Research works

Band-dominated and Fourier-band-dominated operators on locally compact abelian groups

Abstract By relating notions from quantum harmonic analysis and band-dominated operator theory, we prove that, over any locally compact abelian group 𝐺, the operator algebra C 1 \mathcal{C}_{1} from quantum harmonic analysis agrees with the intersection of band-dominated operator...

Particle systems and McKean–Vlasov dynamics with singular interaction through local times

We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all the particles. If this local time drift is too strong, such systems exhibit a breakdown in their solut...

On Generalized Disc-Polygons in Plane Convex Bodies With a Higher Degree of Smoothness

Abstract We prove power series expansions for the expectations of the number of vertices and missed area of random L -convex polygons in planar convex bodies with sufficiently smooth boundaries. Random L -convex polygons arise as the intersection of all translates of a fixed conv...

Full Convergence of Regularized Methods for Unconstrained Optimization

Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we extend the latter property to a broader cl...

Promoting arm movement practice with a novel wheelchair armrest early after stroke: a randomized controlled trial

Abstract Background Chronic upper extremity (UE) impairment is common after stroke. This study aimed to evaluate both the feasibility and preliminary clinical effects of Boost, a novel wheelchair-mounted rehabilitation device designed to assist individuals in UE motor recovery du...

Citation accuracy, citation noise, and citation bias: a foundation of citation analysis

Abstract Citation analysis is widely used in research evaluation to assess the impact of scientific papers. These analyses rest on the assumption that citation decisions by authors are accurate, representing the flow of knowledge from cited to citing papers. However, in practice,...

Radon Exposure: A Comprehensive Review of the Health Risks and Therapeutic Potentials

Radon, a naturally occurring radioactive gas, is classified as a Group 1 carcinogen by the World Health Organization (WHO) and remains a significant environmental health hazard. Traditionally linked to lung cancer, radon exposure is the second leading cause of lung cancer worldwi...

Rabies and rabies prophylaxis in Egypt: a nationwide cross-sectional study that calls for action

BACKGROUND: Rabies is a fatal but preventable viral disease that poses a global health threat, especially in developing countries. Despite the high incidence of animal bites reported annually in Egypt, limited data exist regarding the knowledge, attitudes, and practices (KAP) of...

Interpolating chromatic and homomorphism thresholds

The problem of chromatic thresholds seeks minimum degree conditions that ensure that dense H -free graphs have a bounded chromatic number, or equivalently a bounded size homomorphic image. The strengthened homomorphism thresholds problem further requires that the homomorphic imag...

The Lipschitz-Volume Rigidity Problem for Metric Manifolds

Abstract We prove a Lipschitz-volume rigidity result for 1-Lipschitz maps of non-zero degree between metric manifolds (metric spaces homeomorphic to a closed oriented manifold) and Riemannian manifolds. The proof is based on degree theory and recent developments of Lipschitz-volu...

Controlled rough SDEs, pathwise stochastic control and dynamic programming principles

We study stochastic optimal control of rough stochastic differential equations (RSDEs). This is in the spirit of the pathwise control problem (Lions–Souganidis 1998, Buckdahn–Ma 2007; also Davis–Burstein 1992), with renewed interest and recent works drawing motivation from filter...

KP integrability of non-perturbative differentials

We prove the KP integrability of non-perturbative topological recursion, which can be considered as a formal ℏ -deformation of the Krichever construction of algebro-geometric solutions of the KP hierarchy. This property goes back to a 2011 conjecture of Borot and Eynard.

On the rigidity of random graphs in high-dimensional spaces

We study the maximum dimension $d=d(n,p)$ for which an Erdős-Rényi $G(n,p)$ random graph is $d$-rigid. Our main results reveal two different regimes of rigidity in $G(n,p)$ separated at $p_c=C_*\log n/n,~C_*=2/(1-\log 2)$ -- the point where the graph's minimum degree exceeds half...

Perverse sheaves and $t$-structures on the thin and thick affine flag varieties

We study the categories \mathrm{Perv}_{\mathrm{thin}} , \mathrm{Perv}_{\mathrm{thick}} of Iwahori-equivariant perverse sheaves on the thin and thick affine flag varieties associated to a split reductive group G . An earlier work of the first author describes \mathrm{Perv}_{\mathr...

The spectrum of units of algebraic K-theory

It is well known that the [ 0 , 1 ] and [ 0 , 2 ] Postnikov truncations of the units of the topological K -theories 𝔤 𝔩 1 ⁢ K O and 𝔤 𝔩 1 ⁢ K U , respectively, are split, and that the splitting is provided by the ( ℤ / 2 -graded) line bundles. In this paper we give a similar spli...

Cutoff phenomenon for asymmetric zero range process with monotone rates

We investigate the mixing time of the asymmetric Zero Range process on the segment with a nondecreasing rate. We establish that the cutoff holds in the totally asymmetric case with a convex flux, and also with a concave flux if the asymmetry is strong enough. We show that the mix...

Nonlinear interpolation and the flow map of quasilinear equations

We prove an interpolation theorem for nonlinear functionals defined on scales of Banach spaces that generalize Besov spaces. It applies to functionals defined only locally, requiring only some weak Lipschitz conditions, extending those introduced by Lions and Peetre. Our analysis...

A quantitative central limit theorem for the simple symmetric exclusion process

A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on the d-dimensional discrete torus is proven. The argument is based on the comparison of the generators of the density fluctuation field of the SSEP and the generalized Ornstein–Uhlenbeck proc...

Impact of undernutrition on apoptotic pathways and thymocyte development in rats: insights into caspase activation and mitochondrial dysfunction

Abstract Undernutrition significantly compromises immune function, particularly in vulnerable populations. This study explored the effects of undernutrition on apoptotic pathways and thymocyte development in rats, shedding light on potential mechanisms underlying immunosuppressio...

Simple grammar bisimilarity, with an application to session type equivalence

We provide an algorithm for deciding simple grammar bisimilarity whose complexity is polynomial in the valuation of the grammar (maximum seminorm among production rules). Since the valuation is at most exponential in the size of the grammar, this gives rise to a (single) exponent...