Related papers: Inductive Approach to Loop Vertex Expansion
Some time ago we extended our monogenity investigations and calculations of generators of power integral bases to the relative case. Up to now we considered (usually totally real) extensions of complex quartic fields. In the present paper…
Interpretable Machine Learning (IML) is expected to remove significant barriers for the application of Machine Learning (ML) algorithms in power systems. This letter first seeks to showcase the benefits of SHapley Additive exPlanations…
Based on transformation optics, a strategy is proposed to expose the inner one-dimensional space of a wave field inside a beam volume to the surface of the propagation medium and extend the space from one-dimensional to two-dimensional,…
We construct positive loops of Legendrian submanifolds in several instances. In particular, we partially recover G. Liu's result stating that any loose Legendrian admits a positive loop, under some mild topological assumptions on the…
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…
A concept of a rectangular diagram of a foliation in the three-sphere is introduced. It is shown that any co-orientable finite depth foliation in the complement of a link admits a presentation by a rectangular diagram compatible with the…
Achieving effective test-time scaling requires models to engage in In-Context Exploration -- the intrinsic ability to generate, verify, and refine multiple reasoning hypotheses within a single continuous context. Grounded in State Coverage…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
We present abstract acceleration techniques for computing loop invariants for numerical programs with linear assignments and conditionals. Whereas abstract interpretation techniques typically over-approximate the set of reachable states…
Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the…
We propose a unified approach to addition of some physical quantities (among which resistors and capacitors are the most well-known) that are usually encountered in introductory physics such that the formulae required to solve problems are…
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into…
The recently introduced series of description logics under the common moniker DL-Lite has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and…
The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…
Here, a non-linear analysis method is applied rather than classical one to study projective changes of Finsler metrics. More intuitively, a projectively invariant pseudo-distance is introduced and characterized with respect to the Ricci…
The purpose of this paper is to develop and study recursive proofs of coinductive predicates. Such recursive proofs allow one to discover proof goals in the construction of a proof of a coinductive predicate, while still allowing the use of…
We develop an effective field theory for lattice models, in which the only non-vanishing diagrams exactly reproduce the topology of the lattice. The Bethe-Peierls approximation appears naturally as the saddle point approximation. The…