Average Distance Queries through Weighted Samples in Graphs and Metric Spaces: High Scalability with Tight Statistical Guarantees

The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness centrality of a node, is a popular importance measure in the study of social networks. We develop novel structural insights on the sparsifiability of the distance relation via weighted sampling. Based on that, we present highly practical algorithms with strong statistical guarantees for fundamental problems. We show that the average distance (and hence the centrality) for all nodes in a graph can be estimated using $O(\epsilon^{-2})$ single-source distance computations. For a set $V$ of $n$ points in a metric space, we show that after preprocessing which uses $O(n)$ distance computations we can compute a weighted sample $S\subset V$ of size $O(\epsilon^{-2})$ such that the average distance from any query point $v$ to $V$ can be estimated from the distances from $v$ to $S$. Finally, we show that for a set of points $V$ in a metric space, we can estimate the average pairwise distance using $O(n+\epsilon^{-2})$ distance computations. The estimate is based on a weighted sample of $O(\epsilon^{-2})$ pairs of points, which is computed using $O(n)$ distance computations. Our estimates are unbiased with normalized mean square error (NRMSE) of at most $\epsilon$. Increasing the sample size by a $O(\log n)$ factor ensures that the probability that the relative error exceeds $\epsilon$ is polynomially small.Comment: 21 pages, will appear in the Proceedings of RANDOM 201

An open-label study of herbal topical medication (Psirelax) for patients with chronic plaque psoriasis

Psirelax is an herbal topical medication indicated for the treatment ofpatients with psoriasis. Its efficacy was determined in an open-labelstudy in 22 patients (15 men, 7 women) with a mean age of 48.9±11.8years suffering from chronic plaque psoriasis. The patients weretreated by application of Psirelax twice a day for a period of 4 weeks.Clinical assessment was performed using the Psoriasis Area andSeverity Index (PASI) and the Beer-Sheva Psoriasis Severity Score(BPSS). The results shows that Psirelax was well tolerated and thereno local or systemic side effects. There was 59% reduction in PASI,from a mean of 5.9 ± 4.0 before treatment to 2.4 ± 2.4 after treatment(p<0.001). In 8 patients (36%) PASI decreased in more than 75%(PASI75). In 16 patients (73%) PASI decreased in more than 50%(PASI50). Application of Psirelax was associated with a decrease indisease severity, as assessed by the patients and physicians. It isconcluded that Psirelax treatment was well tolerated in patients withchronic plaque psoriasis

Deterministic Combinatorial Replacement Paths and Distance Sensitivity Oracles

In this work we derandomize two central results in graph algorithms, replacement paths and distance sensitivity oracles (DSOs) matching in both cases the running time of the randomized algorithms. For the replacement paths problem, let G = (V,E) be a directed unweighted graph with n vertices and m edges and let P be a shortest path from s to t in G. The replacement paths problem is to find for every edge e in P the shortest path from s to t avoiding e. Roditty and Zwick [ICALP 2005] obtained a randomized algorithm with running time of O~(m sqrt{n}). Here we provide the first deterministic algorithm for this problem, with the same O~(m sqrt{n}) time. Due to matching conditional lower bounds of Williams et al. [FOCS 2010], our deterministic combinatorial algorithm for the replacement paths problem is optimal up to polylogarithmic factors (unless the long standing bound of O~(mn) for the combinatorial boolean matrix multiplication can be improved). This also implies a deterministic algorithm for the second simple shortest path problem in O~(m sqrt{n}) time, and a deterministic algorithm for the k-simple shortest paths problem in O~(k m sqrt{n}) time (for any integer constant k > 0). For the problem of distance sensitivity oracles, let G = (V,E) be a directed graph with real-edge weights. An f-Sensitivity Distance Oracle (f-DSO) gets as input the graph G=(V,E) and a parameter f, preprocesses it into a data-structure, such that given a query (s,t,F) with s,t in V and F subseteq E cup V, |F| <=f being a set of at most f edges or vertices (failures), the query algorithm efficiently computes the distance from s to t in the graph G F (i.e., the distance from s to t in the graph G after removing from it the failing edges and vertices F). For weighted graphs with real edge weights, Weimann and Yuster [FOCS 2010] presented several randomized f-DSOs. In particular, they presented a combinatorial f-DSO with O~(mn^{4-alpha}) preprocessing time and subquadratic O~(n^{2-2(1-alpha)/f}) query time, giving a tradeoff between preprocessing and query time for every value of 0 < alpha < 1. We derandomize this result and present a combinatorial deterministic f-DSO with the same asymptotic preprocessing and query time

Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms

We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic "approximately-maximal" fractional matching algorithms. Applying this reduction to the recent fractional matching algorithm of Bhattacharya, Henzinger, and Nanongkai (SODA 2017), we obtain a novel result for the integral problem. Specifically, our main result is a randomized fully-dynamic (2+epsilon)-approximate integral matching algorithm with small polylog worst-case update time. For the (2+epsilon)-approximation regime only a fractional fully-dynamic (2+epsilon)-matching algorithm with worst-case polylog update time was previously known, due to Bhattacharya et al. (SODA 2017). Our algorithm is the first algorithm that maintains approximate matchings with worst-case update time better than polynomial, for any constant approximation ratio. As a consequence, we also obtain the first constant-approximate worst-case polylogarithmic update time maximum weight matching algorithm

Eye of the Beholder: The individual and dyadic contributions of empathic accuracy and perceived empathic effort to relationship satisfaction

This study examined links between two distinct facets of empathy – empathic accuracy and perceived empathic effort – and one’s own and one’s partner’s relationship satisfaction. Using a video recall procedure, participants (N = 156 couples in committed relationships) reported on their own emotions and their perceptions of partners’ emotions and partners’ empathic intentions during moments of high affect in laboratory-based discussions of upsetting events. Partners’ data were correlated as a measure of how accurately they were able to read what the other was feeling and to what degree they felt the other was trying to be empathic at those moments. The perception of empathic effort by one’s partner was more strongly linked with both men’s and women’s relationship satisfaction than empathic accuracy. Men’s relationship satisfaction was related to the ability to read their partners’ positive emotions accurately, whereas women’s relationship satisfaction was related to their partners’ ability to read women’s negative emotions accurately. Women’s ability to read their husbands’ negative emotions was positively linked to both men’s and women’s relationship satisfaction. Findings suggest that the perception of a partner’s empathic effort – as distinct from empathic accuracy – is uniquely informative in understanding how partners may derive relationship satisfaction from empathic processes. When working with couples in treatment, heightening partners’ perceptions of each other’s empathic effort, and helping partners learn to demonstrate effort, may represent particularly powerful opportunities for improving satisfaction in relationships

Sources of somatization: Exploring the roles of insecurity in relationships and styles of anger experience and expression

Research has shown strong connections between insecure attachment in close relationships and somatization. In addition, studies have demonstrated connections between somatic symptoms and anger experience and expression. In this study, we integrate perspectives from these two literatures by testing the hypothesis that proneness to anger and suppression of anger mediate the link between insecurity in relationships and somatization. Between 2000 and 2003, a community-based sample of 101 couples in a large U.S. city completed self-report measures, including the Somatic Symptom Inventory, the Relationship Scales Questionnaire, the Multidimensional Anger Inventory, the Revised Conflict Tactics Scale, and the Beck Depression Inventory. Controlling for age, income, and recent intimate partner violence, analyses showed that the link between insecure attachment and somatization was partially mediated by anger proneness for men and by anger suppression for women. Findings are consistent with the hypothesis that men who are insecurely attached are more prone to experience anger that in turn fosters somatization. For women, findings suggest that insecure attachment may influence adult levels of somatization by fostering suppression of anger expression. Specific clinical interventions that help patients manage and express angry feelings more adaptively may reduce insecurely attached individuals’ vulnerability to medically unexplained somatic symptoms

Sources of somatization: Exploring the roles of insecurity in relationships and styles of anger experience and expression

Research has shown strong connections between insecure attachment in close relationships and somatization. In addition, studies have demonstrated connections between somatic symptoms and anger experience and expression. In this study, we integrate perspectives from these two literatures by testing the hypothesis that proneness to anger and suppression of anger mediate the link between insecurity in relationships and somatization. Between 2000 and 2003, a community-based sample of 101 couples in a large U.S. city completed self-report measures, including the Somatic Symptom Inventory, the Relationship Scales Questionnaire, the Multidimensional Anger Inventory, the Revised Conflict Tactics Scale, and the Beck Depression Inventory. Controlling for age, income, and recent intimate partner violence, analyses showed that the link between insecure attachment and somatization was partially mediated by anger proneness for men and by anger suppression for women. Findings are consistent with the hypothesis that men who are insecurely attached are more prone to experience anger that in turn fosters somatization. For women, findings suggest that insecure attachment may influence adult levels of somatization by fostering suppression of anger expression. Specific clinical interventions that help patients manage and express angry feelings more adaptively may reduce insecurely attached individuals’ vulnerability to medically unexplained somatic symptoms

Eye of the Beholder: The individual and dyadic contributions of empathic accuracy and perceived empathic effort to relationship satisfaction

This study examined links between two distinct facets of empathy – empathic accuracy and perceived empathic effort – and one’s own and one’s partner’s relationship satisfaction. Using a video recall procedure, participants (N = 156 couples in committed relationships) reported on their own emotions and their perceptions of partners’ emotions and partners’ empathic intentions during moments of high affect in laboratory-based discussions of upsetting events. Partners’ data were correlated as a measure of how accurately they were able to read what the other was feeling and to what degree they felt the other was trying to be empathic at those moments. The perception of empathic effort by one’s partner was more strongly linked with both men’s and women’s relationship satisfaction than empathic accuracy. Men’s relationship satisfaction was related to the ability to read their partners’ positive emotions accurately, whereas women’s relationship satisfaction was related to their partners’ ability to read women’s negative emotions accurately. Women’s ability to read their husbands’ negative emotions was positively linked to both men’s and women’s relationship satisfaction. Findings suggest that the perception of a partner’s empathic effort – as distinct from empathic accuracy – is uniquely informative in understanding how partners may derive relationship satisfaction from empathic processes. When working with couples in treatment, heightening partners’ perceptions of each other’s empathic effort, and helping partners learn to demonstrate effort, may represent particularly powerful opportunities for improving satisfaction in relationships

Security of attachment to spouses in late life: Concurrent and prospective links with cognitive and emotional wellbeing

Social ties are powerful predictors of late-life health and well-being. Although many adults maintain intimate partnerships into late life, little is known about mental models of attachment to spouses and how they influence aging. A total of 81 elderly heterosexual couples (162 individuals) were interviewed to examine the structure of attachment security to their partners; respondents also completed measures of cognition and well-being concurrently and 2.5 years later. Factor analysis revealed a single factor for security of attachment. Higher security was linked concurrently with greater marital satisfaction, fewer depressive symptoms, better mood, and less frequent marital conflicts. Greater security predicted lower levels of negative affect, less depression, and greater life satisfaction 2.5 years later. For women, greater security predicted better memory 2.5 years later and attenuated the link between frequency of marital conflict and memory deficits. Late in life, mental models of attachment to partners are linked to well-being concurrently and over time

Links between childhood physical abuse and intimate partner aggression: The mediating role of anger expression

Research linking childhood physical abuse (CPA) and adult intimate partner aggression (IPA) has focused on individuals without sufficient attention to couple processes. In this study, 109 couples reported on histories of CPA, IPA, and anger expression. Actor-Partner Interdependence Modeling was used to examine links between CPA and revictimization and perpetration of IPA, with anger suppression as a potential mediator. Women’s CPA histories were associated with more physical aggression towards and more revictimization by partners. Men’s CPA histories were only associated at the trend level with their revictimization. Anger suppression fully mediated the link between women’s CPA and both revictimization and perpetration of IPA. Findings suggest that women with CPA histories are more prone to suppress anger, which leaves them at greater risk for revictimization and perpetration of IPA