Urn models play an important role to express various basic ideas in probability theory. Here we extend this urn model with tubes. An urn contains coloured balls, which can be drawn with probabilities proportional to the numbers of balls of each colou...
The Toffoli gate takes a special place in the quantum information theory. It opens up a path for efficient implementation of complex quantum algorithms. Despite tremendous progress of the quantum processors based on the superconducting qubits, realiz...
The fundamental result of B. Sz. Nazy states that every contraction has a coisometric extension and a unitary dilation. The isometric dilation of a contraction on a Hilbert space motivated whether this theory can be extended sensibly to families of o...
Motivations and challenges jointly shape how individuals enter, persist, and evolve within software engineering (SE), yet their interplay remains underexplored across the transition from education to professional practice. We conducted 15 semi-struct...
Time-decaying currencies have long been discussed in economic theory as a means to discourage hoarding and promote circulation. However, their modern digital implementation as a universal basic income (UBI) mechanism raises unresolved structural ques...
Using a combination of theory, experiment, and simulation, we revisit the dynamics of two coupled metronomes on a moving platform. Our experiments show that the platform's motion is damped by a dry friction force of Coulomb type, not the viscous line...
1 day ago · Videos by According2HipHop The Hip-Hop and neo-soul community is mourning the loss of legendary recording engineer Bob Power, a pivotal figure behind the sound of the Native Tongues …
As currently understood since its discovery, the bare Klein-Gordon theory consists of negative quantum probabilities which are considered to be physically meaningless if not outright obsolete. Despite this annoying setback, these negative probabiliti...
We study the theta decomposition of Jacobi forms of nonintegral lattice index for a representation that arises in the theory of Weil representations associated to even lattices, and suggest possible applications....
We establish a rigorous duality theory, under No Unbounded Profit with Bounded Risk, for an infinite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed time, independ...
We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a proof by...
We introduce the notion of a higher covering diagram in a base $\infty$-category $\mathcal{C}$. The theory of higher covering diagrams in $\mathcal{C}$ will be shown to recover various descent conditions known from the $\infty$-categorical literature...
Improved actions in SU(2) and SU(3) lattice gauge theories are investigated with an emphasis on asymptotic scaling. A new scheme for tadpole improvement is proposed. The standard but heuristic tadpole improvement emerges from a mean field approxima...
Such large-structure tools of cohomology as toposes and derived categories stay close to arithmetic in practice, yet existing foundations for them go beyond the strong set theory ZFC. We formalize the practical insight by founding the theorems of EGA...
The theory of Wasserstein gradient flows in the space of probability measures has made an enormous progress over the last twenty years. It constitutes a unified and powerful framework in the study of dissipative partial differential equations (PDEs)...
In this note, we study an optimal transportation problem arising in density functional theory. We derive an upper bound on the semi-classical Hohenberg-Kohn functional derived by Cotar, Friesecke and Klüppelberg (2012) which can be computed in a str...
Widespread adoption of AI systems hinges on their ability to generate economic value that outweighs their inference costs. Evaluating this tradeoff requires metrics accounting for both performance and costs. Building on production theory, we develop...
In social choice theory, Sen's value restriction condition is a sufficiency condition restricted to individuals' ordinal preferences so as to obtain a transitive social preference under the majority decision rule. In this article, Sen's transitivity...
The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. We present...
In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash equilibrium for...