Pairwise Order Research Articles

Optimal designs for order-of-addition experiments

The order-of-addition (OofA) designs have received significant attention over recent years. It is of great interest to seek for efficient fractional OofA designs especially when the number of components is large. It has been recognized that constructing efficient fractional OofA designs is a challenging work. A systematic construction method for a class of efficient fractional OofA designs, called OofA orthogonal arrays (OofA-OAs), is proposed. It is shown that OofA-OAs are superior over any other type of fractional OofA designs for the predominant pair-wise ordering (PWO) model. The balance property of OofA-OAs is also developed. In addition, the capacity of OofA-OAs for estimating different models is investigated.

Expansions of abelian square-free groups

We investigate finitary functions from [Formula: see text] to [Formula: see text] for a square-free number [Formula: see text]. We show that the lattice of all clones on the square-free set [Formula: see text] which contain the addition of [Formula: see text] is finite. We provide an upper bound for the cardinality of this lattice through an injective function to the direct product of the lattices of all [Formula: see text]-linearly closed clonoids, [Formula: see text], to the [Formula: see text] power, where [Formula: see text]. These lattices are studied in [S. Fioravanti, Closed sets of finitary functions between products of finite fields of pair-wise coprime order, preprint (2020), arXiv:2009.02237] and there we can find an upper bound for their cardinality. Furthermore, we prove that these clones can be generated by a set of functions of arity at most [Formula: see text].

Concordance probability as a meaningful contrast across disparate survival times.

The performance of time-to-event models is frequently assessed in part by estimating the concordance probability, which evaluates the probabilistic pairwise ordering of the model-based risk scores and survival times. The standard definition of this probability conditions on any survival time pair ordering, irrespective of whether the times are meaningfully separated. Inclusion of survival times that would be deemed clinically similar attenuates the concordance and moves the estimate away from the contrast-of-interest: comparing the risk scores between individuals with disparate survival times. In this manuscript, we propose a concordance definition and corresponding method to estimate the probability conditional on survival times being separated by at least a minimum difference. The proposed estimate requires direct input from the analyst to identify a separable survival region and, in doing so, is analogous to the clinically defined subgroups used for binary outcome area under the curve estimates. The method is illustrated in two cancer examples: a prognostic score in clear cell renal cell carcinoma and two biomarkers in metastatic prostate cancer.

Probabilistic framework for integration of mass spectrum and retention time information in small molecule identification.

MotivationIdentification of small molecules in a biological sample remains a major bottleneck in molecular biology, despite a decade of rapid development of computational approaches for predicting molecular structures using mass spectrometry (MS) data. Recently, there has been increasing interest in utilizing other information sources, such as liquid chromatography (LC) retention time (RT), to improve identifications solely based on MS information, such as precursor mass-per-charge and tandem mass spectrometry (MS2).ResultsWe put forward a probabilistic modelling framework to integrate MS and RT data of multiple features in an LC-MS experiment. We model the MS measurements and all pairwise retention order information as a Markov random field and use efficient approximate inference for scoring and ranking potential molecular structures. Our experiments show improved identification accuracy by combining MS2 data and retention orders using our approach, thereby outperforming state-of-the-art methods. Furthermore, we demonstrate the benefit of our model when only a subset of LC-MS features has MS2 measurements available besides MS1.Availability and implementationSoftware and data are freely available at https://github.com/aalto-ics-kepaco/msms_rt_score_integration.Supplementary information Supplementary data are available at Bioinformatics online.

Detection and Segmentation of Unlearned Objects in Unknown Environment

Detecting and segmenting unlearned objects in unknown environment is a very important visual perception ability to enhance industrial intelligence. In this article, we present a novel conditional random field model integrating unimodal and cross-modal terms for detecting and segmenting object instances without knowing their categories and without sampling extra proposals. This model takes a paired image and point cloud as input, from which we first develop a set of novel category-independent features to distinguish objects. Then, a set of unary, pairwise, and higher order potentials are designed according to these category-independent features, and the cross-modal potential is introduced as a novel global constraints to keep the spatial consistency in both 2-D and 3-D modalities. In this novel model, the unlearned object detection and segmentation is treated as the process of pixel labeling. Thus, adjacent or occlusion object instances can also be separated efficiently from a labeled map. By comparison with the baseline methods, experimental results on a public RGB+D dataset show that the proposed model can obtain better performance with improved precision and recall rate. Moreover, we use the proposed method in a real industrial scene and achieve satisfactory performance.

Calibration and Uncertainty in Neural Time-to-Event Modeling.

Models for predicting the time of a future event are crucial for risk assessment, across a diverse range of applications. Existing time-to-event (survival) models have focused primarily on preserving pairwise ordering of estimated event times (i.e., relative risk). We propose neural time-to-event models that account for calibration and uncertainty while predicting accurate absolute event times. Specifically, an adversarial nonparametric model is introduced for estimating matched time-to-event distributions for probabilistically concentrated and accurate predictions. We also consider replacing the discriminator of the adversarial nonparametric model with a survival-function matching estimator that accounts for model calibration. The proposed estimator can be used as a means of estimating and comparing conditional survival distributions while accounting for the predictive uncertainty of probabilistic models. Extensive experiments show that the distribution matching methods outperform existing approaches in terms of both calibration and concentration of time-to-event distributions.

Differential regulation of a placental SAM68 and sFLT1 gene pathway and the relevance to maternal vitamin D sufficiency.

The goal of this study was to determine if an axis of placental gene expression associated with early onset and severe preeclampsia (EOSPE) was operative in term pregnancy and correlated with vitamin D sufficiency. qPCR analysis of NKX2-5, SAM68, sFLT1 and membrane bound VEGFR1/FLT1 mRNA expression was conducted in placentas from 43 subjects enrolled in a vitamin D3 pregnancy supplementation trial. Pair-wise rank order correlations between patient-specific gene expression levels were calculated, and their relationship to maternal 25(OH)D status was assessed by a two-sample Wilcoxon test. Additionally, we probed the mechanistic link between SAM68 and sFLT1 using siRNA depletion in a human trophoblast cell line model. Positive and highly significant correlations were found between SAM68 vs. sFLT1 and SAM68 vs. FLT1 expression levels, as were significant and differential correlations between the expression of these genes and perinatal 25(OH)D status. The variability when stratified by race/ethnicity was qualitatively distinct from those previously observed in EOSPE. Mechanistic studies confirmed a functional role for SAM68 protein in the regulation of sFLT1 expression. NKX2-5 expression was not significantly correlated with sFLT1 or SAM68 expression in these samples, suggesting that its expression may be significant at earlier stages of pregnancy or be restricted to pathological settings. These data further support our overarching hypothesis that SAM68 expression is a key determinant of VEGFR1 isoform expression in the placenta, and provide additional insights into how this gene pathway may be differentially deployed or modified in normal and pathological pregnancies.

On countably saturated linear orders and certain class of countably saturated graphs

The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality mathfrak {c}. We provide some examples of pairwise non-isomorphic countably saturated linear orders of cardinality mathfrak {c}, under different set-theoretic assumptions. We give a new proof of the old theorem of Harzheim, that the class of countably saturated linear orders has a uniquely determined one-element basis. From our proof it follows that this minimal linear order is a Fraïssé limit of certain Fraïssé class. In particular, it is homogeneous with respect to countable subsets. Next we prove the existence and uniqueness of the uncountable version of the random graph. This graph is isomorphic to (H(omega _1),in cup ni ), where H(omega _1) is the set of hereditarily countable sets, and two sets are connected if one of them is an element of the other. In the last section, an example of a prime countably saturated Boolean algebra is presented.

Attention Based Vehicle Trajectory Prediction

Self-driving vehicles need to continuously analyse the driving scene, understand the behavior of other road users and predict their future trajectories in order to plan a safe motion and reduce their reaction time. Motivated by this idea, this paper addresses the problem of vehicle trajectory prediction over an extended horizon. On highways, human drivers continuously adapt their speed and paths according to the behavior of their neighboring vehicles. Therefore, vehicles’ trajectories are very correlated and considering vehicle interactions makes motion prediction possible even before the start of a clear maneuver pattern. To this end, we introduce and analyze trajectory prediction methods based on how they model the vehicles interactions. Inspired by human reasoning, we use an attention mechanism that explicitly highlights the importance of neighboring vehicles with respect to their future states. We go beyond pairwise vehicle interactions and model higher order interactions. Moreover, the existence of different goals and driving behaviors induces multiple potential futures. We exploit a combination of global and partial attention paid to surrounding vehicles to generate different possible trajectory. Experiments on highway datasets show that the proposed model outperforms the state-of-the-art performances.

Enhancing Pointer Network for Sentence Ordering with Pairwise Ordering Predictions

Dominant sentence ordering models use a pointer network decoder to generate ordering sequences in a left-to-right fashion. However, such a decoder only exploits the noisy left-side encoded context, which is insufficient to ensure correct sentence ordering. To address this deficiency, we propose to enhance the pointer network decoder by using two pairwise ordering prediction modules: The FUTURE module predicts the relative orientations of other unordered sentences with respect to the candidate sentence, and the HISTORY module measures the local coherence between several (e.g., 2) previously ordered sentences and the candidate sentence, without the influence of noisy left-side context. Using the pointer mechanism, we then incorporate this dynamically generated information into the decoder as a supplement to the left-side context for better predictions. On several commonly-used datasets, our model significantly outperforms other baselines, achieving the state-of-the-art performance. Further analyses verify that pairwise ordering predictions indeed provide extra useful context as expected, leading to better sentence ordering. We also evaluate our sentence ordering models on a downstream task, multi-document summarization, and the summaries reordered by our model achieve the best coherence scores. Our code is available at https://github.com/DeepLearnXMU/Pairwise.git.

High-Dimensional Bayesian Network Inference From Systems Genetics Data Using Genetic Node Ordering.

Studying the impact of genetic variation on gene regulatory networks is essential to understand the biological mechanisms by which genetic variation causes variation in phenotypes. Bayesian networks provide an elegant statistical approach for multi-trait genetic mapping and modelling causal trait relationships. However, inferring Bayesian gene networks from high-dimensional genetics and genomics data is challenging, because the number of possible networks scales super-exponentially with the number of nodes, and the computational cost of conventional Bayesian network inference methods quickly becomes prohibitive. We propose an alternative method to infer high-quality Bayesian gene networks that easily scales to thousands of genes. Our method first reconstructs a node ordering by conducting pairwise causal inference tests between genes, which then allows to infer a Bayesian network via a series of independent variable selection problems, one for each gene. We demonstrate using simulated and real systems genetics data that this results in a Bayesian network with equal, and sometimes better, likelihood than the conventional methods, while having a significantly higher overlap with groundtruth networks and being orders of magnitude faster. Moreover our method allows for a unified false discovery rate control across genes and individual edges, and thus a rigorous and easily interpretable way for tuning the sparsity level of the inferred network. Bayesian network inference using pairwise node ordering is a highly efficient approach for reconstructing gene regulatory networks when prior information for the inclusion of edges exists or can be inferred from the available data.

Wtest: an integrated R package for genetic epistasis testing

BackgroundWith the increasing amount of high-throughput genomic sequencing data, there is a growing demand for a robust and flexible tool to perform interaction analysis. The identification of SNP-SNP, SNP-CpG, and higher order interactions helps explain the genetic etiology of human diseases, yet genome-wide analysis for interactions has been very challenging, due to the computational burden and a lack of statistical power in most datasets.ResultsThe wtest R package performs association testing for main effects, pairwise and high order interactions in genome-wide association study data, and cis-regulation of SNP and CpG sites in genome-wide and epigenome-wide data. The software includes a number of post-test diagnostic and analysis functions and offers an integrated toolset for genetic epistasis testing.ConclusionsThe wtest is an efficient and powerful statistical tool for integrated genetic epistasis testing. The package is available in CRAN: https://CRAN.R-project.org/package=wtest.

Two-hop walks indicate PageRank order

This paper shows that pairwise PageRank orders emerge from two-hop walks. The main tool used here refers to a specially designed sign-mirror function and a parameter curve, whose low-order derivative information implies pairwise PageRank orders with high probability. We study the pairwise correct rate by placing the Google matrix G in a probabilistic framework, where G may be equipped with different random ensembles for model-generated or real-world networks with sparse, small-world, scale-free features, the proof of which is mixed by mathematical and numerical evidence. We believe that the underlying spectral distribution of aforementioned networks is responsible for the high pairwise correct rate. Moreover, the perspective of this paper naturally leads to an O(1) algorithm for any single pairwise PageRank comparison if assuming both A=G−In, where In denotes the identity matrix of order n, and A2 are ready on hand (e.g., constructed offline in an incremental manner), based on which it is easy to extract the top k list in O(kn), thus making it possible for PageRank algorithm to deal with super large-scale datasets in real time.

Reversible Disjoint Unions of Well Orders and Their Inverses

A poset $\mathbb {P}$ is called reversible iff every bijective homomorphism $f:\mathbb {P} \rightarrow \mathbb {P}$ is an automorphism. Let $\mathcal {W}$ and $\mathcal {W}^{*}$ denote the classes of well orders and their inverses respectively. We characterize reversibility in the class of posets of the form $\mathbb {P} =\bigcup _{i\in I}\mathbb {L}_{i}$, where $\mathbb {L}_{i}, i\in I$, are pairwise disjoint linear orders from $\mathcal {W} \cup \mathcal {W}^{*}$. First, if $\mathbb {L}_{i} \in \mathcal {W}$, for all i ∈ I, and $\mathbb {L}_{i} \cong \alpha _{i} =\gamma _{i}+n_{i}\in \text {Ord}$, where γi ∈Lim ∪{0} and ni ∈ ω, defining Iα := {i ∈ I : αi = α}, for α ∈Ord, and Jγ := {j ∈ I : γj = γ}, for γ ∈Lim ∪{0}, we prove that $\bigcup _{i\in I} \mathbb {L}_{i}$ is a reversible poset iff 〈αi : i ∈ I〉 is a finite-to-one sequence, that is, |Iα| < ω, for all α ∈Ord, or there exists γ = max{γi : i ∈ I}, for α ≤ γ we have |Iα| < ω, and 〈ni : i ∈ Jγ ∖ Iγ〉 is a reversible sequence of natural numbers. The same holds when $\mathbb {L}_{i} \in \mathcal {W}^{*}$, for all i ∈ I. In the general case, the reversibility of the whole union is equivalent to the reversibility of the union of components from $\mathcal {W}$ and the union of components from $\mathcal {W}^{*}$.

Self-Supervised Feature Learning With CRF Embedding for Hyperspectral Image Classification

The challenges in hyperspectral image (HSI) classification lie in the existence of noisy spectral information and lack of contextual information among pixels. Considering the three different levels in HSIs, i.e., subpixel, pixel, and superpixel, offer complementary information, we develop a novel HSI feature learning network (HSINet) to learn consistent features by self-supervision for HSI classification. HSINet contains a three-layer deep neural network and a multifeature convolutional neural network. It automatically extracts the features such as spatial, spectral, color, and boundary as well as context information. To boost the performance of self-supervised feature learning with the likelihood maximization, the conditional random field (CRF) framework is embedded into HSINet. The potential terms of unary, pairwise, and higher order in CRF are constructed by the corresponding subpixel, pixel, and superpixel. Furthermore, the feedback information derived from these terms are also fused into the different-level feature learning process, which makes the HSINet-CRF be a trainable end-to-end deep learning model with the back-propagation algorithm. Comprehensive evaluations are performed on three widely used HSI data sets and our method outperforms the state-of-the-art methods.

The tail dependograph

All characterizations of non-degenerate multivariate tail dependence structures are both functional and infinite-dimensional. Taking advantage of the Hoeffding–Sobol decomposition, we derive new indices to measure and summarize the strength of dependence in a multivariate extreme value analysis. The tail superset importance coefficients provide a pairwise ordering of the asymptotic dependence structure. We then define the tail dependograph, which visually ranks the extremal dependence between the components of the random vector of interest. For the purpose of inference, a rank-based statistic is derived and its asymptotic behavior is stated. These new concepts are illustrated with both theoretical models and real data, showing that our methodology performs well in practice.

Convenient Interface to Inverse Ising (ConIII): A Python 3 Package for Solving Ising-Type Maximum Entropy Models

ConIII (pronounced CON-ee) is an open-source Python project providing a simple interface to solving the pairwise and higher order Ising model and a base for extension to other maximum entropy models. We describe the maximum entropy problem and give an overview of the algorithms that are implemented as part of ConIII ( https://github.com/eltrompetero/coniii ) including Monte Carlo histogram, pseudolikelihood, minimum probability flow, a regularized mean field method, and a cluster expansion method. Our goal is to make a variety of maximum entropy techniques accessible to those unfamiliar with the techniques and accelerate workflow for users. Funding Statement: EDL was supported by an NSF Graduate Fellowship under grant no. DGE-1650441. This research was supported in part by a congressional research grant provided by the Dirksen Congressional Center.

Conjugacy classes, characters and products of elements

AbstractRecently, Baumslag and Wiegold proved that a finite group G is nilpotent if and only if for every of coprime order. Motivated by this result, we study the groups with the property that and those with the property that for every and every nontrivial of pairwise coprime order. We also consider several ways of weakening the hypothesis on x and y. While the result of Baumslag and Wiegold is completely elementary, some of our arguments here depend on (parts of) the classification of finite simple groups.

Correlation analysis: edge betweenness centrality vs. neighbourhood overlap

We explore the correlation between two well-known edge centrality metrics: a computationally-heavy metric called edge betweenness centrality (EBWC) and a computationally-light metric called neighbourhood overlap (NOVER). Three different correlation measures are used for the analysis: Spearman's correlation measure (for network-wide ranking), Kendall's correlation measure (for pair-wise relative ordering) and Pearson's correlation measure (for regression-based prediction). A suite of 47 real-world networks of diverse degree distributions have been used for the correlation study. Results of the correlation analysis indicate that NOVER could be used as a computationally-light alternative to rank the edges (network-wide) in lieu of EBWC, but might not be appropriate to predict the actual EBWC values.

Correlation analysis: edge betweenness centrality vs. neighbourhood overlap

We explore the correlation between two well-known edge centrality metrics: a computationally-heavy metric called edge betweenness centrality (EBWC) and a computationally-light metric called neighbourhood overlap (NOVER). Three different correlation measures are used for the analysis: Spearman's correlation measure (for network-wide ranking), Kendall's correlation measure (for pair-wise relative ordering) and Pearson's correlation measure (for regression-based prediction). A suite of 47 real-world networks of diverse degree distributions have been used for the correlation study. Results of the correlation analysis indicate that NOVER could be used as a computationally-light alternative to rank the edges (network-wide) in lieu of EBWC, but might not be appropriate to predict the actual EBWC values.