arXiv subjects

Andres Mejia

Publications and source records attributed to Andres Mejia.

5 recordsLinked to original sources

arXiv2026

SPEC CPU: The Next Generation

The march toward developing relevant and robust CPU benchmarks continues with the introduction of SPEC CPU 2026, the next generation suite for measuring processor performance. This paper details the methodology behind its creation, showcasing a process centered on community collaboration and principled development. The suite is built upon a foundation of modern, open-source applications, selected and hardened through a process that emphasizes workload diversity, portability, and software longevity. A key contribution is Rolling-Round-Robin Rate, a novel and standardized approach to running heterogeneous, multiprogrammed workloads that addresses a long-standing gap in benchmarking practice. Additionally, the suite features an expanded set of multithreaded benchmarks and introduces workloads with distinct microarchitectural profiles, reflecting the demands of contemporary software. By detailing our principled approach to benchmark selection, adaptation, and validation, we demonstrate how the SPEC CPU 2026 suite sets the standard for performance evaluation in the next era of computer architecture research and development.

cs.PF↗

arXiv2024

The Generalized Makeev Problem Revisited

Based on a result of Makeev, in 2012 Blagojević and Karasev proposed the following problem: given any positive integers $m$ and $1\leq \ell\leq k$, find the minimum dimension $d=Δ(m;\ell/k)$ such that for any $m$ mass distributions on $\mathbb{R}^d$, there exist $k$ hyperplanes, any $\ell$ of which equipartition each mass. The $\ell=k$ case is a central question in geometric and topological combinatorics which remains open except for few values of $m$ and $k$. For $\ell< k$ and arbitrary $m$, we establish new upper bounds on $Δ(m;\ell/k)$ when (1) $\ell=2$ and $k$ is arbitrary and (2) $\ell=3$ and $k=4$. When $\ell=k-1$ and $m+1$ is a power of two these bounds are nearly optimal and are exponentially smaller than the current best upper bounds when $\ell=k$. Similar remarks apply to our upper bounds when the hyperplanes are prescribed to be pairwise orthogonal. Lastly, we provide transversal extensions of our results along the lines recently established by Frick et al.: given $m$ families of compact convex sets in $\mathbb{R}^d$ such that no $2^\ell$ members of any family are pairwise disjoint, we show that every member of each family is pierced by the union of any $\ell$ of some collection of $k$ hyperplanes.

math.CO↗

arXiv2023

A linearization map for genuine equivariant algebraic $K$-theory

We introduce a version of algebraic $K$-theory for coefficient systems of rings which is valued in genuine $G$-spectra for a finite group $G$. We use this construction to build a genuine $G$-spectrum $K_G(\mathbb{Z}[\underline{\pi_1(X)}])$ associated to a $G$-space $X$, which provides a home for equivariant versions of classical invariants like the Wall finiteness obstruction and Whitehead torsion. We provide a comparison between our $K$-theory spectrum and the equivariant $A$-theory of Malkiewich--Merling via a genuine equivariant linearization map.

math.AT↗

arXiv2018

Admissibility and the $C_2$ Spider

A tensor category is multiplicity-free if for any objects $A,B,C$ we have that $\mathrm{Hom}(A\otimes B\otimes C,\mathbb{C})$ is either $0$ or $1$ dimensional. It is known that $Rep^{uni}(U_q(\mathfrak{sp}(4)))$ is not multiplicty-free. We find a full subcategory of $Rep^{uni}(U_q(\mathfrak{sp}(4)))$ which is multiplicty-free. A description of the dimension of these $\mathrm{Hom}$ spaces is given for this subcategory, including when $q$ is a root of unity. The methods used arise from the description, given by Kuperberg, of $Rep^{uni}(U_q(\mathfrak{sp}(4)))$ as a spider. The main tool is the recursive definition of clasps given by Kim. In particular, we provide an appropriate notion of admissibility when looking at the $\mathrm{Sp}(4)_k$ ribbon graph invariants with restricted edge labels.

math.QA↗

arXiv2016

Classically Integral Quadratic Forms Excepting at Most Two Values

Let $S \subseteq \mathbb{N}$ be finite. Is there a positive definite quadratic form that fails to represent only those elements in $S$? For $S = \emptyset$, this was solved (for classically integral forms) by the $15$-Theorem of Conway-Schneeberger in the early 1990s and (for all integral forms) by the $290$-Theorem of Bhargava-Hanke in the mid-2000s. In 1938 Halmos attempted to list all weighted sums of four squares that failed to represent $S=\{m\}$; of his $88$ candidates, he could provide complete justifications for all but one. In the same spirit, we ask, "for which $S = \{m, n\}$ does there exist a quadratic form excepting only the elements of $S$?" Extending the techniques of Bhargava and Hanke, we answer this question for quaternary forms. In the process, we prove what Halmos could not; namely, that $x^2+2y^2+7z^2+13w^2$ represents all positive integers except $5$. We develop new strategies to handle forms of higher dimensions, yielding an enumeration of and proofs for the $73$ possible pairs that a classically integral positive definite quadratic form may except.

math.NT↗