We explore the use of the method of Maximum Entropy (ME) as a technique to generate approximations. In a first use of the ME method the "exact" canonical probability distribution of a fluid is approximated by that of a fluid of hard spheres; ME is...
Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the first probl...
In theorem provers based on dependent type theory such as Coq and Lean, induction is a fundamental proof method and induction tactics are omnipresent in proof scripts. Yet the ergonomics of existing induction tactics are not ideal: they do not reliab...
We generalize pp elimination for modules, or more generally abelian structures, to a continuous logic environment where the abelian structure is equipped with a homomorphism to a compact (Hausdorff) group. We conclude that the continuous logic theory...
Precipitation strengthening is a key strengthening method for metallic materials. However, the temperature effect on precipitation strengthening is still unclear to date. Based on dislocation theory, a thermally-activated precipitation strengthening...
The interplay between variational functionals and the Brunn-Minkowski Theory is a well-established phenomenon widely investigated in the last thirty years. In this work, we prove the existence of solutions to the even logarithmic Minkowski problems a...
We discuss coincidences of pairs (f_1, f_2) of maps between manifolds. We recall briefly the definition of four types of Nielsen numbers which arise naturally from the geometry of generic coincidences. They are lower bounds for the minimum numbers MC...
Contents (Part 1): 1.Derivation of Lorentz Invariance and Three Space Dimensions in Generic Field Theory (C D. Froggatt and H. B. Nielsen) 2.Unitary Representations, Noncompact Groups SO(q; d - q)...(N. Mankoc Borstnik, H. B. Nielsen and D. Lukman)...
The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law...
We investigate the conditions under which Leonid meteoroids might generate short duration (burster) electrophonic sounds. A `first order' theory is employed to estimate the approximate electron number density in the meteoroid ablation column as a f...
How Enumerative Combinatorics met Special Functions, thanks to Joe Gillis...
In this article we report a novel analytic solution for a cosmological model with a matter content described by a one component dissipative fluid, in the framework of the causal Israel-Stewart theory. Some physically well motivated analytical relatio...
In this paper we will look at the book Mathematical Go by Elwyn Berlekamp and David Wolfe \cite{MG}, and argue that the definitions and theories that they use are not the correct ones. We will argue that the new theory of scoring play games as develo...
I give an introduction to the QCD-based theory of the heavy flavor hadrons and their weak decays. Trying to remain at the next-to-elementary level and skip technicalities, I concentrate on the qualitative description of the most important applicati...
Gribov approach to high-energy interactions of hadrons and nuclei is reviewed and applied to calculation of particle production in heavy-ions collisions. It is pointed out that the AGK (Abramovsky, Gribov, Kancheli) cutting rules is a powerful tool...
Quantum ESPRESSO is an open-source distribution of computer codes for quantum-mechanical materials modeling, based on density-functional theory, pseudopotentials, and plane waves, and renowned for its performance on a wide range of hardware architect...
The famous Goldbach conjecture remains open for nearly three centuries. Recently Goldbach graphs are introduced to relate the problem with the literature of Graph Theory. It is shown that the connectedness of the graphs is equivalent to the affirmati...
Numenta Platform for Intelligent Computing is an implementation of Hierarchical Temporal Memory (HTM), a theory of intelligence based strictly on the neuroscience of the neocortex. (⭐ 6357)
These are lecture notes of the QFT-I course I gave in an online mode at Chennai Mathematical Institute. The course focussed on the free relativistic quantum fields, their interactions in the perturbative scattering framework, standard computations of...
A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on polynomi...