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Anthony Sanchez

Publications and source records attributed to Anthony Sanchez.

16 recordsLinked to original sources
arXiv2026

A Tale of Two Calibrators: Comparing Newtonian and Photon Calibration in Advanced LIGO after the Third Observing Run

Precise calibration of LIGO's strain readout plays a vital role in our ability to extract information from gravitational-wave detections. We present a comparative analysis of two independent direct-force calibration methods: the Newtonian Calibrator (NCal) and Photon Calibrator (PCal) systems. Currently, LIGO relies solely on the PCal system as its absolute calibration reference. To facilitate comparison, a series of direct-force injections were performed using the NCal and PCal systems at the LIGO Hanford observatory just after the completion of the third observing run. We compute the ratio of the measured to expected strain amplitudes for every injection. For each injection frequency across a 30 Hz band, the ratios of NCal and PCal differ by $\sim$0.5-1%, demonstrating a small systematic difference between the two systems. This offset highlights the importance of maintaining multiple independent calibration references to validate LIGO's calibration.

gr-qc↗
arXiv2026

Translation Surfaces arising from Right Regular Prisms

We study flat metrics arising from right regular $n$-prisms by viewing them as $n$-differentials and analyzing their associated unfoldings. We show that the unfolding of a right regular $n$-prism is never a lattice surface unless $n=4$, in contrast with the case of Platonic solids. Despite this, we prove that these surfaces admit translation coverings to hyperelliptic surfaces, allowing us to determine their $\mathrm{GL}(2,\mathbb{R})$-orbit closures using the classification of hyperelliptic components of strata. As a consequence, we obtain exact quadratic asymptotics for a certain average of the number of saddle connections on the base surfaces, their unfoldings, and the original prisms, including their Siegel--Veech constants. This provides a natural infinite family of non-lattice surfaces for which orbit closures and counting problems can be computed explicitly.

math.GT↗
arXiv2025

Quantitative finiteness of hyperplanes in hybrid manifolds

We prove a quantitative finiteness theorem for the number of totally geodesic hyperplanes of non-arithmetic hyperbolic $n$-manifolds that arise from a gluing construction of Gromov and Piatetski-Shapiro for $n\ge3$. This extends work of Lindenstrauss-Mohammadi in dimension 3. This follows from effective density theorem for periodic orbits of $\mathrm{SO}(n-1,1)$ acting on quotients of $\mathrm{SO}(n,1)$ by a lattice for $n\ge3$. The effective density result uses a number of a ideas including Margulis functions, a restricted projection theorem, and an effective equidistribution result for measures on the horospherical subgroup that are nearly full dimensional.

math.DS↗
arXiv2023

An arithmetic Kontsevich--Zorich monodromy of a symmetric origami in genus 4

We demonstrate the existence of a certain genus four origami whose Kontsevich--Zorich monodromy is arithmetic in the sense of Sarnak. The surface is interesting because its Veech group is as large as possible and given by $\mathrm{SL}(2,\mathbb Z)$. When compared to other surfaces with Veech group $\mathrm{SL}(2,\mathbb Z)$ such as the Eierlegendre Wollmichsau and the Ornithorynque, an arithmetic Kontsevich--Zorich monodromy is surprising and indicates that there is little relationship between the Veech group and monodromy group of origamis. Additionally, we record the index and congruence level in the ambient symplectic group which gives data on what can appear in genus 4.

math.DS↗
arXiv2023

Effective equidistribution of large dimensional measures on affine invariant submanifolds

The unstable foliation, that locally is given by changing horizontal components of period coordinates, plays an important role in study of translation surfaces, including their deformation theory and in the understanding of horocycle invariant measures. In this article we show that measures of large dimension on the unstable foliation equidistribute in affine invariant submanifolds and give an effective rate. An analogous result in the setting of homogeneous dynamics is crucially used in the effective density and equidistribution results of Lindenstrauss-Mohammadi and Lindenstrauss--Mohammadi--Wang.

math.DS↗
arXiv2022

Kontsevich-Zorich monodromy groups of translation covers of some platonic solids

We compute the Zariski closure of the Kontsevich-Zorich monodromy groups arising from certain square tiled surfaces that are geometrically motivated. Specifically we consider three surfaces that emerge as translation covers of platonic solids and quotients of infinite polyhedra, and show that the Zariski closure of the monodromy group arising from each surface is equal to a power of $\rm{SL}(2, \mathbb{R})$. We prove our results by finding generators for the monodromy groups, using a theorem of Matheus-Yoccoz-Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound"). Moreover, combining our analysis with the Eskin-Kontsevich-Zorich formula, we also compute the Lyapunov spectrum of the Kontsevich-Zorich cocycle for said square-tiled surfaces.

math.DS↗
arXiv2022

An avoidance principle and Margulis functions for expanding translates of unipotent orbits

We prove an avoidance principle for expanding translates of unipotent orbits for some semisimple homogeneous spaces. In addition, we prove a quantitative isolation result of closed orbits and give an upper bound on the number of closed orbits of bounded volume. The proofs of our results rely on the construction of a Margulis function and the theory of finite dimensional representations of semisimple Lie groups.

math.DS↗
arXiv2021

Slope Gap Distributions of Veech Surfaces

The slope gap distribution of a translation surface is a measure of how random the directions of the saddle connections on the surface are. It is known that Veech surfaces, a highly symmetric type of translation surface, have gap distributions that are piecewise real analytic. Beyond that, however, very little is currently known about the general behavior of the slope gap distribution, including the number of points of non-analyticity or the tail. We show that the limiting gap distribution of slopes of saddle connections on a Veech translation surface is always piecewise real-analytic with \emph{finitely} many points of non-analyticity. We do so by taking an explicit parameterization of a Poincar\'{e} section to the horocycle flow on $\text{SL}(2,\mathbb{R})/\text{SL}(X,\omega)$ associated to an arbitrary Veech surface $\text{SL}(X,\omega)$ and establishing a key finiteness result for the first return map under this flow. We use the finiteness result to show that the tail of the slope gap distribution of Veech surfaces always has quadratic decay.

math.DS↗
arXiv2020

MK-SQuIT: Synthesizing Questions using Iterative Template-filling

The aim of this work is to create a framework for synthetically generating question/query pairs with as little human input as possible. These datasets can be used to train machine translation systems to convert natural language questions into queries, a useful tool that could allow for more natural access to database information. Existing methods of dataset generation require human input that scales linearly with the size of the dataset, resulting in small datasets. Aside from a short initial configuration task, no human input is required during the query generation process of our system. We leverage WikiData, a knowledge base of RDF triples, as a source for generating the main content of questions and queries. Using multiple layers of question templating we are able to sidestep some of the most challenging parts of query generation that have been handled by humans in previous methods; humans never have to modify, aggregate, inspect, annotate, or generate any questions or queries at any step in the process. Our system is easily configurable to multiple domains and can be modified to generate queries in natural languages other than English. We also present an example dataset of 110,000 question/query pairs across four WikiData domains. We then present a baseline model that we train using the dataset which shows promise in a commercial QA setting.

cs.CL↗
arXiv2020

Gaps of saddle connection directions for some branched covers of tori

We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the first explicit computations of gap distributions for non-lattice translation surfaces. We show that this distribution has support at 0 and quadratic tail decay. We also construct examples of translation surfaces in any genus $d>1$ that have the same gap distribution as the gap distribution of two identical tori glued along a slit. The second class we consider are twice-marked tori and saddle connections between distinct marked points. These results can be interpreted as the gap distribution of slopes of affine lattices. We obtain our results by translating the question of gap distributions to a dynamical question of return times to a transversal under the horocycle flow on an appropriate moduli space.

math.DS↗
arXiv2018

W-measurable sensitivity of semigroup actions

This paper studies the notion of W-measurable sensitivity in the context of semigroup actions. W-measurable sensitivity is a measurable generalization of sensitive dependence on initial conditions. In 2012, Grigoriev et. al. proved a classification result of conservative ergodic dynamical systems that states all are either W-measurably sensitive or act by isometries with respect to some metric and have refined structure. We generalize this result to a class of semigroup actions. Furthermore, a counterexample is provided that shows W-measurable sensitivity is not preserved under factors. We also consider the restriction of W-measurably sensitive semigroup actions to sub-semigroups and show that the restriction remains W-measurably sensitive when the sub-semigroup is large enough (e.g. when the sub-semigroups are syndetic or thick).

math.DS↗
arXiv2017

Brain Damage and Motor Cortex Impairment in Chronic Obstructive Pulmonary Disease: Implication of Nonrapid Eye Movement Sleep Desaturation

Nonrapid eye movement (NREM) sleep desaturation may cause neuronal damage due to the withdrawal of cerebrovascular reactivity. The current study (1) assessed the prevalence of NREM sleep desaturation in nonhypoxemic patients with chronic obstructive pulmonary disease (COPD) and (2) compared a biological marker of cerebral lesion and neuromuscular function in patients with and without NREM sleep desaturation.

q-bio.TO↗
arXiv2014

Invariant Measures for Hybrid Stochastic Systems

In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as time-homogeneous Markov processes. In particular, we prove the existence of invariant measures for each embedded system and relate the invariant measures for the various systems through the flow. We calculate these invariant measures explicitly in several illustrative examples.

math.DS↗
arXiv2014

Limit and Morse Sets for Deterministic Hybrid Systems

The term "hybrid system" refers to a continuous time dynamical system that undergoes Markovian perturbations at discrete time intervals. In this paper, we find that under the right formulation, a hybrid system can be treated as a dynamical system on a compact space. This allows one to study its limit sets. We examine the Morse decompositions of hybrid systems, find a sufficient condition for the existence of a non-trivial Morse decomposition, and study the Morse sets of such a decomposition. Finally, we consider the case in which the Markovian perturbations are small, showing that trajectories in a hybrid system with small perturbations behave similarly to those of the unperturbed dynamical system.

math.DS↗
arXiv2014

Generic extensions and generic Polynomials for multiplicative groups

Let $\mathcal{A}$ be a finite-dimensional algebra over a finite field $\mathbf{F}_q$ and let $G=\mathcal{A}^\times$ be the multiplicative group of $\mathcal{A}$. In this paper, we construct explicitly a generic Galois $G$-extension $S/R$, where $R$ is a localized polynomial ring over $\mathbf{F}_q$, and an explicit generic polynomial for $G$ in $\dim_{\mathbf{F}_q}(\mathcal{A})$ parameters.

math.AG↗