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Linear models for the radiative transfer equation have been well developed, while nonlinear models are seldom investigated even for slab geometry due to some essential difficulties. We have proposed a moment model in MPN for slab geometry…
Supersymmetric models with a strongly interacting superconformal hidden sector (HS) may drive soft SUSY breaking scalar masses, bilinear soft term B\mu and Higgs combinations m_{H_{u,d}}^2+\mu^2 to small values at some intermediate scale,…
Theoretical understanding of deep learning remains elusive despite its empirical success. In this study, we propose a novel "synaptic field theory" that describes the training dynamics of synaptic weights and biases in the continuum limit.…
We examine the procedure for integrating out heavy fields in supersymmetric (both global and local) theories. We find that the usual conditions need to be modified in general and we discuss the restrictions under which they are valid. These…
Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e. are sensitive to) only a subset of those parameters. Rigorously…
The complete quantum theory of closed superstrings is constructed using string diagrams endowed with metric having constant curvature $-1$. The elementary string diagrams are equipped with the analytic local coordinates induced from the…
Single--particle spectra of $\Lambda $ and $\Sigma $ hypernuclei are calculated within a relativistic mean--field theory. The hyperon couplings used are compatible with the $\Lambda $ binding in saturated nuclear matter, neutron-star masses…
Nonperturbative solutions to the nonlinear field equations in the NS sector of cubic as well as nonpolynomial superstring field theory can be obtained from a linear equation which includes a "spectral" parameter \lambda and a coboundary…
We study how the resonant decay of moduli fields arising in the Minimal Supersymmetric Standard Model (MSSM) could affect large scale curvature perturbations in the early universe. It has been known for some time that the presence of…
We show that any measurable solution of the cohomological equation for a H\"older linear cocycle over a hyperbolic system coincides almost everywhere with a H\"older solution. More generally, we show that every measurable invariant…
For population systems modeled by age-structured hyperbolic partial differential equations (PDEs) that are bilinear in the input and evolve with a positive-valued infinite-dimensional state, global stabilization of constant yield set points…
We introduce a Monte Carlo scheme for fully nonlinear parabolic nonlocal PDE's whose nonlinearity in of Hamilton-Jacobi-Bellman-Isaacs (HJBI for short). We avoid the difficulties of infinite L\'evy measure by truncation of the L\'evy…
We prove a Closing Lemma for nonuniformly hyperbolic measures of meromorphic maps. We prove also a theorem of approximation of the dynamics of such measures by Bernoulli coding maps.
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
We present a rough path analog of the classical Gronwall Lemma introduced recently by A. Deya, M. Gubinelli, M. Hofmanov\'a, S. Tindel in [arXiv:1604.00437] and discuss two of its applications. First, it is applied in the framework of rough…
We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
We show that geometric integrals of the type $\int_\Omega f\, d g^1\wedge \, d g^2$ can be defined over a two-dimensional domain $\Omega$ when the functions $f$, $g^1$, $g^2\colon \mathbb{R}^2\to \mathbb{R}$ are just H\"{o}lder continuous…
The following article is an application of commutative algebra to the study of multiparameter persistent homology in topological data analysis. In particular, the theory of finite free resolutions of modules over polynomial rings is applied…
We study the Lefschetz fixed point formula for constructible sheaves with higher-dimensional fixed point sets. We give another proof to the explicit description of Lefschetz cycles in our previous paper. For this purpose, we introduce a new…