Related papers: 447 Instances of Hypergeometric 3F2(1)
We propose a framework that allows us to analyze different variants of HDG methods for the static Maxwell equations using one simple analysis. It reduces all the work to the construction of projections that best fit the structures of the…
The method of dimensional recurrences proposed by one of the authors [1,2] is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result…
Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we…
A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the…
This study addresses the challenge of accurately forecasting geometric deviations in manufactured components using advanced 3D surface analysis. Despite progress in modern manufacturing, maintaining dimensional precision remains difficult,…
We call a cusped hyperbolic 3-manifold tetrahedral if it can be decomposed into regular ideal tetrahedra. Following an earlier publication by three of the authors, we give a census of all tetrahedral manifolds and all of their combinatorial…
Data sets that are specified by a large number of features are currently outside the area of applicability for quantum machine learning algorithms. An immediate solution to this impasse is the application of dimensionality reduction methods…
Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the…
Using superspace projection operators we provide a classification of (3/2,2) off-shell supermultiplets which are realized in terms of a real axial vector superfield, with or without compensating superfields. Any linearized supergravity…
Geometric constraints between feature matches are critical in 3D point cloud registration problems. Existing approaches typically model unordered matches as a consistency graph and sample consistent matches to generate hypotheses. However,…
We present a new implementation of the numerical integration of the classical, gravitational, N-body problem based on a high order Hermite's integration scheme with block time steps, with a direct evaluation of the particle-particle forces.…
We introduce PHYSICS, a comprehensive benchmark for university-level physics problem solving. It contains 1297 expert-annotated problems covering six core areas: classical mechanics, quantum mechanics, thermodynamics and statistical…
The rise of vision-language foundation models marks an advancement in bridging the gap between human and machine capabilities in 3D scene reasoning. Existing 3D reasoning benchmarks assume real-time scene accessibility, which is impractical…
We compute some numerical invariants of the lines on hyperplane sections of a smooth cubic threefold over complex numbers. We also prove that for any smooth hypersurface $X\subset \mathbb P^{n+1}$ of degree $d$ over an algebraically closed…
This study presents a new high-fidelity multi-modal dataset containing 16000+ geometric variants of automotive hoods useful for machine learning (ML) applications such as engineering component design and process optimization, and…
We introduce partial duality of hypermaps, which include the classical Euler-Poincar\'e duality as a particular case. Combinatorially, hypermaps may be described in one of three ways: as three involutions on the set of flags (bi-rotation…
In the past 20 years, compactifications of the families of curves in algebraic varieties X have been studied via stable maps, Hilbert schemes, stable pairs, unramified maps, and stable quotients. Each path leads to a different enumeration…
The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…
In this paper it will be shown that the Standard Model in 3+1 dimensions is a gauge fixed version of a 2T-physics field theory in 4+2 dimensions, thus establishing that 2T-physics provides a correct description of Nature from the point of…
We measure the 3PCF of 300 halo catalogs from the Minerva simulations covering a total volume of $~1000 h^{-3} \mathrm{Gpc}^3$. Each 3PCF measurement includes all possible triangular configurations with sides between 20 and…