Related papers: A method of constructing pairwise balanced designs…
A weighted $t$-design in $\mathbb{R}^d$ is a finite weighted set that exactly integrates all polynomials of degree at most $t$ with respect to a given probability measure. A fundamental problem is to construct weighted $t$-designs with as…
Deep clustering as an important branch of unsupervised representation learning focuses on embedding semantically similar samples into the identical feature space. This core demand inspires the exploration of contrastive learning and…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…
In this note, we give direct constructions of some group divisible designs (GDDs) with block size $4$ that have up to $50$ points.
Rectangular designs are classified as regular, Latin regular, semiregular, Latin semiregular and singular designs. Some series of selfdual as well as alpharesolvable designs are obtained using matrix approaches which belong to the above…
The collinear factorization theorem, combined with finite-order calculations in perturbative QCD, provides a powerful framework to obtain predictions for many collider observables. However, for observables which involve multiple energy…
Balanced incomplete block designs (BIBDs) are a class of designs with v treatments and b blocks of size k that are optimal with regards to a wide range of optimality criteria, but it is not clear which designs to choose for combinations of…
Within PCB design, the reuse of circuit design blocks is a major preventing factor inhibiting beginners from reusing designs made by experts, a common practice in software but non-existent in circuit design at large. Despite efforts to…
In federated learning, models are learned from users' data that are held private in their edge devices, by aggregating them in the service provider's "cloud" to obtain a global model. Such global model is of great commercial value in, e.g.,…
The aim of this paper is to present a recursive construction of simple t-designs for arbitrary t. The construction is of purely combinatorial nature and it requires finding solutions for the indices of the ingredient designs that satisfy a…
Predefined evenly-distributed class centroids (PEDCC) can be widely used in models and algorithms of pattern classification, such as CNN classifiers, classification autoencoders, clustering, and semi-supervised learning, etc. Its basic idea…
Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…
Discovering new physical products and processes often demands enormous experimentation and expensive simulation. To design a new product with certain target characteristics, an extensive search is performed in the design space by trying out…
Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…
A generalization of the Gr\"{u}nwald difference approximation for fractional derivatives in terms of a real sequence and its generating function is presented. Properties of the generating function are derived for consistency and order of…
We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…
Motion planning is an important and well-studied field of robotics. A typical approach to finding a route is to construct a {\em cell graph} representing a scene and then to find a path in such a graph. In this paper we present and analyze…
Constant dimension codes (CDCs), as special subspace codes, have received a lot of attention due to their application in random network coding. This paper introduces a family of new codes, called rank metric codes with given ranks (GRMCs),…
Tensors are ubiquitous in science and engineering and tensor factorization approaches have become important tools for the characterization of higher order structure. Factorizations includes the outer-product rank Canonical Polyadic…