Related papers: Number theory combination: natural density and SMT
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Dempster-Shafer theory of evidence is widely applied to uncertainty modelling and knowledge reasoning because of its advantages in dealing with uncertain information. But some conditions or requirements, such as exclusiveness hypothesis and…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
We will discuss the key concepts in density functional theory (DFT), how it can be used to model experimental data, and consider how the synergy between DFT and experiment can give significant insights. The discussion will centre on the…
It involves the completely novel ways of integrating ML algorithms with traditional statistical modelling that has changed the way we analyze data, do predictive analytics or make decisions in the fields of the data. In this paper, we study…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The…
We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the S-matrix. In the…
Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
One possible ramification of unified theories of nature such as string theory that may underlie the conventional standard model is the possible spontaneous breakdown of Lorentz and CPT symmetry. In this talk, the formalism for inclusion of…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently…
In this article, we study about the $\lambda$-statistical convergence with respect to the density of moduli and find some results related to statistical convergence as well. Also we introduce the concept of $f_\lambda$-summable sequence and…
Smoothing is an estimation technique that takes into account both past and future observations, and can be more accurate than filtering alone. In this Letter, a quantum theory of smoothing is constructed using a time-symmetric formalism,…