Related papers: Past and future of the cap set problem

Coupled cluster Green's function (CCGF) approach has drawn much attention in recent years for targeting the molecular and material electronic structure problems from a many-body perspective in a systematically improvable way. Here, we will…

Set function learning has emerged as a crucial area in machine learning, addressing the challenge of modeling functions that take sets as inputs. Unlike traditional machine learning that involves fixed-size input vectors where the order of…

In this paper we study research trends in condensed matter physics. Trends are analyzed by means of the the number of publications in the different sub-fields as function of the years. We found that many research topics have a similar…

We consider the model selection problem for a large class of time series models, including, multivariate count processes, causal processes with exogenous covariates. A procedure based on a general penalized contrast is proposed. Some…

We give a survey on the concept of Poissonian pair correlation (PPC) of sequences in the unit interval, on existing and recent results and we state a list of open problems. Moreover, we present and discuss a quite recent multi-dimensional…

We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…

In this paper, we generalize the well known cut-set bound to the problem of lossy transmission of functions of arbitrarily correlated sources over a discrete memoryless multiterminal network.

We survey some of the state of the art regarding singularities in Lagrangian mean curvature flow. Some open problems are suggested at the end.

Status of the problem of neutrino masses, mixing and oscillations is discussed. Future perspectives are briefly considered.

We survey some recent work on topological quantum computation with gapped boundaries and boundary defects and list some open problems.

In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.

Results from molecular dynamics simulations of simple, structured particles capable of self-assembling into polyhedral shells are described. The analysis focuses on the growth histories of individual shells in the presence of an explicit…

We provide a brief topical outline of the persisting problem of the hyperon polarization and consider some future experimental prospects. The predictions which deserve experimental verification are proposed.

In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.

This is a survey of old and new problems and results in additive number theory.

The necessity of the FORM project is discussed. Then the evolutionary needs in particle physics are considered, looking at the trends over the years. A guess is made at what will be needed in the (near) future. The whole is concluded with…

We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that…

In this paper, we develop a series of boundary pointwise regularity for Dirichlet problems and oblique derivative problems. As applications, we give direct and simple proofs of the higher regularity of the free boundaries in obstacle-type…

We present some questions and suggestion on the second part of the Hilbert 16th problem

We pursue the study of families of functions on the natural numbers, with emphasis here on the bounded families. The situation being more complicated than the unbounded case, we attack the problem by classifying the families according to…