Research
Research
Research
Research
1,336+ open-access research outputs.
We prove that a class of classical lattice models on $\mathbb{Z}^d$ ($d \geq 2$) with on-site space $\mathbb{N}_0$ exhibits long-range checkerboard order at sufficiently high temperature. The model ha…
The type IIB matrix model has been proposed as a nonperturbative formulation of superstring theory. While numerical simulations of this model are essential for probing nonperturbative effects, such as…
In our work, we show how, for a network of bosonic modes, canonical commutation relations constrain the coefficients relating input and internal modes. Based on these constraints, we derive a lower bo…
Given a pair of finite posets $A \subseteq P$, the function counting integer-valued order preserving extensions of an order preserving map $\lambda : A\rightarrow \mathbb{Z}$ from $A$ to $P$ is given …
Despite the long history of the theory of Bose-Einstein condensation, there exist till nowadays some slippery points that are often misunderstood and result in confusion. The report touches some of th…
Alladi's duality identities (1977) provide a fundamental relation between the smallest and the $k$-th largest prime factors of integers. In this paper, we establish these dualities in the setting of g…
In this paper, we consider integral linear constraints and the dissipation inequality with linear supply rates for certain sets of trajectories confined pointwise in time to a convex cone which belong…
Attention Deficit Hyperactivity Disorder (ADHD) is a highly prevalent neurodevelopmental condition; however, its neurobiological diagnosis remains challenging due to the lack of reliable imaging-based…
The Pareto sum of two-dimensional point sets $P$ and $Q$ in $\mathbb{R}^2$ is defined as the skyline of the points in their Minkowski sum. The problem of efficiently computing the Pareto sum arises fr…
Quantum graphs have been introduced by Duan, Severini, and Winter to describe the zero-error behaviour of quantum channels. Since then, quantum graph theory has become a field of study in its own righ…
The inclusion of a mass-like term for the gluon in Yang-Mills theories quantized in the Landau gauge has proven to be an effective way of reproducing lattice results for gauge-fixed correlation functi…
What if a world simulation model could render not an imagined environment but a city that actually exists? Prior generative world models synthesize visually plausible yet artificial environments by im…
We present a pedagogical and self contained account of the functional formulation of non-Abelian gauge theories, aimed at the construction of a process independent effective charge for Yang--Mills the…
In this paper, we study the global well-posedness of the Boltzmann equation within the $L_{v}^{p}L_{x}^{\infty}$ framework for soft potential models with angular cutoff in a periodic box $\mathbb{T}^3…
For solving constrained (pseudo)-monotone variational inequality, we prove that the upper bound of stepsize $\frac{1}{2L}$ established for the Popov's algorithm and the forward-reflected-backward algo…
We show that the Serreau--Tissier (ST) replica sector can dynamically generate a Gribov--Zwanziger (GZ)--type horizon functional in Yang--Mills (YM) theories. After integrating out the replica superfi…
Hyper-Positive Real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclus…
We consider the ``minimum degree spanning tree'' problem. As input, we receive an undirected, connected graph $G=(V, E)$ with $n$ nodes and $m$ edges, and our task is to find a spanning tree $T$ of $G…
Classical controllability and observability characterise reachability and reconstructibility of the full system state and admit equivalent geometric and eigenvalue-based Popov-Belevitch-Hautus (PBH) t…
Large language models (LLMs) have recently achieved remarkable success in generating rigorous mathematical proofs, with "AI for Math" emerging as a vibrant field of research (Ju et al., 2026). While t…
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