Related papers: FORM version 4.0
Standpoint logics offer unified modal logic-based formalisms for representing multiple heterogeneous viewpoints. At the same time, many non-monotonic reasoning frameworks can be naturally captured using modal logics, in particular using the…
Recent advances in generative AI have significantly enhanced the realism of multimodal media manipulation, thereby posing substantial challenges to manipulation detection. Existing manipulation detection and grounding approaches…
The release of SOSTOOLS v4.00 comes as we approach the 20th anniversary of the original release of SOSTOOLS v1.00 back in April, 2002. SOSTOOLS was originally envisioned as a flexible tool for parsing and solving polynomial optimization…
Optical systems are becoming increasingly important by resolving many bottlenecks in today's communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical…
Since its introduction in 2012, the factorization theory for rational motions quickly evolved and found applications in theoretical and applied mechanism science. We provide an accessible introduction to motion factorization with many…
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions.…
We present version 3.0 of the Mathematica package DoFun for the derivation of functional equations. In this version, the derivation of equations for correlation functions of composite operators was added. In the update, the general workflow…
In this paper we present a unification-based lexical platform designed for highly inflected languages (like Roman ones). A formalism is proposed for encoding a lemma-based lexical source, well suited for linguistic generalizations. From…
We present Version 9 of the Feynman-diagram calculator FormCalc and a flexible new suite of shell scripts and Mathematica packages based on FormCalc, which can be adapted and used as a template for calculations.
We present the Mathematical Functions Grimoire (FunGrim), a website and database of formulas and theorems for special functions. We also discuss the symbolic computation library used as the backend and main development tool for FunGrim, and…
Generating simulations to train intelligent agents in game-playing and robotics from natural language input, from user input or task documentation, remains an open-ended challenge. Existing approaches focus on parts of this challenge, such…
Datalog has become a popular language for writing static analyses. Because Datalog is very limited, some implementations of Datalog for static analysis have extended it with new language features. However, even with these features it is…
We explain the construction of Forcer, a FORM program for the reduction of four-loop massless propagator-type integrals to master integrals. The resulting program performs parametric IBP reductions similar to the three-loop Mincer program.…
Recently, a general tool called a holographic transformation, which transforms an expression of the partition function to another form, has been used for polynomial-time algorithms and for improvement and understanding of the belief…
Collecting and annotating morphological data present significant challenges, requiring linguistic expertise, methodological rigour, and substantial resources. These barriers are particularly acute for low-resource languages and varieties.…
In this paper, we show a new approach to transformations of an imperative program with function calls and global variables into a logically constrained term rewriting system. The resulting system represents transitions of the whole…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
The calculus of variations applied to the image processing requires some numerical models able to perform the variations of images and the extremization of appropriate actions. To produce the variations of images, there are several…
The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex…
This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their…