Computational Point Of View Research Articles

Two algorithms for computing the general component of jet scheme and applications

Let k be a perfect field. Let X be an integral k-variety. Let m∈N. In this article, we study, from the theoretical and computational points of view, the component Gm(X) of the jet scheme Lm(X) defined to be the Zariski closure of the set of truncated arcs with a regular base-point. We prove that Gm(X) can be described from any smooth birational model of X. When X is supposed to be affine embedded in AkN, this description allows us to provide an algorithm, valid in arbitrary characteristic, which computes a Gröbner basis of a presentation of Gm(X) in Ak(m+1)N from the datum of a given explicit smooth affine birational model of X. Then, we show how to use the datum of a presentation of Gm(X) (in the suitable affine space) to deduce algebraic and geometric properties in two contexts from the theoretical and computational points of view. Firstly, we apply our main result to obtain bases for a class of homogeneous differential operators logarithmic along plane curves in arbitrary characteristics. Secondly, we introduce a motivic power series which encodes the geometry of all the Gm(X) and prove its rationality in the specific case of homogeneous plane curve singularities thanks to our description of Gm(X)via the normalization of X.

A New Stochastic Model for Bus Rapid Transit Scheduling with Uncertainty

Nowadays, authorities of large cities in the world implement bus rapid transit (BRT) services to alleviate traffic problems caused by the significant development of urban areas. Therefore, a controller is required to control and dispatche buses in such BRT systems.. However, controllers are facing new challenges due to the inherent uncertainties of passenger parameters such as arrival times, demands, alighting fraction as well as running time of vehicles between stops. Such uncertainties may significantly increase the operational cost and the inefficiencies of BRT services. In this paper, we focus on the controller’s perspective and propose a stochastic mixed-integer nonlinear programming (MINLP) model for BRT scheduling to find the optimal departure time of buses under uncertainty. The objective function of the model consists of passenger waiting and traveling time and aims to minimize total time related to passengers at any stop. From the modeling perspective, we propose a new method to generate scenarios for the proposed stochastic MINLP model. Furthermore, from the computational point of view, we implement an outer approximation algorithm to solve the proposed stochastic MINLP model and demonstrate the merits of the proposed solution method in the numerical results. This paper accurately reflect the complexity of BRT scheduling problem and is the first study, to the best of our knowledge, that presents and solves a mixed-integer nonlinear programming model for BRT scheduling.

CRFlowLib — Chemically Reacting Flow Library

The simulation of reactive flows is a very challenging task from the computational point of view, as in addition to taking into account all the complex aspects of fluid dynamics, it requires a detailed description of the chemical kinetics involved in the process. Thus, the use of strategies to reduce simulation time is essential. Among the existing reduction techniques, the In Situ Adaptive Tabulation (ISAT) is one of the most promising since it offers a good compromise between accuracy and cost reduction. This paper presents the CRFlowLib, a computational package to simulate chemically reacting flows using ISAT algorithm

Freezing, Bounded-Change and Convergent Cellular Automata

This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes a bounded number of state changes in any orbit, and finally cellular automata where each orbit converges to some fixed point. Many examples studied in the literature fit into these definitions, in particular the works on cristal growth started by S. Ulam in the 60s. The central question addressed here is how the computational power and computational hardness of basic properties is affected by the constraints of convergence, bounded number of change, or local decreasing of states in each cell. By studying various benchmark problems (short-term prediction, long term reachability, limits) and considering various complexity measures and scales (LOGSPACE vs. PTIME, communication complexity, Turing computability and arithmetical hierarchy) we give a rich and nuanced answer: the overall computational complexity of such cellular automata depends on the class considered (among the three above), the dimension, and the precise problem studied. In particular, we show that all settings can achieve universality in the sense of Blondel-Delvenne-K\r{u}rka, although short term predictability varies from NLOGSPACE to P-complete. Besides, the computability of limit configurations starting from computable initial configurations separates bounded-change from convergent cellular automata in dimension~1, but also dimension~1 versus higher dimensions for freezing cellular automata. Another surprising dimension-sensitive result obtained is that nilpotency becomes decidable in dimension~ 1 for all the three classes, while it stays undecidable even for freezing cellular automata in higher dimension.

An Application of Instantaneous Spectral Entropy for the Condition Monitoring of Wind Turbines

For economic and environmental reasons, the use of renewable energy sources is a key aspect of the ongoing transition to a sustainable industrialised society. Wind energy represents a major player among these natural, carbon-neutral sources. Nevertheless, wind turbines are often subject to mechanical faults, especially due to ageing. To alleviate Operation and Maintenance costs, Vibration-Based Inspection and Condition Monitoring have been proposed in recent times. This research proposes Instantaneous Spectral Entropy and Continuous Wavelet Transform for anomaly detection and fault diagnosis, departing from gearbox vibration time histories. The approach is validated on experimental data recorded from a turbine suffering bearing failure and total gearbox replacement. From a computational point of view, the proposed algorithm was found to be efficient and therefore even potentially applicable for real-time monitoring.

Fundamental limitations on efficiently forecasting certain epidemic measures in network models

The ongoing COVID-19 pandemic underscores the importance of developing reliable forecasts that would allow decision makers to devise appropriate response strategies. Despite much recent research on the topic, epidemic forecasting remains poorly understood. Researchers have attributed the difficulty of forecasting contagion dynamics to a multitude of factors, including complex behavioral responses, uncertainty in data, the stochastic nature of the underlying process, and the high sensitivity of the disease parameters to changes in the environment. We offer a rigorous explanation of the difficulty of short-term forecasting on networked populations using ideas from computational complexity. Specifically, we show that several forecasting problems (e.g., the probability that at least a given number of people will get infected at a given time and the probability that the number of infections will reach a peak at a given time) are computationally intractable. For instance, efficient solvability of such problems would imply that the number of satisfying assignments of an arbitrary Boolean formula in conjunctive normal form can be computed efficiently, violating a widely believed hypothesis in computational complexity. This intractability result holds even under the ideal situation, where all the disease parameters are known and are assumed to be insensitive to changes in the environment. From a computational complexity viewpoint, our results, which show that contagion dynamics become unpredictable for both macroscopic and individual properties, bring out some fundamental difficulties of predicting disease parameters. On the positive side, we develop efficient algorithms or approximation algorithms for restricted versions of forecasting problems.

DFT, ADMET and Molecular Docking Investigations for the Antimicrobial Activity of 6,6'-Diamino-1,1',3,3'-tetramethyl-5,5'-(4-chlorobenzylidene)bis[pyrimidine-2,4(1H,3H)-dione

Heterocyclic compounds, including pyrimidine derivatives, exhibit a broad variety of biological and pharmacological activities. In this paper, a previously synthesized novel pyrimidine molecule is proposed, and its pharmaceutical properties are investigated. Computational techniques such as the density functional theory, ADMET evaluation, and molecular docking were applied to elucidate the chemical nature, drug likeness and antibacterial function of molecule. The viewpoint of quantum chemical computations revealed that the molecule was relatively stable and has a high electrophilic nature. The contour maps of HOMO-LUMO and molecular electrostatic potential were analyzed to illustrate the charge density distributions that could be associated with the biological activity. Natural bond orbital (NBO) analysis revealed details about the interaction between donor and acceptor within the bond. Drug likeness and ADMET analysis showed that the molecule possesses the agents of safety and the effective combination therapy as pharmaceutical drug. The antimicrobial activity was investigated using molecular docking. The investigated molecule demonstrated a high affinity for binding within the active sites of antibacterial and antimalarial proteins. The high affinity of the antibacterial protein was proved by its low binding energy (−7.97 kcal/mol) and a low inhibition constant value (1.43 µM). The formation of four conventional hydrogen bonds in ligand–protein interactions confirmed the high stability of the resulting complexes. When compared to known standard drugs, the studied molecule displayed a remarkable antimalarial activity, as indicated by higher binding affinity (B.E. −5.86 kcal/mol & Ki = 50.23 M). The pre-selected molecule could be presented as a promising drug candidate for the development of novel antimicrobial agents.

Weapon-target assignment problem: exact and approximate solution algorithms

The Weapon-Target Assignment (WTA) problem aims to assign a set of weapons to a number of assets (targets), such that the expected value of survived targets is minimized. The WTA problem is a nonlinear combinatorial optimization problem known to be NP-hard. This paper applies several existing techniques to linearize the WTA problem. One linearization technique (Camm et al. in Oper Res 50(6):946–955, 2002) approximates the nonlinear terms of the WTA problem via convex piecewise linear functions and provides heuristic solutions to the WTA problem. Such approximation problems are, though, relatively easy to solve from the computational point of view even for large-scale problem instances. Another approach proposed by O’Hanley et al. (Eur J Oper Res 230(1):63–75, 2013) linearizes the WTA problem exactly at the expense of incorporating a significant number of additional variables and constraints, which makes many large-scale problem instances intractable. Motivated by the results of computational experiments with these existing solution approaches, a specialized new exact solution approach is developed, which is called branch-and-adjust. The proposed solution approach involves the compact piecewise linear convex under-approximation of the WTA objective function and solves the WTA problem exactly. The algorithm builds on top of any existing branch-and-cut or branch-and-bound algorithm and can be implemented using the tools provided by state-of-the-art mixed integer linear programming solvers. Numerical experiments demonstrate that the proposed specialized algorithm is capable of handling very large scale problem instances with up to 1500 weapons and 1000 targets, obtaining solutions with optimality gaps of up to \(2.0\%\) within 2 h of computational runtime.

The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality

The measurement of technical efficiency is a topic of great interest in microeconomics and engineering. Data Envelopment Analysis (DEA) is one of the existing techniques for measuring technical efficiency. One of the challenges related to DEA is to introduce a “well-defined” efficiency measure. Overall, it means that the technical efficiency measure should satisfy a list of mathematical and economical properties. Regarding this point, an unresolved question in the DEA literature to date, is whether any measure can satisfy both Indication, also called Pareto-efficiency identification, and uniqueness of the projection point generated by the corresponding efficiency optimization model. With this issue in mind, this paper introduces a new family of measures, inspired on the Range-Adjusted Measure (RAM), which satisfy a list of six properties. This family of measures will be called Generalized Range-Adjusted Measure (GRAM). Additionally, we show in this paper how GRAM can be implemented from a computational point of view and we also provide an economical interpretation of its dual program in terms of (shadow) profit maximization. Finally, an empirical example extracted from the literature serves to illustrate the new methodology.

Knowledge representation for explainable artificial intelligence

Alongside the particular need to explain the behavior of black box artificial intelligence (AI) systems, there is a general need to explain the behavior of any type of AI-based system (the explainable AI, XAI) or complex system that integrates this type of technology, due to the importance of its economic, political or industrial rights impact. The unstoppable development of AI-based applications in sensitive areas has led to what could be seen, from a formal and philosophical point of view, as some sort of crisis in the foundations, for which it is necessary both to provide models of the fundamentals of explainability as well as to discuss the advantages and disadvantages of different proposals. The need for foundations is also linked to the permanent challenge that the notion of explainability represents in Philosophy of Science. The paper aims to elaborate a general theoretical framework to discuss foundational characteristics of explaining, as well as how solutions (events) would be justified (explained). The approach, epistemological in nature, is based on the phenomenological-based approach to complex systems reconstruction (which encompasses complex AI-based systems). The formalized perspective is close to ideas from argumentation and induction (as learning). The soundness and limitations of the approach are addressed from Knowledge representation and reasoning paradigm and, in particular, from Computational Logic point of view. With regard to the latter, the proposal is intertwined with several related notions of explanation coming from the Philosophy of Science.

МЕТОД СТРУКТУРНОЇ ІДЕНТИФІКАЦІЇ НЕЛІНІЙНИХ ІНТЕРВАЛЬНИХ МОДЕЛЕЙ СТАТИЧНИХ ОБ’ЄКТІВ

The process of building mathematical models of static objects and systems, which includes the solution of two problems: structural and parametric identification, is considered. At the same time, the task of identifying the structure of the model is more difficult and primary. The problem of structural identification of interval models of the characteristic of a static object is the problem of multiple solving of problems of parametric identification of this model, and therefore, from a computational point of view, it is NP complex. The procedure for finding the optimal structure of the model is considered as a directed selection of a defined set of structures in such a way as to minimize the number of iterations of the formation of interval systems of nonlinear algebraic equations. The article formulates the problem of structural identification of interval models of static objects, as a problem of repeatedly searching for solutions of interval systems of nonlinear algebraic equations, in the form of optimization problems with a nonlinear objective function and nonlinear constraints. For the first time, a method of structural identification of interval models of the characteristics of static objects based on the analysis of interval data is proposed and substantiated, which, unlike the existing ones, is based on self-organization and self-adaptation procedures of computing procedures by analogy with artificial bee colony (АBC), which gives the ability to implement model structure identification procedures with lower computational complexity and obtain interval models with simpler structures compared to known methods. The proposed method was tested on the example of building an interval model of the characteristics of a small hydroelectric plant for the purpose of research and ensuring the maximum efficiency of the use of hydropower resources, which demonstrated the effectiveness of using computational procedures based on the artificial bee colony. Accordingly, the proposed method makes it possible to obtain simple, from the point of view of complexity, interval models of complex static objects with a given guaranteed accuracy and with a lower computational complexity of identifying these models. Such features of the method ensure the effective development of the mathematical apparatus, which is used both in decision-making processes and in the processes of preparing decisions in intellectualized data-oriented systems.

Lupaş post quantum Bernstein operators over arbitrary compact intervals

This paper deals with Lupaş post quantum Bernstein operators over arbitrary closed and bounded interval constructed with the help of Lupaş post quantum Bernstein bases. Due to the property that these bases are scale invariant and translation invariant, the derived results on arbitrary intervals are important from computational point of view. Approximation properties of Lupaş post quantum Bernstein operators on arbitrary compact intervals based on Korovkin type theorem are studied. More general situation along all possible cases have been discussed favouring convergence of sequence of Lupaş post quantum Bernstein operators to any continuous function defined on compact interval. Rate of convergence by modulus of continuity and functions of Lipschitz class are computed. Graphical analysis has been presented with the help of MATLAB to demonstrate approximation of continuous functions by Lupaş post quantum Bernstein operators on different compact intervals.

Resolution attributes for geophysical inversion models: Depth of investigation and novel measures

ABSTRACTAssessing the reliability of inversion models derived from geophysical measurements is crucial for a reliable interpretation. An interpretation depends critically on the interpreter being able to discern between the characteristics of the inversion model that can be trusted as more or less well resolved and the ones that are more dubious. This paper analyses the resolution measure ‘depth of investigation’ from a conceptual and a computational viewpoint and proposes two definitions that incorporate all aspects of the inversion and that are free of a user‐defined ad hoc parameter. Two more resolution attributes are introduced: a qualified depth of investigation and the depth of required structure . The first one answers the question: What is the minimum depth to a homogeneous halfspace with an interpreter‐defined conductivity that will not increase the data residual more than a certain amount? The second one is an ‘unqualified’ depth of investigation that addresses the question: What is the minimum depth to a homogeneous halfspace with any conductivity that will not increase the data residual more than a certain amount? This latter measure indicates the depth below which no structure is needed to fit the data. Finally, measures are defined that will provide estimates of the vertical resolution width as a function of depth. All of the resolution measures presented in this paper are based on the posterior model resolution matrix.

Generating an ensemble of mutually exclusive and exhaustive waves targeted for extreme responses

To examine the reliability or performance of marine systems related to dynamic time-varying responses, time domain simulation may be required. But for long durations, brute-force simulation is clearly not feasible from a computational point of view to examine converged extreme value statistics. An additional challenge is defining a set of mutually exclusive and exhaustive wave excitation records which excite the desired extreme response(s). To address these challenges, this work develops a non-linear Design Loads Generator (NL-DLG) process which links wave profiles targeted for extreme responses generated via response-conditioning wave techniques to a probabilistic framework which examines the possible correlation or mutual exclusivity between those wave profiles. The end result is an ensemble of short targeted wave profiles which excite converged extreme value return-period statistics of a defined response that may be excited by multiple correlated processes. The method of the NL-DLG process is explained by applying it towards rare wave groups, where the result is an ensemble of short wave profiles which contain extreme occurrences of different wave groups targeted for the defined exposure duration. These generated wave excitation profiles are compared to physical data from the Pt. Reyes buoy and then numerical simulations are employed to consider rarer events.

Local Charge Distributions, Electric Dipole Moments, and Local Electric Fields Influence Reactivity Patterns and Guide Regioselectivities in α-Ketoglutarate-Dependent Non-heme Iron Dioxygenases.

Non-heme iron dioxygenases catalyze vital processes for human health related to the biosynthesis of essential products and the biodegradation of toxic metabolites. Often the natural product biosyntheses by these non-heme iron dioxygenases is highly regio- and chemoselective, which are commonly assigned to tight substrate-binding and positioning. However, recent high-level computational modeling has shown that substrate-binding and positioning is only part of the story and long-range electrostatic interactions can play a major additional role.In this Account, we review and summarize computational viewpoints on the high regio- and chemoselectivity of α-ketoglutarate-dependent non-heme iron dioxygenases and how external perturbations affect the catalysis. In particular, studies from our groups have shown that often a regioselectivity in enzymes can be accomplished by stabilization of the rate-determining transition state for the reaction through external charges, electric dipole moments, or local electric field effects. Furthermore, bond dissociation energies in molecules are shown to be influenced by an electric field effect, and through targeting a specific bond in an electric field, this can lead to an unusually specific reaction. For instance, in the carbon-induced starvation protein, we studied two substrate-bound conformations and showed that regardless of what C-H bond of the substrate is closest to the iron(IV)-oxo oxidant, the lowest hydrogen atom abstraction barrier is always for the pro-S C2-H abstraction due to an induced dipole moment of the protein that weakens this bond. In another example of the hygromycin biosynthesis enzyme, an oxidative ring-closure reaction in the substrate forms an ortho-δ-ester ring. Calculations on this enzyme show that the selectivity is guided by a protonated lysine residue in the active site that, through its positive charge, triggers a low energy hydrogen atom abstraction barrier. A final set of examples in this Account discuss the viomycin biosynthesis enzyme and the 2-(trimethylammonio)ethylphosphonate dioxygenase (TmpA) enzyme. Both of these enzymes are shown to possess a significant local dipole moment and local electric field effect due to charged residues surrounding the substrate and oxidant binding pockets. The protein dipole moment and local electric field strength changes the C-H bond strengths of the substrate as compared to the gas-phase triggers the regioselectivity of substrate activation. In particular, we show that in the gas phase and in a protein environment C-H bond strengths are different due to local electric dipole moments and electric field strengths. These examples show that enzymes have an intricately designed structure that enables a chemical reaction under ambient conditions through the positioning of positively and negatively charged residues that influence and enhance reaction mechanisms. These computational insights create huge possibilities in bioengineering to apply local electric field and dipole moments in proteins to achieve an unusual selectivity and specificity and trigger a fit-for-purpose biocatalyst for unique biotransformations.

Supervised Methods for Biomarker Detection from Microarray Experiments.

Biomarkers are valuable indicators of the state of a biological system. Microarray technology has been extensively used to identify biomarkers and build computational predictive models for disease prognosis, drug sensitivity and toxicity evaluations. Activation biomarkers can be used to understand the underlying signaling cascades, mechanisms of action and biological cross talk. Biomarker detection from microarray data requires several considerations both from the biological and computational points of view. In this chapter, we describe the main methodology used in biomarkers discovery and predictive modeling and we address some of the related challenges. Moreover, we discuss biomarker validation and give some insights into multiomics strategies for biomarker detection.

Computational analysis of the particle size effect on the pressure profiles and type of flow regimes of TiO2 microparticles in a fluidized bed

Abstract The effect of particle size on the pressure profiles and flow regimes of the bed containing TiO2 microparticles (MPs) was investigated in a fluidized bed. The fluidization behavior of particles with mean diameters, d p , of 170, 200, 225, and 300 μm at different gas velocities, U g , was investigated both experimental and computational viewpoints. A computational fluid dynamic (CFD) model was developed by the Eulerian–Eulerian approach to evaluate the sensitivity of the Syamlal–O’Brien, and Gidaspow drag models on the predicted results of the bed pressure profiles. The results showed that with increasing particle size, the amplitude of pressure fluctuations increases and the type of flow regime in the bed tended from bubbling to slugging flow regime. The error analysis showed that the use of the Gidaspow model led to more accurate results than the Syamlal–O’Brien model in predicting the bed pressure drop and pressure fluctuations in the slugging flow regime. However, the Syamlal–O’Brien model was more suitable for predicting the pressure profiles in the bubbling flow regime. The results were more suitable for the bed containing particles of 300 μm than the beds with d p ≤ 225 μm. The highest and lowest deviations between the experimental data and simulation outputs were obtained at U g of 0.295 and 0.650 m/s, respectively. The findings confirmed that the mutual effects existed between the d p pressure profiles, and the type of flow regimes in the bed.

Parsimonious Optimization of Multitask Neural Network Hyperparameters.

Neural networks are rapidly gaining popularity in chemical modeling and Quantitative Structure–Activity Relationship (QSAR) thanks to their ability to handle multitask problems. However, outcomes of neural networks depend on the tuning of several hyperparameters, whose small variations can often strongly affect their performance. Hence, optimization is a fundamental step in training neural networks although, in many cases, it can be very expensive from a computational point of view. In this study, we compared four of the most widely used approaches for tuning hyperparameters, namely, grid search, random search, tree-structured Parzen estimator, and genetic algorithms on three multitask QSAR datasets. We mainly focused on parsimonious optimization and thus not only on the performance of neural networks, but also the computational time that was taken into account. Furthermore, since the optimization approaches do not directly provide information about the influence of hyperparameters, we applied experimental design strategies to determine their effects on the neural network performance. We found that genetic algorithms, tree-structured Parzen estimator, and random search require on average 0.08% of the hours required by grid search; in addition, tree-structured Parzen estimator and genetic algorithms provide better results than random search.

Efficient solution of many-objective Home Energy Management systems

Home Energy Management systems have become an essential tool on pursuing an efficient energy consumption besides the implantation of demand response programs in residential consumers. This kind of systems have evolved from a single-objective paradigm, in which only the electricity bill was concerned, to many-objective frameworks that involve different targets such as grid supporting programs or user convenience premises. From the computational point of view, many-objective optimization problems are more challenging than single-, and multiple-objective ones due to higher computational burden and the necessity of advanced tools capable to reach a compromise solution among objectives. This paper tackles this issue by developing an efficient but effective stochastic many-objective solution framework based on Mixed Integer Linear Programming formulation. The new proposal is based on lexicographic optimization and scalarizing functions, thus allowing to distinguish one of the targets as the most important one. This feature makes the new approach very suitable for Home Energy Management systems in which the energy cost is normally the most important objective while other goals can be considered secondary. The developed tool is validated on a standard home layout benchmark considering up to six typical objectives. The results obtained put on manifest the effectiveness and efficiency of the developed approach.

Branching interval algebra: An almost complete picture

Branching Algebra is the natural branching-time generalization of Allen's Interval Algebra. As in the linear case, the consistency problem for Branching Algebra is NP-hard. Branching Algebra has many potential applications in different areas of Artificial Intelligence; therefore, being able to efficiently solve classical problems expressed in Branching Algebra is very important. This can be achieved in two steps: first, by identifying expressive enough, yet tractable fragments of the whole algebra, and, second, by using such fragments to boost the performances of a backtracking algorithm for the whole language. In this paper we study the properties of several such fragments, both from the algebraic and the computational point of view, and we give an almost complete picture of tractable and non-tractable fragments of the Branching Algebra.