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We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…
We introduce the \emph{Correlated Preference Bandits} problem with random utility-based choice models (RUMs), where the goal is to identify the best item from a given pool of $n$ items through online subsetwise preference feedback. We…
Schema matching is the process of identifying correspondences between the elements of two given schemata, essential for database management systems, data integration, and data warehousing. For datasets across different scenarios, the…
This paper proposes a novel method for randomized bin-picking based on learning. When a two-fingered gripper tries to pick an object from the pile, a finger often contacts a neighboring object. Even if a finger contacts a neighboring…
For $2\le k\in\mathbb{N}$, consider the following adaptation of the classical secretary problem. There are $k$ items at each of $n$ linearly ordered ranks. The $kn$ items are revealed, one item at a time, in a uniformly random order, to an…
The topic of the article is the parametric study of the complexity of algorithms on arrays of pairwise distinct integers. We introduce a model that takes into account the non-uniformness of data, which we call the Ewens-like distribution of…
How many fair coin tosses to choose 1 of $n$ options with uniform probability? Although a probability problem, the solution is essentially number-theoretic, with special roles for Mersenne numbers, Fermat numbers, and the haupt exponent. We…
A common paradigm to improve the performance of large language models is optimizing for a reward model. Reward models assign a numerical score to an LLM's output that indicates, for example, how likely it is to align with user preferences…
In one-class recommendation systems, the goal is to learn a model from a small set of interacted users and items and then identify the positively-related user-item pairs among a large number of pairs with unknown interactions. Most previous…
Large Language Models (LLMs) deliver state-of-the-art performance on complex reasoning tasks, but their inference costs limit deployment at scale. Small Language Models (SLMs) offer dramatic cost savings yet lag substantially in accuracy.…
The existing research on physical layer security commonly assumes the number of eavesdropper antennas to be known. Although this assumption allows one to easily compute the achievable secrecy rate, it can hardly be realized in practice. In…
We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of…
We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…
We analyze the competitive ratio and the advice complexity of the online unbounded knapsack problem. An instance is given as a sequence of n items with a size and a value each, and an algorithm has to decide how often to pack each item into…
The famous Johnson-Lindenstrauss lemma states that for any set of n vectors, there is a linear transformation into a space of dimension O(log n) that approximately preserves all their lengths. In fact, a Haar random unitary transformation…
A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…
We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree…
Effective problem solving with Large Language Models (LLMs) can be enhanced when they are paired with external search algorithms. By viewing the space of diverse ideas and their follow-up possibilities as a tree structure, the search…