBH). As in stripped nuclear star clusters, the SMBHs in UCDs may be fed by stellar winds from old stellar populations, in the absence of substantial gas reservoirs and...
We study surplus division in network constrained bilateral matching markets with transferable utility. We introduce a new solution concept, the credible bargaining solution, which refines stability by requiring that, for each matched pair of buyer and seller, surplus be divided according to the Nash bargaining solution with respect to...
In this paper we extend the notion of $\varphi$-mixing to set-valued random sequences that take values in the family of closed subsets of a Banach space. Several strong laws of large numbers for such $\varphi$-mixing sequences are stated and proved. Illustrative examples show that the hypotheses of the theorems are both natural and sharp.
In two-sampling testing, one observes two independent sequences of independent and identically distributed random variables distributed according to the distributions $P_1$ and $P_2$ and wishes to decide whether $P_1=P_2$ (null hypothesis) or $P_1\neq P_2$ (alternative hypothesis). The Gutman test for this problem compares the...
Large Language Models (LLMs) have been increasingly employed for query expansion. However, their generative nature often undermines performance on complex multi-hop retrieval tasks by introducing irrelevant or noisy information. To address this challenge, we propose DeCoR (Decompose and Compress for Retrieval), a framework grounded in...
Triad magnetometer components change with sensor attitude even when the IGRF total intensity target stays invariant. NavFormer forecasts this invariant target with rotation invariant scalar features and a Canonical SPD module that stabilizes the spectrum of window level second moments of the triads without sign discontinuities. The...
Supervised fine-tuning (SFT) is a fundamental post-training strategy to align Large Language Models (LLMs) with human intent. However, traditional SFT often ignores the one-to-many nature of language by forcing alignment with a single reference answer, leading to the model overfitting to non-core expressions. Although our empirical...
Purpose: The model allocates the system components orders to the suppliers to minimize the parts price and the system construction delay penalties and maximize the system availability during its use. It considers the quantity-based discount and variation of delivery lead time by ordering similar components. The model also reflects the...
We study null controllability for linear heat-type systems in finite dimensions that incorporate both memory and time-delay effects. A strengthened notion of controllability, referred to as delay and memory-type null controllability, is introduced, which requires the state, the memory functional, and the delayed history to vanish at...
In pursuit of a colloidal analogue to quantum density functional theory (DFT) predictions of atomic crystal structures, we report a new, classical DFT that predicts the relative thermodynamic stability of colloidal crystals of hard, convex particle shapes. In contrast to standard classical DFT approaches, our theory maps the hard...
Deploying medical image segmentation models in routine clinical workflows is often constrained by on-premises infrastructure, where computational resources are fixed and cloud-based inference may be restricted by governance and security policies. While high-capacity models achieve strong segmentation accuracy, their computational...
We consider parabolic variational inequalities in a Hilbert space $V$, which have a non-monotone nonlinearity of Navier--Stokes type represented by a bilinear operator $B: V \times V \to V'$ and a monotone type nonlinearity described by a convex, proper, and lower-semicontinuous functional $\varphi : V \to (-\infty, +\infty]$....
Adiabatic invariants are fundamental to plasma physics but are often treated as purely theoretical concepts in undergraduate courses due to the difficulty of experimentally demonstrating them. This paper presents a pedagogical experiment to visualize and quantitatively verify the conservation of the magnetic moment ($μ$) and the...
Cooperative MSR codes are a kind of storage codes which enable optimal-bandwidth repair of any $h\geq2$ node erasures in a cooperative way, while retaining the minimum storage as an $[n,k]$ MDS code. Each code coordinate (node) is assumed to store an array of $\ell$ symbols, where $\ell$ is termed as sub-packetization. Large...
We propose the integral-equation formalism of population dynamics (IEPDYN) to describe the population dynamics of distinct configurational states. According to classical reaction dynamics theory, the probability density associated with a given state obeys the Liouville equation, including influx from and efflux to neighboring states....