Related papers: A pre-order principle and set-valued Ekeland varia…

In this paper I attempt to summarize the fundamental principles which underlie to Arrangement Field Theory. In my intention the exposition would be the most possible intelligible and self-contained. However the exposed concepts are…

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…

The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the…

This paper first makes an attempt to investigate the partial information near optimal control of systems governed by forward-backward stochastic differential equations with observation noise under the assumption of a convex control domain.…

Recently there has been an increased interest in unsupervised learning of disentangled representations using the Variational Autoencoder (VAE) framework. Most of the existing work has focused largely on modifying the variational cost…

This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…

An exactly solvable time-dependent quantum mechanical problem is employed to study the convergence properties of transition amplitudes calculated by using the Schwinger variational principle. A detailed comparison between the amplitudes…

We introduce the notion of order projections using the order unit property of a positive element in an order unit space and characterize them in terms of (geometric) orthogonality. We describe order projections of the order unit space…

This paper is concerned with an elliptic system of Kirchhoff type, driven by the variable-order fractional $p(x)$-operator. With the help of the direct variational method and Ekeland variational principle, we show the existence of a weak…

Conventional machine learning algorithms have traditionally been designed under the assumption that input data follows a vector-based format, with an emphasis on vector-centric paradigms. However, as the demand for tasks involving set-based…

The new integrable mapping with a simple geometric interpretation is presented. This mapping arise from the nonlinear superposition principle for the B\"acklund transformations of some vector evolution equation.

For many years, the intuitions underlying partial-order planning were largely taken for granted. Only in the past few years has there been renewed interest in the fundamental principles underlying this paradigm. In this paper, we present a…

We develop a generalisation of disentanglement in VAEs---decomposition of the latent representation---characterising it as the fulfilment of two factors: a) the latent encodings of the data having an appropriate level of overlap, and b) the…

Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…

This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…

Many key quantities in statistics and probability theory such as the expectation, quantiles, expectiles and many risk measures are law-determined maps from a space of random variables to the reals. We call such a law-determined map, which…

In this paper, we compute the iterated derived sets of the set of multiple t-values under the usual topology of R. Our results imply that the set of multiple t-values, ordered by >=, is a well-ordered set.

Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…

This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…

We present an elementary pedagogical derivation of the Brillouin-Wigner and the Rayleigh-Schr\"odinger perturbation theories with Epstein-Nesbet partitioning. A variant of the Brillouin-Wigner perturbation theory is also introduced, which…