Pairwise Order Research Articles

Beyond directed hypergraphs: heterogeneous hypergraphs and spectral centralities

Abstract The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article, we introduce the notion of heterogeneous hypergraphs from an algebraic point of view, which have traditional directed hypergraphs as a particular case. We furthermore analytically study the spectral centralities associated to some types of heterogeneous hypergraphs, extending previously defined eigenvector-like centrality measures to this new realm. We supplement the analytical arguments with some numerical comparisons of pairwise and higher order rankings, and we construct directed higher order networks from real data, which we then use for discussion and analysis.

Clinical and Functional Effects of Rehabilitation of Patients after COVID-19 Infection.

Background/Objectives: The most common post-acute consequences of SARS-CoV-2 include lung dysfunction, the impairment of cognitive functions and mental health, as well as the impairment of the musculoskeletal system in the form of fatigue and muscle weakness. Post-COVID-19 patients often experience impaired balance and reduced physical capacity. It is important to implement a rehabilitation program that eliminates the side effects of COVID-19 and allows for significant improvement in the patient's functionality. The aim of our study was to assess patient functionality after a 6-week rehabilitation program on balance, foot pressure distribution, and physical capacity in post-COVID-19 patients. Methods: The clinical study group consisted of 53 people 3 months after COVID-19 infection, confirmed by a positive PCR test. Exclusion from the study included people with comorbidities that impaired balance and gait. The patients underwent a posturographic assessment-Romberg test, a baropodometric assessment-static and dynamic, and a performance assessment-a 6 min walk test determining shortness of breath on the mMRC scale, blood pressure, heart rate, and saturation. Patients participated in rehabilitation until the sixth week, after which they were assessed again. Comparisons were made using IBM SPSS Statistics 27.0 software using the Wilcoxon pairwise order test, at a significance level of p < 0.05. Results: The result of the postural control assessment showed an improvement in the ability to maintain the centre of gravity in terms of the foot support area-statistical decreases were observed in the ellipse area, from 745.28 mm2 to 453.52 mm2 (p = 0.009), as well as maximum (from 3133.5 gr/cm2 to 2994.2 gr/cm2; p = 0.065) and average load on the left foot (from 1010.1 gr/cm2 to 969.38 gr/cm2; p = 0.028). In the 6 min walk test before and after exercise, the heart rate decreased after the therapy (shortness of breath on the mMRC scale also decreased from 79.12 to 74.95). This means that patients achieved better physical fitness and efficiency. Conclusions: Rehabilitation significantly improved balance, as measured by a decrease in ellipse area during the Romberg test.

Reconstructing the evolution history of networked complex systems

The evolution processes of complex systems carry key information in the systems’ functional properties. Applying machine learning algorithms, we demonstrate that the historical formation process of various networked complex systems can be extracted, including protein-protein interaction, ecology, and social network systems. The recovered evolution process has demonstrations of immense scientific values, such as interpreting the evolution of protein-protein interaction network, facilitating structure prediction, and particularly revealing the key co-evolution features of network structures such as preferential attachment, community structure, local clustering, degree-degree correlation that could not be explained collectively by previous theories. Intriguingly, we discover that for large networks, if the performance of the machine learning model is slightly better than a random guess on the pairwise order of links, reliable restoration of the overall network formation process can be achieved. This suggests that evolution history restoration is generally highly feasible on empirical networks.

How much freedom does an effectiveness metric really have?

AbstractIt is tempting to assume that because effectiveness metrics have free choice to assign scores to search engine result pages (SERPs) there must thus be a similar degree of freedom as to the relative order that SERP pairs can be put into. In fact that second freedom is, to a considerable degree, illusory. That is because if one SERP in a pair has been given a certain score by a metric, fundamental ordering constraints in many cases then dictate that the score for the second SERP must be either not less than, or not greater than, the score assigned to the first SERP. We refer to these fixed relationships as innate pairwise SERP orderings. Our first goal in this work is to describe and defend those pairwise SERP relationship constraints, and tabulate their relative occurrence via both exhaustive and empirical experimentation. We then consider how to employ such innate pairwise relationships in IR experiments, leading to a proposal for a new measurement paradigm. Specifically, we argue that tables of results in which many different metrics are listed for champion versus challenger system comparisons should be avoided; and that instead a single metric be argued for in principled terms, with any relationships identified by that metric then reinforced via an assessment of the innate relationship as to whether other metrics are likely to yield the same system‐versus‐system outcome.

Inference for the Optimum Using Linear Regression Models with Discrete Inputs

We present a multiple-comparison-with-the-best procedure to provide inference for the optimum from regression models with discrete inputs. Two applications are given to illustrate the methodology: two-level factorial designs to identify the best drug combination and order-of-addition experiments where the primary objective is to identify the sequence with the largest mean response. The methods easily accommodate restrictions limiting the inference set of conditions. We use simulation to determine the critical values. While the methods apply to any linear regression model, we identify cases that require just a single critical value, and we also show where approximations and upper bounds mitigate the need for intensive computation. We tabulate the required critical values for a variety of common applications: the main-effect model and two-factor interaction model estimated by certain two-level factorial designs, and the pairwise order model and several component-position models for estimation based on optimal order-of-addition designs. Our work greatly simplifies the problem of rigorous inference for the optimum from regression models with discrete inputs.

Constructing Optimal Designs for Order-of-Addition Experiments Using a Hybrid Algorithm

For order-of-addition experiments, the response is affected by the addition order of the experimental materials. Consequently, the main interest focuses on creating a predictive model and an optimal design for optimizing the response. Van Nostrand proposed the pairwise-order (PWO) model for detecting PWO effects. Under the PWO model, the full PWO design is optimal under various criteria but is often unaffordable because of the large run size. In this paper, we consider the D-, A- and M.S.-optimal fractional PWO designs. We first present some results on information matrices. Then, a flexible and efficient algorithm is given for generating these optimal PWO designs. Numerical simulation shows that the generated design has an appealing efficiency in comparison with the full PWO design, though with only a small fraction of runs. Several comparisons with existing designs illustrate that the generated designs achieve better efficiencies, and the best PWO designs and some selected 100% efficient PWO designs generated by the new algorithm are reported.

Interaction effects in pairwise ordering model

In an order-of-addition (OofA) experiment, the response is a function of the addition order of components. The key objective of the OofA experiments is to find the optimal order of addition. The most popularly used model for OofA experiments is perhaps the pairwise ordering (PWO) model, which assumes that the response can be fully accounted by the pairwise ordering of components. Recently, the PWO model has been extended by adding the interactions of PWO factors, to account for variations caused by the ordering of sets of three or more components, where the interaction term is defined by the multiplication of two PWO factors. This paper introduces a novel class of conditional PWO effect to study the interaction effect between PWO factors. The advantages of the proposed interaction terms are studied. Based on these conditional effects, a new model is proposed. The optimal order of addition can be straightforwardly obtained via the proposed model.

Dual-Orthogonal Arrays for Order-of-Addition Two-Level Factorial Experiments

A new class of orthogonal arrays called dual-orthogonal arrays is proposed in this paper to design order-of-addition two-level factorial experiments in which both component addition orders and component levels can be varied over treatments. Dual-orthogonal arrays can be viewed as an optimal combination of order-of-addition orthogonal arrays and two-level orthogonal arrays. Based on these two different concepts of orthogonality, when a compound model is used to fit the observed data, both pairwise order effects and component main effects can be estimated with optimal efficiency. Under the assumption of normality, these two kinds of parametric effects can also be inferred independently. A three-drug combination study is first used to show that dual-orthogonal arrays can be practical for real-world studies. Both combinatorial and computational methods are then introduced to construct dual-orthogonal arrays. Additionally, a design catalogue is generated for future work.

Crucial role of Fe in determining the hard magnetic properties of Nd2Fe14B

${\mathrm{Nd}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$'s unsurpassed, hard magnetic properties for a wide range of temperatures result from a combination of a large volume magnetization from Fe and a strong single-ion anisotropy from Nd. Here, using finite temperature first-principles calculations, we focus on the other crucial roles played by the Fe atoms in maintaining the magnetic order on the Nd sublattices, and hence the large magnetic anisotropy, and directly generating significant uniaxial anisotropy at high temperatures. We identify effective spins for atomistic modeling from the material's interacting electrons and quantify pairwise and higher order, nonpairwise magnetic interactions among them. We find the Nd spins couple most strongly to spins on sites belonging to two specific Fe sublattices: $8{j}_{1}$ and $8{j}_{2}$. Moreover, the Fe $8{j}_{1}$ sublattice also provides the electronic origin of the unusual, nonmonotonic temperature dependence of the anisotropy of ${\mathrm{Y}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$. Our work provides atomic-level resolution of the properties of this fascinating magnetic material.

Hierarchical multi-criteria decision making with group voting information: New Tanino’s additive consistency intuitionistic fuzzy translation and utility vector acquisition

The frame of intuitionistic fuzzy preference relations (IFPRs) is an effective tool of representing pairwise preference order based group voting information. However, existing intuitionistic fuzzy translations of Tanino’s additive consistency and previous methods of acquiring utility vectors from IFPRs are often unable to achieve a satisfactory solution for hierarchical multi-criteria decision making (HMCDM) with IFPRs. This study analyzes existing notions of additively consistent IFPRs (ACIFPRs) and shows their shortages. A novel intuitionistic fuzzy translation of Tanino’s additive consistency is developed and an index computational formula is provided to measure additive inconsistency of IFPRs. A new approach is offered to generate ACIFPRs from vectors with intuitionistic fuzzy elements and a frame is put forward to normalize intuitionistic fuzzy vectors. Subsequently, a closed-form solution based method is presented to secure normalized intuitionistic fuzzy utility vectors from ACIFPRs and a linear program is built to acquire an optimal and normalized intuitionistic fuzzy utility vector from any IFPR. An approach is proposed to tackle HMCDM problems with pairwise preference order based group voting information. The reasonability and performance of the models developed are validated by an illustrative example and a case study about outstanding teacher recommendation based on large-scale group votes on teaching satisfaction.

Ordering motivation and Likert scale ratings: When a numeric scale is not necessarily better.

Measuring psychological attributes, such as motivation, typically involves rating scales, assuming that an attribute can be ordered, and that ratings represent this order. Previously, only the first assumption had been tested, albeit limited. First, we checked the ordinal structure of motivation, looking at whether people can establish transitive relations between motivation levels in pairwise comparisons; and we found different ordering patterns: strict transitive, weak transitive, changing order, and intransitivity. The rate of intransitivity was similar to that found previously and was somewhat higher than we obtained when we asked participants to compare definitely quantitative attributes (such as weight). Second, we checked if specific ordering patterns were related to individual interpretations of the statements that deviated from expected motivation types. Indeed, about a third of participants miscategorized statements, and these deviant interpretations were related to intransitivity as well as weak transitivity. Third, we checked whether Likert ratings represent the order of motives obtained from pairwise comparisons. We found rather homomorphic representation: ratings correlated with the order, but they did not differentiate between different ordering patterns and hierarchies of motives. We conclude that the Likert rating scale provides less information about respondents than pairwise ordering. The findings question the mainstream practice of using rating scales without testing underlying assumptions.

Automated Assessment of Photoreceptor Visibility in Adaptive Optics Split-Detection Images Using Edge Detection.

PurposeAdaptive optics scanning laser ophthalmoscopy (AOSLO) is a high-resolution imaging modality that allows measurements of cellular-level retinal changes in living patients. In retinal diseases, the visibility of photoreceptors in AOSLO images is affected by pathology, patient motion, and optics, which can lead to variability in analyses of the photoreceptor mosaic. Current best practice for AOSLO mosaic quantification requires manual assessment of photoreceptor visibility across overlapping images, a laborious and time-consuming task.MethodsWe propose an automated measure for quantification of photoreceptor visibility in AOSLO. Our method detects salient edge features, which can represent visible photoreceptor boundaries in each image. We evaluate our measure against two human graders and two standard automated image quality assessment algorithms.ResultsWe evaluate the accuracy of pairwise ordering (PO) and the correlation of ordinal rankings (ORs) of photoreceptor visibility in 29 retinal regions, taken from five subjects with choroideremia. The proposed measure had high association with manual assessments (Grader 1: PO = 0.71, OR = 0.61; Grader 2: PO = 0.67, OR = 0.62), which is comparable with intergrader reliability (PO = 0.76, OR = 0.75) and outperforms the top standard approach (PO = 0.57; OR = 0.46).ConclusionsOur edge-based measure can automatically assess photoreceptor visibility and order overlapping images within AOSLO montages. This can significantly reduce the manual labor required to generate high-quality AOSLO montages and enables higher throughput for quantitative studies of photoreceptors.Translational RelevanceAutomated assessment of photoreceptor visibility allows us to more rapidly quantify photoreceptor morphology in the living eye. This has applications to ophthalmic medicine by allowing detailed characterization of retinal degenerations, thus yielding potential biomarkers of treatment safety and efficacy.

Kendall transformation brings a robust categorical representation of ordinal data

Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation allows for generalisation of methods requiring strictly categorical input, especially in the limit of small number of observations, when quantisation becomes problematic. In particular, many approaches of information theory can be directly applied to Kendall-transformed continuous data without relying on differential entropy or any additional parameters. Moreover, by filtering information to this contained in ranking, Kendall transformation leads to a better robustness at a reasonable cost of dropping sophisticated interactions which are anyhow unlikely to be correctly estimated. In bivariate analysis, Kendall transformation can be related to popular non-parametric methods, showing the soundness of the approach. The paper also demonstrates its efficiency in multivariate problems, as well as provides an example analysis of a real-world data.

Formalization and implementation of credibility dynamics through prioritized multiple revision

In this work, we focus on credibility dynamics. The trust or credibility associated with a set of agents is represented by a pairwise comparison partial order of agents called credibility order. In this paper, we formalize a prioritized multiple revision operator that can be used to revise one credibility order by another credibility order. We introduce a set of postulates for this change operator, and we show that our proposed operator satisfies those postulates. We will also introduce a computer application we have developed to provide a complete implementation of our approach. The application has an intuitive graphical user interface to handle credibility orders, apply the change operator, and has some visual tools to explain the revision process.

Epidemics on multilayer simplicial complexes

Simplicial complexes describe the simple fact that in social networks a link can connect more than two individuals. As we show here, this has far-reaching consequences for epidemic spreading, in particular in the context of a multilayer network model, where one layer is a virtual social network and the other one is a physical contact network. The social network layer is responsible for the transmission of information via pairwise or higher order 2-simplex interactions among individuals, while the physical layer is responsible for the epidemic spreading. We use the microscopic Markov chain approach to derive the probability transition equations and to determine epidemic outbreak thresholds. We further support these results with Monte Carlo simulations, which are in good agreement, thus confirming the analytical tractability of the proposed model. We find that information transmission rates are frequently low when actual disease transmission rates in the physical network are low or medium, and we show that this can be mitigated effectively by introducing 2-simplex interactions in the social network. The relative ease of introducing higher-order interactions in virtual social networks means that this could be exploited to inhibit epidemic outbreaks.

Local and global context-based pairwise models for sentence ordering

Sentence Ordering refers to the task of rearranging a set of sentences into the appropriate coherent order. For this task, most previous approaches have explored global context-based end-to-end methods using Sequence Generation techniques. In this paper, we put forward a set of robust local and global context-based pairwise ordering strategies, leveraging which our prediction strategies outperform all previous works in this domain. Our proposed encoding method utilizes the paragraph’s rich global contextual information to predict the pairwise order using novel transformer architectures. Analysis of the two proposed decoding strategies helps better explain error propagation in pairwise models. This approach is the most accurate pure pairwise model and our encoding strategy also significantly improves the performance of other recent approaches that use pairwise models, including the previous state-of-the-art, demonstrating the research novelty and generalizability of this work. Additionally, we show how the pre-training task for ALBERT helps it to significantly outperform BERT, despite having considerably lesser parameters. The extensive experimental results, architectural analysis and ablation studies demonstrate the effectiveness and superiority of the proposed models compared to the previous state-of-the-art, besides providing a much better understanding of the functioning of pairwise models.

Saturated and supersaturated order-of-addition designs

Van Nostrand’s pairwise order model has been the most popular model for analyzing order-of-addition experiments. Here we construct designs of minimal size for the pairwise order model, considering both D-optimality, as well as the prediction-based I- and G-optimality criteria. Even these saturated designs grow large when the number of components exceeds 10. Thus, we also propose Bayesian D-optimal designs, which may have fewer runs than the number of parameters for the pairwise order model. These supersaturated designs may be used as screening designs for applications where the number of components is large.

A statistical perspective on non-deterministic polynomial-time hard ordering problems: Making use of design for order-of-addition experiments

The need for solving NP-hard problems emerges from many fields, including configuration, process monitoring, scheduling, planning, among others. One type of NP-hard problem is the ordering problem, where the goal is to find the optimal sequence. This is, in fact, identical to the purpose of Order-of-Addition (OofA) problem. Based on this connection, this paper proposes a statistical methodology to infer solutions of NP-hard ordering problems via design of OofA experiments. An efficient pairwise-order (PWO) modeling approach is able to identify statistically significant PWO effects, and consequentially find the optimal order(s). In general, the proposed method could solve any NP-hard ordering problems, as long as its underlying structure can be adequately approximated by the PWO model. Empirical studies (Job scheduling problems and run orders problems) show that the proposed methodology often yields the optimal (or nearly optimal) orders. Theoretical support is given under specific setups. This paper is an interdisciplinary collaboration between statistics and optimization, and it pioneers an approach that connects two seemingly unrelated research topics together: the NP-hard ordering problems and the OofA experiments. We hope that the idea of this paper will provide a fresh perspective on NP-hard ordering problems and also motivate fruitful applications of the techniques related to OofA experiments.

Binding affinity landscapes constrain the evolution of broadly neutralizing anti-influenza antibodies.

Over the past two decades, several broadly neutralizing antibodies (bnAbs) that confer protection against diverse influenza strains have been isolated. Structural and biochemical characterization of these bnAbs has provided molecular insight into how they bind distinct antigens. However, our understanding of the evolutionary pathways leading to bnAbs, and thus how best to elicit them, remains limited. Here, we measure equilibrium dissociation constants of combinatorially complete mutational libraries for two naturally isolated influenza bnAbs (CR9114, 16 heavy-chain mutations; CR6261, 11 heavy-chain mutations), reconstructing all possible evolutionary intermediates back to the unmutated germline sequences. We find that these two libraries exhibit strikingly different patterns of breadth: while many variants of CR6261 display moderate affinity to diverse antigens, those of CR9114 display appreciable affinity only in specific, nested combinations. By examining the extensive pairwise and higher order epistasis between mutations, we find key sites with strong synergistic interactions that are highly similar across antigens for CR6261 and different for CR9114. Together, these features of the binding affinity landscapes strongly favor sequential acquisition of affinity to diverse antigens for CR9114, while the acquisition of breadth to more similar antigens for CR6261 is less constrained. These results, if generalizable to other bnAbs, may explain the molecular basis for the widespread observation that sequential exposure favors greater breadth, and such mechanistic insight will be essential for predicting and eliciting broadly protective immune responses.

Regression models for order-of-addition experiments.

The purpose of order-of-addition (OofA) experiments is to identify the best order in a sequence of m components in a system. Such experiments may be analyzed by various regression models, the most popular ones being based on pairwise ordering (PWO) factors or on component-position (CP) factors. This paper reviews these models and extensions and proposes a new class of models based on response surface (RS) regression using component position numbers as predictor variables. Using two published examples, it is shown that RS models can be quite competitive. In case of model uncertainty, we advocate the use of model averaging for analysis. The averaging idea leads naturally to a design approach based on a compound optimality criterion assigning weights to each candidate model.