Ranking Function Research Articles

Dense Text Retrieval Based on Pretrained Language Models: A Survey

Text retrieval is a long-standing research topic on information seeking, where a system is required to return relevant information resources to user’s queries in natural language. From heuristic-based retrieval methods to learning-based ranking functions, the underlying retrieval models have been continually evolved with the ever-lasting technical innovation. To design effective retrieval models, a key point lies in how to learn text representations and model the relevance matching. The recent success of pretrained language models (PLM) sheds light on developing more capable text-retrieval approaches by leveraging the excellent modeling capacity of PLMs. With powerful PLMs, we can effectively learn the semantic representations of queries and texts in the latent representation space, and further construct the semantic matching function between the dense vectors for relevance modeling. Such a retrieval approach is called dense retrieval , since it employs dense vectors to represent the texts. Considering the rapid progress on dense retrieval, this survey systematically reviews the recent progress on PLM-based dense retrieval. Different from previous surveys on dense retrieval, we take a new perspective to organize the related studies by four major aspects, including architecture, training, indexing and integration, and thoroughly summarize the mainstream techniques for each aspect. We extensively collect the recent advances on this topic, and include 300+ reference papers. To support our survey, we create a website for providing useful resources, and release a code repository for dense retrieval. This survey aims to provide a comprehensive, practical reference focused on the major progress for dense text retrieval.

Mostly Automated Verification of Liveness Properties for Distributed Protocols with Ranking Functions

Distributed protocols have long been formulated in terms of their safety and liveness properties. Much recent work has focused on automatically verifying the safety properties of distributed protocols, but doing so for liveness properties has remained a challenging, unsolved problem. We present LVR, the first framework that can mostly automatically verify liveness properties for distributed protocols. Our key insight is that most liveness properties for distributed protocols can be reduced to a set of safety properties with the help of ranking functions. Such ranking functions for practical distributed protocols have certain properties that make them straightforward to synthesize, contrary to conventional wisdom. We prove that verifying a liveness property can then be reduced to a simpler problem of verifying a set of safety properties, namely that the ranking function is strictly decreasing and nonnegative for any protocol state transition, and there is no deadlock. LVR automatically synthesizes ranking functions by formulating a parameterized function of integer protocol variables, statically analyzing the lower and upper bounds of the variables as well as how much they can change on each state transition, then feeding the constraints to an SMT solver to determine the coefficients of the ranking function. It then uses an off-the-shelf verification tool to find inductive invariants to verify safety properties for both ranking functions and deadlock freedom. We show that LVR can mostly automatically verify the liveness properties of several distributed protocols, including various versions of Paxos, with limited user guidance.

Towards neutrosophic Circumstances goal programming approach for solving multi-objective linear fractional programming problems

Indeterminacy is common in practical decision-making circumstances. So the mathematical models of decision making represent the situations in a better way if the parameters are considered as neutrosophic. This article studies a general framework of multi-objective neutrosophic linear fractional programming problem (MONLFPP) and proposes unique approach. The issue's parameters are thought of as triangular neutrosophic numbers. The problem is converted into an equal crisp multi-objective linear programming problem (MOLPP) with the help of variable transformation technique and a ranking function. Fuzzy goal programming is used to solve the MOLPP that has been obtained. Finally, the usefulness of the proposed technique is established using two mathematical models.

Time-sequential probabilistic fermatean hesitant approach in multi-objective green solid transportation problems for sustainable enhancement

In order to delineate the randomness and imprecision in a single framework of time-sequential information, we proposed the notion of a time-sequential probabilistic fermatean hesitant set (TS-PFHS). Triangular time-sequential probabilistic fermatean hesitant number (Tr-TS-PFHN) is also initiated as a triangular version of TS-PFHS along with its fundamental operations and a ranking function. For the employment of our proposed set, we formulated a solid transportation problem (STP) with multiple objectives with TS-PFHS parameters for a sustainable green environment. Consequently, we proposed an algorithm by utilizing fuzzy programming (FP) and weighted sum technique (WST) to address proposed green transportation model. Additionally, to highlight the significance of the suggested technique, a numerical instance based on the transportation of electric vehicles in India is also investigated. Finally, conclusion along with the future prospects and limitations of the work done are discussed.

A New Approach to Solve Transportation Problems Under Neutrosophic Environment

The transportation problem has received a lot of attention in the field of operations research. In many circumstances, transportation planners may lack clear information on supply, demand, and transportation costs. Fuzzy sets can accept incomplete information by allowing for degrees of membership, which describe the level of certainty or uncertainty associated with each parameter. Three components—truth-membership, indeterminacy-membership, and falsity-membership degrees—are added to fuzzy numbers to create neutrosophic fuzzy numbers, which enables a more complex depiction of uncertainty. In this paper, we discuss the fuzzy transportation problem in a neutrosophic environment. Here the transportation costs, demands, and supplies are represented by neutrosophic trapezoidal fuzzy numbers. The neutrosophic trapezoidal fuzzy numbers are transformed into crisp numbers by using a ranking function and providing numerical examples to show the proposed method's efficiency to get the minimum optimal cost. Finally, we have demonstrated that our proposed method produced a better optimal solution to existing approaches by comparing its results to those of the existing ones.

Histopathology Image Classification With Noisy Labels via The Ranking Margins.

Clinically, histopathology images always offer a golden standard for disease diagnosis. With the development of artificial intelligence, digital histopathology significantly improves the efficiency of diagnosis. Nevertheless, noisy labels are inevitable in histopathology images, which lead to poor algorithm efficiency. Curriculum learning is one of the typical methods to solve such problems. However, existing curriculum learning methods either fail to measure the training priority between difficult samples and noisy ones or need an extra clean dataset to establish a valid curriculum scheme. Therefore, a new curriculum learning paradigm is designed based on a proposed ranking function, which is named The Ranking Margins (TRM). The ranking function measures the 'distances' between samples and decision boundaries, which helps distinguish difficult samples and noisy ones. The proposed method includes three stages: the warm-up stage, the main training stage and the fine-tuning stage. In the warm-up stage, the margin of each sample is obtained through the ranking function. In the main training stage, samples are progressively fed into the networks for training, starting from those with larger margins to those with smaller ones. Label correction is also performed in this stage. In the fine-tuning stage, the networks are retrained on the samples with corrected labels. In addition, we provide theoretical analysis to guarantee the feasibility of TRM. The experiments on two representative histopathologies image datasets show that the proposed method achieves substantial improvements over the latest Label Noise Learning (LNL) methods.

Minimum cost flow problems in generalized fuzzy environments. Credibilistic CVaR minimization approach

The paper focuses on the problems of linear programming (LP) with generalized fuzzy numbers (GFNs) as coefficients of the objective function. It is necessary to characterize consistent arithmetic operations to lower the error and information loss compared to the minimum operator usage and normalization in cases where experts are not completely certain of their subjective opinions. The uncertainty is eliminated using the total cost as a loss function and credibilistic conditional value at risk (CVaR) minimization. To crispify and generate a GFN, we utilize a ranking function that allows us to consider risky realizations. By solving many deterministic problems with LP solvers, projections of the error in the objective function can be presented. To describe and implement our methodology, we mainly focus on network optimization problems, especially generalized fuzzy transportation, assignment, and shortest path problems.

Problem fazi linearnog frakcionog programiranja pomoću leksikografskog metoda

Introduction/purpose: In solving real-life fractional programming problems, uncertainty and hesitation are often encountered due to various uncontrollable factors. To overcome these limitations, the fuzzy logic approach is applied to these problems. Methods: The discussion focused on solving the fuzzy linear fractional programming problem (FLFPP). First, the FLFP problem was converted into a lexicographic optimization problem, which was then solved to obtain the solution. Results: A numerical example was presented to simplify the explanation of the algorithm. While most researchers solve FLFPPs using the ranking function method, this approach reduces the efficiency of the fuzzy problem. Conclusion: This research contributes a comprehensive methodology for addressing fuzzy linear fractional programming problems using the lexicography method. The findings offer valuable insights for researchers, practitioners, and decision-makers grappling with optimization challenges in settings where imprecise information significantly influences the decision landscape.

Fuzzy Programming Approach to Solve Multi-Objective Fully Fuzzy Transportation Problem

The aim of this study is presenting the solution methodology of multi-objective fuzzy transportation problem with fuzzy decision variables, where all the input parameters and decisions variables of the programming problems are assumed to be triangular fuzzy number and triangular fuzzy decision variables respectively. Moreover the objectives under considerations are minimization of cost of transportation and minimization of shipping time under fuzzy environment. The fuzziness of the objective functions and the fuzzy constraints of the programming problem are defuzzified using the ranking function and the equality property between two fuzzy numbers, respectively. The consequent crisp multi-objective fuzzy transportation problem is tackled by employing fuzzy mathematical programming approach. Finally fuzzy decision is made after solving the resultant mathematical programming problem using LINGO(Schrage and LINDO Systems (1997)) software. Illustrative numerical example is presented in support of the proposed methodology.

The rank of the numbers of the A-function

The famous Indian mathematician D. Kaprekar came up with a method for obtaining new numbers K(n) = n + S(n) where S(n) is the sum of the digits of a number n in decimal notation. Following D. Kaprekar, the paper presents a new way to obtain numbers It is proved that the function A(n) is non-decreasing. Similarly to the function K(n), the concepts of a-generated and a-self-generated numbers are defined. The rank of numbers is investigated and it is proved that the rank function is non-decreasing. The rank formula for the numbers n = 10S

Image cartoon-texture decomposition by a generalized non-convex low-rank minimization method

Image cartoon-texture decomposition is an important problem in image processing. In recent years, by exploiting low-rank priors of images, low-rank minimization methods have been widely adopted for image cartoon-texture decomposition. Since matrix rank minimization is an NP-hard problem, the convex nuclear norm is often used as a substitute for the matrix’s rank to realize the low-rank minimization methods. In this paper, we utilize a generalized non-convex surrogate of the matrix rank function to develop a novel low-rank minimization model for image cartoon-texture decomposition. We design a proximal alternating algorithm to solve the non-convex model and further demonstrate the global convergence of the algorithm. Numerical experiments illustrate that the proposed method can show much better performances than the existing state-of-the-art methods for image cartoon-texture decomposition.

Hardness and approximation of submodular minimum linear ordering problems

AbstractThe minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost $$f(\cdot )$$ f ( · ) due to an ordering $$\sigma $$ σ of the items (say [n]), i.e., $$\min _{\sigma } \sum _{i\in [n]} f(E_{i,\sigma })$$ min σ ∑ i ∈ [ n ] f ( E i , σ ) , where $$E_{i,\sigma }$$ E i , σ is the set of items mapped by $$\sigma $$ σ to indices [i]. Despite an extensive literature on MLOP variants and approximations for these, it was unclear whether the graphic matroid MLOP was NP-hard. We settle this question through non-trivial reductions from mininimum latency vertex cover and minimum sum vertex cover problems. We further propose a new combinatorial algorithm for approximating monotone submodular MLOP, using the theory of principal partitions. This is in contrast to the rounding algorithm by Iwata et al. (in: APPROX, 2012), using Lovász extension of submodular functions. We show a $$(2-\frac{1+\ell _{f}}{1+|E|})$$ ( 2 - 1 + ℓ f 1 + | E | ) -approximation for monotone submodular MLOP where $$\ell _{f}=\frac{f(E)}{\max _{x\in E}f(\{x\})}$$ ℓ f = f ( E ) max x ∈ E f ( { x } ) satisfies $$1 \le \ell _f \le |E|$$ 1 ≤ ℓ f ≤ | E | . Our theory provides new approximation bounds for special cases of the problem, in particular a $$(2-\frac{1+r(E)}{1+|E|})$$ ( 2 - 1 + r ( E ) 1 + | E | ) -approximation for the matroid MLOP, where $$f = r$$ f = r is the rank function of a matroid. We further show that minimum latency vertex cover is $$\frac{4}{3}$$ 4 3 -approximable, by which we also lower bound the integrality gap of its natural LP relaxation, which might be of independent interest.

Moment functions of higher rank on some types of hypergroups

We consider moment functions of higher order. In our earlier paper, we have already investigated the moment functions of higher order on groups. The main purpose of this work is to prove characterization theorems for moment functions on the multivariate polynomial hypergroups and on the Sturm–Liouville hypergroups. In the first case, the moment generating functions of higher rank are partial derivatives (taken at zero) of the composition of generating polynomials of the hypergroup and functions whose coordinates are given by the formal power series. On Sturm–Liouville hypergroups the moment functions of higher rank are restrictions of even smooth functions that also satisfy certain boundary value problems. The second characterization of moment functions of higher rank on Sturm–Liouville hypergroups is given by means of an exponential family. In this case, the moment functions of higher rank are partial derivatives of an appropriately modified exponential family again taken at zero.

Propagation of chaos for topological interactions by a coupling technique

We consider a system of particles that interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have been shown relevant for the modelling of bird flocks. We show that, in the large number of particles limit and under minimal smoothness assumptions on the data, the model converges to a kinetic equation which was derived in earlier works both formally and rigorously under more stringent regularity assumptions. The proof relies on the coupling method which assigns to the particle and limiting processes a joint process posed on the cartesian product of the two configuration spaces of the former processes. By appropriate estimates in a suitable Wasserstein metric, we show that the distance between the two processes tends to zero as the number of particles tends to infinity, with an error typical of the law of large numbers.

Singular vectors of sums of rectangular random matrices and optimal estimation of high-rank signals: The extensive spike model.

Across many disciplines spanning from neuroscience and genomics to machine learning, atmospheric science, and finance, the problems of denoising large data matrices to recover hidden signals obscured by noise, and of estimating the structure of these signals, is of fundamental importance. A key to solving these problems lies in understanding how the singular value structure of a signal is deformed by noise. This question has been thoroughly studied in the well-known spiked matrix model, in which data matrices originate from low-rank signal matrices perturbed by additive noise matrices, in an asymptotic limit where matrix size tends to infinity but the signal rank remains finite. We first show, strikingly, that the singular value structure of large finite matrices (of size ∼1000) with even moderate-rank signals, as low as 10, is not accurately predicted by the finite-rank theory, thereby limiting the application of this theory to real data. To address these deficiencies, we analytically compute how the singular values and vectors of an arbitrary high-rank signal matrix are deformed by additive noise. We focus on an asymptotic limit corresponding to an extensive spike model, in which both the signal rank and the size of the data matrix tend to infinity at a constant ratio. We map out the phase diagram of the singular value structure of the extensive spike model as a joint function of signal strength and rank. We further exploit these analytics to derive optimal rotationally invariant denoisers to recover the hidden high-rank signal from the data, as well as optimal invariant estimators of the signal covariance structure. Our extensive-rank results yield several conceptual differences compared to the finite-rank case: (1) as signal strength increases, the singular value spectrum does not directly transition from a unimodal bulk phase to a disconnected phase, but instead there is a bimodal connected regime separating them; (2) the signal singular vectors can be partially estimated even in the unimodal bulk regime, and thus the transitions in the data singular value spectrum do not coincide with a detectability threshold for the signal singular vectors, unlike in the finite-rank theory; (3) signal singular values interact nontrivially to generate data singular values in the extensive-rank model, whereas they are noninteracting in the finite-rank theory; and (4) as a result, the more sophisticated data denoisers and signal covariance estimators we derive, which take into account these nontrivial extensive-rank interactions, significantly outperform their simpler, noninteracting, finite-rank counterparts, even on data matrices of only moderate rank. Overall, our results provide fundamental theory governing how high-dimensional signals are deformed by additive noise, together with practical formulas for optimal denoising and covariance estimation.

Maximal matroids in weak order posets

Let X be a family of subsets of a finite set E. A matroid on E is called an X-matroid if each set in X is a circuit. We develop techniques for determining when there exists a unique maximal X-matroid in the weak order poset of all X-matroids on E and formulate a conjecture which would characterise the rank function of this unique maximal matroid when it exists. The conjecture suggests a new type of matroid rank function which extends the concept of weakly saturated sequences from extremal graph theory. We verify the conjecture for various families X and show that, if true, the conjecture could have important applications in such areas as combinatorial rigidity and low rank matrix completion.

Methodological observations concerning word rankings and z-score refinements

Abstract This article evaluates word rankings suggested by Ary L. Goldberger, Albert C. Yang, and C. Peng as a means of establishing the authorship of texts in the light of Delta, developed by John Burrows at about the same time. The tests carried out with high ranking function words and results established with the more modern approaches of Rolling Delta, Rolling Classify, and the General Imposters method give clear evidence that word rankings only return crude and unreliable results that cannot keep up with non-traditional modern methods. Even though the stylistic difference between Marlowe and Shakespeare plays could be stated, word rankings failed to recognize Shakespearean stylistics in The Jew of Malta, Edward II, and Doctor Faustus. It was only through the use of z-scores that a wider vocabulary provided a larger degree of differentiation.

Clinical Evaluation of a Functional Combinatorial Precision Medicine Platform to Predict Patient-Specific Treatment Outcomes in Acute Myeloid Leukemia

Introduction: Acute myeloid leukemia (AML) is an aggressive form a leukemia that remains difficult to treat, often with rapid and frequent disease relapse due to drug-resistant clonal selection. A range of combination therapies have been designed to overcome this hurdle, however, identifying the most appropriate combination therapy at each line of treatment remains a challenge. Functional precision medicine platforms that use ex vivo drug sensitivity data from primary patient samples have shown potential to guide treatments in a range of cancers. We have recently developed an ex vivo combinatorial drug sensitivity platform, quadratic phenotypic optimization platform (QPOP), that analyses a predesigned array of 155 test combinations performed on a primary patient sample to rank and compare all possible therapeutic combinations from a 12-drug set. In this study, we evaluated the use of QPOP to predict treatment outcomes in an AML cohort treated with a variety of combination therapies. Furthermore, we also explored QPOP's combination therapy ranking function to identify novel or under-utilized combinations that may benefit larger groups of AML patients when appropriately guided. Methods: Prospective clinical feasibility study of QPOP in AML was performed at National University Hospital (NUH) in Singapore. Peripheral blood or bone marrow aspirations were collected from AML patients, recruited between 26 th November 2019 and June 15 th 2023. Following CD34+ cell selection, the enriched malignant blast population was subjected to an array of 155 test combinations derived from an orthogonal array composite design. Phenotypic cell viability data from this test was subsequently used by QPOP to derive drug combination scores and rankings for all possible combinations. Median turnaround time for QPOP patient-specific reports was 8 (±2.1) days. Patients were treated with current standard of care options as guided by the clinician. The primary outcomes of this study were to determine the concordance between treatment outcomes as guided by clinicians and QPOP drug combination scores and rankings. Secondary outcomes of this study were to identify high-ranking, potentially effective combinations that may be nover or under-utilized for future studies. Results: 40 patients were recruited to the study with 49 samples analyzed by QPOP. Samples collected until 21 January 2022 were also used to refined ex vivo drug dosing levels for 12-drug, 3-level test combination arrays. Excluding patients diagnosed as non-AML and patient without available clinical concordance data, QPOP response concordance was evaluable for 19 patients. A 75% positive predictive value (PPV) and a 72.7% negative predictive value (NPV) was determined for a QPOP normalized cell viability (NCV) cutoff of 0.65. The area under the curve of the receiver operator curve, AUC = 0.75, suggesting acceptable predictivity. Concordance analysis of with samples (n = 10) collected after 21January 2022 demonstrated an 80% PPV, 80% NPV, AUC = 0.80 for an NCV cutoff of 0.62, suggesting that current ex vivo dosage settings for test array can further improve test accuracy. Combination therapy with the BCL2 inhibitor venetoclax and hypomethylating agent azacytidine is standard-of-care for AML. QPOP NCV cutoff of 0.62 also exhibited 100% concordance (5/5) with venetoclax+azacytidine treatment further demonstrating the accuracy of QPOP to predict treatment outcomes in AML. Amongst top ranked QPOP-derived combinations, venetoclax/fludarabine was amongst the most frequently reoccurring top-ranked combinations. With appropriate functional combinatorial precision medicine testing, patients who may benefit from addition of venetoclax to fludarabine-based chemotherapy regimens, such as fludarabine/busulfan reduced-intensity conditioning chemotherapy, may be accurately identified. Conclusions: This clinical study demonstrates the feasibility of QPOP to predict treatment outcomes and accurately identify both response and resistance to combination therapy. Following platform workflow optimization, initial concordance analysis suggests excellent predictivity. Expansion of this clinical study is needed to confirm these results. This study also suggests that underutilized combinations may be effective across a larger population of AML patients with appropriate ex vivo drug testing and deserve further clinical interrogation.

Wachs permutations, Bruhat order and weak order

We study the partial orders induced on Wachs and signed Wachs permutations by the Bruhat and weak orders of the symmetric and hyperoctahedral groups. We show that these orders are graded, determine their rank function, characterize their ordering and covering relations, and compute their characteristic polynomials, when partially ordered by Bruhat order, and determine their structure explicitly when partially ordered by right weak order.

A New Approach for Solving a Heptagonal Intuitionistic Fuzzy Transportation Problem by Using Proposed Method

In this paper, we approach the transportation problem whose supplies and demands are in intuitionistic fuzzy number. We formulate and utilize the heptagonal intuitionistic fuzzy number to deal with uncertainty. We discuss about the new ranking function for intuitionistic fuzzy number. Finally, we approach an algorithm for finding the optimal solution of heptagonal intuitionistic fuzzy transportation problem with relevant numerical example.