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With quantum computers promising advantages even in the near-term NISQ era, there is a lively community that develops software and toolkits for the design of corresponding quantum circuits. Although the underlying problems are different,…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions.…
We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler's perceived…
Local explanation frameworks aim to rationalize particular decisions made by a black-box prediction model. Existing techniques are often restricted to a specific type of predictor or based on input saliency, which may be undesirably…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
We describe a method that allows, under some hypotheses, to compute all the rational points of some genus 5 curves defined over a number field. This method is used to solve some arithmetic problems that remained open.
We introduce a notion of strategies based on averaging for nonlocal games in quantum information theory. These so-called statistical strategies come in a commuting type and a more specific spatial type, which are respectively special cases…
In adversarial settings, a mobile agent may strategically plan its motion to influence an opponent's inference about its intended goal. We study deceptive path planning in a scenario where a mobile agent aims to reach a privately selected…
The optimal allocation of resources is a crucial task for their efficient use in a wide range of practical applications in science and engineering. This paper investigates the optimal allocation of resources in multipartite quantum systems.…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Quantum optimization algorithms are inherently probabilistic, yet they are most often used to search for a single high-quality solution. In this paper, we instead study hypergraph partitioning problems in which the desired output is itself…
We recall the physical features of the parton distributions in the quantum statistical approach of the nucleon, which allows to describe simultaneously, unpolarized and polarized Deep Inelastic Scattering data. Some predictions from a…
Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance. Importation of these ideas, combined with an existing rich body of…
Game theory provides a framework for studying communication dynamics and emergent phenomena arising from rational agent interactions. We present a model framework for the Volunteer's Dilemma with four key contributions: (1) formulating it…
In this paper we continue the study of $Q$-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin $R$-matrix associated with the affine quantum algebra…
By means of the Ehrhart theory of inside-out polytopes we establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, on a polygonal convex board. The number of ways…