arXiv subjects

Matthew Davis

Publications and source records attributed to Matthew Davis.

6 recordsLinked to original sources

arXiv2026

Relating tournaments and permutations with xrays

In a 2005 paper, Bebeacua et al. investigated the xrays of permutations, and conjectured a correspondence between binary xrays and score sequences of tournaments. In 2014, Brualdi and Fritscher conjectured a possible correspondence between score sequences of $2$-tournaments and (not necessarily binary) xrays of permutations. In this paper, we first introduce the concept of a transitive tournament decomposition of $k$-tournaments, then present a construction by which a permutation is used to build $1$- and $2$-tournaments whose score sequences agree with the xray of the permutation in the manner outlined by Bebeacua et al. and Brualdi and Fritscher. We close with an investigation of xrays with restricted terms, including binary xrays, and show that the recent conjectures by Bebeacua et al. and Brualdi and Fritscher are special cases of a more general statement, which we conjecture and for which we provide supporting evidence.

math.CO↗

arXiv2025

Automatically Detecting Heterogeneous Bugs in High-Performance Computing Scientific Software

Scientific advancements rely on high-performance computing (HPC) applications that model real-world phenomena through simulations. These applications process vast amounts of data on specialized accelerators (eg., GPUs) using special libraries. Heterogeneous bugs occur in these applications when managing data movement across different platforms, such as CPUs and GPUs, leading to divergent behavior when using heterogeneous platforms compared to using only CPUs. Existing software testing techniques often fail to detect such bugs because either they do not account for platform-specific characteristics or target specific platforms. To address this problem, we present HeteroBugDetect, an automated approach to detect platform-dependent heterogeneous bugs in HPC scientific applications. HeteroBugDetect combines natural-language processing, off-target testing, custom fuzzing, and differential testing to provide an end-to-end solution for detecting platform-specific bugs in scientific applications. We evaluate HeteroBugDetect on LAMMPS, a molecular dynamics simulator, where it detected multiple heterogeneous bugs, enhancing its reliability across diverse HPC environments.

cs.SE↗

arXiv2024

A Bijection Between All Shi Regions and Core Partitions

We extend the bijection of Fishel-Vazirani on dominant regions of the $m$-Shi arrangement. Our map puts the set of all minimal chambers of the $m$-Shi arrangement of Type $A_{n}$ in bijection with a certain set of (equivalence classes of) $n$-core partitions. As a step to our proof, we give a potentially interesting classification of the alcoves in the $S_{n}$-orbit of an $m$-minimal alcove which are themselves $m$-minimal.

math.CO↗

arXiv2017

Optical Network Virtualisation using Multi-technology Monitoring and SDN-enabled Optical Transceiver

We introduce the real-time multi-technology transport layer monitoring to facilitate the coordinated virtualisation of optical and Ethernet networks supported by optical virtualise-able transceivers (V-BVT). A monitoring and network resource configuration scheme is proposed to include the hardware monitoring in both Ethernet and Optical layers. The scheme depicts the data and control interactions among multiple network layers under the software defined network (SDN) background, as well as the application that analyses the monitored data obtained from the database. We also present a re-configuration algorithm to adaptively modify the composition of virtual optical networks based on two criteria. The proposed monitoring scheme is experimentally demonstrated with OpenFlow (OF) extensions for a holistic (re-)configuration across both layers in Ethernet switches and V-BVTs.

cs.NI↗

arXiv2017

Insular microbiogeography

The diversity revealed by large scale genomics in microbiology is calling into question long held beliefs about genome stability, evolutionary rate, even the definition of a species. MacArthur and Wilson's theory of insular biogeography provides an explanation for the diversity of macroscopic animal and plant species as a consequence of the associated hierarchical web of species interdependence. We report a large scale study of microbial diversity that reveals that the cumulative number of genes discovered increases with the number of genomes studied as a simple power law. This result is demonstrated for three different genera comparing over 15,000 isolates. We show that this power law is formally related to the MacArthur-Wilson exponent, suggesting the emerging diversity of microbial genotypes arises because the scale independent behavior first reported by MacArthur and Wilson extends down to the scale of microbes and their genes. Assessing the depth of available whole genome sequences implies a dynamically changing core genome, suggesting that traditional taxonomic classifications should be replaced with a quasispecies model that captures the diversity and dynamic exchange of genes. We report Species population "clouds" in a defined microbiome, with scale invariance extending down to the level of single-nucleotide polymorphisms (SNPs).

q-bio.GN↗

arXiv2007

Rotator and extender ferroelectrics: Importance of the shear coefficient to the piezoelectric properties of domain-engineered crystals and ceramics

The importance of a high shear coefficient d15 (or d24) to the piezoelectric properties of domain-engineered and polycrystalline ferroelectrics is discussed. The extent of polarization rotation, as a mechanism of piezoelectric response, is directly correlated to the shear coefficient. The terms "rotator" and "extender" are introduced to distinguish the contrasting behaviors of crystals such as 4mm BaTiO3 and PbTiO3. In "rotator" ferroelectrics, where d15 is high relative to the longitudinal coefficient d33, polarization rotation is the dominant mechanism of piezoelectric response; the maximum longitudinal piezoelectric response is found away from the polar axis. In "extender" ferroelectrics, d15 is low and the collinear effect dominates; the maximum piezoelectric response is found along the polar axis. A variety of 3m, mm2 and 4mm ferroelectrics, with various crystal structures based on oxygen octahedra, are classified in this way. It is shown that the largest piezoelectric anisotropies d15/d33 are always found in 3m crystals; this is a result of the intrinsic electrostrictive anisotropy of the constituent oxygen octahedra. Finally, for a given symmetry, the piezoelectric anisotropy increases close to ferroelectric-ferroelectric phase transitions; this includes morphotropic phase boundaries and temperature induced polymorphic transitions.

cond-mat.mtrl-sci↗