arXiv subjects

Guy Katriel

Publications and source records attributed to Guy Katriel.

At least 19 recordsLinked to original sources

arXiv2026

Modeling the Impact of Immune Boosting on Population-Level Vaccine Effectiveness

We extend the standard susceptible-infected-recovered framework to incorporate natural immune boosting during a short-scale outbreak. By deriving closed-form final size relations, we analytically link total attack rates to boosting dynamics and vaccine coverage. This framework identifies a critical boosting threshold: above it, higher vaccine coverage paradoxically decreases relative vaccine effectiveness. This occurs because successful epidemic suppression deprives vaccinated individuals of the silent pathogen exposures required to maintain their relative immunological advantage. Crucially, the overall population-level impact remains beneficial, consistently reducing absolute disease burden. For highly transmissible variants, asymptotic analysis reveals that relative vaccine effectiveness converges to a positive limit entirely independent of coverage.

q-bio.PE↗

arXiv2025

The Cayley-Moser problem with Poissonian arrival of offers

We study a version of the classical Cayley-Moser optimal stopping problem, in which a seller must sell an asset by a given deadline, with the offers, which are independent random variables with a known distribution, arriving at random times, as a Poisson process. This continuous-time formulation of the problem is much more analytically tractable than the analogous discrete-time problem which is usually considered, leading to a simple differential equation that can be explicitly solved to find the optimal policy. We study the performance of this optimal policy, and obtain explicit expressions for the distribution of the realized sale price, as well as for the distribution of the stopping time. The general results are used to explore characteristics of the optimal policy and of the resulting bidding process, and are illustrated by application to several specific instances of the offer distribution.

math.PR↗

arXiv2025

Optimal regulation in a periodic environment: insights from a simple model

We perform a detailed study of a simple mathematical model addressing the problem of optimally regulating a process subject to periodic external forcing, which is interesting both in view of its direct applications and as a prototype for more general problems. In this model one must determine an optimal time-periodic `effort' profile, and the natural setting for the problem is in a space of periodic non-negative measures. We prove that there exists a unique solution for the problem in the space of measures, and then turn to characterizing this solution. Under some regularity conditions on the problem's data, we prove that its solution is an absolutely continuous measure, and provide an explicit formula for the measure's density. On the other hand, when the problem's data is discontinuous, the solution measure can also include atomic components. Complementing our analytical results, we carry out numerical computations to obtain solutions of the problem in various instances, which enable us to examine the interesting ways in which the solution's structure varies as the problem's data is varied.

math.OC↗

arXiv2024

Non-local origin and correlations in the Johnson noise at nonuniform temperatures

We propose an alternative scenario for the propagation of thermal noise in a conductor. In this scenario, the noise in the emf (electromotive force) between two terminals cannot be described as a sum of contributions from uncorrelated regions, each in local thermal equilibrium. We review previous studies of thermal noise in circuits with nonuniform temperature. We suggest experiments that could distinguish between different scenarios. We build a workable 1D model for a gas of particles that undergo stochastic collisions with the lattice and exert distance-dependent forces on each other. We enunciate definitions of current, voltage, and emf, appropriate to a wire with limited number of particles. For uniform temperature, within appropriate length and temperature ranges, our simulations comply with Nyquist's result. Analytic results can be obtained in the limit of strong interparticle interaction. The simulations indicate that (1) thermal noise in a resistor at uniform temperature within an electric circuit can be larger (smaller) than predicted by Nyquist due to the presence of a resistor with higher (lower) temperature in the circuit; (2) for sufficiently long circuits, the deviation from the Nyquist prediction is inversely proportional to the distance between the centers of the resistors; (3) if the resistors differ in temperature, their emf can be correlated, even if they are detached. The long-range repulsion between charges in electrically connected resistors may have conceptual and technological impact in nanodevices.

cond-mat.stat-mech↗

arXiv2023

Optimizing antimicrobial treatment schedules: some fundamental analytical results

This work studies fundamental questions regarding the optimal design of antimicrobial treatment protocols, using standard pharmacodynamic and pharmacokinetic mathematical models. We consider the problem of designing an antimicrobial treatment schedule to achieve eradication of a microbial infection, while minimizing the area under the time-concentration curve (AUC). We first solve this problem under the assumption that an arbitrary antimicrobial concentration profile may be chosen, and prove that the 'ideal' concentration profile consists of a constant concentration over a finite time duration, where explicit expressions for the optimal concentration and the time duration are given in terms of the pharmacodynamic parameters. Since antimicrobial concentration profiles are induced by a dosing schedule and the antimicrobial pharmacokinetics, the ideal concentration profile is not strictly feasible. We therefore also investigate the possibility of achieving outcomes which are close to those provided by the ideal concentration profile,using a bolus+continuous dosing schedule, which consists of a loading dose followed by infusion of the antimicrobial at a constant rate. We explicitly find the optimal bolus+continuous dosing schedule, and show that, for realistic parameter ranges, this schedule achieves results which are nearly as efficient as those attained by the ideal concentration profile. The optimality results obtained here provide a baseline and reference point for comparison and evaluation of antimicrobial treatment plans.

q-bio.PE↗

arXiv2022

Optimal vaccination at high reproductive numbers: sharp transitions and counter-intuitive allocations

Optimization of vaccine allocations among different segments of a heterogeneous population is important for enhancing the effectiveness of vaccination campaigns in reducing the burden of epidemics. Intuitively, it would seem that allocations designed to minimize infections should prioritize those with the highest risk of being infected and infecting others. This prescription is well supported by vaccination theory, e.g., when the vaccination campaign aims to reach herd immunity. In this work, we show, however, that for vaccines providing partial protection (leaky vaccines) and for sufficiently high values of the basic reproduction number, intuition is overturned: the optimal allocation for minimizing the number of infections prioritizes the vaccination of those who are least likely to be infected. Furthermore, we show that this phenomenon occurs at a range of basic reproduction numbers relevant for the currently circulating strains of SARS-CoV-19. The work combines numerical investigations, asymptotic analysis for a general model, and complete mathematical analysis in a simple two-group model. The results point to important considerations in managing vaccination campaigns for infections with high transmissibility.

q-bio.QM↗

arXiv2021

Dispersal-induced growth in a time-periodic environment

Dispersal-induced growth (DIG) occurs when two populations with time-varying growth rates, each of which, when isolated, would become extinct, are able to persist and grow exponentially when dispersal among the two populations is present. This work provides a mathematical exploration of this surprising phenomenon, in the context of a deterministic model with periodic variation of growth rates, and characterizes the factors which are important in generating the DIG effect and the corresponding conditions on the parameters involved.

q-bio.PE↗

arXiv2020

Optimality of constant inflow for a linear system with a bottleneck entrance

Sadeghi et al. considered a bottleneck system with periodic inflow rate, and proved that a constant-rate input maximizes the time-averaged output rate among all periodic inflow rates. Here we provide a short and elementary proof of this result, without use of optimal control theory. The new approach developed here allows us to prove an extension of the result to the case of a general non-periodic inflow rate.

math.CA↗

arXiv2019

Linearization of holomorphic semicocycles in Banach spaces

We consider holomorphic semicocycles on the open unit ball in a Banach space taking values in a Banach algebra. We establish criteria for a semicocycle to be linearizable, that is, cohomologically equivalent to one independent of the spatial variable.

math.DS↗

arXiv2019

Estimating the rate of defects under imperfect sampling inspection - a new approach

We consider the problem of estimating the rate of defects (mean number of defects per item), given the counts of defects detected by two independent imperfect inspectors on one sample of items. In contrast with the setting for the well-known method of Capture-Recapture, we {\it{do not}} have information regarding the number of defects jointly detected by {\it{both}} inspectors. We solve this problem by constructing two types of estimators - a simple moment-type estimator, and a complicated maximum-likelihood estimator. The performance of these estimators is studied analytically and by means of simulations. It is shown that the maximum-likelihood estimator is superior to the moment-type estimator. A systematic comparison with the Capture-Recapture method is also made.

stat.ME↗

arXiv2018

The dynamics of two-stage contagion

We explore simple models aimed at the study of social contagion, in which contagion proceeds through two stages. When coupled with demographic turnover, we show that two-stage contagion leads to nonlinear phenomena which are not present in the basic `classical' models of mathematical epidemiology. These include: bistability, critical transitions, endogenous oscillations, and excitability, suggesting that contagion models with stages could account for some aspects of the complex dynamics encountered in social life. These phenomena, and the bifurcations involved, are studied by a combination of analytical and numerical means.

physics.soc-ph↗

arXiv2018

Gambler's ruin probability - a general formula

We derive an explicit formula for the probability of ruin of a gambler playing against an infinitely-rich adversary, when the games have payoff given by a general integer-valued probability distribution.

math.PR↗

arXiv2018

Continuous and holomorphic semicocycles in Banach spaces

We study some fundamental properties of semicocycles over semigroups of self-mappings of a domain in a Banach space. We prove that any semicocycle over a jointly continuous semigroup is itself jointly continuous. For semicocycles over semigroups which have generator, we establish a sufficient condition for differentiablity with respect to the time variable, and hence for the semicocycle to satisfy a linear evolution problem, giving rise to the notion of `generator' of a semicocycle. Bounds on the growth of a semicocycle with respect to the time variable are given in terms of this generator. Special consideration is given to the case of holomorphic semicocycles, for which we prove an exact correspondence between certain uniform continuity properties of a semicocyle and boundedness properties of its generator.

math.FA↗

arXiv2018

A quantitative discounted central limit theorem using the Fourier metric

The discounted central limit theorem concerns the convergence of an infinite discounted sum of i.i.d. random variables to normality as the discount factor approaches $1$. We show that, using the Fourier metric on probability distributions, one can obtain the discounted central limit theorem, as well as a quantitative version of it, in a simple and natural way, and under weak assumptions.

math.PR↗

arXiv2017

Non-commutative holomorphic semicocycles

This paper studies holomorphic semicocycles over semigroups in the unit disk, which take values in an arbitrary unital Banach algebra. We prove that every such semicocycle is a solution to a corresponding evolution problem. We then investigate the linearization problem: which semicocycles are cohomologous to constant semicocycles? In contrast with the case of commutative semicocycles, in the non-commutative case non-linearizable semicocycles are shown to exist. Simple conditions for linearizability are derived and are shown to be sharp.

math.CV↗

arXiv2017

Spline functions, the discrete biharmonic operator and approximate eigenvalues

The biharmonic operator plays a central role in a wide array of physical models, notably in elasticity theory and the streamfunction formulation of the Navier-Stokes equations. The need for corresponding numerical simulations has led, in recent years, to the development of a discrete biharmonic calculus. The primary object of this calculus is a high-order compact discrete biharmonic operator (DBO). The numerical results have been remarkably accurate, and have been corroborated by some rigorous proofs. However, there remained the "mystery" of the "underlying reason" for this success. This paper is a contribution in this direction, expounding the strong connection between cubic spline functions (on an interval) and the DBO. It is shown in particular that the (scaled) fourth-order distributional derivative of the cubic spline is identical to the action of the DBO on grid functions. The DBO is constructed in terms of the discrete Hermitian derivative. A remarkable fact is that the kernel of the inverse of the discrete operator is (up to scaling) equal to the grid evaluation of the kernel of $\Big[\Big(\frac{d}{dx}\Big)^4\Big]^{-1} .$ Explicit expressions are presented for both kernels. The relation between the (infinite) set of eigenvalues of the fourth-order Sturm-Liouville problem and the finite set of eigenvalues of the discrete biharmonic operator is studied, and the discrete eigenvalues are proved to converge (at an "optimal" $O(h^4)$ rate) to the continuous ones. Another remarkable consequence is the validity of a comparison principle. It is well known that there is no maximum principle for the fourth-order equation. However, a positivity result is derived, both for the continuous and the discrete biharmonic equation, showing that in both cases the kernels are order preserving.

math.NA↗

arXiv2014

Estimating the number of eigenvalues of linear operators on Banach spaces

Let $L_0$ be a bounded operator on a Banach space, and consider a perturbation $L=L_0+K$, where $K$ is compact. This work is concerned with obtaining bounds on the number of eigenvalues of $L$ in subsets of the complement of the essential spectrum of $L_0$, in terms of the approximation numbers of the perturbing operator $K$. Our results can be considered as wide generalizations of classical results on the distribution of eigenvalues of compact operators, which correspond to the case $L_0=0$. They also extend previous results on operators in Hilbert space. Our method employs complex analysis and a new finite-dimensional reduction, allowing us to avoid using the existing theory of determinants in Banach spaces, which would require strong restrictions on $K$. Several open questions regarding the sharpness of our results are raised, and an example is constructed showing that there are some essential differences in the possible distribution of eigenvalues of operators in general Banach spaces, compared to the Hilbert space case.

math.SP↗

arXiv2014

The Immediate Exchange model: an analytical investigation

We study the Immediate Exchange model, recently introduced by Heinsalu and Patriarca [Eur. Phys. J. B 87: 170 (2014)], who showed by simulations that the wealth distribution in this model converges to a Gamma distribution with shape parameter $2$. Here we justify this conclusion analytically, in the infinite-population limit. An infinite-population version of the model is derived, describing the evolution of the wealth distribution in terms of iterations of a nonlinear operator on the space of probability densities. It is proved that the Gamma distributions with shape parameter $2$ are fixed points of this operator, and that, starting with an arbitrary wealth distribution, the process converges to one of these fixed points. We also discuss the mixed model introduced in the same paper, in which exchanges are either bidirectional or unidirectional with fixed probability. We prove that, although, as found by Heinsalu and Patriarca, the equilibrium distribution can be closely fit by Gamma distributions, the equilibrium distribution for this model is {\it{not}} a Gamma distribution.

q-fin.GN↗