Related papers: A Recipe for Symbolic Geometric Computing: Long Ge…
A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. The basic idea is to map each pair of data points into a real-valued feature function defined on $[0,1]$. The construction of these feature…
The method of direct computation of universal (fibred) product in the category of commutative associative algebras of finite type with unity over a field is given and proven. The field of coefficients is not supposed to be algebraically…
We study Euclidean designs from the viewpoint of the potential energy. For a finite set in Euclidean space, We formulate a linear programming bound for the potential energy by applying harmonic analysis on a sphere. We also introduce the…
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…
Closed form expressions for a logarithm of general multivector (MV) in base-free form in real geometric algebras (GAs) Cl(p,q) are presented for all n=p+q=3. In contrast to logarithm of complex numbers (isomorphic to Cl(0,1), 3D logarithmic…
In this article, we consider the following capacitated covering problem. We are given a set $P$ of $n$ points and a set $\mathcal{B}$ of balls from some metric space, and a positive integer $U$ that represents the capacity of each of the…
Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying…
Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for constructing quantum error-correcting codes with desirable…
A hard hadron-collider event is treated here as a single geometric object - the kinematics and the discrete object-type labels of all reconstructed final-state particles encoded in one multivector $\evMV\in\Cl(1,3)\otimes\Vflav$ - rather…
The steepness property is a local geometric transversality condition on the gradient of a $C^2$-function which is fundamental in order to ensure the stability of sufficiently-regular nearly-integrable Hamiltonian systems over long…
An ensemble of symbolic, numeric and graphic computations developed to construct the Octonionic and compact G2 structures in Mathematica 8.0. Cayley-Dickenson Construction symbolically applied from Reals to Octonions. Baker-…
The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with…
Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…
Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and then lift the modular results to the rationals. This method…
As deep generative models have progressed, recent work has shown them to be capable of memorizing and reproducing training datapoints when deployed. These findings call into question the usability of generative models, especially in light…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
This volume contains papers presented at the Ninth International Symposium on Symbolic Computation in Software Science, SCSS 2021. Symbolic Computation is the science of computing with symbolic objects (terms, formulae, programs,…
This paper contains an attempt to formulate rigorously and to check predictions in enumerative geometry of curves following from Mirror Symmetry. The main tool is a new notion of stable map. We give an outline of a contsruction of…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not depend on the representation (aka coding)…