Combinatorial Generation Research Articles

An Alternate Form of Merino-Mǐcka-Mütze’s Solution to a Knuth’s Combinatorial Generation Problem

A modification of Merino-Mǐcka-Mütze’s solution to a combinatorial generation problem of Knuth is proposed in this survey. The resulting alternate form to such solution is compatible with a reinterpretation by the author of a proof of existence of Hamilton cycles in the middle-levels graphs. Such reinterpretation is given in terms of a dihedral quotient graph associated to each middle-levels graph. The vertices of such quotient graph represent Dyck words and their associated ordered trees. Those Dyck words are linearly ordered via a rooted tree that covers all their tight, or irreducible, forms, offering an universal reference point of view to express and integrate the periodic paths, or blocks, whose concatenation leads to Hamilton cycles resulting from the said solution.

Design and Synthesis of Red-Absorbing Fluoran Leuco Dyes Supported by Computational Screening.

We report here on the design and synthesis of red-absorbing fluoran leuco dyes (LD). An essential part of the present dye development process is a computational screening of the candidate molecules, which allows for both time-efficient and accurate in silico characterization of the dyes. We focus our study here on the robust benzo[a]fluoran scaffold frequently used in leuco dyes. For the computational screening of LD candidates, an automated DFT-based simulation protocol has been developed and applied. The protocol consists of a combinatorial generation of the molecular structures of possible LD candidates, followed by simulations of their optimized molecular geometries, with their UV-Vis spectra as the main figure of merit. In the present application of the simulation protocol, more than 1600 structures of possible LD candidates have been evaluated. Finally, two structures, LD01 and LD02, have been chosen from the list of the best computed LD candidates to be synthesized and characterized. Our study demonstrates how the synergy between experiment and simulation can facilitate the design of novel leuco dyes.

Combinatorial generators for the cohomology of toric arrangements

We give a new combinatorial description of the cohomology ring structure of H⁎(M(A);Z) of the complement M(A) of a real complexified toric arrangement A in (C⁎)d. In particular, we correct an error in the paper [4].

Combinatorial Generation Algorithms for Directed Lattice Paths

Combinatorial Generation Algorithms for Directed Lattice Paths

Expanding Chemical Frontiers: Approaches for Generating Diverse and Bioactive Natural Product-Like Compounds Libraries from Extracts.

The realms of natural products and synthetic compounds exhibit distinct chemical spaces that not only differ but also complement each other. While the convergence of these two domains has been explored through semisynthesis and conventional pharmacomodulation endeavours applied to natural frameworks, a recent and innovative approach has emerged that involves the combinatorial generation of libraries of 'natural product-like compounds' (NPLCs) through the direct synthetic derivatization of natural extracts. This has led to the production of numerous NPLCs that incorporate structural elements from both their natural (multiple saturated rings, oxygen content, chiral centres) and synthetic (aromatic rings, nitrogen and halogen content, drug-like properties) precursors. Through careful selection of extracts and reagents, specific bioactivities have been achieved, and this strategy has been deployed in various ways, showing great promise without reaching its full potential to date. This review seeks to provide an overview of reported examples involving the chemical engineering of extracts, showcasing a spectrum of natural product alterations spanning from simple substitutions to complete scaffold remodelling. It also includes an analysis of the accomplishments, perspectives and technical challenges within this field.

Combinatorial Generation Algorithms for Some Lattice Paths Using the Method Based on AND/OR Trees

Methods of combinatorial generation make it possible to develop algorithms for generating objects from a set of discrete structures with given parameters and properties. In this article, we demonstrate the possibilities of using the method based on AND/OR trees to obtain combinatorial generation algorithms for combinatorial sets of several well-known lattice paths (North-East lattice paths, Dyck paths, Delannoy paths, Schroder paths, and Motzkin paths). For each considered combinatorial set of lattice paths, we construct the corresponding AND/OR tree structure where the number of its variants is equal to the number of objects in the combinatorial set. Applying the constructed AND/OR tree structures, we have developed new algorithms for ranking and unranking their variants. The performed computational experiments have confirmed the obtained theoretical estimation of asymptotic computational complexity for the developed ranking and unranking algorithms.

Editorial

Dear Readers,  It gives me great pleasure to announce the second regular issue of 2023. I would like to thank all the authors for their sound research and the editorial board for the extremely valuable reviews and suggestions for improvement. These contributions together with the generous support of the consortium members enable us to run our journal and maintain its quality.  Still, I would like to expand our editorial board: If you are a tenured associate professor or above with a good publication record, please apply to join our editorial board. We are also interested in high-quality proposals for special issues on new topics and emerging trends.  In this regular issue, I am very pleased to introduce 4 accepted papers involving 16 authors from 6 different countries.  In a collaboration between researchers from South Africa and the USA, Trienko Grobler, Manfred Habeck, Lynette van Zijl and Jaco Geldenhuys address improved algorithms for combinatorial generation of bordered box repetition-free words based on tree-based search space and graph-based search space. In another joint research between Algeria and France, Mehdi Rouissat, Mohammed Belkheir, Hicham Sid Ahmed Belkhira, Sofiane Boukli Hacen, Pascal Lorenz and Merahi Bouziani describe a new technique to mitigate the version number attack for IoT networks, reducing control overhead by 83% and energy consumption by 74%. Amira Samir, Huda Amin Maghawry and Nagwa Badr from Egypt aim in their research to increase the effectiveness of the graphical user interface testing process of mobile applications by proposing an enhanced combinatorial-based metaheuristic approach that has been compared with monkey, frequency, random and greedy approaches. Qusai Y. Shambour, Mosleh M. Abualhaj and Ahmad Adel Abu-Shareha from Jordan propose an effective multi-criteria recommender algorithm for personalized restaurant recommendations by exploiting users’ and items’ implicit similarities to eliminate the sparseness of rating information.   Enjoy Reading!  Cordially, 

Dynamic 3D Combinatorial Generation of hPSC-Derived Neuromesodermal Organoids With Diverse Regional and Cellular Identities.

Neuromesodermal progenitors represent a unique, bipotent population of progenitors residing in the tail bud of the developing embryo, which give rise to the caudal spinal cord cell types of neuroectodermal lineage as well as the adjacent paraxial somite cell types of mesodermal origin. With the advent of stem cell technologies, including induced pluripotent stem cells (iPSCs), the modeling of rare genetic disorders can be accomplished in vitro to interrogate cell-type specific pathological mechanisms in human patient conditions. Stem cell-derived models of neuromesodermal progenitors have been accomplished by several developmental biology groups; however, most employ a 2D monolayer format that does not fully reflect the complexity of cellular differentiation in the developing embryo. This article presents a dynamic 3D combinatorial method to generate robust populations of human pluripotent stem cell-derived neuromesodermal organoids with multi-cellular fates and regional identities. By utilizing a dynamic 3D suspension format for the differentiation process, the organoids differentiated by following this protocol display a hallmark of embryonic development that involves a morphological elongation known as axial extension. Furthermore, by employing a combinatorial screening assay, we dissect essential pathways for optimally directing the patterning of pluripotent stem cells into neuromesodermal organoids. This protocol highlights the influence of timing, duration, and concentration of WNT and fibroblast growth factor (FGF) signaling pathways on enhancing early neuromesodermal identity, and later, downstream cell fate specification through combined synergies of retinoid signaling and sonic hedgehog activation. Finally, through robust inhibition of the Notch signaling pathway, this protocol accelerates the acquisition of terminal cell identities. This enhanced organoid model can serve as a powerful tool for studying normal developmental processes as well as investigating complex neurodevelopmental disorders, such as neural tube defects. © 2022 Wiley Periodicals LLC. Basic Protocol 1: Robust generation of 3D hPSC-derived spheroid populations in dynamic motion settings Support Protocol 1: Pluronic F-127 reagent preparation and coating to generate low-attachment suspension culture dishes Basic Protocol 2: Enhanced specification of hPSCs into NMP organoids Support Protocol 2: Combinatorial pathway assay for NMP organoid protocol optimization Basic Protocol 3: Differentiation of NMP organoids along diverse cellular trajectories and accelerated terminal fate specification into neurons, neural crest, and sclerotome derivatives.

Методика использования базы знаний производящих функций двух переменных

Mathematical knowledge bases are the development of classical mathematical reference books and encyclopedias, which, in turn, makes them an important tool for conducting various research in mathematical sciences and related fields. At present, there are various knowledge bases of mathematical objects. In this paper, we consider the knowledge base of the generating functions of two variables, which allows us to operate with multivariate objects. The relevance and significance of the work lies in solving various problems related to the mathematical apparatus of generating functions. In the paper we consider the use of the knowledge base of generating functions of two variables for solving problems of operating generating functions and obtaining coefficients for composition, reciprocal and compositional inverse generating functions of two variables and their powers, as well as obtaining explicit expressions for the coefficients of logarithmic derivatives of the generating functions. In addition, an inverse problem is considered aimed at obtaining generating functions for explicit expressions describing their coefficients. The use of the knowledge base of generating two-variable functions contributes to the process of constructing combinatorial generation algorithms for combinatorial objects defined by generating functions of many variables. As an example, the construction of combinatorial generation algorithms for sets defined by the generalized Narayana numbers is shown. The Narayana numbers describe classes of subsets for combinatorial sets defined by the Catalan numbers. In this paper, one of the combinatorial interpretations for the Narayana numbers is chosen - the set of the Dyck paths of length n, which have m peaks.

Unranking Small Combinations of a Large Set in Co-Lexicographic Order

The presented research is devoted to the problem of developing new combinatorial generation algorithms for combinations. In this paper, we develop a modification of Ruskey’s algorithm for unranking m-combinations of an n-set in co-lexicographic order. The proposed modification is based on the use of approximations to make a preliminary search for the values of the internal parameter k of this algorithm. In contrast to the original algorithm, the obtained algorithm can be effectively applied when n is large and m is small because the running time of this algorithm depends only on m. Furthermore, this algorithm can be effectively used when n and m are both large but n−m is small, since we can consider unranking (n−m)-combinations of an n-set. The conducted computational experiments confirm the effectiveness of the developed modification.

Quantum Mechanics and Machine Learning Synergies: Graph Attention Neural Networks to Predict Chemical Reactivity

There is a lack of scalable quantitative measures of reactivity that cover the full range of functional groups in organic chemistry, ranging from highly unreactive C-C bonds to highly reactive naked ions. Measuring reactivity experimentally is costly and time-consuming, and no single method has sufficient dynamic range to cover the astronomical size of chemical reactivity space. In previous quantum chemistry studies, we have introduced Methyl Cation Affinities (MCA*) and Methyl Anion Affinities (MAA*), using a solvation model, as quantitative measures of reactivity for organic functional groups over the broadest range. Although MCA* and MAA* offer good estimates of reactivity parameters, their calculation through Density Functional Theory (DFT) simulations is time-consuming. To circumvent this problem, we first use DFT to calculate MCA* and MAA* for more than 2,400 organic molecules thereby establishing a large data set of chemical reactivity scores. We then design deep learning methods to predict the reactivity of molecular structures and train them using this curated data set in combination with different representations of molecular structures. Using 10-fold cross-validation, we show that graph attention neural networks applied to a relational model of molecular structures produce the most accurate estimates of reactivity, achieving over 91% test accuracy for predicting the MCA* ± 3.0 or MAA* ± 3.0, over 50 orders of magnitude. Finally, we demonstrate the application of these reactivity scores to two tasks: (1) chemical reaction prediction and (2) combinatorial generation of reaction mechanisms. The curated data sets of MCA* and MAA* scores is available through the ChemDB chemoinformatics web portal at cdb.ics.uci.edu under Chemical Reactivities data sets.

Combinatorial test case generation from sequence diagram using optimization algorithms

Combinatorial test case generation from sequence diagram using optimization algorithms

Модификация метода построения алгоритмов комбинаторной генерации на основе применения производящих функций многих переменных и приближенных вычислений

This article proposes a modified method for developing combinatorial generation algorithms based on AND/OR trees. The proposed method differs from the original method and its modifications by using the method of obtaining explicit expressions for the coefficients of multivariate generating functions to find the expression for the cardinality function of a given combinatorial set (including combinatorial sets defined by several parameters). Also, the proposed method is distinguished by the use of approximation methods and the binary search to find the selected son of the OR node. This reduces the computational complexity of the unranking algorithms. In order to test the proposed method, a new ranking and unranking algorithms were developed for a combinatorial set of selfavoiding lattice paths. In this case, the use of binary search reduced on average the number of required computational operations and a better computational complexity compared to the original version of the algorithm were obtained.

Coupling between oxidation kinetics and anisothermal oil flow during deep-fat frying

Deep-fat frying is a cooking technique that has been used continuously since prehistoric times. A domestic deep-fryer heated from the bottom develops significant convection inside the bath cavity. It is responsible for very high heat transfer coefficients and the exposure of the deep-frying oil to the atmospheric oxygen. The continuous conversion of gaseous dioxygen into unstable and reactive hydroperoxides and their subsequent advection throughout the bulk volume is at the origin of the main complaints made of frying which includes issues such as odors, fouling, and generation of several toxic compounds. This study analyzes the coupling between natural convection of triacylglycerols and the combinatorial chemistry controlling their autoxidation. At macroscopic scale, anisothermal flow within a typical kitchen appliance, including a cold zone beneath the heating element, was simulated in 3D under the Boussinesq approximation with a Eulerian description during initial heating and temperature holding. At molecular and intermediate scales, the endothermic decomposition of fatty-ester hydroperoxides in various mixtures was simulated over several hours using a Lagrangian description. Simulations and the proposed description of the combinatorial generation of hydroperoxides highlighted the complex relationship between deep-fryer design, residence times at different temperatures, and oil composition. The half-life of hydroperoxides (>15 min) is intermediate between vertical mixing times (<3 min) and longitudinal ones (>2 h). Hydroperoxides of unsaturated fatty esters are generated at the surface, which are preferentially decomposed in heated plumes and accumulate between production cycles in cold stagnant regions. Experimental validation is proposed for the eddy structure, temperature fluctuations, and hydroperoxides decomposition kinetics.

MODEL-Based Performance Quality Assessment for IoT Applications

<p class="0abstractCxSpFirst">The number of applications incorporating Internet of Things (IoT) concepts increases extraordinarily. This increase cannot continue without high-quality assurance. There are some difficulties in testing IoT applications; the system heterogeneity, test cost and time are taken to test the system, and the precision percentage of test results.</p><p class="0abstractCxSpLast">A well-known and possibly the best solution to overcoming these difficulties is to model the system for evaluation purposes, known as model-based testing (MBT). This paper aims to design a model-based testing approach to assess IoT applications performance quality attributes. The ISO 25000 quality model is used as a standard for software quality assurance applications. IoTMaaS is used as a case study to implement the methodological approach. The possible test cases were generated using the ACTS combinatorial test generation tool. The performance metrics of each test case were monitored until the optimum test case was identified, with the shortest response time and the least amount of resources used. The proposed testing method appears to be successful, according to the results.</p>

Heuristic based binary grasshopper optimization algorithm to solve unit commitment problem

The unit commitment problem in power system is a highly nonlinear, nonconvex, multiconstrained, complex,highly dimensional, mixed integer and combinatorial generation selection problem. The phenomenon of committing anddecommitting represents a discrete problem that requires binary/discrete optimization techniques to tackle with unitcommitment optimization problem. The key functions of the unit commitment optimization problem involve decidingwhich units to commit and then to decide their optimum power (economic dispatch). This paper confers a binarygrasshopper optimization algorithm to solve the unit commitment optimization problem under multiple constraints.The grasshopper optimization algorithm is a metaheuristic, multiple solutions-based algorithm inspired by the naturalswarming behavior of grasshopper towards food. For solving the binary unit commitment optimization problem, thereal/continues value grasshopper optimization algorithm is mapped into binary/discrete search-space by using an S-shaped sigmoid function. The proposed algorithm is tested on IEEE benchmark systems of 4, 5, 6, 10, 20, 26, 40, 60,80, and 100 generating units including the IEEE 118-bus system and the results are compared with different classical,heuristics, metaheuristics, quantum, and hybrid approaches. The results confer better performance of binary grasshopperoptimization algorithm to solve the unit commitment optimization problem.

Software test data generation technology based on polymorphic particle swarm evolutionary algorithm

Combinatorial testing is a statute-based software testing method that aims to select a small number of valid test cases from a large combinatorial space of software under test to generate a set of test cases with high coverage and strong error debunking ability. However, combinatorial test case generation is an NP-hard problem that requires solving the combinatorial problem in polynomial time, so a meta-heuristic search algorithm is needed to solve the problem. Compared with other meta-heuristic search algorithms, the particle swarm algorithm is more competitive in terms of coverage table generation scale and execution time. In this paper, we systematically review and summarize the existing research results on generating combinatorial test case sets using particle swarm algorithm, and propose a combinatorial test case generation method that can handle arbitrary coverage strengths by combining the improved one-test-at-a-time strategy and the adaptive particle swarm algorithm for the variable strength combinatorial test problem and the parameter selection problem of the particle swarm algorithm. To address the parameter configuration problem of the particle swarm algorithm, the four parameters of inertia weight, learning factor, population size and iteration number are reasonably set, which makes the particle swarm algorithm more suitable for the generation of coverage tables. For the inertia weights.

Deriving Theorems in Implicational Linear Logic, Declaratively

The problem we want to solve is how to generate all theorems of a given size in the implicational fragment of propositional intuitionistic linear logic. We start by filtering for linearity the proof terms associated by our Prolog-based theorem prover for Implicational Intuitionistic Logic. This works, but using for each formula a PSPACE-complete algorithm limits it to very small formulas. We take a few walks back and forth over the bridge between proof terms and theorems, provided by the Curry-Howard isomorphism, and derive step-by-step an efficient algorithm requiring a low polynomial effort per generated theorem. The resulting Prolog program runs in O(N) space for terms of size N and generates in a few hours 7,566,084,686 theorems in the implicational fragment of Linear Intuitionistic Logic together with their proof terms in normal form. As applications, we generate datasets for correctness and scalability testing of linear logic theorem provers and training data for neural networks working on theorem proving challenges. The results in the paper, organized as a literate Prolog program, are fully replicable. Keywords: combinatorial generation of provable formulas of a given size, intuitionistic and linear logic theorem provers, theorems of the implicational fragment of propositional linear intuitionistic logic, Curry-Howard isomorphism, efficient generation of linear lambda terms in normal form, Prolog programs for lambda term generation and theorem proving.

Method for Developing Combinatorial Generation Algorithms Based on AND/OR Trees and Its Application

In this paper, we study the problem of developing new combinatorial generation algorithms. The main purpose of our research is to derive and improve general methods for developing combinatorial generation algorithms. We present basic general methods for solving this task and consider one of these methods, which is based on AND/OR trees. This method is extended by using the mathematical apparatus of the theory of generating functions since it is one of the basic approaches in combinatorics (we propose to use the method of compositae for obtaining explicit expression of the coefficients of generating functions). As a result, we also apply this method and develop new ranking and unranking algorithms for the following combinatorial sets: permutations, permutations with ascents, combinations, Dyck paths with return steps, labeled Dyck paths with ascents on return steps. For each of them, we construct an AND/OR tree structure, find a bijection between the elements of the combinatorial set and the set of variants of the AND/OR tree, and develop algorithms for ranking and unranking the variants of the AND/OR tree.

Enumeration of stereo, position and chiral isomers of polysubstituted giant fullerenes: applications to C180 and C240

We have developed combinatorial generation function methods that combine Mȍbius inversion and character cycle indices for the enumeration of stereo, position and chiral isomers of icosahedral giant fullerenes C180 and C240. Techniques are also developed for the machine perception of symmetries of especially giant fullerenes. The techniques yield, symmetries, position, stereo and chiral isomers of giant fullerenes which we illustrate with applications to icosahedral C180(Ih), and C240(Ih). We have obtained combinatorial tables for the isomers of C180Xk and C240Xk. Our results point to errors in previous computations on C240 permutations. We have also outlined applications to NMR and ESR spectroscopy.