Research works

Gradient Descent Avoids Strict Saddles with a Simple Line-Search Method Too

It is known that gradient descent (GD) on a [Formula: see text] cost function generically avoids strict saddle points when using a small, constant step size. However, no such guarantee existed for GD with a line-search method. We provide one for a modified version of the standard...

Enhanced measurements on quantum computers via the simultaneous probing of non-commuting Pauli operators

Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. A promising avenue is multi-copy schemes, where identical copies of a quantum state are measured jointly so that all Pauli operators within the considere...

Arf rings, simple singularities, and reflexive modules

Abstract In a pandemic era preprint, Dao showed two remarkable properties of Arf rings: under some mild conditions, they admit finitely many indecomposable reflexive modules up to isomorphism and every reflexive module is actually isomorphic to its own dual. In fact, the latter p...

Multi-species McKean–Vlasov dynamics in non-convex landscapes

Abstract In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean–Vlasov partial differential equations (PDEs) in non-convex landscapes. Under general assumptions on non-convex confining and interaction potentials with polynomial g...

Robust adaptive discrete-time control barrier certificate

This work develops a robust adaptive control strategy for discrete-time systems using Control Barrier Functions (CBFs) to ensure safety under parametric model uncertainty and disturbances. A key contribution of this work is establishing a barrier function certificate in discrete...

Functional Inequalities and Random Walks on Increasing Subsets of the Hypercube

Abstract. Motivated by random walks on subsets of the hypercube, we prove two discrete functional inequalities on the hypercube by the technique of induction-by-restrictions. First, we give a short, elementary proof of the Poincaré inequality on increasing subsets of the cube rec...

Electromagnetism: An intrinsic approach to Hadamard's method of descent

We present a systematic geometric framework for the dimensional reduction of classical electromagnetism based on the concept of descent along vector fields of invariance. By exploring the interplay between the Lie derivative and the Hodge star operator, we implement descent condi...

Spatial sign based direct sparse linear discriminant analysis for high dimensional data

This paper investigates the robust linear discriminant analysis (LDA) problem with elliptical distributions in high-dimensional data. We propose a robust classification method, named SSLDA, that is intended to withstand heavy-tailed distributions. We demonstrate that SSLDA achiev...

Human-like content analysis for generative AI with language-grounded sparse encoders

The rapid development of generative AI has transformed content creation, communication, and human development. However, this technology raises profound concerns in high-stakes domains, demanding rigorous methods to analyze and evaluate AI-generated content. While existing analyti...

Multiscale modeling of the electroviscoelasticity of charged polymers in combined flow and electric fields

The behavior of polymers in combined flow and electric fields underlies many manufacturing processes but remains poorly understood. We model charged polymers across scales, extending the Rouse model for a bead-spring chain to include a charge density distributed along the polymer...

Impact of cosmic-ray acceleration on the early evolution of bow shocks around massive runaway stars

Bow shocks generated from the interaction of winds from massive runaway stars with the interstellar medium have been shown to be prominent particle accelerators through recent γ-ray and radio synchrotron observations. They are ideal candidates for exploring the space- and time-de...

Experimental impact study on a micro-grid project in rural Madagascar: The Café Lumière project

This paper evaluates the impact of a pilot innovative project aiming at promoting a replicable model to create access to distributed electricity in rural areas where grid extension is economically infeasible. The project proposes building solar-powered micro-grids to provide affo...

Zero-shot personalized camera motion control for image-to-video synthesis

Specifying nuanced and compelling camera motion remains a significant hurdle for non-expert creators using generative tools, creating an “expressive gap” where generic text prompts fail to capture cinematic vision. This barrier limits individual creativity and restricts the acces...

Linearization-Based Feedback Stabilization of McKean−Vlasov PDEs

Abstract. We develop a feedback control framework for stabilizing the McKean–Vlasov PDE on the torus. Our goal is to steer the dynamics toward a prescribed stationary distribution or accelerate convergence to it using a time-dependent control potential. We reformulate the control...

Mostly Nonuniformly Sectional Expanding Systems

Abstract We introduce the notion of mostly nonuniform sectional expanding (MNUSE) for singular flows which encompasses the notions of sectional hyperbolicity, asymptotically sectional and multisingular hyperbolicity. We construct examples of a vector field of class $$C^r, r \ge 1...

Parselets: An Abstraction for Fast, General-Purpose Algorithmic Information Calculus

This work describes the principled design of a theoretical framework leading to fast and accurate algorithmic information measures on finite multisets of finite strings by means of compression. One distinctive feature of our approach is to manipulate reified representations of th...

High-order Magnus expansion for Hamiltonian simulation

Efficient simulation of quantum dynamics with time-dependent Hamiltonians is important not only for time-varying systems but also for time-independent Hamiltonians in the interaction picture. Such simulations are more challenging than their time-independent counterparts due to th...

Ultrafast X-ray sonography reveals the spatial heterogeneity of the laser-induced magneto-structural phase transition in FeRh

Abstract Even on the nanoscale, phase transitions are governed by both intrinsic and extrinsic heterogeneities, yet capturing their spatio-temporal dynamics remains a challenge. While ultrafast techniques track phase changes on femtosecond timescales, the spatial complexity and s...

Perturbative Variational Quantum Eigensolver via Reduced Density Matrices

Abstract Current noisy intermediate-scale quantum (NISQ) devices remain limited in their ability to perform accurate quantum chemistry simulations because of restricted numbers of high-fidelity qubits and short coherence times. To overcome these challenges, we introduce a reduced...

Partially hyperbolic geodesic flow via conformal deformation

This paper presents a new construction of non-Anosov partially hyperbolic geodesic flows. Our construction is closely related to the construction presented in [10] , the novelty is the use of conformal deformations to produce the examples. Some of the necessary conditions appear...