Combinatorial Procedure Research Articles

Generalised Gabriel-Roiter measure and thin representations

For Dynkin and Euclidean quivers, it is shown that Gabriel-Roiter measures of thin representations equal the induced chain length functions on the corresponding system of subquivers. This allows a combinatorial procedure to find GR filtrations of thin representations, showing that GR measures of thin representations are field-independent. It is proved that an indecomposable filtration of a thin representation is a GR filtration for a suitable choice of a length function on the category of finite-dimensional representations.

Benders decomposition algorithms for minimizing the spread of harmful contagions in networks

The COVID-19 pandemic has been a recent example for the spread of a harmful contagion in large populations. Moreover, the spread of harmful contagions is not only restricted to an infectious disease, but is also relevant to computer viruses and malware in computer networks. Furthermore, the spread of fake news and propaganda in online social networks is also of major concern. In this study, we introduce the measure-based spread minimization problem (MBSMP), which can help policy makers in minimizing the spread of harmful contagions in large networks. We develop exact solution methods based on branch-and-Benders-cut algorithms that make use of the application of Benders decomposition method to two different mixed-integer programming formulations of the MBSMP: an arc-based formulation and a path-based formulation. We show that for both formulations the Benders optimality cuts can be generated using a combinatorial procedure rather than solving the dual subproblems using linear programming. Additional improvements such as using scenario-dependent extended seed sets, initial cuts, and a starting heuristic are also incorporated into our branch-and-Benders-cut algorithms. We investigate the contribution of various components of the solution algorithms to the performance on the basis of computational results obtained on a set of instances derived from existing ones in the literature.

Note on the moment generating function of the multivariate normal distribution

We present a streamlined proof of a formula for the derivatives of the moment generating function of the multivariate normal distribution. We formulate it in terms of the summation of the contractions by pairings, which encodes a combinatorial computation procedure. We give two applications. First, we provide a simple proof of Isserlis’ theorem and derive a formula for the moments of the multivariate normal distribution. Second, we calculate the moments of the product of a finite number of correlated normally and lognormally distributed random variables.

Zorro: Valid, Sparse, and Stable Explanations in Graph Neural Networks

With the ever-increasing popularity and applications of graph neural networks, several proposals have been made to explain and understand the decisions of a graph neural network. Explanations for graph neural networks differ in principle from other input settings. It is important to attribute the decision to input features and other related instances connected by the graph structure. We find that the previous explanation generation approaches that maximize the mutual information between the label distribution produced by the model and the explanation to be restrictive. Specifically, existing approaches do not enforce explanations to be valid, sparse, or robust to input perturbations. In this paper, we lay down some of the fundamental principles that an explanation method for graph neural networks should follow and introduce a metric <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RDT-Fidelity</i> as a measure of the explanation's effectiveness. We propose a novel approach Zorro based on the principles from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rate-distortion theory</i> that uses a simple combinatorial procedure to optimize for RDT-Fidelity. Extensive experiments on real and synthetic datasets reveal that Zorro produces sparser, stable, and more faithful explanations than existing graph neural network explanation approaches.

Dynamic Resilience Quantification of Hydropower Infrastructure in Multihazard Environments

Ensuring the continued functionality of hydropower infrastructure is of the greatest importance, considering the devastating socioeconomic and environmental impacts of dam operation failures. Among the different approaches currently adopted in hydropower dam operational safety, those that are resilience-based are at the leading edge because they focus on assessing the dynamic system performance pre-, during-, and post-hazard exposures. However, the main challenge for such assessment pertains to the complexity associated with the dynamic operation simulation of hydropower dam systems that consist of several components with nonlinear interdependencies. Moreover, the infrastructure’s exposure to a multihazard environment, which may impact one or more hydropower critical system components, poses further challenges to understanding possible subsequent dam operation failure scenarios. This study develops a resilience-centric system dynamics simulation model that provides a holistic representation of hydropower dam system components to estimate the system’s dynamic resilience in multihazard environments. The study also discusses a combinatorial procedure to generate multihazard scenarios, where a primary hazard can trigger one or more subsequent hazards. Finally, an actual hydropower dam is employed to demonstrate the developed model utility in assessing the resilience of complex infrastructure under a wide range of multihazard scenarios. The proposed model provides valuable decision support tools for infrastructure systemic risk mitigation in multihazard environments—facilitating the development of effective resilience planning strategies.

On toral posets and contact Lie algebras

A (2k+1)-dimensional Lie algebra is called contact if it admits a one-form φ such that φ∧(dφ)k≠0. Here, we extend recent work to describe a combinatorial procedure for generating contact, type-A Lie poset algebras whose associated posets have chains of arbitrary cardinality, and we conjecture that our construction leads to a complete characterization.

Dynamic analysis of multi-cracked truss and frame structures with uncertain-but-bounded damage

The present paper aims to provide a contribution in the study of the dynamic response of cracked truss-like and frame-like structures with uncertain damage modeled by following a non-probabilistic approach. By adopting a finite element model to describe the cracked members with fully open cracks, in the framework of the interval analysis, the parameters identifying the cracks depths are modeled as uncertain‑but-bounded variables.The proposed procedure allows to evaluate lower and upper bounds of the time-varying response of multi-cracked trusses and frames subjected to deterministic excitation by applying two parallel generalized modal analyses corresponding to two appropriate combinations of the endpoints of the interval uncertainties. The method is validated through numerical tests and its accuracy is confirmed by the excellent agreement between the response bounds calculated via the present approach compared with the exact reference bounds derived by a combinatorial procedure (vertex method) merged with the Monte Carlo method.

Combinatorics, Composition, Copia: Mersenne’s Permutations as Rhetoric of Abundance

Abstract This article seeks to explain the meaning and function of Mersenne’s exhaustive lists of note permutations. As is true for all of Mersenne’s labors, the permutations are at their deepest level explicable in terms of his religious commitments—in this case, his faith in the ineffable plenitude of God’s creation. Yet, Mersenne also intended the permutations and the combinatorial procedures that generate them to serve as the foundation of a pedagogy of compositional invention. That pedagogy, this article proposes, is tacitly informed by the rhetorical notion of copia, most comprehensively theorized by Erasmus in his influential De copia.

Determination of the most informative chemical elements for discrimination of rice samples according to the producing region

Several approaches to assess the authenticity of food products have been developed, given that fraudulent products may impact consumers' confidence, affect commercial trades and lead to health risks. This paper proposes an approach to identify the chemical elements that optimally discriminate rice samples according to their producing region in the South of Brazil, the largest rice producer outside Asia. A combinatorial procedure on the concentration of 26 elements determined using inductively coupled mass spectrometry (ICP-MS) and liquid chromatography hyphenated with ICP-MS from 640 rice samples was coupled with Support Vector Machine. The assessed elements included nonmetal and metal elements of 3 types of rice collected from 5 rice-producing regions. The framework selected Mn, Fe, Cu, Zn, Ni, Mo, Cd, Cs, As, Rb, Se, and iAs as the most informative elements for tracking samples’ origin. The concentration of such elements is strongly affected by fertilization procedures and soil composition.

Robust and self-healing polydimethylsiloxane/carbon nanotube foams for electromagnetic interference shielding and thermal insulation

Polymer-based electromagnetic interference (EMI) shielding materials with low density, low thermal conductivity, strong mechanical properties, good self-healing and high shielding performance are ideal candidates for military and aviation applications. However, conflicts between the desired properties result in tremendous challenges in the design and fabrication of these polymer materials. Here, we develop a novel approach to the preparation of excellent elastomeric foams that can meet the aforementioned requirements. A segregated carbon nanotube (CNT) network and porous structure are constructed synchronously in a polydimethylsiloxane (PDMS) matrix by employing a combinatorial procedure of suspension mixing and the template foaming method. The resulting foams exhibit a novel “sea-island” structure, in which the rubber phase with a segregated CNT network and ultrathin-shell expanded polymer microspheres are regarded as the continuous phase and the disperse phase, respectively. The obtained foam possesses an adjustable density (0.26–0.6 g/cm3), considerably low thermal conductivity (0.028–0.064 W/(m·K)), preeminent electrical conductivity (44.23 S/m), outstanding compressive strength (14.67 MPa), and good impact strength (2.80 kJ/m2). Furthermore, the EMI shielding effectiveness is excellent, reaching 44.51 dB, and 88.76% of the shielding effectiveness can be maintained after the self-healing procedure. These results confirm that the obtained foam has great potential for modern electronics and aerospace applications.

Feeder Load Balancing Using Genetic Algorithms and Artificial Neural Network

Low voltage power distribution system problems such as system planning, energy loss minimization and restoration usually involve proper load balancing or network reconfiguration procedures. To achieve an appreciable level of load phase balance, feeder reconfiguration using appropriate switching control strategy such as: Simulated Annealing, Tabu Search, Particle Swarm Optimization, and heuristic algorithms are viable preferences. However, the systematic solution to load phase balancing can be greatly enhanced optimally through implementation of an appropriate combinatorial optimization procedure such as Genetic Algorithms and Artificial Neural Network. Accordingly, this paper presents a genetic algorithms procedure to enhance the load phase balancing optimization and then train an artificial neural network to automate the reconfiguration of the distribution network loads, thus ensuring an optimal phase balancing in the system. An Intel® 2.0 GHz, 4GB RAM HP255 computer-based MATLAB® 14 was used for the neural network training, testing, and the implementation of the genetic algorithms. The outputs of the algorithms are the switching sequence for a balanced network. The parameters ΔIph (max - min) and Δ(Iph – Imax) which is the maximum difference between the phase currents, which are ideally zero if there are no imbalances in the network, shows considerable improvement in the balancing when compared with other literatures. This work presents the application examples of the proposed methods using real test data.

Combined effect of donor doping and RGO (reduced graphene oxide) coating in La/Nb-doped SrTiO3 thermoelectrics

SrTiO3 (STO) is one of the most promising oxide thermoelectric (TE) materials with high thermopower, but the low electrical conductivity and high thermal conductivity are still issues to be solved. Recently, grain boundary engineering using reduced graphene oxide (RGO) has been demonstrated to have capable of simultaneously improving both the electrical and thermal properties of STO. In this study, we investigated the combined effect of La/Nb doping and RGO coating in STO to improve further the electrical conductivity and the TE efficiency of STO materials. Two series of La- and Nb-doped Sr1-xLaxTi1-yNbyO3 (x, y = 0–0.02) samples incorporated with RGO were prepared by a combinatorial procedure of solid-state reaction, RGO coating, and the spark plasma sintering (SPS) process. The structural, morphological and temperature-dependent thermoelectric properties of the Sr1-xLaxTi1-yNbyO3/RGO were studied and as a result, the figure of merit was enhanced ∼6.5 times by the combined effect of donor doping and lowering the double Schottky barrier height due to RGO at grain boundaries.

Neural correlates of semantic integration in Spanish verb-noun compounds: an ERP study

ABSTRACT It is assumed that semantic transparency in compounds depends on integration of constituents and head transparency. Spanish verb-noun compounds are semantically and morphologically exocentric, lacking a head. We studied if verb argument structure determines differences in semantic integration and morphological decomposition. During a lexical decision task, Agentives (referent takes the role of agent), and Metaphoricals (involving methaphorical patterns to construct meaning), were displayed as whole words or separated into constituents. Agentives were responded better and faster than Metaphoricals, with no interaction between compound type and presentation mode, suggesting constituent decomposition for both compounds. Early electrophysiological effects related to visual recognition, and an N400 component for Metaphoricals, suggest constituent semantic integration. Differences seemed related to combinatorial procedures: in Agentives the meaning of constituents is easily integrated to form compound meaning; in Metaphoricals, this procedure is inhibited, and compound meaning is accessed through the metaphoric relation that links both constituents.

Scientific Creativity: Discovery and Invention as Combinatorial.

Although scientific creativity has often been described as combinatorial, the description is usually insufficiently formulated to count as a precise scientific explanation. Therefore, the current article is devoted to elaborating a formalization defined by three combinatorial parameters: the initial probability p, the final utility u, and the scientist’s prior knowledge of that utility v. These parameters then lead logically to an 8-fold typology involving two forms of expertise, two irrational combinations, and four “blind” combinations. One of the latter provides the basis for the definition of personal creativity as c=(1−p)u(1−v), that is, the multiplicative product of originality, utility, and surprise. This three-criterion definition then has six critical implications. Those implications lead to a discussion of various combinatorial processes and procedures that include a treatment of the No Free Lunch Theorems regarding optimization algorithms as well as the creativity-maximizing phenomena of mind wandering and serendipity. The article closes with a discussion of how scientific creativity differs from artistic creativity. Besides the obvious contrasts in the ideas entering the combinatorial processes and procedures, scientific combinations, products, and communities strikingly differ from those typical of the arts. These differences also imply contrasts in developmental experiences and personality characteristics. In sum, the formal combinatorial analysis enhances our understanding of scientific creativity.

Non-Extensive Fragmentation of Natural Products and Pharmacophore-Based Virtual Screening as a Practical Approach to Identify Novel Promising Chemical Scaffolds.

Fragment-based drug design (FBDD) and pharmacophore modeling have proven to be efficient tools to discover novel drugs. However, these approaches may become limited if the collection of fragments is highly repetitive, poorly diverse, or excessively simple. In this article, combining pharmacophore modeling and a non-classical type of fragmentation (herein called non-extensive) to screen a natural product (NP) library may provide fragments predicted as potent, diverse, and developable. Initially, we applied retrosynthetic combinatorial analysis procedure (RECAP) rules in two versions, extensive and non-extensive, in order to deconstruct a virtual library of NPs formed by the databases Traditional Chinese Medicine (TCM), AfroDb (African Medicinal Plants database), NuBBE (Nuclei of Bioassays, Biosynthesis, and Ecophysiology of Natural Products), and UEFS (Universidade Estadual de Feira de Santana). We then developed a virtual screening (VS) using two groups of natural-product-derived fragments (extensive and non-extensive NPDFs) and two overlapping pharmacophore models for each of 20 different proteins of therapeutic interest. Molecular weight, lipophilicity, and molecular complexity were estimated and compared for both types of NPDFs (and their original NPs) before and after the VS proceedings. As a result, we found that non-extensive NPDFs exhibited a much higher number of chemical entities compared to extensive NPDFs (45,355 vs. 11,525 compounds), accounting for the larger part of the hits recovered and being far less repetitive than extensive NPDFs. The structural diversity of both types of NPDFs and the NPs was shown to diminish slightly after VS procedures. Finally, and most interestingly, the pharmacophore fit score of the non-extensive NPDFs proved to be not only higher, on average, than extensive NPDFs (56% of cases) but also higher than their original NPs (69% of cases) when all of them were also recognized as hits after the VS. The findings obtained in this study indicated that the proposed cascade approach was useful to enhance the probability of identifying innovative chemical scaffolds, which deserve further development to become drug-sized candidate compounds. We consider that the knowledge about the deconstruction degree required to produce NPDFs of interest represents a good starting point for eventual synthesis, characterization, and biological activity studies.

Symplectic Keys and Demazure Atoms in Type C

We compute, mimicking the Lascoux-Schützenberger type A combinatorial procedure, left and right keys for a Kashiwara-Nakashima tableau in type C. These symplectic keys have a similar role as the keys for semistandard Young tableaux. More precisely, our symplectic keys give a tableau criterion for the Bruhat order on the hyperoctahedral group and cosets, and describe Demazure atoms and characters in type C. The right and the left symplectic keys are related through the Lusztig involution. A type C Schützenberger evacuation is defined to realize that involution.

A computational model for gestalt proximity principle on dot patterns and beyond.

The human visual system has the ability to group parts of stimuli into larger, inherently structured units. In this article, a computational model inspired by tolerance space theory simulating the human perceptual grouping of dot patterns is proposed. Tolerance space theory introduces a tolerance relation to a discrete set to formulate the continuity of the discrete patterns. The model proposed herein includes one- and two-reach methods based on the assumption that dot patterns can be represented in the proposed extended tolerance space (ETS). Both methods are used to construct a ratio neighborhood graph (RANG), calculate tolerance from the diagram, compute the new RANG, and then rebuild continuous structures from the new RANG with a combinatorial procedure. Experiments are conducted to show the high consistency of the proposed model with human perception for various shapes of dot patterns, its ability to simulate Gestalt proximity and similarity principles, and its potential application in computer vision. In addition, the close relationship of the proposed model with the Pure Distance Law is comprehensively revealed, and the hierarchical representation of perceptual grouping is simulated with an adaptation of the proposed model based on the ETS.

Combinatorial Reid's recipe for consistent dimer models

Reid's recipe for a finite abelian subgroup $G\subset \text{SL}(3,\mathbb{C})$ is a combinatorial procedure that marks the toric fan of the $G$-Hilbert scheme with irreducible representations of $G$. The geometric McKay correspondence conjecture of Cautis--Logvinenko that describes certain objects in the derived category of $G\text{-Hilb}$ in terms of Reid's recipe was later proved by Logvinenko et al. We generalise Reid's recipe to any consistent dimer model by marking the toric fan of a crepant resolution of the vaccuum moduli space in a manner that is compatible with the geometric correspondence of Bocklandt--Craw--Quintero-V\'{e}lez. Our main tool generalises the jigsaw transformations of Nakamura to consistent dimer models.

Combinatorial K-Means Clustering as a Machine Learning Tool Applied to Diabetes Mellitus Type 2.

A new original procedure based on k-means clustering is designed to find the most appropriate clinical variables able to efficiently separate into groups similar patients diagnosed with diabetes mellitus type 2 (DMT2) and underlying diseases (arterial hypertonia (AH), ischemic heart disease (CHD), diabetic polyneuropathy (DPNP), and diabetic microangiopathy (DMA)). Clustering is a machine learning tool for discovering structures in datasets. Clustering has been proven to be efficient for pattern recognition based on clinical records. The considered combinatorial k-means procedure explores all possible k-means clustering with a determined number of descriptors and groups. The predetermined conditions for the partitioning were as follows: every single group of patients included patients with DMT2 and one of the underlying diseases; each subgroup formed in such a way was subject to partitioning into three patterns (good health status, medium health status, and degenerated health status); optimal descriptors for each disease and groups. The selection of the best clustering is obtained through the parameter called global variance, defined as the sum of all variance values of all clinical variables of all the clusters. The best clinical parameters are found by minimizing this global variance. This methodology has to identify a set of variables that are assumed to separate each underlying disease efficiently in three different subgroups of patients. The hierarchical clustering obtained for these four underlying diseases could be used to build groups of patients with correlated clinical data. The proposed methodology gives surmised results from complex data based on a relationship with the health status of the group and draws a picture of the prediction rate of the ongoing health status.

Keys and Demazure crystals for Kac–Moody algebras

The Key map is an important tool in the determination of the Demazure crystals associated to Kac–Moody algebras. In finite type A, it can be computed in the tableau realization of crystals by a simple combinatorial procedure due to Lascoux and Schützenberger. We show that this procedure is a part of a more general construction holding in the Kac–Moody case that we illustrate in finite types and affine type A. In affine type A, we introduce higher level generalizations of core partitions which are expected to play an important role in the representation theory of Ariki–Koike algebras.