Journal articles on the topic 'QBF solver'
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Weihua, Su, Yin Minghao, Wang Jianan, and Zhou Junping. "Message Passing Algorithm for Solving QBF Using More Reasoning." Mathematical Problems in Engineering 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/165927.
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We present a novel solver for solving Quantified Boolean Formulae problem (QBF). In order to improve the performance, we introduce some reasoning rules into the message passing algorithm for solving QBF. When preprocessing the formulae, the solver incorporates the equality reduction and the hyperbinary resolution. Further, the solver employs the message passing method to obtain more information when selecting branches. By using the unit propagation, conflict driven learning, and satisfiability directed implication and learning, the solver handles the branches. The experimental results also show that the solver can solve QBF problem efficiently.
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Lonsing, Florian, and Armin Biere. "DepQBF: A Dependency-Aware QBF Solver." Journal on Satisfiability, Boolean Modeling and Computation 7, no. 2-3 (August 1, 2010): 71–76. http://dx.doi.org/10.3233/sat190077.
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Chen, Pei-Wei, Yu-Ching Huang, and Jie-Hong R. Jiang. "A Sharp Leap from Quantified Boolean Formula to Stochastic Boolean Satisfiability Solving." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 5 (May 18, 2021): 3697–706. http://dx.doi.org/10.1609/aaai.v35i5.16486.
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Stochastic Boolean Satisfiability (SSAT) is a powerful representation for the concise encoding of quantified decision problems with uncertainty. While it shares commonalities with quantified Boolean formula (QBF) satisfiability and has the same PSPACE-complete complexity, SSAT solving tends to be more challenging as it involves expensive model counting, a.k.a. Sharp-SAT. To date, SSAT solvers, especially those imposing no restrictions on quantification levels, remain much lacking. In this paper, we present a new SSAT solver based on the framework of clause selection and cube distribution previously proposed for QBF solving. With model counting integrated and learning techniques strengthened, our solver is general and effective. Experimental results demonstrate the overall superiority of the proposed algorithm in both solving performance and memory usage compared to the state-of-the-art solvers on a number of benchmark formulas.
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Goultiaeva, Alexandra, and Fahiem Bacchus. "Exploiting QBF Duality on a Circuit Representation." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 3, 2010): 71–76. http://dx.doi.org/10.1609/aaai.v24i1.7548.
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Search based solvers for Quantified Boolean Formulas (QBF) have adapted the SAT solver techniques of unit propagation and clause learning to prune falsifying assignments. The technique of cube learning has been developed to help them prune satisfying assignments. Cubes, however, have not been able to achieve the same degree of effectiveness as clauses. In this paper we demonstrate how a circuit representation for QBF can support the propagation of dual truth values. The dual values support the identical techniques of unit propagation and clause learning, except now it is satisfying assignments rather than falsifying assignments that are pruned. Dual value propagation thus exploits the circuit representation and the duality of QBF formulas so that the same effective SAT techniques can now be used to prune both falsifying and satisfyingly assignments. We show empirically that dual propagation yields significantperformance improvements and advances the state of the art in QBF solving.
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Schuppan, Viktor. "Enhanced Unsatisfiable Cores for QBF: Weakening Universal to Existential Quantifiers." International Journal on Artificial Intelligence Tools 29, no. 03n04 (June 2020): 2060012. http://dx.doi.org/10.1142/s021821302060012x.
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We introduce an enhanced notion of unsatisfiable cores for QBF in prenex CNF that allows to weaken universal quantifiers to existential quantifiers in addition to the traditional removal of clauses. The resulting unsatisfiable cores can be different from those of the traditional notion in terms of syntax, standard semantics, and proof-based semantics. This not only gives rise to explanations of unsatisfiability but, via duality, also leads to diagnoses and repairs of unsatisfiability that are not obtained with traditional unsatisfiable cores. We use a source-to-source transformation on QBF in PCNF such that the weakening of universal quantifiers to existential quantifiers in the original formula corresponds to the removal of clauses in the transformed formula. This makes any tool or method for the computation of unsatisfiable cores of the traditional notion available for the computation of unsatisfiable cores of our enhanced notion. We implement our approach as an extension to the QBF solver DepQBF, and we perform an extensive experimental evaluation on a subset of QBFLIB. We illustrate with several case studies that helpful information can be provided by unsatisfiable cores of our enhanced notion.
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Giunchiglia, E., M. Narizzano, and A. Tacchella. "Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas." Journal of Artificial Intelligence Research 26 (August 17, 2006): 371–416. http://dx.doi.org/10.1613/jair.1959.
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Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as a set of clauses. Deduction starts by inferring new clauses by resolution, and goes on until the empty clause is generated or satisfiability of the set of clauses is proven, e.g., because no new clauses can be generated. In this paper, we restrict our attention to the problem of evaluating Quantified Boolean Formulas (QBFs). In this setting, the above outlined deduction process is known to be sound and complete if given a formula in CNF and if a form of resolution, called ``Q-resolution'', is used. We introduce Q-resolution on terms, to be used for formulas in disjunctive normal form. We show that the computation performed by most of the available procedures for QBFs --based on the Davis-Logemann-Loveland procedure (DLL) for propositional satisfiability-- corresponds to a tree in which Q-resolution on terms and clauses alternate. This poses the theoretical bases for the introduction of learning, corresponding to recording Q-resolution formulas associated with the nodes of the tree. We discuss the problems related to the introduction of learning in DLL based procedures, and present solutions extending state-of-the-art proposals coming from the literature on propositional satisfiability. Finally, we show that our DLL based solver extended with learning, performs significantly better on benchmarks used in the 2003 QBF solvers comparative evaluation.
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Narizzano, Massimo, Luca Pulina, and Armando Tacchella. "Report of the Third QBF Solvers Evaluation1." Journal on Satisfiability, Boolean Modeling and Computation 2, no. 1-4 (March 1, 2006): 145–64. http://dx.doi.org/10.3233/sat190019.
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Tentrup, Leander. "CAQE and QuAbS: Abstraction Based QBF Solvers." Journal on Satisfiability, Boolean Modeling and Computation 11, no. 1 (September 1, 2019): 155–210. http://dx.doi.org/10.3233/sat190121.
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Lonsing, Florian, and Armin Biere. "Efficiently Representing Existential Dependency Sets for Expansion-based QBF Solvers." Electronic Notes in Theoretical Computer Science 251 (September 2009): 83–95. http://dx.doi.org/10.1016/j.entcs.2009.08.029.
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Peitl, Tomáš, Friedrich Slivovsky, and Stefan Szeider. "Dependency Learning for QBF." Journal of Artificial Intelligence Research 65 (June 18, 2019): 181–208. http://dx.doi.org/10.1613/jair.1.11529.
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Quantified Boolean Formulas (QBFs) can be used to succinctly encode problems from domains such as formal verification, planning, and synthesis. One of the main approaches to QBF solving is Quantified Conflict Driven Clause Learning (QCDCL). By default, QCDCL assigns variables in the order of their appearance in the quantifier prefix so as to account for dependencies among variables. Dependency schemes can be used to relax this restriction and exploit independence among variables in certain cases, but only at the cost of nontrivial interferences with the proof system underlying QCDCL. We introduce dependency learning, a new technique for exploiting variable independence within QCDCL that allows solvers to learn variable dependencies on the fly. The resulting version of QCDCL enjoys improved propagation and increased flexibility in choosing variables for branching while retaining ordinary (long-distance) Q-resolution as its underlying proof system. We show that dependency learning can achieve exponential speedups over ordinary QCDCL. Experiments on standard benchmark sets demonstrate the effectiveness of this technique.
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Gasquet, Olivier, Dominique Longin, Fr´ed´eric Maris, Pierre R´egnier, and Ma¨el Valais. "Compact Tree Encodings for Planning as QBF." Inteligencia Artificial 21, no. 62 (October 1, 2018): 103–13. http://dx.doi.org/10.4114/intartif.vol21iss62pp103-113.
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Considerable improvements in the technology and performance of SAT solvers has made their use possible for the resolution of various problems in artificial intelligence, and among them that of generating plans. Recently, promising Quantified Boolean Formula (QBF) solvers have been developed and we may expect that in a near future they become as efficient as SAT solvers. So, it is interesting to use QBF language that allows us to produce more compact encodings. We present in this article a translation from STRIPS planning problems into quantified propositional formulas. We introduce two new Compact Tree Encodings: CTE-EFA based on Explanatory frame axioms, and CTE-OPEN based on causal links. Then we compare both of them to CTE-NOOP based on No-op Actions proposed in [Cashmore et al. 2012]. In terms of execution time over benchmark problems, CTE-EFA and CTE-OPEN always performed better than CTE-NOOP.
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Gasquet, Olivier. "Compact Tree Encodings for Planning as QBF." Inteligencia Artificial 21, no. 62 (October 1, 2018): 103. http://dx.doi.org/10.4114/intartif.vol21iss62pp103-114.
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Considerable improvements in the technology and performance of SAT solvers has made their use possible for the resolution of various problems in artificial intelligence, and among them that of generating plans. Recently, promising Quantified Boolean Formula (QBF) solvers have been developed and we may expect that in a near future they become as efficient as SAT solvers. So, it is interesting to use QBF language that allows us to produce more compact encodings. We present in this article a translation from STRIPS planning problems into quantified propositional formulas. We introduce two new Compact Tree Encodings: CTE-EFA based on Explanatory frame axioms, and CTE-OPEN based on causal links. Then we compare both of them to CTE-NOOP based on No-op Actions proposed in [Cashmore et al. 2012]. In terms of execution time over benchmark problems, CTE-EFA and CTE-OPEN always performed better than CTE-NOOP.
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Shaik, Irfansha, and Jaco Van de Pol. "Classical Planning as QBF without Grounding." Proceedings of the International Conference on Automated Planning and Scheduling 32 (June 13, 2022): 329–37. http://dx.doi.org/10.1609/icaps.v32i1.19817.
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Most classical planners use grounding as a preprocessing step, essentially reducing planning to propositional logic. However, grounding involves instantiating all rules and actions with concrete object combinations, and results in large encodings for SAT/QBF-based planners. This severe cost in memory becomes a main bottleneck when actions have many parameters, such as in the Organic Synthesis problems from the IPC 2018 competition. We provide a compact QBF encoding that is logarithmic in the number of objects and avoids grounding completely by using universal quantification for object combinations. We show that we can solve some of the Organic Synthesis problems, which could not be handled before by any SAT/QBF based planners due to grounding.
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Egly, Uwe, Martina Seidl, and Stefan Woltran. "A solver for QBFs in negation normal form." Constraints 14, no. 1 (July 13, 2008): 38–79. http://dx.doi.org/10.1007/s10601-008-9055-y.
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Pulina, Luca, and Martina Seidl. "The 2016 and 2017 QBF solvers evaluations (QBFEVAL'16 and QBFEVAL'17)." Artificial Intelligence 274 (September 2019): 224–48. http://dx.doi.org/10.1016/j.artint.2019.04.002.
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Cashmore, Michael, Maria Fox, and Enrico Giunchiglia. "Partially Grounded Planning as Quantified Boolean Formula." Proceedings of the International Conference on Automated Planning and Scheduling 23 (June 2, 2013): 29–36. http://dx.doi.org/10.1609/icaps.v23i1.13549.
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This paper describes a technique for translating bounded propositional reachability problems, such as Planning, into Quantified Boolean Formulae (QBF). The key feature of this translation is that the problem, and the resultant encoding is only partially grounded. The technique is applicable to other SAT or QBF encodings as an additional improvement, potentially reducing the size of the resulting formula by an exponential amount. We present experimental results showing that the approach applied to a simple SAT translation greatly improves the time taken to encode and solve problems in which there are many objects of a single type, even solving some problems that cannot be reasonably encoded as SAT.
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PEARCE, DAVID, HANS TOMPITS, and STEFAN WOLTRAN. "Characterising equilibrium logic and nested logic programs: Reductions and complexity,." Theory and Practice of Logic Programming 9, no. 05 (July 31, 2009): 565–616. http://dx.doi.org/10.1017/s147106840999010x.
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AbstractEquilibrium logic is an approach to non-monotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case ofnested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kinds of theories. In this paper, we present polynomial reductions of the main reasoning tasks associated with equilibrium logic and nested logic programs intoquantified propositional logic, an extension of classical propositional logic where quantifications over atomic formulas are permitted. Thus, quantified propositional logic is a fragment of second-order logic, and its formulas are usually referred to asquantified Boolean formulas(QBFs). We provide reductions not only for decision problems, but also for the central semantical concepts of equilibrium logic and nested logic programs. In particular, our encodings map a given decision problem into some QBF such that the latter is valid precisely in case the former holds. The basic tasks we deal with here are theconsistency problem,brave reasoningandskeptical reasoning. Additionally, we also provide encodings for testing equivalence of theories or programs under different notions of equivalence, viz.ordinary,stronganduniform equivalence. For all considered reasoning tasks, we analyse their computational complexity and give strict complexity bounds. Hereby, our encodings yield upper bounds in a direct manner. Besides this useful feature, our approach has the following benefits: First, our encodings yield auniform axiomatisationfor a variety of problems in a common language. Second, extant solvers for QBFs can be used as back-end inference engines to realise implementations of the encoded task in a rapid prototyping manner. Third, our axiomatisations also allow us to straightforwardly relate equilibrium logic with circumscription.
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Maratea, Marco, Francesco Ricca, Wolfgang Faber, and Nicola Leone. "Look-back techniques and heuristics in DLV: Implementation, evaluation, and comparison to QBF solvers." Journal of Algorithms 63, no. 1-3 (January 2008): 70–89. http://dx.doi.org/10.1016/j.jalgor.2008.02.006.
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Scholl, Christoph, Jie-Hong Roland Jiang, Ralf Wimmer, and Aile Ge-Ernst. "A PSPACE Subclass of Dependency Quantified Boolean Formulas and Its Effective Solving." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1584–91. http://dx.doi.org/10.1609/aaai.v33i01.33011584.
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Dependency quantified Boolean formulas (DQBFs) are a powerful formalism, which subsumes quantified Boolean formulas (QBFs) and allows an explicit specification of dependencies of existential variables on universal variables. This enables a succinct encoding of decision problems in the NEXPTIME complexity class. As solving general DQBFs is NEXPTIME complete, in contrast to the PSPACE completeness of QBF solving, characterizing DQBF subclasses of lower computational complexity allows their effective solving and is of practical importance.Recently a DQBF proof calculus based on a notion of fork extension, in addition to resolution and universal reduction, was proposed by Rabe in 2017. We show that this calculus is in fact incomplete for general DQBFs, but complete for a subclass of DQBFs, where any two existential variables have either identical or disjoint dependency sets over the universal variables. We further characterize this DQBF subclass to be ΣP3 complete in the polynomial time hierarchy. Essentially using fork extension, a DQBF in this subclass can be converted to an equisatisfiable 3QBF with only a linear increase in formula size. We exploit this conversion for effective solving of this DQBF subclass and point out its potential as a general strategy for DQBF quantifier localization. Experimental results show that the method outperforms state-of-the-art DQBF solvers on a number of benchmarks, including the 2018 DQBF evaluation benchmarks.
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Vasant, Pandian, Fahad Parvez Mahdi, Jose Antonio Marmolejo-Saucedo, Igor Litvinchev, Roman Rodriguez Aguilar, and Junzo Watada. "Quantum-Behaved Bat Algorithm for Solving the Economic Load Dispatch Problem Considering a Valve-Point Effect." International Journal of Applied Metaheuristic Computing 11, no. 3 (July 2020): 41–57. http://dx.doi.org/10.4018/ijamc.2020070102.
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Quantum computing-inspired metaheuristic algorithms have emerged as a powerful computational tool to solve nonlinear optimization problems. In this paper, a quantum-behaved bat algorithm (QBA) is implemented to solve a nonlinear economic load dispatch (ELD) problem. The objective of ELD is to find an optimal combination of power generating units in order to minimize total fuel cost of the system, while satisfying all other constraints. To make the system more applicable to the real-world problem, a valve-point effect is considered here with the ELD problem. QBA is applied in 3-unit, 10-unit, and 40-unit power generation systems for different load demands. The obtained result is then presented and compared with some well-known methods from the literature such as different versions of evolutionary programming (EP) and particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), simulated annealing (SA) and hybrid ABC_PSO. The comparison of results shows that QBA performs better than the above-mentioned methods in terms of solution quality, convergence characteristics and computational efficiency. Thus, QBA proves to be an effective and a robust technique to solve such nonlinear optimization problem.
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Liu, Tong, Roberto Amadini, Maurizio Gabbrielli, and Jacopo Mauro. "sunny-as2: Enhancing SUNNY for Algorithm Selection." Journal of Artificial Intelligence Research 72 (October 12, 2021): 329–76. http://dx.doi.org/10.1613/jair.1.13116.
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SUNNY is an Algorithm Selection (AS) technique originally tailored for Constraint Programming (CP). SUNNY is based on the k-nearest neighbors algorithm and enables one to schedule, from a portfolio of solvers, a subset of solvers to be run on a given CP problem. This approach has proved to be effective for CP problems.
In 2015, the ASlib benchmarks were released for comparing AS systems coming from disparate fields (e.g., ASP, QBF, and SAT) and SUNNY was extended to deal with generic AS problems. This led to the development of sunny-as, a prototypical algorithm selector based on SUNNY for ASlib scenarios. A major improvement of sunny-as, called sunny-as2, was then submitted to the Open Algorithm Selection Challenge (OASC) in 2017, where it turned out to be the best approach for the runtime minimization of decision problems.
In this work we present the technical advancements of sunny-as2, by detailing through several empirical evaluations and by providing new insights. Its current version, built on the top of the preliminary version submitted to OASC, is able to outperform sunny-as and other state-of-the-art AS methods, including those who did not attend the challenge.
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Zhang, Yong, and Dapeng Wang. "A Cost-Sensitive Ensemble Method for Class-Imbalanced Datasets." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/196256.
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In imbalanced learning methods, resampling methods modify an imbalanced dataset to form a balanced dataset. Balanced data sets perform better than imbalanced datasets for many base classifiers. This paper proposes a cost-sensitive ensemble method based on cost-sensitive support vector machine (SVM), and query-by-committee (QBC) to solve imbalanced data classification. The proposed method first divides the majority-class dataset into several subdatasets according to the proportion of imbalanced samples and trains subclassifiers using AdaBoost method. Then, the proposed method generates candidate training samples by QBC active learning method and uses cost-sensitive SVM to learn the training samples. By using 5 class-imbalanced datasets, experimental results show that the proposed method has higher area under ROC curve (AUC), F-measure, and G-mean than many existing class-imbalanced learning methods.
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BOGAERTS, BART, TOMI JANHUNEN, and SHAHAB TASHARROFI. "Stable-unstable semantics: Beyond NP with normal logic programs." Theory and Practice of Logic Programming 16, no. 5-6 (September 2016): 570–86. http://dx.doi.org/10.1017/s1471068416000387.
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AbstractStandard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic programs offers the most prominent way of reaching the second level of the PH, but encoding respective hard problems as disjunctive programs typically requires sophisticated techniques such as saturation or meta-interpretation. The application of such techniques easily leads to encodings that are inaccessible to non-experts. Furthermore, while disjunctive ASP solvers often rely on calls to a (co-)NP oracle, it may be difficult to detect from the input program where the oracle is being accessed. In other formalisms, such as Quantified Boolean Formulas (QBFs), the interface to the underlying oracle is more transparent as it is explicitly recorded in the quantifier prefix of a formula. On the other hand, ASP has advantages over QBFs from the modeling perspective. The rich high-level languages such as ASP-Core-2 offer a wide variety of primitives that enable concise and natural encodings of search problems. In this paper, we present a novel logic programming–based modeling paradigm that combines the best features of ASP and QBFs. We develop so-calledcombined logic programsin which oracles are directly cast as (normal) logic programs themselves. Recursive incarnations of this construction enable logic programming on arbitrarily high levels of the PH. We develop a proof-of-concept implementation for our new paradigm.
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Rozhnova, S. A., and A. V. Tsypkina. "Comparative Analysis of the QbD Approach in the Pharmaceutical Industry." Drug development & registration 8, no. 4 (November 26, 2019): 20–26. http://dx.doi.org/10.33380/2305-2066-2019-8-4-20-26.
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Introduction. In the development and introduction of medicines into production, the aim of pharmaceutical manufacturers is to comply with the principle of «Quality-by-Design» (QbD). The International Council for Harmonisation (ICH) has created a number of GxP standards, which have become the regulatory framework for the development of documentation regulating the requirements for the development and production of drug products for countries focused on bringing their products to the world pharmaceutical market. The analysis of the system of regulation of pharmaceutical stages of development of new drugs in the territory of the Eurasian Economic Union was not considered, but for the formation of a systematic approach to the management of the process of pharmaceutical development it is necessary to describe them.Aim. To analyze the possibility of applying the QbD principle to the process of drug development at domestic pharmaceutical enterprises.Materials and methods. Content analysis of scientific publications, system and comparative analysis, sociological methods of research in the field of pharmaceutical development.Results and discussions. Regulatory state requirements to the organization and conduct of drug development procedures are analyzed and described. A number of systemic and sectoral problems typical for domestic pharmaceutical manufacturers in the organization of the development and implementation of new drug products. It is established that one of the main problems for Russian enterprises was the organization of the process as a whole and its individual procedures. To solve the problem of organization of procedures for the development and implementation of new medicines, we formed a methodological support, developed on the basis of a systematic approach and international requirements from the quality system.Conclusion. The main problem identified by the manufacturers is the lack of methodological support for the organization of the processes of pharmaceutical development and the introduction of new drugs in the part of research going to the stage of preclinical and clinical development. The decisions adopted by the Eurasian Economic Union do not affect such aspects of pharmaceutical development regulation as the organization of processes, their management and methodological support aimed at the implementation of the QbD principle. To solve this problem, we have developed guidelines for the implementation of the processes of pharmaceutical development and the introduction of new drug products, which allowed us to apply unified and formalized approaches to their organization.
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Wang, Liting, Jiwen Wang, Ke Gong, Qing Shen, Hao Fu, Hui Huang, Chuanrong Chen, Lin Zhang, Yourong Duan, and Tao Suo. "Amyloid Precursor Protein Influences Gallbladder Cancer Cell Behaviors and may be an Effective Prognostic Factor." Nano LIFE 10, no. 01n02 (March 2020): 2040002. http://dx.doi.org/10.1142/s1793984420400024.
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Gallbladder cancer is one of the most aggressive carcinomas of digestive system. The conventional surgical resection, radiotherapy and chemotherapy limit therapeutic effects on gallbladder cancer, so it is urgent to further explore the mechanism of the development of gallbladder cancer. To solve this problem, we have studied the application value of amyloid precursor protein (APP) in the diagnosis and treatment of gallbladder cancer. Small interfering ribonucleic acid (siRNA) was used to knock down APP in SGC-996 and QBC-939 cells. Then, the effects of APP on SGC-996 and QBC-939 cells proliferation, migration, invasion and cell cycle were evaluated. The results showed that APP was overexpressed in gallbladder cancer tissues and cell lines. The cell proliferation, migration and invasion were effectively inhibited and the cell cycle was influenced to a certain extent after knockdown of APP. And the expression of tumor metastatic associated protein, MMP-2, MMP-9, E-cadherin, N-cadherin, was associated with the level of APP. The present data confirmed that APP played a crucial role in gallbladder cancer cells function. This study strongly suggests that APP is a potential target for gallbladder cancer treatment.
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García Velasco, Daniel. "Cognitive status and referential acts in functional discourse grammar." Quaderns de Filologia - Estudis Lingüístics 23, no. 23 (December 24, 2018): 155. http://dx.doi.org/10.7203/qf.23.13525.
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In Functional Discourse Grammar, both Ascription and Reference are characterized as actional processes and are captured at the Interpersonal Level of linguistic description. Additionally, the temporal sequencing of Discourse Acts seems relevant to establishing dependency relations among them. However, the remainder of the levels of representation in the theory contain static descriptions of linguistic structures and not of processes. In this paper, I will argue that this is the result of an inherent contradiction between FDG’s characterization as a static grammar and the dynamicity of verbal interaction, which is best solved if the theory commits itself to the procedural nature of the Interpersonal Level. In order to do so, the different categories that have been identified in the literature on the cognitive status of referents should find relevance in the grammar. Elaborating upon García Velasco (2014), I will show that the temporal dimension of the text creating activity and referent accessibility, are relevant for a full account of constituent preposing in Spanish.
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Lindauer, Marius, Holger H. Hoos, Frank Hutter, and Torsten Schaub. "AutoFolio: An Automatically Configured Algorithm Selector." Journal of Artificial Intelligence Research 53 (August 31, 2015): 745–78. http://dx.doi.org/10.1613/jair.4726.
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Algorithm selection (AS) techniques -- which involve choosing from a set of algorithms the one expected to solve a given problem instance most efficiently -- have substantially improved the state of the art in solving many prominent AI problems, such as SAT, CSP, ASP, MAXSAT and QBF. Although several AS procedures have been introduced, not too surprisingly, none of them dominates all others across all AS scenarios. Furthermore, these procedures have parameters whose optimal values vary across AS scenarios. This holds specifically for the machine learning techniques that form the core of current AS procedures, and for their hyperparameters. Therefore, to successfully apply AS to new problems, algorithms and benchmark sets, two questions need to be answered: (i) how to select an AS approach and (ii) how to set its parameters effectively. We address both of these problems simultaneously by using automated algorithm configuration. Specifically, we demonstrate that we can automatically configure claspfolio 2, which implements a large variety of different AS approaches and their respective parameters in a single, highly-parameterized algorithm framework. Our approach, dubbed AutoFolio, allows researchers and practitioners across a broad range of applications to exploit the combined power of many different AS methods. We demonstrate AutoFolio can significantly improve the performance of claspfolio 2 on 8 out of the 13 scenarios from the Algorithm Selection Library, leads to new state-of-the-art algorithm selectors for 7 of these scenarios, and matches state-of-the-art performance (statistically) on all other scenarios. Compared to the best single algorithm for each AS scenario, AutoFolio achieves average speedup factors between 1.3 and 15.4.
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Apers, Simon, and Alain Scarlet. "Quantum fast-forwarding: Markov chains and graph property testing." Quantum Information and Computation 19, no. 3&4 (March 2019): 181–213. http://dx.doi.org/10.26421/qic19.3-4-1.
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We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with P the Markov chain transition matrix and D = \sqrt{P\circ P^T} its discriminant matrix (D=P if P is symmetric), we construct a quantum walk algorithm that for any quantum state |v> and integer t returns a quantum state \epsilon-close to the state D^t|v>/\|D^t|v>. The algorithm uses O(|D^t|v>|^{-1}\sqrt{t\log(\epsilon\|D^t|v>})^{-1}}) expected quantum walk steps and O(\|D^t|v>|^{-1}) expected reflections around |v>. This shows that quantum walks can accelerate the transient dynamics of Markov chains, complementing the line of results that proves the acceleration of their limit behavior. We show that this tool leads to speedups on random walk algorithms in a very natural way. Specifically we consider random walk algorithms for testing the graph expansion and clusterability, and show that we can quadratically improve the dependency of the classical property testers on the random walk runtime. Moreover, our quantum algorithm exponentially improves the space complexity of the classical tester to logarithmic. As a subroutine of independent interest, we use QFF for determining whether a given pair of nodes lies in the same cluster or in separate clusters. This solves a robust version of s-t connectivity, relevant in a learning context for classifying objects among a set of examples. The different algorithms crucially rely on the quantum speedup of the transient behavior of random walks.
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Panda, Santosh Kumar, Manoranjan Sahu, Kahnu Charan Panigrahi, Chinam Niranjan Patra, and Goutam Kumar Jena. "The Development of Floating Multiple Unit Mini Tablets of Bosentan Using QbD: Characterisation and Pharmacokinetic Study." Drug Delivery Letters 11, no. 2 (June 28, 2021): 179–94. http://dx.doi.org/10.2174/2210303111666210226142015.
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Background: In order to achieve steady state concentration multiple dosing is required for bosentan. Hence formulating bosentan controlled release formulation could be an approach to solve this issue. Objective: The objective is to develop floating multiple unit minitablets of bosentan using Quality by design approach. Methods: Failure mode effect analysis (FMEA) and Taguchi design are employed in order to screen highly critical factors. Box-Behnken design (BBD) was adopted for the process of optimization. Results: The quantity of gelucire 39/01, HPMC K15 M, and sodium bicarbonate was found to be one of the significant factors using Taguchi design. The Box-Behnken design results in the optimised formulation showing floating lag time within 3 min, floating time of nearly 15 h, time to release 50% of drug of 3.6 h, time to release 90% of drug of 11h and better bioavailability compared to pure drug. Conclusion: It can be concluded that floating multiple unit minitablet can be used as an encouraging approach for sustaining the drug release of bosentan.
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Yang, Shu, San Kiang, Parham Farzan, and Marianthi Ierapetritou. "Optimization of Reaction Selectivity Using CFD-Based Compartmental Modeling and Surrogate-Based Optimization." Processes 7, no. 1 (December 29, 2018): 9. http://dx.doi.org/10.3390/pr7010009.
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Mixing is considered as a critical process parameter (CPP) during process development due to its significant influence on reaction selectivity and process safety. Nevertheless, mixing issues are difficult to identify and solve owing to their complexity and dependence on knowledge of kinetics and hydrodynamics. In this paper, we proposed an optimization methodology using Computational Fluid Dynamics (CFD) based compartmental modelling to improve mixing and reaction selectivity. More importantly, we have demonstrated that through the implementation of surrogate-based optimization, the proposed methodology can be used as a computationally non-intensive way for rapid process development of reaction unit operations. For illustration purpose, reaction selectivity of a process with Bourne competitive reaction network is discussed. Results demonstrate that we can improve reaction selectivity by dynamically controlling rates and locations of feeding in the reactor. The proposed methodology incorporates mechanistic understanding of the reaction kinetics together with an efficient optimization algorithm to determine the optimal process operation and thus can serve as a tool for quality-by-design (QbD) during product development stage.
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Marcot, Bruce G. "EcoQBNs: First Application of Ecological Modeling with Quantum Bayesian Networks." Entropy 23, no. 4 (April 9, 2021): 441. http://dx.doi.org/10.3390/e23040441.
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A recent advancement in modeling was the development of quantum Bayesian networks (QBNs). QBNs generally differ from BNs by substituting traditional Bayes calculus in probability tables with the quantum amplification wave functions. QBNs can solve a variety of problems which are unsolvable by, or are too complex for, traditional BNs. These include problems with feedback loops and temporal expansions; problems with non-commutative dependencies in which the order of the specification of priors affects the posterior outcomes; problems with intransitive dependencies constituting the circular dominance of the outcomes; problems in which the input variables can affect each other, even if they are not causally linked (entanglement); problems in which there may be >1 dominant probability outcome dependent on small variations in inputs (superpositioning); and problems in which the outcomes are nonintuitive and defy traditional probability calculus (Parrondo’s paradox and the violation of the Sure Thing Principle). I present simple examples of these situations illustrating problems in prediction and diagnosis, and I demonstrate how BN solutions are infeasible, or at best require overly-complex latent variable structures. I then argue that many problems in ecology and evolution can be better depicted with ecological QBN (EcoQBN) modeling. The situations that fit these kinds of problems include noncommutative and intransitive ecosystems responding to suites of disturbance regimes with no specific or single climax condition, or that respond differently depending on the specific sequence of the disturbances (priors). Case examples are presented on the evaluation of habitat conditions for a bat species, representing state-transition models of a boreal forest under disturbance, and the entrainment of auditory signals among organisms. I argue that many current ecological analysis structures—such as state-and-transition models, predator–prey dynamics, the evolution of symbiotic relationships, ecological disturbance models, and much more—could greatly benefit from a QBN approach. I conclude by presenting EcoQBNs as a nascent field needing the further development of the quantum mathematical structures and, eventually, adjuncts to existing BN modeling shells or entirely new software programs to facilitate model development and application.
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Benenson, M. Z., and E. A. Alekseeva. "Building a database for complex industrial monitoring systems." Radio industry (Russia) 31, no. 1 (April 7, 2021): 65–73. http://dx.doi.org/10.21778/2413-9599-2021-31-1-65-73.
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Problem statement. When creating monitoring systems for industrial facilities for a range of purposes, it becomes necessary to solve processing and storing objects with a complex data structure. The user must be provided with tools for processing and storing the defined data and object types that they have defined.Objective. Development of a software implementation of the interface for interaction with the database built into industrial facilities’ monitoring system.Results. A software interface for interacting with an object-oriented database has been developed. Three programming classes are used to describe various types of industrial system objects. Class methods have been developed that allow setting a variable number of attributes for different object types. The authors propose a method for extracting an object with specified attribute values, similar to the QBE method, and a method for complex (natural) queries written in the application development language.Practical implications. The proposed software implementation of the interface for interaction with the built-in database can be used to create a wide range of industrial monitoring systems. This approach allows to significantly reduce the computing resources required for the implementation of such systems, reduces the time and cost of their development.
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Sun, Sicong, Wei Wei, Xianqi Yuan, and Rougang Zhou. "Research on Calibration Methods of Long-Wave Infrared Camera and Visible Camera." Journal of Sensors 2022 (December 22, 2022): 1–13. http://dx.doi.org/10.1155/2022/8667606.
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Long-wave infrared (LWIR) and visible (VIS) cameras can image information at different dimensions, but the way to calibrate these two types of cameras while registering and fusing the acquired images is difficult. We propose a calibration plate and a calibration method for thermal imaging and visible imaging to solve three problems: (1) the inability of the existing calibration plates to address LWIR and VIS cameras simultaneously; (2) severe heat interference in the calibration images of LWIR cameras; (3) difficulty in finding feature points for registration due to the different imaging spectra between thermal imaging and visible imaging. Simulation tests and error analysis show the error of outline central point computation is less than 0.1 pixel. Average errors of Euclidean distances from the margin outline scattered point sets of the closed circle and closed ellipse to the outline central points decrease by 10% and 9.9%, respectively. The Mean Reprojection Error in the calibration of LWIR and VIS cameras are 0.1 and 0.227 pixels, respectively. Through image registration design and fusion experiments, the FMIdct, MS-SSIM, Qabf, SCD, and SSIM of the images fused after distortion correction are all higher than those of the images fused before distortion correction, with the highest increases being 4.6%, 0.3%, 3.1%, 7.2%, and 1.4%. These results prove the effectiveness and feasibility of our method.
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Gautam, Sumit, Sourabh Solanki, Shree Krishna Sharma, Symeon Chatzinotas, and Björn Ottersten. "Boosting Quantum Battery-Based IoT Gadgets via RF-Enabled Energy Harvesting." Sensors 22, no. 14 (July 19, 2022): 5385. http://dx.doi.org/10.3390/s22145385.
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The search for a highly portable and efficient supply of energy to run small-scale wireless gadgets has captivated the human race for the past few years. As a part of this quest, the idea of realizing a Quantum battery (QB) seems promising. Like any other practically tractable system, the design of QBs also involve several critical challenges. The main problem in this context is to ensure a lossless environment pertaining to the closed-system design of the QB, which is extremely difficult to realize in practice. Herein, we model and optimize various aspects of a Radio-Frequency (RF) Energy Harvesting (EH)-assisted, QB-enabled Internet-of-Things (IoT) system. Several RF-EH modules (in the form of micro- or nano-meter-sized integrated circuits (ICs)) are placed in parallel at the IoT receiver device, and the overall correspondingly harvested energy helps the involved Quantum sources achieve the so-called quasi-stable state. Concretely, the Quantum sources absorb the energy of photons that are emitted by a photon-emitting device controlled by a micro-controller, which also manages the overall harvested energy from the RF-EH ICs. To investigate the considered framework, we first minimize the total transmit power under the constraints on overall harvested energy and the number of RF-EH ICs at the QB-enabled wireless IoT device. Next, we optimize the number of RF-EH ICs, subject to the constraints on total transmit power and overall harvested energy. Correspondingly, we obtain suitable analytical solutions to the above-mentioned problems, respectively, and also cross-validate them using a non-linear program solver. The effectiveness of the proposed technique is reported in the form of numerical results, which are both theoretical and simulations based, by taking a range of operating system parameters into account.
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Bloem, Roderick, Nicolas Braud-Santoni, Vedad Hadzic, Uwe Egly, Florian Lonsing, and Martina Seidl. "Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternations." Formal Methods in System Design, August 23, 2021. http://dx.doi.org/10.1007/s10703-021-00371-7.
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AbstractIn recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over Boolean variables. Such approaches partially expand one type of variable (either existential or universal) for obtaining a propositional abstraction of the QBF. If this formula is false, the truth value of the QBF is decided, otherwise further refinement steps are necessary. Classically, expansion-based solvers process the given formula quantifier-block wise and use one SAT solver per quantifier block. In this paper, we present a novel algorithm for expansion-based QBF solving that deals with the whole quantifier prefix at once. Hence recursive applications of the expansion principle are avoided and only two incremental SAT solvers are required. While our algorithm is naturally based on the $$\forall $$ ∀ Exp+Res calculus that is the formal foundation of expansion-based solving, it is conceptually simpler than present recursive approaches. Experiments indicate that the performance of our simple approach is comparable with the state of the art of QBF solving, especially in combination with other solving techniques.
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FANDINNO, JORGE, FRANCOIS LAFERRIERE, JAVIER ROMERO, TORSTEN SCHAUB, and TRAN CAO SON. "Planning with Incomplete Information in Quantified Answer Set Programming." Theory and Practice of Logic Programming, September 24, 2021, 1–17. http://dx.doi.org/10.1017/s1471068421000259.
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Abstract We present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.
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Beyersdorff, Olaf, and Benjamin Böhm. "Understanding the Relative Strength of QBF CDCL Solvers and QBF Resolution." Logical Methods in Computer Science Volume 19, Issue 2 (April 14, 2023). http://dx.doi.org/10.46298/lmcs-19(2:2)2023.
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QBF solvers implementing the QCDCL paradigm are powerful algorithms that successfully tackle many computationally complex applications. However, our theoretical understanding of the strength and limitations of these QCDCL solvers is very limited. In this paper we suggest to formally model QCDCL solvers as proof systems. We define different policies that can be used for decision heuristics and unit propagation and give rise to a number of sound and complete QBF proof systems (and hence new QCDCL algorithms). With respect to the standard policies used in practical QCDCL solving, we show that the corresponding QCDCL proof system is incomparable (via exponential separations) to Q-resolution, the classical QBF resolution system used in the literature. This is in stark contrast to the propositional setting where CDCL and resolution are known to be p-equivalent. This raises the question what formulas are hard for standard QCDCL, since Q-resolution lower bounds do not necessarily apply to QCDCL as we show here. In answer to this question we prove several lower bounds for QCDCL, including exponential lower bounds for a large class of random QBFs. We also introduce a strengthening of the decision heuristic used in classical QCDCL, which does not necessarily decide variables in order of the prefix, but still allows to learn asserting clauses. We show that with this decision policy, QCDCL can be exponentially faster on some formulas. We further exhibit a QCDCL proof system that is p-equivalent to Q-resolution. In comparison to classical QCDCL, this new QCDCL version adapts both decision and unit propagation policies.
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Hossain, Akash, and François Laroussinie. "QCTL model-checking with QBF solvers." Information and Computation, October 2020, 104642. http://dx.doi.org/10.1016/j.ic.2020.104642.
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Balabanov, Valeriy, Jie-Hong Jiang, Mikolas Janota, and Magdalena Widl. "Efficient Extraction of QBF (Counter)models from Long-Distance Resolution Proofs." Proceedings of the AAAI Conference on Artificial Intelligence 29, no. 1 (March 4, 2015). http://dx.doi.org/10.1609/aaai.v29i1.9750.
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Many computer science problems can be naturally and compactly expressed using quantified Boolean formulas (QBFs). Evaluating thetruth or falsity of a QBF is an important task, and constructing the corresponding model or countermodel can be as important and sometimes even more useful in practice. Modern search and learning based QBF solvers rely fundamentally on resolution and can be instrumented to produce resolution proofs, from which in turn Skolem-function models and Herbrand-function countermodels can be extracted. These (counter)models are the key enabler of various applications. Not until recently the superiority of long-distanceresolution (LQ-resolution) to short-distance resolution(Q-resolution) was demonstrated. While a polynomial algorithm exists for (counter)model extraction from Q-resolution proofs, it remains open whether it exists forLQ-resolution proofs. This paper settles this open problem affirmatively by constructing a linear-time extraction procedure. Experimental results show the distinct benefits of the proposed method in extracting high quality certificates from some LQ-resolution proofs that are not obtainable from Q-resolution proofs.
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Ning, Tao, Xiaodong Duan, and Lu An. "Study on the strategy of multimodal transportation of medical aid materials for public health emergencies: a case study basing on COVID-19." International Journal of Low-Carbon Technologies, June 10, 2021. http://dx.doi.org/10.1093/ijlct/ctab046.
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Abstract The emergency response to sudden public health incident often encounters problems such as the long distance between the medical material supply node and the demand point or the destruction of key roads, which makes it difficult to transport materials directly to the disaster area by vehicles in time. Helicopters are increasingly being used to transport critical medical emergency resources, but it is not easy to distribute medical supplies through helicopter in large-scale public health incidents. In order to solve the above problems, a two-stage combined transportation method for medical supplies based on clustering is proposed in this paper. In the first stage, the quantum bacterial foraging (QBF) algorithm is used to select emergency transit points and divide the medical assistance points. In view of the imbalance of remaining capacity in QBF division, an improved division method (quantum bacterial foraging with capacity constraints (QBFwCC)) is proposed and a ‘helicopter–vehicle’ medical material combined transportation network structure is constructed in consideration of capacity constraints. In the second stage, a transportation route optimization model based on clustering is established to determine the specific transportation route from the emergency transit point to the medical assistance point. The performance of the method proposed in the paper was analyzed through experimental COVID-19 simulation and compared between QBF and QBFwCC. The results show that the method not only achieves the goal of optimization, but also effectively reduces the number of vehicles.
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Hecher, Markus. "Advanced tools and methods for treewidth-based problem solving." it - Information Technology, February 10, 2023. http://dx.doi.org/10.1515/itit-2023-0004.
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Abstract Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula’s structural properties during solving. One of such structural indicators is the so-called treewidth, which tries to measure how close a formula instance is to being easy (tree-like). This work focuses on logic-based problems and treewidth-based methods and tools for solving them. Many of these problems are also relevant for knowledge representation and reasoning (KR) as well as artificial intelligence (AI) in general. We present a new type of problem reduction, which is referred to by decomposition-guided (DG). This reduction type forms the basis to solve a problem for quantified Boolean formulas (QBFs) of bounded treewidth that has been open since 2004. The solution of this problem then gives rise to a new methodology for proving precise lower bounds for a range of further formalisms in logic, KR, and AI. Despite the established lower bounds, we implement an algorithm for solving extensions of Sat efficiently, by directly using treewidth. Our implementation is based on finding abstractions of instances, which are then incrementally refined in the process. Thereby, our observations confirm that treewidth is an important measure that should be considered in the design of modern solvers.
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Grech, Leander, Gianluca Valentino, Diogo Alves, and Simon Hirlaender. "Application of reinforcement learning in the LHC tune feedback." Frontiers in Physics 10 (September 7, 2022). http://dx.doi.org/10.3389/fphy.2022.929064.
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The Beam-Based Feedback System (BBFS) was primarily responsible for correcting the beam energy, orbit and tune in the CERN Large Hadron Collider (LHC). A major code renovation of the BBFS was planned and carried out during the LHC Long Shutdown 2 (LS2). This work consists of an explorative study to solve a beam-based control problem, the tune feedback (QFB), utilising state-of-the-art Reinforcement Learning (RL). A simulation environment was created to mimic the operation of the QFB. A series of RL agents were trained, and the best-performing agents were then subjected to a set of well-designed tests. The original feedback controller used in the QFB was reimplemented to compare the performance of the classical approach to the performance of selected RL agents in the test scenarios. Results from the simulated environment show that the RL agent performance can exceed the controller-based paradigm.
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Battula, Venkatesh, Haranath Chinthaginjala, Mousami Bhavasar Telkar, Udit Narayan Singh, Nagashubha Bobbarjang, and Bhargav Eranti. "Insights of Lipid-Based Drug Delivery Systems with an Emphasis on Quality by Design." International Journal of Life Science and Pharma Research, February 13, 2023, P83—P98. http://dx.doi.org/10.22376/ijlpr.2023.13.2.p83-p98.
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Lipid-based drug delivery systems offer several advantages and have wide solubility, permeation, and bioavailability enhancement applications. This review provides detailed information on the fabrication, application and aspects of QbD of various lipid-based vesicles. Most of the review studies focused on lipid-based vesicles without the QbD aspect. This review article covers all the lipid-based systems in escalating on the method of QbD, which enhances the bioavailability of active pharmaceutical ingredients in different formulation approaches. Among all the different available approaches towards formulation development, lipid-based drug delivery systems (LBDDS) have continually maintained the limelight on themselves. One of the reasons for the popularity of LBDDS is their ability to solve problems with poorly water-soluble drugs and their bioavailability. Several drugs' efficacy was improved by utilizing this type of delivery system. Vesosomes, Phytosomes, Solid Lipid Nanoparticles (SLNs), Nanostructured Lipid Carriers (NLCs), and Archaeosomes are novel lipid-based systems with unique applications in drug delivery. Hence, the present perspective is to review the various LBDDS approaches utilized to enhance the formulations' performance while dissecting the studies systematically to get a clear outline of various LBDD subsystems, their applications, methods of preparation, and the mechanism of drug delivery. In addition to this, the review also focuses on overcoming the lacunas of the past literature by making an attempt to identify Quality target product profile (QTPP), Critical quality attributes (CQAs) and applying them for the statistical design of experiments and continuous strategy by QbD at the same time harnessing their potential in risk assessment. Applying QbD in developing lipid-based drug delivery systems reduces the number of trials and yields a product with in-built quality as it deliberates various critical variables, process parameters, risk assessment, and control strategy in formulation development.
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Huntul, M. J., and Muhammad Abbas. "An inverse problem of fourth-order partial differential equation with nonlocal integral condition." Advances in Continuous and Discrete Models 2022, no. 1 (September 1, 2022). http://dx.doi.org/10.1186/s13662-022-03727-3.
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AbstractIn this study, the time-dependent potential coefficient in a higher-order PDE with initial and boundary conditions is numerically constructed for the first time from a nonlocal integral condition. Even though the inverse identification problem investigated in this study is ill-posed, it has a unique solution. For discretizing the direct problem and finding stable and accurate solutions, we employ the Quintic B-spline (QBS) collocation and Tikhonov regularization methods, respectively. The following nonlinear minimization problem is solved using MATLAB. The collected findings demonstrate that accurate and stable solutions can be found.
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Ward, Jonathan A., and Martín López-García. "Exact analysis of summary statistics for continuous-time discrete-state Markov processes on networks using graph-automorphism lumping." Applied Network Science 4, no. 1 (November 20, 2019). http://dx.doi.org/10.1007/s41109-019-0206-4.
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AbstractWe propose a unified framework to represent a wide range of continuous-time discrete-state Markov processes on networks, and show how many network dynamics models in the literature can be represented in this unified framework. We show how a particular sub-set of these models, referred to here as single-vertex-transition (SVT) processes, lead to the analysis of quasi-birth-and-death (QBD) processes in the theory of continuous-time Markov chains. We illustrate how to analyse a number of summary statistics for these processes, such as absorption probabilities and first-passage times. We extend the graph-automorphism lumping approach [Kiss, Miller, Simon, Mathematics of Epidemics on Networks, 2017; Simon, Taylor, Kiss, J. Math. Bio. 62(4), 2011], by providing a matrix-oriented representation of this technique, and show how it can be applied to a very wide range of dynamical processes on networks. This approach can be used not only to solve the master equation of the system, but also to analyse the summary statistics of interest. We also show the interplay between the graph-automorphism lumping approach and the QBD structures when dealing with SVT processes. Finally, we illustrate our theoretical results with examples from the areas of opinion dynamics and mathematical epidemiology.
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Hanukov, Gabi, and Uri Yechiali. "EXPLICIT SOLUTIONS FOR CONTINUOUS-TIME QBD PROCESSES BY USING RELATIONS BETWEEN MATRIX GEOMETRIC ANALYSIS AND THE PROBABILITY GENERATING FUNCTIONS METHOD." Probability in the Engineering and Informational Sciences, January 3, 2020, 1–16. http://dx.doi.org/10.1017/s0269964819000470.
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Two main methods are used to solve continuous-time quasi birth-and-death processes: matrix geometric (MG) and probability generating functions (PGFs). MG requires a numerical solution (via successive substitutions) of a matrix quadratic equation A0 + RA1 + R2A2 = 0. PGFs involve a row vector $\vec{G}(z)$ of unknown generating functions satisfying $H(z)\vec{G}{(z)^\textrm{T}} = \vec{b}{(z)^\textrm{T}},$ where the row vector $\vec{b}(z)$ contains unknown “boundary” probabilities calculated as functions of roots of the matrix H(z). We show that: (a) H(z) and $\vec{b}(z)$ can be explicitly expressed in terms of the triple A0, A1, and A2; (b) when each matrix of the triple is lower (or upper) triangular, then (i) R can be explicitly expressed in terms of roots of $\det [H(z)]$ ; and (ii) the stability condition is readily extracted.