Related papers: River Crossing Problems: Algebraic Approach

In this article, we study connections between representation theory and efficient solutions to the conjugacy problem on finitely generated groups. The main focus is on the conjugacy problem in conjugacy separable groups, where we measure…

A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…

The problem of allocating tasks to workers is of long standing fundamental importance. Examples of this include the classical problem of assigning computing tasks to nodes in a distributed computing environment, as well as the more recent…

We investigate, at the fundamental level, the questions of `why', `when' and `how' one could or should reach out to poor and vulnerable people to support them in the absence of governmental institutions. We provide a simple and new approach…

The occurrence of discrimination is an important problem in the social and economical sciences. Much of the discrimination observed in empirical studies can be explained by the theory of in-group favoritism, which states that people tend to…

Prisoner's Dilemma is a game theory model used to describe altruistic behavior seen in various populations. This theoretical game is important in understanding why a seemingly selfish strategy does persist and spread throughout a population…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

(shortened version) Religions and languages are social variables, like age, sex, wealth or political opinions, to be studied like any other organizational parameter. In fact, religiosity is one of the most important sociological aspects of…

There are two main opposing schools of statistical reasoning, Frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong…

We study the adjudication of water rights in international rivers. We characterize allocation rules that formalize focal principles to deal with water disputes in a basic model. Central to our analysis is a family of geometric rules that…

Fully pairing all elements of a set while attempting to maximize the total benefit is a combinatorically difficult problem. Such pairing problems naturally appear in various situations in science, technology, economics, and other fields. In…

Decades of scientific inquiry have sought to understand how evolution fosters cooperation, a concept seemingly at odds with the belief that evolution should produce rational, self-interested individuals. Most previous work has focused on…

Causality and causal inference have emerged as core research areas at the interface of modern statistics and domains including biomedical sciences, social sciences, computer science, and beyond. The field's inherently interdisciplinary…

Network flows over time are a fascinating generalization of classical (static) network flows, introducing an element of time. They naturally model problems where travel and transmission are not instantaneous and flow may vary over time. Not…

Designing systems for autonomous transport of groups of living agents has received a lot of attention in recent years due to a wealth of important potential applications. Biomimetic approaches are often sought, and a range of herding…

Classical planning aims to find a sequence of actions, a plan, that maps a starting state into one of the goal states. If a trajectory appears to be leading to the goal, should we prioritise exploring it? Seminal work in goal recognition…

Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine…

The Nile problem by Ronald Fisher may be interpreted as the problem of making statistical inference for a special curved exponential family when the minimal sufficient statistic is incomplete. The problem itself and its versions for general…

Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…

We consider $\G$-graded commutative algebras, where $\G$ is an abelian group. Starting from a remarkable example of the classical algebra of quaternions and, more generally, an arbitrary Clifford algebra, we develop a general viewpoint on…