Related papers: Current Open Questions in Complete Mixability
Since Choo and Siow (2006), a burgeoning literature has analyzed matching markets when utility is perfectly transferable and the joint surplus is separable. We take stock of recent methodological developments in this area. Combining…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.
The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal…
It is revealed that distribution functions of practical gases relate to singularities and such singularities can, with molecular motion, spread to the entire region of interest. It is also shown that even common continuous distribution…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories,…
In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced…
Traditionally, solubility and mixing belong to the realm of chemistry and material sciences and many standard textbooks on physical chemistry treat this problem, usually within the scope of thermodynamics. Here apart from thermodynamics we…
Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…
We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.
Categories enriched over a commutative unital quantale can be studied as generalized, or many-valued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain…
Cooperation information sharing is important to theories of human learning and has potential implications for machine learning. Prior work derived conditions for achieving optimal Cooperative Inference given strong, relatively restrictive…
The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional…
Say that a finite group $G$ is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on $G$. We present conditions and obstructions to mixability. We show that $2$-groups, the…
We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to…
We know that neutrino mass and mixing provide a window to physics beyond the Standard Model. Now this window is open, at least partly. And the questions are: what do we see, which kind of new physics, and how far "beyond"? I summarize the…
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
We explore the consequences of exactness or K-mixing on the notions of mixing (a.k.a. infinite-volume mixing) recently devised by the author for infinite-measure-preserving dynamical systems.
The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…