Ranking Function Research Articles

Quantum Kernel Machine Learning With Continuous Variables

The popular qubit framework has dominated recent work on quantum kernel machine learning, with results characterising expressivity, learnability and generalisation. As yet, there is no comparative framework to understand these concepts for continuous variable (CV) quantum computing platforms. In this paper we represent CV quantum kernels as closed form functions and use this representation to provide several important theoretical insights. We derive a general closed form solution for all CV quantum kernels and show every such kernel can be expressed as the product of a Gaussian and an algebraic function of the parameters of the feature map. Furthermore, in the multi-mode case, we present quantification of a quantum-classical separation for all quantum kernels via a hierarchical notion of the “stellar rank" of the quantum kernel feature map. We then prove kernels defined by feature maps of infinite stellar rank, such as GKP-state encodings, can be approximated arbitrarily well by kernels defined by feature maps of finite stellar rank. Finally, we simulate learning with a single-mode displaced Fock state encoding and show that (i) accuracy on our specific task (an annular data set) increases with stellar rank, (ii) for underfit models, accuracy can be improved by increasing a bandwidth hyperparameter, and (iii) for noisy data that is overfit, decreasing the bandwidth will improve generalisation but does so at the cost of effective stellar rank.

Solving a Fully Intuitionistic Fuzzy Transportation Problem Using a Hybrid Multi-Objective Optimization Approach

In this study, a typical transportation problem involving intuitionistic fuzzy-type variables and parameters is focused on. The approaches proposed in the literature for such transportation problems have many shortcomings, such as the use of ranking functions and obtaining an infeasible solution with negative values for variables and objective functions in the presence of non-negative unit transportation charges. To overcome such weaknesses, a new approach without a ranking function is introduced in this paper. The proposed approach first constructs an equivalent crisp multi-objective form of the intuitionistic fuzzy transportation problem and then proposes a new hybrid multi-objective solution procedure to tackle the obtained crisp multi-objective problem. The conducted computer experiments with benchmark problems from the existing studies of the literature reflect the effectiveness of the proposed solution approach of this study in terms of the quality of the results when compared to the available approaches of the literature.

Tensor linearity of two-dimensional isotropic functions in the plane problem of nonlinear theory of elasticity

It is shown that a nonlinear isotropic tensor function of the second rank in two-dimensional space, which is a power series in its tensor argument, is representable by a finite binomial tensor linear relation. Expressions of two coefficients of this relation are given in terms of an infinite set of coefficients of the original series and two independent invariants of the tensor argument. In relation to continuum mechanics, the reducibility of the constitutive relations in the plane problem of tensor nonlinear elasticity theory to the tensor linear connection of the corresponding second-order minors of stresses and strains is established.

On complete classes of valuated matroids

We characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network. We exhibit a family of valuated matroids that are not R-minor based on sparse paving matroids. Valuated matroids are inherently related to gross substitute valuations in mathematical economics. By the same token we refute the Matroid Based Valuation Conjecture by Ostrovsky and Paes Leme (Theoretical Economics 2015) asserting that every gross substitute valuation arises from weighted matroid rank functions by repeated applications of merge and endowment operations. Our result also has implications in the context of Lorentzian polynomials: it reveals the limitations of known construction operations.

Sequential merging and construction of rankings as cognitive logic

We introduce and evaluate a cognitively inspired formal reasoning approach that sequentially applies a combination of a belief merging operator and a ranking construction operator. The approach is inspired by human propositional reasoning, which is understood here as a sequential process in which the agent constructs a new epistemic state in each task step according to newly acquired information. Formally, we model epistemic states by Spohn's ranking functions. The posterior representation of the epistemic state is obtained by merging the prior ranking function and a ranking function constructed from the new piece of information. We denote this setup as the sequential merging approach. The approach abstracts from the concrete merging operation and abstracts from the concrete way of constructing a ranking function according to new information. We formally show that sequential merging is capable of predicting with theoretical maximum achievable accuracy. Various instantiations of our approach are benchmarked on data from a psychological experiment, demonstrating that sequential merging provides formal reasoning methods that are cognitively more adequate than classical logic.

Ranked Enumeration for Database Queries

Ranked enumeration is a query-answering paradigm where the query answers are returned incrementally in order of importance (instead of returning all answers at once). Importance is defined by a ranking function that can be specific to the application, but typically involves either a lexicographic order (e.g., "ORDER BY R.A, S.B" in SQL) or a weighted sum of attributes (e.g., "ORDER BY 3*R.A + 2*S.B"). Recent work has introduced any-k algorithms for (multi-way) join queries, which push ranking into joins and avoid materializing intermediate results until necessary. The top-ranked answers are returned asymptotically faster than the common join-then-rank approach of database systems, resulting in orders-of-magnitude speedup in practice.

Minor-closed classes of binary functions

Binary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid deletion and contraction. We give the excluded minor characterisations for the classes of binary functions with well defined minors, and those with an associated rank function. Within these classes, we also characterise the classes of binary functions corresponding to polymatroids, matroids and binary matroids by their excluded minors. This gives a new proof of Tutte's excluded minor characterisation of binary matroids in the more generalised space of binary functions.

A modified multiple-criteria decision-making approach based on a protein-protein interaction network to diagnose latent tuberculosis

BackgroundDNA microarrays provide informative data for transcriptional profiling and identifying gene expression signatures to help prevent progression of latent tuberculosis infection (LTBI) to active disease. However, constructing a prognostic model for distinguishing LTBI from active tuberculosis (ATB) is very challenging due to the noisy nature of data and lack of a generally stable analysis approach.MethodsIn the present study, we proposed an accurate predictive model with the help of data fusion at the decision level. In this regard, results of filter feature selection and wrapper feature selection techniques were combined with multiple-criteria decision-making (MCDM) methods to select 10 genes from six microarray datasets that can be the most discriminative genes for diagnosing tuberculosis cases. As the main contribution of this study, the final ranking function was constructed by combining protein-protein interaction (PPI) network with an MCDM method (called Decision-making Trial and Evaluation Laboratory or DEMATEL) to improve the feature ranking approach.ResultsBy applying data fusion at the decision level on the 10 introduced genes in terms of fusion of classifiers of random forests (RF) and k-nearest neighbors (KNN) regarding Yager’s theory, the proposed algorithm reached a sensitivity of 0.97, specificity of 0.90, and accuracy of 0.95. Finally, with the help of cumulative clustering, the genes involved in the diagnosis of latent and activated tuberculosis have been introduced.ConclusionsThe combination of MCDM methods and PPI networks can significantly improve the diagnosis different states of tuberculosis.Clinical trial numberNot applicable.

A Study of Word Bigrams for Pseudo-relevance Feedback in Information Retrieval

Traditional information retrieval models mostly adopt a term independence assumption and are based on single terms or unigrams. Past efforts have attempted to go beyond this assumption, such as by using contiguous terms (i.e. word n-grams) or terms appearing in proximity. One such approach employs pseudo-relevance feedback (PRF) in an extended BM25 model, with an expanded query containing bigrams and proximity word pairs besides unigrams. However, the benefit of this approach over the traditional unigram PRF remains inconclusive. We speculate the uncertain effectiveness of bigram PRF in this past work is due to: (1) The new bigrams obtained from the expanded query may be formed by pairing unigrams drawn from different documents. These are potentially noise instead of relevant concepts; (2) The collection statistics of n-grams needed to calculate the document ranking functions, such as their document frequency, is not available in retrieval. Only estimates of these quantities are used instead. We suggest that these issues may be overcome by extracting word n-grams as single units in query expansion, and employing a document index that contains both unigrams and word n-grams. We demonstrate the approach for the case of bigram PRF in an extended BM25. Retrieval experiments are conducted on a range of standard test collections. For the majority of tested collections, the difference between values of the evaluation metrics (Mean Average Precision and the precision-oriented NDCG@20) obtained by our bigram PRF and the unigram PRF baseline is not statistically significant. Thus, our bigram PRF fails to improve over unigram PRF robustly across collections. An analysis of our results reveals ‘query drift’ due to bigram query expansion terms that represent too-broad topics as a cause for the failure of our approach.

Comparative Study of R Programming and Lingo Software in Fully Fuzzy Linear Programming Problems

Authors: The paper begins with an introduction to the concept of fuzzy optimization, providing an in-depth explanation of its significance and applications. It then proceeds to define two distinct ranking functions that is Yager’s and vR – ranking functions within the context of fuzzy optimization along with the properties of vR- ranking function. Following this, a comprehensive overview of Lingo software and R programming is presented, delving into their respective features and capabilities. This paper further delves into a detailed comparison of Lingo and R programming, offering a thorough exploration of their strengths and limitations through the use of example problems. These examples illustrate the process of computing optimal solutions for fully fuzzy linear programming problems using both Lingo and R programming, providing a comprehensive and practical comparison of their effectiveness in this context.

Optimization of Chinese Postman Problem Using Fuzzy-Based Priority Weighted Graph

: In the early 1960s, Chinese mathematician Mei-Ko Kwan (M. Guan) introduced a method aimed at minimizing mail carriers’ route lengths. This method led to the exploration of various formulations of the Chinese Postman Problem (CPP), resulting in at least eight distinct formulations. In response to a practical concern, a new problem formulation called the Priority Constrained Chinese Postman Problem (PCCPP) emerged. In PCCPP, a linear order is provided for a set of significant nodes, and the objective is to traverse all edges at least once while prioritizing the prompt visitation of higher-priority nodes. This paper presents a modified approach to Chinese Postman Problems (CPP) using priorities in a fuzzy environment ranking function applied to priority nodes in CPP to get the optimal result. Finally, this paper also illustrates and justifies the implementation of the modified approach with a numerical problem. The consideration of multi-factors in a multi-graph with priorities gives another scope of research. JEL Codes: C44 Received: 18/07/2024. Accepted: 29/09/2024. Published: 13/10/2024.

Randomized SearchRank: A semiclassical approach to a quantum search engine

The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the N/M ratio between the network size N and the number of marked nodes M is sufficiently large. We propose a modification of the algorithm, replacing the underlying Szegedy quantum walk with a semiclassical walk. To maintain the same time complexity as the quantum SearchRank algorithm we propose a simplification of the algorithm. This new algorithm is called randomized SearchRank, since it corresponds to a quantum walk over a randomized mixed state. The performance of the SearchRank algorithms is first analyzed on an example network and then statistically on a set of different networks of increasing size and different number of marked nodes. On the one hand, to test the search ability of the algorithms, it is computed how the probability of measuring the marked nodes decreases with N/M for the quantum SearchRank, but remarkably it remains at a high value around 0.9 for our semiclassical algorithms, solving the quantum SearchRank problem. The time complexity of the algorithms is also analyzed, obtaining a quadratic speedup with respect to the classical ones. On the other hand, the ranking functionality of the algorithms has been investigated, obtaining a good agreement with the classical PageRank distribution. Finally, the dependence of these algorithms on the intrinsic PageRank damping parameter has been clarified. Our results suggest that this parameter should be below a threshold so that the execution time does not increase drastically. Published by the American Physical Society 2024

Addressing Fuzzy Linear Programming Problems Through Ranking Functions

In contemporary decision-making, reliance on information is paramount, yet much of it is fraught with uncertainty, making logical decision-making challenging. To tackle this uncertainty, various methods, including the use of fuzzy numbers, have been employed. This paper specifically delves into addressing linear programming (LP) problems characterized by fuzzy coefficients in the objective function, fuzzy values in the right-hand side, and fuzzy coefficients of constraints. The proposed approach involves employing linear ranking functions such as Maleki, Campos, Yager’s F1 and Yager linear ranking functions to solve these fuzzy linear programming (FLP) problems and attain optimal solutions. Furthermore, the paper elucidates the resolution steps through the presentation of numerical examples, in this study, a comprehensive methodology is presented for effectively addressing a wide range of linear programming problems.

Vocal-visual combinations in wild chimpanzees

Living organisms throughout the animal kingdom habitually communicate with multi-modal signals that use multiple sensory channels. Such composite signals vary in their communicative function, as well as the extent to which they are recombined freely. Humans typically display complex forms of multi-modal communication, yet the evolution of this capacity remains unknown. One of our two closest living relatives, chimpanzees, also produce multi-modal combinations and therefore may offer a valuable window into the evolutionary roots of human communication. However, a currently neglected step in describing multi-modal systems is to disentangle non-random combinations from those that occur simply by chance. Here we aimed to provide a systematic quantification of communicative behaviour in our closest living relatives, describing non-random combinations produced across auditory and visual modalities. Through recording the behaviour of wild chimpanzees from the Kibale forest, Uganda we generated the first repertoire of non-random combined vocal and visual components. Using collocation analysis, we identified more than 100 vocal-visual combinations which occurred more frequently than expected by chance. We also probed how multi-modal production varied in the population, finding no differences in the number of visual components produced with vocalisations as a function of age, sex or rank. As expected, chimpanzees produced more visual components alongside vocalizations during longer vocalization bouts, however, this was only the case for some vocalization types, not others. We demonstrate that chimpanzees produce a vast array of combined vocal and visual components, exhibiting a hitherto underappreciated level of multi-modal complexity.

Dynamic ranking function to optimize transshipment costs in intuitionistic Type-2 and Type-1 fuzzy environments

In the dynamic realm of organizational logistics, accurately minimizing transportation and transshipment costs is crucial, yet often challenging due to inherent uncertainties. This paper introduces a novel application of fuzzy logic to provide a more precise analysis of these costs. Specifically, it develops an innovative ranking function for trapezoidal fuzzy numbers (TrFNs) for Type-2 and Type-1 fuzzy environments, a tool yet unexplored in existing literature. The main contributions of this paper are the idea that a ranking function for TrFNs can significantly improve decision-maker's freedom in cost analysis due to an adherence on all (a, b, c d) parameters of TrFN. A new decision-oriented ranking method for these fuzzy numbers is developed which consists of an inventive algorithm. The method is also considered for intuitionistic TrFNs and applied to solve transshipment costs in fuzzy area. To verify the proposed methodology's efficiency, effectiveness and accuracy a numerical example in Wolfram Mathematica 9.0 is demonstrated showing superior computational performance over existing methods.

Learning bivariate scoring functions for ranking

State-of-the-art Learning-to-Rank algorithms, e.g., λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}MART, rely on univariate scoring functions to score a list of items. Univariate scoring functions score each item independently, i.e., without considering the other available items in the list. Nevertheless, ranking deals with producing an effective ordering of the items and comparisons between items are helpful to achieve this task. Bivariate scoring functions allow the model to exploit dependencies between the items in the list as they work by scoring pairs of items. In this paper, we exploit item dependencies in a novel framework—we call it the Lambda Bivariate (LB) framework—that allows to learn effective bivariate scoring functions for ranking using gradient boosting trees. We discuss the three main ingredients of LB: (i) the invariance to permutations property, (ii) the function aggregating the scores of all pairs into the per-item scores, and (iii) the optimization process to learn bivariate scoring functions for ranking using any differentiable loss functions. We apply LB to the λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}Rank loss and we show that it results in learning a bivariate version of λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}MART—we call it Bi-λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}MART—that significantly outperforms all neural-network-based and tree-based state-of-the-art algorithms for Learning-to-Rank. To show the generality of LB with respect to other loss functions, we also discuss its application to the Softmax loss.

An implementation of nonmonotonic reasoning with c-representations using an SMT solver

A qualitative conditional “If A then usually B” establishes a plausible connection between the antecedent A and the consequent B. As a semantics for conditional knowledge bases containing such conditionals, ranking functions order possible worlds by mapping them to a degree of plausibility. c-Representations are special ranking functions that are obtained by assigning individual integer impacts to the conditionals in a knowledge base R and by defining the rank of each possible world as the sum of these impacts of falsified conditionals. c-Inference is the nonmonotonic inference relation taking all c-representations of a given knowledge base R into account. In this paper, we show how c-inference can be realized as a satisfiability modulo theories problem (SMT), which allows an implementation by an appropriate SMT solver. Moreover, we show that this leads to the first implementation fully realizing c-inference because it does not require a predefined upper limit for the impacts assigned to the conditionals. We develop a transformation of the constraint satisfaction problem characterizing c-inference into a solvable-equivalent SMT problem, prove its correctness, and illustrate it by a running example. Furthermore, we provide a corresponding implementation using the SMT solver Z3. We develop and implement a randomized generation scheme for knowledge bases and queries, and evaluate our SMT-based implementation of c-inference with respect to such randomly generated knowledge bases. Our evaluation demonstrates the feasibility of our approach as well as the superiority in comparison to former implementations of c-inference.

Optimized Selective Assembly using Hungarian Algorithm

Assembly of discrete parts guided by hardware design specification constitutes the final phase in product manufacturing. In the course of mass production of components, mating parts with geometric or dimensional deviation from their intended design can be made acceptable by the identification of suitable pairs after analysing design fit and tolerance limits. By transforming this application-specific problem into a unified mathematical model, an optimal solution can be achieved that minimizes the rejection of non-conforming fabricated parts. Regardless of the type and range of a design fit, the problem can be mapped into a matrix using a ranking function defined by the user. The ranking function is modifiable as per the user requirements and may vary based on the selection criteria for an assembly. Based on the type of ranking function used, the tabulated matrix is solved using the Hungarian minimization/maximization algorithm, which is a powerful combinatorial optimization algorithm that solves the classical assignment problem in mathematics. This approach ensures maximum number of suiting pairs as well as nominal suiting of parts with each other resulting in high-quality products and maximum utilization of fabricated resources.

An Approach for Solving Fuzzy Sequencing Problem with Triangular Fuzzy Neutrosophic Numbers Using Ranking Function

This study presents a modified approach to address the sequencing problem, specifically when the values are expressed using Triangular Fuzzy Neutrosophic Numbers. First, we have to convert Triangular Neutrosophic fuzzy numbers into crisp one by using Score function. A numerical example has been considered and solved for illustration purpose.

An efficient algorithm for solving multilevel multi-objective linear fractional optimization problem with neutrosophic parameters

This work demonstrates the modeling of the multilevel-multiobjective linear fractional optimization (ML-MOLFO) problem in a neutrosophic decision environment. The primary driving force behind this work is to determine how to handle a ML-MOLFO problem while taking into account a real-life decision-making scenario. There is a hierarchy of decision-makers and many decision-making processes, such as agree, not-sure, and disagree, in a real-life decision-making setting. By taking into account such genuine situations, all resource, coefficient of objective, and constraint functions are represented as single-valued trapezoidal neutrosophic numbers. As far as we can tell, there is no established technique for resolving the ML-MOLFO problem with neutrosophic parameters in the literature review. Therefore, by outlining goal programming methods in the intuitionistic fuzzy environment, we create our new intuitionistic fuzzy Chebyshev goal programming (IFCGP) method to address the introduced problem. In the proposed method, first we used a modified ranking function to transform the problem into an analogous crisp ML-MOLFO problem, and then it was converted into a multilevel multiobjective linear optimization problem through linearized techniques. The linearization procedure in the proposed method, unlike the existing one, does not require derivatives, additional variables, or inequality constraints, which makes it simpler. To illustrate the adequacy and performance of the proposed new method, we considered numerical tests and application problems. We also compared the performance of the resulting optimal solution with existing approaches using the distance metric, which indicates our method is non-dominated.