arXiv subjects

Wenlong Jiang

Publications and source records attributed to Wenlong Jiang.

5 recordsLinked to original sources

arXiv2026

An AFLT-type generalization of the $q$-Baker--Forrester ex-conjecture

The Habsieger--Kadell $q$-Morris constant term identity, which is equivalent to the famous $q$-Selberg integral, has been generalized in numerous ways since the 1980s. Among these, there are two important generalizations: (i) the $q$-Baker--Forrester ex-conjecture, which was conjectured by Baker and Forrester in 1998 and proved by K\'{a}rolyi, Nagy, Petrov and Volkov in 2015; (ii) the AFLT-type $q$-Morris identity (equivalently, the AFLT-type $q$-Selberg integral), which was obtained by Albion, Rains and Warnaar in 2021, as a $q$-analog of the result of Alba, Fateev, Litvinov and Tarnopolskiy (AFLT). In this paper, by the Gessel--Xin method and the Macdonald polynomials with prescribed symmetry, we unify these two generalizations.

math.CO↗

arXiv2026

A generalization of Kadell's orthogonality ex-conjecture

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson constant term identity. The non-zero part of Kadell's conjecture is a constant term identity indexed by a weak composition $v$. This conjecture was first proved by K\'{a}rolyi, Lascoux and Warnaar in 2015. They further formulated a closed-form expression for the above constant term when all parts of the composition $v$ are distinct. In 2021, Zhou obtained a recursion for this constant term for an arbitrary composition $v$. In this paper, by categorizing the variables into two parts, we generalize Zhou's result.

math.CO↗

arXiv2025

Simultaneous estimation of connectivity and dimensionality in samples of networks

An overarching objective in contemporary statistical network analysis is extracting salient information from datasets consisting of multiple networks. To date, considerable attention has been devoted to node and network clustering, while comparatively less attention has been devoted to downstream connectivity estimation and parsimonious embedding dimension selection. Given a sample of potentially heterogeneous networks, this paper proposes a method to simultaneously estimate a latent matrix of connectivity probabilities and its embedding dimensionality or rank after first pre-estimating the number of communities and the node community memberships. The method is formulated as a convex optimization problem and solved using an alternating direction method of multipliers algorithm. We establish estimation error bounds under the Frobenius norm and nuclear norm for settings in which observable networks have blockmodel structure, even when node memberships are imperfectly recovered. When perfect membership recovery is possible and dimensionality is much smaller than the number of communities, the proposed method outperforms conventional averaging-based methods for estimating connectivity and dimensionality. Numerical studies empirically demonstrate the accuracy of our method across various scenarios. Additionally, analysis of a primate brain dataset demonstrates that posited connectivity is not necessarily full rank in practice, illustrating the need for flexible methodology.

stat.ME↗

arXiv2025

Lost-in-Distance: Impact of Contextual Proximity on LLM Performance in Graph Tasks

Despite significant advancements, Large Language Models (LLMs) exhibit blind spots that impair their ability to retrieve and process relevant contextual data effectively. We demonstrate that LLM performance in graph tasks with complexities beyond the "needle-in-a-haystack" scenario-where solving the problem requires cross-referencing and reasoning across multiple subproblems jointly-is influenced by the proximity of relevant information within the context, a phenomenon we term "lost-in-distance". We examine two fundamental graph tasks: identifying common connections between two nodes and assessing similarity among three nodes, and show that the model's performance in these tasks significantly depends on the relative positioning of common edges. We evaluate three publicly available LLMs using various graph encoding techniques that represent graph structures for LLM input. We propose a formulation for the lost-in-distance phenomenon and demonstrate that lost-in-distance and lost-in-the middle phenomenas occur independently. Results indicate that model accuracy can decline by up to 6x as the distance between node connections increases, independent of graph encoding and model size.

cs.AI↗

arXiv2024

Two characteristic constants of the supercooled liquid transitions of amorphous substances

Supercooled liquid state is a particularly interesting state in that it exhibits several unusual physical properties. To illustrate, the liquid displays a single peak relaxation frequency at high temperatures, which splits into $α$ relaxation and $β$ relaxation in the moderately supercooled regime, with relaxation a disappearing at the glass transition temperature. The mechanism underlying these unusual physical properties of liquids has always been one of the important research topics in condensed matter. Here, a new mechanism is proposed. A distinctive physical state is built, and its most salient feature is that its independent variables are difficult or impossible to measure. Theoretical calculations indicate that there exist two sets of measurable variables in this physical state that cannot be measure exactly simultaneously. Moreover, it is easy to reach an erroneous conclusion, namely that ``a system in this physical state is in a superposition of some real states, until it is measured''. Further theoretical calculations demonstrate that there are two new transitions and that $\mathrm{e}^{3}$ and $2\mathrm{e}^{3}$ are characteristic values of these two transitions, respectively, where $\mathrm{e}$ is Euler's number. Considerable experimental data shows that the characteristic value of glass transition appears to be concentrated near $2\mathrm{e}^{3}$ and the characteristic value of another transition (for example, the splitting of relaxation peak) appears to be concentrated near $\mathrm{e}^{3}$.

cond-mat.soft↗