arXiv subjects

Jerry Zhang

Publications and source records attributed to Jerry Zhang.

10 recordsLinked to original sources

arXiv2026

Asymptotics of the Average Stack-Sorting Depth

Let $\mathcal{D}_n$ denote the average number of passes of the stack-sorting map $s$ required to sort a permutation in $S_n$. We use the recently introduced framework of stack-sorting diagrams and tableaux to prove that the limit $\lim_{n\to\infty}\mathcal{D}_n/n$ exists. This resolves a longstanding conjecture of West originally proposed in $1990$. As a consequence, we also provide a monotonically increasing sequence that converges to $\lim_{n\to\infty}\mathcal{D}_n/n$, improving upon Defant's lower bound of $\lambda\approx 0.62433$.

math.CO↗

arXiv2026

ExecuTorch -- A Unified PyTorch Solution to Run AI Models On-Device

Local execution of AI on edge devices is important for low latency and offline operation. However, deploying models on diverse hardware remains fragmented, often requiring model conversion or complete reimplementation outside the PyTorch ecosystem where the model was originally authored. We introduce ExecuTorch, a unified PyTorch-native deployment framework for edge AI. ExecuTorch enables seamless deployment of machine learning models across heterogeneous compute environments. It scales from embedded microcontrollers to complex system-on-chips (SoCs) with dedicated accelerators, powering devices ranging from wearables and smartphones to large compute clusters. ExecuTorch preserves PyTorch semantics while allowing customization, support for optimizations like quantization, and pluggable execution "backends". These features together enable fast experimentation, allowing researchers to validate deployment behavior entirely within PyTorch, bridging the gap between research and production.

cs.LG↗

arXiv2026

Polynomial Time Enumeration of t-Stack-Sortable Permutations Ending in Their Least Entry

We study the behavior of West's stack-sorting map $s$ on permutations whose last entry is also their least. Let $S_{n}':=\{\pi0\mid \pi\in S_n\}$ where $\pi0$ denotes the concatenation of $\pi$ and $0$. For each permutation $\pi\in S_n'$, we introduce a new combinatorial object known as the stack-sorting tableau $T_{\pi}$, which ultimately serves as the key ingredient in the first polynomial time algorithm for counting the number of $t$-stack-sortable permutations in $S_n'$. We then establish a precise relationship between the behavior of $s$ on $S_{n}'$ and on $S_{n}$.

math.CO↗

arXiv2026

Environment-in-the-Loop: Rethinking Code Migration with LLM-based Agents

Modern software systems continuously undergo code upgrades to enhance functionality, security, and performance, and Large Language Models (LLMs) have demonstrated remarkable capabilities in code migration tasks. However, while research on automated code migration which including refactoring, API adaptation, and dependency updates has advanced rapidly, the exploration of the automated environment interaction that must accompany it remains relatively scarce. In practice, code and its environment are intricately intertwined. Relying solely on static analysis of the environment leads to an inadequate understanding of the target setting, prolongs feedback cycles, and consequently causes significant rework and project delays, thereby reducing overall efficiency. We contend that successful software evolution demands a holistic perspective that integrates both code and environment migration. To understand the current landscape and challenges, we first provide an overview of the status of automated environment construction. We then propose a novel framework paradigm that tightly integrates automated environment setup with the code migration workflow. Finally, we explore the challenges and future directions for automated environment interaction within the code migration domain. Our findings emphasize that without automated environment interaction, the automation of code migration is only half complete.

cs.SE↗

arXiv2025

Evolution of Adaptive Force Chains in Reconfigurable Granular Metamaterials

Under an externally applied load, granular packings form force chains that depend on the contact network and moduli of the grains. In this work, we investigate packings of variable modulus (VM) particles, where we can direct force chains by changing the Young's modulus of individual particles within the packing on demand. Each VM particle is made of a silicone shell that encapsulates a core made of a low-melting-point metallic alloy (Field's metal). By sending an electric current through a co-located copper heater, the Field's metal internal to each particle can be melted via Joule heating, which softens the particle. As the particle cools to room temperature, the alloy solidifies and the particle recovers its original modulus. To optimize the mechanical response of granular packings containing both soft and stiff particles, we employ an evolutionary algorithm coupled with discrete element method simulations to predict the patterns of particle moduli that will yield specific force outputs on the assembly boundaries. The predicted patterns of particle moduli from the simulations were realized in experiments using 2D assemblies of VM particles and the force outputs on the assembly boundaries were measured using photoelastic techniques. These studies represent a step towards making robotic granular metamaterials that can dynamically adapt their mechanical properties in response to different environmental conditions or perform specific tasks on demand.

cond-mat.soft↗

arXiv2024

Demazure product and hopping in type D

The Demazure product, also called the 0-Hecke product, is an associative operation on Coxeter groups with interesting properties and applications. In (Li et al 2024) it was shown that the Demazure product of two permutations can be described purely combinatorially: using only their one-line notation and not relying on reduced words. In this paper, we extend this to type D Coxeter groups.

math.CO↗

arXiv2023

Tessellated granular metamaterials with tunable elastic moduli

Most granular packings possess shear moduli ($G$) that increase with the applied external pressure, and bulk moduli ($B$) that increase or remain constant with pressure. This paper presents "tessellated" granular metamaterials for which both $G$ and the ratio $G/B$ decrease with increasing pressure. The granular metamaterials are made from flexible tessellations forming a ring of closed cells, each containing a small number of solid particles. For under-constrained tessellations, the dominant contributions to $G$ and $B$ are the particle-particle and particle-cell interactions. With specific particle configurations in the cells, we limit the number of possible particle rearrangements to achieve decreasing $G$ as we increase the pressure difference between the inside and outside of the tessellation, leading to $G/B \ll 1$ at large pressures. We further study tessellated granular metamaterials with cells containing a single particle and many particles to determine the variables that control the mechanical response of particle-filled tessellations as a function of pressure.

cond-mat.soft↗

arXiv2023

Designing the pressure-dependent shear modulus using tessellated granular metamaterials

Jammed packings of granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus $\left\langle G \right\rangle$ increases as a power-law in pressure $p$ for static packings of soft spherical particles that can rearrange during compression. We seek to design granular materials with shear moduli that can either increase {\it or} decrease with pressure without particle rearrangements even in the large-system limit. To do this, we construct {\it tessellated} granular metamaterials by joining multiple particle-filled cells together. We focus on cells that contain a small number of bidisperse disks in two dimensions. We first study the mechanical properties of individual disk-filled cells with three types of boundaries: periodic boundary conditions (PBC), fixed-length walls (FXW), and flexible walls (FLW). Hypostatic jammed packings are found for cells with FLW, but not in cells with PBC and FXW, and they are stabilized by quartic modes of the dynamical matrix. The shear modulus of a single cell depends linearly on $p$. We find that the slope of the shear modulus with pressure, $\lambda_c < 0$ for all packings in single cells with PBC where the number of particles per cell $N \ge 6$. In contrast, single cells with FXW and FLW can possess $\lambda_c > 0$, as well as $\lambda_c < 0$, for $N \le 16$. We show that we can force the mechanical properties of multi-cell granular metamaterials to possess those of single cells by constraining the endpoints of the outer walls and enforcing an affine shear response. These studies demonstrate that tessellated granular metamaterials provide a novel platform for the design of soft materials with specified mechanical properties.

cond-mat.soft↗

arXiv2023

Adaptive Dynamic Global Illumination

We present an adaptive extension of probe based global illumination solution that enhances the response to dynamic changes in the scene while while also enabling an order of magnitude increase in probe count. Our adaptive sampling strategy carefully places samples in regions where we detect time varying changes in radiosity either due to a change in lighting, geometry or both. Even with large number of probes, our technique robustly updates the irradiance and visibility cache to reflect the most up to date changes without stalling the overall algorithm. Our bandwidth aware approach is largely an improvement over the original \textit{Dynamic Diffuse Global Illumination} while also remaining orthogonal to the recent advancements in the technique.

cs.GR↗

arXiv2014

Immersive and Collaborative Data Visualization Using Virtual Reality Platforms

Effective data visualization is a key part of the discovery process in the era of big data. It is the bridge between the quantitative content of the data and human intuition, and thus an essential component of the scientific path from data into knowledge and understanding. Visualization is also essential in the data mining process, directing the choice of the applicable algorithms, and in helping to identify and remove bad data from the analysis. However, a high complexity or a high dimensionality of modern data sets represents a critical obstacle. How do we visualize interesting structures and patterns that may exist in hyper-dimensional data spaces? A better understanding of how we can perceive and interact with multi dimensional information poses some deep questions in the field of cognition technology and human computer interaction. To this effect, we are exploring the use of immersive virtual reality platforms for scientific data visualization, both as software and inexpensive commodity hardware. These potentially powerful and innovative tools for multi dimensional data visualization can also provide an easy and natural path to a collaborative data visualization and exploration, where scientists can interact with their data and their colleagues in the same visual space. Immersion provides benefits beyond the traditional desktop visualization tools: it leads to a demonstrably better perception of a datascape geometry, more intuitive data understanding, and a better retention of the perceived relationships in the data.

cs.HC↗