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Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…
Although machine learning has been successfully used to propose novel molecules that satisfy desired properties, it is still challenging to explore a large chemical space efficiently. In this paper, we present a conditional molecular design…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm allows the use of the same piece of computer code to evaluate any particular diagram in any…
This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.…
Generating novel molecules with optimal properties is a crucial step in many industries such as drug discovery. Recently, deep generative models have shown a promising way of performing de-novo molecular design. Although graph generative…
Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using…
Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…
ScaleLat (Scale Lattice) is a computer program written in C for performing the atomic structure analysis of multi-phase system or high entropy alloys (HEAs). The program implements an atomic cluster extraction algorithm to obtain all…
We present a general framework to generate trees every vertex of which has a non-negative weight and a color. The colors are used to impose certain restrictions on the weight and colors of other vertices. We first extend the enumeration…
Designing molecular structures with desired chemical properties is an essential task in drug discovery and material design. However, finding molecules with the optimized desired properties is still a challenging task due to combinatorial…
Patterns, which are collections of elements arranged in regular or near-regular arrangements, are an important graphic art form and widely used due to their elegant simplicity and aesthetic appeal. When a pattern is encoded as a flat image…
This article builds on Thurston's height functions. His tiling algorithm is reinterpreted using lattice theory and then generalized in order to generate any tiling of a hole-free region. Combined with a natural encoding of tilings by words,…
We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show…
This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:L\to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications…
The paper discusses the construction of high dimensional spatial discretizations for arbitrary multivariate trigonometric polynomials, where the frequency support of the trigonometric polynomial is known. We suggest a construction based on…
In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…
Efficient algorithms for searching for optimal saturated designs are widely available. They maximize a given efficiency measure (such as D-optimality) and provide an optimum design. Nevertheless, they do not guarantee a \emph{global}…
A promising approach for scaling-up trapped-ion quantum computer platforms is by storing multiple trapped-ion qubit sets ('ion crystals') in segmented microchip traps and to interconnect these via physical movement of the ions…