Related papers: Formalization of Transform Methods using HOL Light
This paper introduces a new method for solving the planar heat equation based on the Lightning Method. The lightning method is a recent development in the numerical solution of linear PDEs which expresses solutions using sums of polynomials…
The Fourier transform method can be applied to obtain electromagnetic knots, which are solutions of Maxwell equations in vacuum with non-trivial topology of the field lines and especial properties. The program followed in this work allows…
Event Tree (ET) analysis is widely used as a forward deductive safety analysis technique for decision-making at the critical-system design stage. ET is a schematic diagram representing all possible operating states and external events in a…
Formal methods are widely recognized as a powerful engineering method for the specification, simulation, development, and verification of distributed interactive systems. However, most formal methods rely on a two-valued logic, and are…
Optoacoustic imaging technologies require fast and accurate signal pre-processing algorithms to enable widespread deployment in clinical and home-care settings. However, they still rely on the Discrete Fourier Transform (DFT) as the default…
The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method…
We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the…
In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
Deep learning models such as the Transformer are often constructed by heuristics and experience. To provide a complementary foundation, in this work we study the following problem: Is it possible to find an energy function underlying the…
We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…
Model transformation tools assist system designers by reducing the labor--intensive task of creating and updating models of various aspects of systems, ensuring that modeling assumptions remain consistent across every model of a system, and…
Transformers have made significant strides across various artificial intelligence domains, including natural language processing, computer vision, and audio processing. This success has naturally garnered considerable interest from both…
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…
We obtain closed-form solutions of several inhomogeneous Lienard equations by the factorization method. The two factorization conditions involved in the method are turned into a system of first-order differential equations containing the…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…
Two methods for fast Fourier transforms are used in a quantum context. The first method is for systems with dimension of the Hilbert space $D=d^n$ with $d$ an odd integer, and is inspired by the Cooley-Tukey formalism. The `large Fourier…
A new transform over finite fields, the finite field Hartley transform (FFHT), was recently introduced and a number of promising applications on the design of efficient multiple access systems and multilevel spread spectrum sequences were…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…