Related papers: Computing Periods of Hypersurfaces
We compute Przyjalkowski-Shramov's resolution of the Calabi-Yau compactification of Givental's mirror Landau-Ginzburg model of the quadric hypersurfaces. We deduce the Picard-Fuchs equation for the narrow periods, which mirror the ambient…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…
This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…
Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…
Hypersurfaces of arbitrary causal character embedded in a spacetime are studied with the aim of extracting necessary and sufficient free data on the submanifold suitable for reconstructing the spacetime metric and its first derivative along…
The growing need for creating surfaces with specific wetting properties, such as superhyrdophobic behavior, asks for novel methods for their efficient design. In this work, a fast computational method for the evaluation of patterned…
We present a quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions. The latter are always fulfilled for infrastructures obtained…
Some of the most remarkable tilings and discrete quasiperiodic sets used in quasicrystal physics can be obtained by using strip projection method in a superspace of dimension four, five or six, and the projection of a unit hypercube as a…
In this paper, we will consider the period index problems of elliptic curves and introduce a value called generic index which is closed related to the essential dimension of Picard stacks. In particular, we will use examples to see that…
We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time points. The algorithm is obtained through a delicate…
Available algorithms for the initialization of volume fractions typically utilize exact functions to model fluid interfaces, or they rely on computationally costly intersections between volume meshes. Here, a new algorithm is proposed that…
Several natural complex configuration spaces admit surprising uniformizations as arithmetic ball quotients, by identifying each parametrized object with the periods of some auxiliary object. In each case, the theory of canonical models of…
We give two algorithms to compute linear determinantal representations of smooth plane curves of any degree over any field. As particular examples, we explicitly give representatives of all equivalence classes of linear determinantal…
We define a period map for classical Campedelli surfaces, using a covering trick as in the case of Enriques surfaces: the period map is shown to come from a family of Enriques surfaces, obtained as quotients of the Campedelli surface by an…
We show that smooth hypersurfaces in complex projective spaces with automorphism groups of maximum size are isomorphic to Fermat hypersurfaces, with a few exceptions. For the exceptions, we give explicitly the defining equations and…
Time series analysis finds wide applications in fields such as weather forecasting, anomaly detection, and behavior recognition. Previous methods attempted to model temporal variations directly using 1D time series. However, this has been…
This work presents a deep learning surrogate model for the fast simulation of high-dimensional frequency selective surfaces. We consider unit-cells which are built as multiple concatenated stacks of screens and their design requires the…
In characteristic $p>0$ and for $q$ a power of $p$, we compute the number of nonplanar rational curves of arbitrary degrees on a smooth Hermitian surface of degree $q+1$ under the assumption that the curves have a parametrization given by…
In their precedent work, the authors constructed closed oriented hyperbolic surfaces with pseudo-Anosov homeomorphisms from certain class of integral matrices. In this paper, we present a very simple algorithm to compute the Teichmueller…
A geometric algorithm is introduced for finding a symplectic basis of the first integral homology group of a compact Riemann surface, which is a $p$-cyclic covering of ${\mathbb C} P^1$ branched over 3 points. The algorithm yields a…