Related papers: A Recipe for Symbolic Geometric Computing: Long Ge…
Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic…
In this paper, we present a deep learning-based framework for solving geometric construction problems through visual reasoning, which is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the…
3D shape abstraction has drawn great interest over the years. Apart from low-level representations such as meshes and voxels, researchers also seek to semantically abstract complex objects with basic geometric primitives. Recent deep…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
This paper explains how, following the representation of 3D crystallographic space groups in Clifford's geometric algebra, it is further possible to similarly represent the 162 so called subperiodic groups of crystallography in Clifford's…
Following the success of the so-called algebraic approach to the study of decision constraint satisfaction problems (CSPs), exact optimization of valued CSPs, and most recently promise CSPs, we propose an algebraic framework for valued…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this…
The power of Clifford or, geometric, algebra lies in its ability to represent geometric operations in a concise and elegant manner. Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into…
The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
Bounded model finding is a key technique for validating software designs, usually obtained by translating high-level specifications into SAT/SMT problems. Although effective, such translations introduce a semantic gap and a dependency on…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often suffer from…
We give a proof of the $A_2$ conjecture in geometrically doubling metric spaces (GDMS), i.e. a metric space where one can fit not more than a fixed amount of disjoint balls of radius $r$ in a ball of radius $2r$. Our proof consists of three…
In stochastic quantization, ordinary 4-dimensional Euclidean quantum field theory is expressed as a functional integral over fields in 5 dimensions with a fictitious 5th time. This is advantageous, in particular for gauge theories, because…
This paper describes a computational, declarative approach to prosodic morphology that uses inviolable constraints to denote small finite candidate sets which are filtered by a restrictive incremental optimization mechanism. The new…
The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…