Searcharxiv⌕ Search

arXiv subjects

Izabella Stuhl

Publications and source records attributed to Izabella Stuhl.

13 recordsLinked to original sources
arXiv2026

Queueing models with random resetting

We introduce and study some queueing models with random resetting, including Markovian and non--Markovian models under the first-come first-served (FCFS) discipline. The Markovian models include M/M/$r$ and M/M/1+M queues with random resetting, in which a continuous-time Markov chain is formulated, with transitions including a resetting to state zero in addition to arrivals and services. We explicitly characterize the stationary distributions of the queueing processes in these models by using parting balance equations. We derive expressions for standard performance measures such as the delay probability, expected queue length and waiting time, as well as probability of a customer completing service before resetting in the M/M/$r$ model, and probability of abandonment before service or resetting in the M/M/1+M model. The non--Markovian models include GI/GI/1, GI/GI/$r$ and GI/GI/$\infty$ queues with random resetting to state zero at arrival times. For GI/GI/1 and GI/GI/$r$ queues under the FCFS discipline, we introduce modified Lindley and Kiefer--Wolfowitz recursions, respectively. Using an operator representation for these recursions, we characterize the stationary distributions via convergent series, as solutions to the modified Wiener--Hopf equations. For GI/GI/$\infty$ queues with resettings, we utilize a version of the Kiefer--Wolfowitz recursion, and also characterize the corresponding stationary distribution.

math.PR↗
arXiv2026

On weighted partial triangulations of convex polygons

We study the problem of sampling weighted partial triangulations of a convex polygon with $n+2$ sides. We consider the distribution $π_{n,λ}$ under which each partial triangulation $σ$ is assigned probability proportional to $λ^{|σ|}$, where $λ>0$ is a model parameter and $|σ| \in \{0,\dots,n-1\}$ denotes the number of diagonals in $σ$. This model belongs to a broad class of weighted geometric partition problems that include lattice triangulations and dyadic tilings, and is closely related to several classical combinatorial structures, including the full triangulations of a convex polygon and the associated Catalan structures. Our main result is a simple exact sampling algorithm for $π_{n,λ}$ with expected running time $O\big((\min\{n,n\sqrtλ\}+1)\log n\big)$, which is optimal up to the logarithmic factor.

cs.DM↗
arXiv2026

Percolation and Criticality in Hyperuniform Networks

Hyperuniform many-particle systems, which encompass crystals, quasicrystals and certain exotic disordered systems, exhibit an anomalous suppression of density fluctuations on macroscopic length scales relative to those of conventional disordered systems. Here we investigate the percolation behaviors of disordered stealthy hyperuniform systems (SHU), a subclass of hyperuniform configurations for which the structure factor vanishes for a finite range of wavevectors near the origin, with the degree of stealthiness controlled via a parameter $χ$. We construct Delaunay triangulation networks derived from SHU configurations with varying $χ$ as well as Poisson point configurations for the purpose of comparison. We investigate a non-uniform bond percolation process, in which bond occupation probabilities decrease with the Euclidean distance between the connected vertices. In this setting, percolation is induced by varying a tuning parameter $z$. We estimate the percolation thresholds $z_c$ and critical exponents of the networks via finite-size scaling and the Newman-Ziff algorithm. We find that SHU networks exhibit lower percolation thresholds than Poisson networks. Notably, the percolation threshold of SHU networks decreases with the stealthiness parameter $χ$, indicating that global connectivity emerges more readily as short-range order increases. Moreover, we show that SHU networks with large $χ$ belong to the same universality class as lattices, while Poisson and low-$χ$ systems show deviations. We relate the shift in critical exponents to the degree of suppression of density fluctuations in the point configurations. Our work extends previous studies on transport properties of SHU systems from continuum two-phase media to networks. These results open new avenues for optimizing the resilience of statistically homogeneous disordered networks.

cond-mat.stat-mech↗
arXiv2019

Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order

There is a one-to-one correspondence between involutory latin quandles and uniquely $2$-divisible Bruck loops. Bruck loops of odd prime power order are centrally nilpotent. Using linear-algebraic approach to central extensions, we enumerate Bruck loops (and hence involutory latin quandles) of order $3^k$ for $k\le 5$, except for those loops that are central extensions of the cyclic group of order $3$ by the elementary abelian group of order $3^4$. Among the constructed loops there is a Bruck loop of order $3^5$ whose associated $Γ$-loop is not a commutative automorphic loop. We independently enumerate commutative automorphic loops of order $3^k$ for $k\le 5$, with the same omission as in the case of Bruck loops.

math.GR↗
arXiv2018

How fragile are information cascades?

It is well known that sequential decision making may lead to information cascades. That is, when agents make decisions based on their private information, as well as observing the actions of those before them, then it might be rational to ignore their private signal and imitate the action of previous individuals. If the individuals are choosing between a right and a wrong state, and the initial actions are wrong, then the whole cascade will be wrong. This issue is due to the fact that cascades can be based on very little information. We show that if agents occasionally disregard the actions of others and base their action only on their private information, then wrong cascades can be avoided. Moreover, we study the optimal asymptotic rate at which the error probability at time $t$ can go to zero. The optimal policy is for the player at time $t$ to follow their private information with probability $p_{t} = c/t$, leading to a learning rate of $c'/t$, where the constants $c$ and $c'$ are explicit.

math.PR↗
arXiv2017

Weighted entropy: basic inequalities

This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of the Fisher information inequality and entropy power inequality for the weighted entropy and discuss connections with weighted Lieb's splitting inequality. The concepts of rates of the weighted entropy and information are also discussed.

math.PR↗
arXiv2017

Weighted entropy and optimal portfolios for risk-averse Kelly investments

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study.

math.PR↗
arXiv2016

Weighted information and entropy rates

The weighted entropy $H^{\rm w}_ϕ(X)=H^{\rm w}_ϕ(f)$ of a random variable $X$ with values $x$ and a probability-mass/density function $f$ is defined as the mean value ${\mathbb E} I^{\rm w}_ϕ(X)$ of the weighted information $I^{\rm w}_ϕ(x)=-ϕ(x)\log\,f(x)$. Here $x\mapstoϕ(x)\in{\mathbb R}$ is a given weight function (WF) indicating a 'value' of outcome $x$. For an $n$-component random vector ${\mathbf{X}}_0^{n-1}=(X_0,\ldots ,X_{n-1})$ produced by a random process ${\mathbf{X}}=(X_i,i\in{\mathbb Z})$, the weighted information $I^{\rm w}_{ϕ_n}({\mathbf x}_0^{n-1})$ and weighted entropy $H^{\rm w}_{ϕ_n}({\mathbf{X}}_0^{n-1})$ are defined similarly, with an WF $ϕ_n({\mathbf x}_0^{n-1})$. Two types of WFs $ϕ_n$ are considered, based on additive and a multiplicative forms ($ϕ_n({\mathbf x}_0^{n-1})=\sum\limits_{i=0}^{n-1}φ (x_i)$ and $ϕ_n({\mathbf x}_0^{n-1})=\prod\limits_{i=0}^{n-1}φ (x_i)$, respectively). The focus is upon ${\it rates}$ of the weighted entropy and information, regarded as parameters related to ${\mathbf{X}}$. We show that, in the context of ergodicity, a natural scale for an asymptotically additive/multiplicative WF is $\frac{1}{n^2}H^{\rm w}_{ϕ_n}({\mathbf{X}}_0^{n-1})$ and $\frac{1}{n}\log\;H^{\rm w}_{ϕ_n}({\mathbf{X}}_0^{n-1})$, respectively. This gives rise to ${\it primary}$ ${\it rates}$. The next-order terms can also be identified, leading to ${\it secondary}$ ${\it rates}$. We also consider emerging generalisations of the Shannon-McMillan-Breiman theorem.

cs.IT↗
arXiv2016

On principles of large deviation and selected data compression

The Shannon Noiseless coding theorem (the data-compression principle) asserts that for an information source with an alphabet $\mathcal X=\{0,\ldots ,\ell -1\}$ and an asymptotic equipartition property, one can reduce the number of stored strings $(x_0,\ldots ,x_{n-1})\in {\mathcal X}^n$ to $\ell^{nh}$ with an arbitrary small error-probability. Here $h$ is the entropy rate of the source (calculated to the base $\ell$). We consider further reduction based on the concept of utility of a string measured in terms of a rate of a weight function. The novelty of the work is that the distribution of memory is analyzed from a probabilistic point of view. A convenient tool for assessing the degree of reduction is a probabilistic large deviation principle. Assuming a Markov-type setting, we discuss some relevant formulas, including the case of a general alphabet.

cs.IT↗
arXiv2016

Basic inequalities for weighted entropies

The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies (general as well as specific), mirroring similar bounds on standard (Shannon) entropies and related quantities. The required assumptions are written in terms of various expectations of the weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cramér-Rao inequalities involving the weighted Fisher information matrix.

cs.IT↗
arXiv2015

Half-isomorphisms of Moufang loops

We prove that if the squaring map in the factor loop of a Moufang loop $Q$ over its nucleus is surjective, then every half-isomorphism of $Q$ onto a Moufang loop is either an isomorphism or an anti-isomorphism. This generalizes all earlier results in this vein.

math.GR↗
arXiv2014

Oriented Steiner quasigroups

We introduce the notion of an oriented Steiner quasigroup and develop elements of a relevant algebraic apparatus. The approach is based upon (modified) Schreier-type $f$-extensions for quasigroups (cf. earlier works \cite{S, NSt, NSt2}) achieved through oriented Steiner triple systems. This is done in a fashion similar to in \cite{SS} where an analogous construction was established for loops. As a justification of this concept briefly discuss an application of oriented Steiner triple systems in cryptography using oriented Steiner quasigroups.

math.GR↗