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Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
Can the cross product be generalized? Why are the trace and determinant so important in matrix theory? What do all the coefficients of the characteristic polynomial represent? This paper describes a technique for `doodling' equations from…
Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…
With the continuous increase in the computational power and resources of modern high-performance computing (HPC) systems, large-scale ensemble simulations have become widely used in various fields of science and engineering, and especially…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
We reduce CR-structures on smooth elliptic and hyperbolic manifolds of CR-codimension 2 to parallelisms thus solving the problem of global equivalence for such manifolds. The parallelism that we construct is defined on a sequence of two…
While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations.…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
A "reduced" differential geometry adapted to the presence of abelian isometries is constructed.Classical T-duality diagonalizes in this setting, allowing us to get conveniently the transformation of the relevant geometrical objects such as…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
Many of the classic graph problems cannot be solved in the Massively Parallel Computation setting (MPC) with strongly sublinear space per machine and $o(\log n)$ rounds, unless the 1-vs-2 cycles conjecture is false. This is true even on…
We present a certified algorithm that takes a smooth algebraic curve in $\mathbb{R}^n$ and computes an isotopic approximation for a generic projection of the curve into $\mathbb{R}^2$. Our algorithm is designed for curves given implicitly…
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…
It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
After having investigated the real conic sections and their isoptic curves in the hyperbolic plane $\bH^2$ we consider the problem of the isoptic curves of generalized conic sections in the extended hyperbolic plane. This topic is widely…