arXiv subjects

Christopher Perez

Publications and source records attributed to Christopher Perez.

8 recordsLinked to original sources

arXiv2026

Theoretical Foundations of Principal Manifold Estimation with Non-Euclidean Templates

We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with general, potentially non-Euclidean topology, which can be inferred using tools from topological data analysis. Using the theory of Sobolev spaces on Riemannian manifolds, we establish that the proposed principal manifolds are well defined, prove convergence of the iterative algorithm used to compute them, and show consistency of the finite-sample estimator. Furthermore, we introduce a novel method for selecting the complexity level of a fitted manifold, which addresses the shortcomings of the classical fitting-error criterion. We also provide a detailed geometric interpretation of the penalty term in our framework. In addition to the theoretical developments, we present extensive numerical experiments supporting our results. This article provides theoretical foundations for approaches that have been used in applications such as robotics. More importantly, it extends these approaches to general topological settings with potential applications across a broad range of disciplines, including neuroimaging and shape data analysis.

math.ST↗

arXiv2025

Resolving the Electron Plume within a Scanning Electron Microscope

Scanning electron microscopy (SEM), a century-old technique, is today a ubiquitous method of imaging the surface of nanostructures. However, most SEM detectors simply count the number of secondary electrons from a material of interest, and thereby overlook the rich material information contained within them. Here, by simple modifications to a standard SEM tool, we resolve the momentum and energy information of secondary electrons by directly imaging the electron plume generated by the electron beam of the SEM. Leveraging these spectroscopic imaging capabilities, our technique is able to image lateral electric fields across a prototypical silicon p-n junctions and to distinguish differently doped regions, even when buried beyond depths typically accessible by SEM. Intriguingly, the sub-surface sensitivity of this technique reveals unexpectedly strong surface band bending within nominally passivated semiconductor structures, providing useful insights for complex layered component designs, in which interfacial dynamics dictate device operation. These capabilities for non-invasive, multi-modal probing of complicated electronic components are crucial in today's electronic manufacturing but is largely inaccessible even with sophisticated techniques. These results show that seemingly simple SEM can be extended to probe complex and useful material properties.

cond-mat.mtrl-sci↗

arXiv2023

Non-volatile electrically programmable integrated photonics with a 5-bit operation

Scalable programmable photonic integrated circuits (PICs) can potentially transform the current state of classical and quantum optical information processing. However, traditional means of programming, including thermo-optic, free carrier dispersion, and Pockels effect result in either large device footprints or high static energy consumptions, significantly limiting their scalability. While chalcogenide-based non-volatile phase-change materials (PCMs) could mitigate these problems thanks to their strong index modulation and zero static power consumption, they often suffer from large absorptive loss, low cyclability, and lack of multilevel operation. Here, we report a wide-bandgap PCM antimony sulfide (Sb2S3)-clad silicon photonic platform simultaneously achieving low loss, high cyclability, and 5-bit operation. We switch Sb2S3 via an on-chip silicon PIN diode heater and demonstrate components with low insertion loss (<1.0 dB), high extinction ratio (>10 dB), and high endurance (>1,600 switching events). Remarkably, we find that Sb2S3 can be programmed into fine intermediate states by applying identical and thermally isolated pulses, providing a unique approach to controllable multilevel operation. Through dynamic pulse control, we achieve on-demand and accurate 5-bit (32 levels) operations, rendering 0.50 +- 0.16 dB contrast per step. Using this multilevel behavior, we further trim random phase error in a balanced Mach-Zehnder interferometer. Our work opens an attractive pathway toward non-volatile large-scale programmable PICs with low-loss and on-demand multi-bit operations.

physics.optics↗

arXiv2022

An NLP-Assisted Bayesian Time Series Analysis for Prevalence of Twitter Cyberbullying During the COVID-19 Pandemic

COVID-19 has brought about many changes in social dynamics. Stay-at-home orders and disruptions in school teaching can influence bullying behavior in-person and online, both of which leading to negative outcomes in victims. To study cyberbullying specifically, 1 million tweets containing keywords associated with abuse were collected from the beginning of 2019 to the end of 2021 with the Twitter API search endpoint. A natural language processing model pre-trained on a Twitter corpus generated probabilities for the tweets being offensive and hateful. To overcome limitations of sampling, data was also collected using the count endpoint. The fraction of tweets from a given daily sample marked as abusive is multiplied to the number reported by the count endpoint. Once these adjusted counts are assembled, a Bayesian autoregressive Poisson model allows one to study the mean trend and lag functions of the data and how they vary over time. The results reveal strong weekly and yearly seasonality in hateful speech but with slight differences across years that may be attributed to COVID-19.

cs.SI↗

arXiv2021

Uncovering Thermal and Electrical Properties of Sb2Te3/GeTe Superlattice Films

Superlattice-like phase change memory (SL-PCM) promises lower switching current than conventional PCM based on Ge2Sb2Te5 (GST). However, a fundamental understanding of SL-PCM requires detailed characterization of the interfaces within such a SL. Here, we explore the electrical and thermal transport of SLs with deposited Sb2Te3 and GeTe alternating layers of various thicknesses. We find up to ~4X reduction of the effective cross-plane thermal conductivity of the SL stack (as-deposited polycrystalline) compared to polycrystalline GST (as-deposited amorphous and later annealed) due to the thermal interface resistances within the SL. Thermal measurements with varying periods of our SLs show a signature of phonon coherence with a transition from wave-like to particle-like phonon transport, further described by our modeling. Electrical resistivity measurements of such SLs reveal strong anisotropy (~2000X) between the in-plane and cross-plane directions due to the weakly interacting van der Waals gaps. This work uncovers electro-thermal transport in SLs based on Sb2Te3 and GeTe, for improved design of low-power PCM.

cond-mat.mtrl-sci↗

arXiv2021

Towers and elementary embeddings in toral relatively hyperbolic groups

In a remarkable series of papers, Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers. It was later proved by Chloé Perin that if $H$ is an elementarily embedded subgroup (or elementary submodel) of a torsion-free hyperbolic group $G$, then $G$ is a tower over $H$. We prove a generalization of Perin's result to toral relatively hyperbolic groups using JSJ and shortening techniques.

math.GR↗

arXiv2019

Phase change dynamics and 2-dimensional 4-bit memory in Ge2Sb2Te5 via telecom-band encoding

As modern computing gets continuously pushed up against the von Neumann Bottleneck -- limiting the ultimate speeds for data transfer and computation -- new computing methods are needed in order to bypass this issue and keep our computer's evolution moving forward, such as hybrid computing with an optical co-processor, all-optical computing, or photonic neuromorphic computing. In any of these protocols, we require an optical memory: either a multilevel/accumulator memory, or a computational memory. Here, we propose and demonstrate a 2-dimensional 4-bit fully optical non-volatile memory using Ge2Sb2Te5 (GST) phase change materials, with encoding via a 1550 nm laser. Using the telecom-band laser, we are able to reach deeper into the material due to the low-loss nature of GST at this wavelength range, hence increasing the number of optical write/read levels compared to previous demonstrations, while simultaneously staying within acceptable read/write energies. We verify our design and experimental results via rigorous numerical simulations based on finite element and nucleation theory, and we successfully write and read a string of characters using direct hexadecimal encoding.

physics.app-ph↗

arXiv2011

Codes as fractals and noncommutative spaces

We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can associate geometric spaces constructed using methods from noncommutative geometry, arising from rational noncommutative tori and finite abelian group actions on Cuntz algebras and fractals associated to the classical codes.

cs.IT↗