Related papers: FORM facts
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
We present a simple and concise semantics for temporal planning. Our semantics are developed and formalised in the logic of the interactive theorem prover Isabelle/HOL. We derive from those semantics a validation algorithm for temporal…
In this work, on the one hand, we survey and amplify old results concerning tame dynamical systems and, on the other, prove some new results and exhibit new examples of such systems. In particular, we study tame symbolic systems and…
The article provides a brief survey of the mathematics of some of the newly being developed so called "hybrid" (also called "multi-physics" or "multi-wave") imaging techniques.
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…
An overview of current multiple alignment systems to date are described.The useful algorithms, the procedures adopted and their limitations are presented.We also present the quality of the alignments obtained and in which cases(kind of…
The form factor of hadronic systems in various forms of relativistic quantum mechanics is considered. Motivated by the agreement of the nucleon ``point-form'' results with experiment, results for a toy model corresponding to the simplest…
Thousands of different forms (words) are associated with thousands of different meanings (concepts) in a language computer model. Reasonable agreement with reality is found for the number of languages in a family and the Hamming distances…
A multiparameter class of integrable systems is introduced.
Some features of modern simulation tools for high-energy physics are reviewed.
In this work, we offer a historical stroll through the vast topic of binary quadratic forms. We begin with a quick review of their history and then an overview of contemporary algebraic developments on the subject.
Transformer model architectures have garnered immense interest lately due to their effectiveness across a range of domains like language, vision and reinforcement learning. In the field of natural language processing for example,…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
A closed formula multiallelic Walsh (or Hadamard) transform is introduced. Basic results are derived, and a statistical interpretation of some of the resulting linear forms is discussed.
We introduce a formalism that exploits the many-input many-output nature of nodes in quantum circuits. There is a diagrammatic and an algebraic version, the latter similar to the spinor formalism of general relativity. This allows us to…
We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present some results and examples and conclude our paper with a…
Understanding how cells respond to external stimuli is a central challenge in biomedical research and drug development. Current computational frameworks for modelling cellular responses remain restricted to two-dimensional representations,…
The principle of virtual work for dissipative systems is stated. Partially controlled systems are discussed and the concept of a generating families of forms is introduced. The notion of a critical point of a family of convex forms is…
The article suggests a description of a system of tables with a set of special lists absorbing a semantics of data and reflects a fullness of data. It shows how their parallel processing can be constructed based on the descriptions. The…