A Transformation Approach To Implementing Aggregate Operations

We study adding aggregate operators, such as summing up elements of a column of a relation, to logics with counting mechanisms. The primary motivation comes from database applications, where aggregate operators are present in all real life query languages. Unlike other features of query languages, aggregates are not adequately captured by the existing logical formalisms. Consequently, all previous approaches to analyzing the expressive power of aggregation were only capable of producing partial results, depending on the allowed class of aggregate and arithmetic operations. We consider a powerful counting logic, and extend it with the set of all aggregate operators. We show that the resulting logic satisfies analogs of Hanf's and Gaifman's theorems, meaning that it can only express local properties. We consider a database query language that expresses all the standard aggregates found in commercial query languages, and show how it can be translated into the aggregate logic, thereby providing a number of expressivity bounds, that do not depend on a particular class of arithmetic functions, and that subsume all those previously known. We consider a restricted aggregate logic that gives us a tighter capture of database languages, end also use it to show that some questions on expressivity of aggregation cannot be answered without resolving some deep problems in complexity theory.

Strictly stable families of aggregation operators

Atomic Weighted Vectors (AWVs) are vectors that contain the codified information of molecular structures, which can apply to a set of Aggregation Operators (AOs) to calculate total and local molecular descriptors (MDs). This article presents an exploratory study of a new tool useful for drug discovery using different datasets, such as DRAGON and Sutherland’s datasets, as well as their comparison with other well-known approaches. In order to evaluate the performance of the tool, several statistics and QSAR/QSPR experiments were performed. Variability analyses are used to quantify the information content of the AWVs obtained from the tool, by the way of an information theory-based algorithm. Principal Components Analysis (PCA) is used to analyze the orthogonality of these descriptors, for which the new MDs from AWVs provide different information from those codified by DRAGON descriptors (0-2D). The QSAR models are obtained for every Sutherland’s dataset, according to the original division into training/test sets, by means of the Multiple Linear Regression with Genetic Algorithm (MLR-GA). These models have been validated and compare favorably to several approaches previously published, using the same benchmark datasets. The obtained results show that this tool should be a useful strategy for the QSAR/QSPR studies, despite its simplicity.

We introduce a first-order language with real polynomial arithmetic and aggregation operators (count, iterated sum and multiply), which is well suited for the definition of aggregate queries involving complex statistical functions. It offers a good trade-off between expressive power and complexity, with a tractable data complexity. Interestingly, some fundamental properties of first-order with real arithmetic are preserved in the presence of aggregates. In particular, there is an effective quantifier elimination for formulae with aggregation. We then consider the problem of querying data that has already been aggregated in aggregate views, and focus on queries with an aggregation over a conjunctive query (namely single-block aggregate group-by queries without having clause). Our main conceptual contribution is the introduction of a new equivalence relation among conjunctive queries, the isomorphism modulo a product. We prove that the equivalence of aggregate queries such as for instance averages reduces to it. Deciding if two queries are isomorphic modulo a product is shown to be NP-complete. We then analyze the equivalence problem in the case of aggregate conjunctive queries with comparisons. We introduce the concept of cross isomorphic linear expansions, which generalizes isomorphim modulo a product, and we show that equivalence reduces to it and that it can be decided in PSPACE. Finally, we show that the problem of complete rewriting of count queries using count views is NP-complete, and we introduce new rewriting techniques based on the isomorphism modulo a product. to recover the values of counts by complex arithmetical computation from the views.

Judgment aggregation is a field in which individuals are required to vote for or against a certain decision (the conclusion) while providing reasons for their choice. The reasons and the conclusion are logically connected propositions. The problem is how a collective judgment on logically interconnected propositions can be defined from individual judgments on the same propositions. It turns out that, despite the fact that the individuals are logically consistent, the aggregation of their judgments may lead to an inconsistent group outcome, where the reasons do not support the conclusion. However, in this paper we claim that collective irrationality should not be the only worry of judgment aggregation. For example, judgment aggregation would not reject a consistent combination of reasons and conclusion that no member voted for. In our view this may not be a desirable solution. This motivates our research about when a social outcome is `compatible' with the individuals' judgments. The key notion that we want to capture is that any individual member has to be able to defend the collective decision. This is guaranteed when the group outcome is compatible with its members views. Judgment aggregation problems are usually studied using classical propositional logic. However, for our analysis we use an argumentation approach to judgment aggregation problems. Indeed the question of how individual evaluations can be combined into a collective one can also be addressed in abstract argumentation. We introduce three aggregation operators that satisfy the condition above, and we offer two definitions of compatibility. Not only does our proposal satisfy a good number of standard judgment aggregation postulates, but it also avoids the problem of individual members of a group having to become committed to a group judgment that is in conflict with their own individual positions.

Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough sets, soft sets, etc. Indeed, they are successfully employed to address partial knowledge, consensus, and borderline cases. One of the generalized versions of orthopairs is intuitionistic fuzzy sets which is a well-known theory for researchers interested in fuzzy set theory. To extend the area of application of fuzzy set theory and address more empirical situations, the limitation that the grades of membership and non-membership must be calibrated with the same power should be canceled. To this end, we dedicate this manuscript to introducing a generalized frame for orthopair fuzzy sets called “(m,n)-Fuzzy sets”, which will be an efficient tool to deal with issues that require different importances for the degrees of membership and non-membership and cannot be addressed by the fuzzification tools existing in the published literature. We first establish its fundamental set of operations and investigate its abstract properties that can then be transmitted to the various models they are in connection with. Then, to rank (m,n)-Fuzzy sets, we define the functions of score and accuracy, and formulate aggregation operators to be used with (m,n)-Fuzzy sets. Ultimately, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making problems in the environment of (m,n)-Fuzzy sets. The proposed technique has been illustrated and analyzed via a numerical example.

This article uses the Aczel-Alsina t-norm and t-conorm to make several new linguistic interval-valued intuitionistic fuzzy aggregation operators. First, we devised some rules for how linguistic interval-valued intuitionistic fuzzy numbers should work. Then, using these rules as a guide, we created a set of operators, such as linguistic interval-valued intuitionistic fuzzy Aczel-Alsina weighted averaging (LIVIFAAWA) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina weighted geometric (LIVIFAAWG) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina ordered weighted averaging (LIVIFAAOWA) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina ordered weighted geometric (LIVIFAAOWG) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina hybrid weighted averaging (LIVIFAAHWA) operator and linguistic interval-valued intuitionistic fuzzy Aczel-Alsina hybrid weighted geometric (LIVIFAAHWG) operators are created. Several desirable qualities of the newly created operators are thoroughly studied. Moreover, a multi-criteria group decision-making (MCGDM) method is proposed based on the developed operators. The proposed operators are then applied to real-world decision-making situations to demonstrate their applicability and validity to the reader. Finally, the suggested model is contrasted with the currently employed method of operation.

Multi-criteria decision-making (MCDM) involves evaluating alternatives under uncertain, vague, and conflicting criteria. While fuzzy set theories, such as intuitionistic, pythagorean, fermatean, and q-rung orthopair fuzzy sets have advanced uncertainty modeling, they remain limited to capturing extreme judgments where membership reaches a value of one alongside significant non-membership. The recently introduced q-fractional fuzzy set (q-FrFS) addresses these shortcomings via a flexible constraint, making it suitable for extreme contexts. However, existing q-FrFS methodologies lack robust aggregation mechanisms capable of balancing trade-offs and modulating compensation during information fusion. To overcome this, this study proposes a novel class of Frank-based aggregation operators tailored specifically to q-FrFS environments. Leveraging the parameterized structure of Frank t-norms and t-conorms, we develop two operators: q-FrFFWA (Frank weighted averaging) and q-FrFFWG (Frank weighted geometric) alongside their essential algebraic properties. These operators enhance the representation and fusion of complex and uncertain data. Furthermore, we present a comprehensive MCDM framework utilizing the proposed operators and demonstrate its applicability by selecting optimal vehicle routing software for last-mile delivery. Sensitivity and comparative analyses affirm the stability and credibility of the proposed methodology. This research contributes to the evolving landscape of fuzzy decision-making by integrating the expressive power of q-FrFS with the adaptive flexibility of Frank aggregation, offering a potent tool for modeling and analyzing multidimensional uncertainties in complex decision environments.

In the present study, a generalized approach for molecular structure characterization is introduced, based on the relation frequency matrix (F) representation of the molecular graph and the subsequent calculation of the corresponding discrete derivative (finite difference) over a pair of elements (atoms). In earlier publications (22- 24), an unique event, named connected subgraphs, (based on the Kier-Hall's subgraphs) was systematically employed for the computation of the matrix F. The present report is a generalization of this notion, in which eleven additional events are introduced, classified in three categories, namely, topological (terminal paths, vertex path incidence, quantum subgraphs, walks of length k, Sach's subgraphs), fingerprints (MACCs, E-state and substructure fingerprints) and atomic contributions (Ghose and Crippen atom-types for hydrophobicity and refractivity) for F generation. The events are intended to capture diverse information by the generation or search of different kinds of substructures from the graph representation of a molecule. The discrete derivative over duplex atom relations are calculated for each event, and the resulting derivatives, local vertex invariants (LOVIs) are finally obtained. These LOVIs are subsequently employed as the basis for the calculation of global and local indices over groups of atoms (heteroatoms, halogens, methyl carbons, etc.), by using norms, means, statistics and classical algorithms as aggregator (fusion) operators. These indices were implemented in our house software DIVATI (Derivative Type Indices, a new module of TOMOCOMDCARDD system). DIVATI provides a friendly and cross-platform graphical user interface, developed in the Java programming language and is freely available at: http: //www.tomocomd.com. Factor analysis shows that the presented events are rather orthogonal and collect diverse information about the chemical structure. Finally, QSPR models were built to describe the logP and logK of 34 furylethylenes derivatives using the eleven events. Generally, the equations obtained according to these events showed high correlations, with the Sach's sub-graphs and Multiplicity events showing the best behavior in the description of logK (Q2 LOO value of 99.06%) and logP (Q2 LOO value of 98.1 %), respectively. These results show that these new eventbased indices constitute a powerful approach for chemoinformatics studies.

Reflective programming is becoming popular due to the increasing set of dynamic services provided by execution environments like JVM and CLR. With custom attributes Microsoft introduced an extensible model of reflection for CLR: they can be used as additional decorations on element declarations. The same notion has been introduced in Java 1.5. The extensible model proposed in both platforms limits annotations to class members. In this paper we describe [a]C#, 1 an extension of the C# programming language, that allows programmers to annotate statements or code blocks and retrieve these annotations at run-time. We show how this extension can be reduced to the existing model. A set of operations on annotated code blocks to retrieve annotations and manipulate bytecode is introduced. Finally, we discuss how to use [a]C# to annotate programs giving hints on how to parallel a sequential method and how it can be implemented by means of the abstractions provided by the run-time of the language.

This paper describes a technique for implementing the part of a compiler that processes the semantics of a programming language. It presents a concise, easy to understand notation for describing this semantic processing. The notation utilizes semantic charts which are similar to the separable transition diagrams [Conway63, Barnard75] that are used to define the syntax of programming languages. The charts describe semantic processing in terms of a set of operations that manipulate a small number of special-purpose data structures. They form a variable-free programming language, which accesses data via a set of operations organized into mechanisms to manage the associated data structure. These mechanisms can be modelled (and thus formalized) using abstract data types.

Aggregating linear complementarity problems under a general definition of constrained consistency leads to the possibility of consistent aggregation of linear and quadratic programming models and bimatrix games. Under this formulation, consistent aggregation of dual variables is also achieved. Furthermore, the existence of multiple sets of aggregation operators is discussed and illustrated with a numerical example. Constrained consistency can also be interpreted as a disaggregation rule. This aspect of the problem may be important for implementing macro (economic) policies by means of micro (economic) agents.

We investigate the limitations that emerge in thermodynamic tasks as a result of having local control only over the components of a thermal machine. These limitations are particularly relevant for devices composed of interacting many-body systems. Specifically, we study protocols of work extraction that employ a many-body system as a working medium whose evolution can be driven by tuning the on-site Hamiltonian terms. This provides a restricted set of thermodynamic operations, giving rise to alternative bounds for the performance of engines. Our findings show that those limitations in control render it, in general, impossible to reach Carnot efficiency; in its extreme ramification it can even forbid to reach a finite efficiency or finite work per particle. We focus on the one-dimensional Ising model in the thermodynamic limit as a case study. We show that in the limit of strong interactions the ferromagnetic case becomes useless for work extraction, while the antiferromagnetic case improves its performance with the strength of the couplings, reaching Carnot in the limit of arbitrary strong interactions. Our results provide a promising connection between the study of quantum control and thermodynamics and introduce a more realistic set of physical operations well suited to capture current experimental scenarios.

This paper proposes a set of specific crossover and mutation operators for the delineation of functional regions through evolutionary computation. We consider a problem of dividing a given territory into local labor market areas based on spatial interaction data. Such areas are defined so that a high degree of inter-regional separation and intra-regional integration - in both cases in terms of commuting flows - exist. A genetic algorithm has been designed based on the maximization of a fitness function that measures aggregate intra-region interaction under constraints of inter-region separation and minimum size. Additional requirements, typical of any functional regionalization, include the absence of overlapping between delineated regions and an exhaustive coverage of the whole territory (so all basic spatial units must be allocated to one and only one-region). The complex set of restrictions results in conventional operators often generating invalid solutions, impeding or delaying the evolutionary process. This is the reason why an extensive set of operators has been designed that incorporates knowledge about the problem, allowing the evolution of the set of solutions towards the final result.

We compute the anomalous dimensions of a set of composite operators which involve derivatives at four loops in \(\bar{\rm MS}\) in \(\phi^4\) theory as a function of the operator moment \(n\). These operators are similar to the twist-2 operators which arise in QCD in the operator product expansion in deep inelastic scattering. By regarding their inverse Mellin transform as being equivalent to the DGLAP splitting functions we explore to what extent taking a restricted set of operator moments can give a good approximation to the exact four loop result.