Conditional Reliability in Uncertain Graphs

Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of existence. Many approaches and problem variants have been considered in the literature, all assuming that edge-existence probabilities are fixed. Nevertheless, in real-world graphs, edge probabilities typically depend on external conditions. In metabolic networks a protein can be converted into another protein with some probability depending on the presence of certain enzymes. In social influence networks the probability that a tweet of some user will be re-tweeted by her followers depends on whether the tweet contains specific hashtags. In transportation networks the probability that a network segment will work properly or not might depend on external conditions such as weather or time of the day. In this paper we overcome this limitation and focus on conditional reliability, that is assessing reliability when edge-existence probabilities depend on a set of conditions. In particular, we study the problem of determining the k conditions that maximize the reliability between two nodes. We deeply characterize our problem and show that, even employing polynomial-time reliability-estimation methods, it is NP-hard, does not admit any PTAS, and the underlying objective function is non-submodular. We then devise a practical method that targets both accuracy and efficiency. We also study natural generalizations of the problem with multiple source and target nodes. An extensive empirical evaluation on several large, real-life graphs demonstrates effectiveness and scalability of the proposed methods.Comment: 14 pages, 13 figure

Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications

Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem of extracting dense subgraphs has remained largely unexplored so far. In this work we study the problem of core decomposition of a multilayer network. The multilayer context is much challenging as no total order exists among multilayer cores; rather, they form a lattice whose size is exponential in the number of layers. In this setting we devise three algorithms which differ in the way they visit the core lattice and in their pruning techniques. We then move a step forward and study the problem of extracting the inner-most (also known as maximal) cores, i.e., the cores that are not dominated by any other core in terms of their core index in all the layers. Inner-most cores are typically orders of magnitude less than all the cores. Motivated by this, we devise an algorithm that effectively exploits the maximality property and extracts inner-most cores directly, without first computing a complete decomposition. Finally, we showcase the multilayer core-decomposition tool in a variety of scenarios and problems. We start by considering the problem of densest-subgraph extraction in multilayer networks. We introduce a definition of multilayer densest subgraph that trades-off between high density and number of layers in which the high density holds, and exploit multilayer core decomposition to approximate this problem with quality guarantees. As further applications, we show how to utilize multilayer core decomposition to speed-up the extraction of frequent cross-graph quasi-cliques and to generalize the community-search problem to the multilayer setting

Protecting entanglement via the quantum Zeno effect

We study the exact entanglement dynamics of two atoms in a lossy resonator. Besides discussing the steady-state entanglement, we show that in the strong coupling regime the system-reservoir correlations induce entanglement revivals and oscillations and propose a strategy to fight against the deterioration of the entanglement using the quantum Zeno effect.Comment: 4 pages, 3 figure

Surgical Management of Retraction Pockets: Does Mastoidectomy have a Role?

Abstract Introduction Retraction pocket is a condition in which the eardrum lies deeper within the middle ear. Its management has no consensus in literature. Objective To assess the role of mastoidectomy in the management of retraction pockets added to a tympanoplasty. Methods Prospective study of patients with retraction pocket and referred to surgery. The patients were randomly assigned to two groups: one managed with tympanoplasty and mastoidectomy and the other group with tympanoplasty only. The minimum follow-up considered was 12 months. The outcomes were: integrity of eardrum, recurrence, and hearing status. Results This study included 43 patients. In 24 cases retraction occurred in the posterior half of the eardrum, and in 19 patients there was clinical evidence of ossicular interruption. The two groups of treatment were composed by: 21 patients that underwent tympanoplasty with mastoidectomy and 22 patients had only tympanoplasty. One case of the first group had a recurrence. In 32 cases patients follow up was longer than 48 months. The average air-bone gap changed from 22.1 dB to 5 dB. The percentage of air-bone gap improvement was assessed at 60% in those patients treated with mastoidectomy, and 64.3% in those without it (p > 0.5). Conclusion Tympanoplasty and ossiculoplasty should be considered to treat atelectatic middle ear and ossicular chain interruption. Mastoidectomy as a way to increase air volume in the ear seems to be a paradox; it does not add favorable prognostic factor to management of retraction pockets

Span-core Decomposition for Temporal Networks: Algorithms and Applications

When analyzing temporal networks, a fundamental task is the identification of dense structures (i.e., groups of vertices that exhibit a large number of links), together with their temporal span (i.e., the period of time for which the high density holds). In this paper we tackle this task by introducing a notion of temporal core decomposition where each core is associated with two quantities, its coreness, which quantifies how densely it is connected, and its span, which is a temporal interval: we call such cores \emph{span-cores}. For a temporal network defined on a discrete temporal domain $T$, the total number of time intervals included in $T$ is quadratic in $|T|$, so that the total number of span-cores is potentially quadratic in $|T|$ as well. Our first main contribution is an algorithm that, by exploiting containment properties among span-cores, computes all the span-cores efficiently. Then, we focus on the problem of finding only the \emph{maximal span-cores}, i.e., span-cores that are not dominated by any other span-core by both their coreness property and their span. We devise a very efficient algorithm that exploits theoretical findings on the maximality condition to directly extract the maximal ones without computing all span-cores. Finally, as a third contribution, we introduce the problem of \emph{temporal community search}, where a set of query vertices is given as input, and the goal is to find a set of densely-connected subgraphs containing the query vertices and covering the whole underlying temporal domain $T$. We derive a connection between this problem and the problem of finding (maximal) span-cores. Based on this connection, we show how temporal community search can be solved in polynomial-time via dynamic programming, and how the maximal span-cores can be profitably exploited to significantly speed-up the basic algorithm.Comment: ACM Transactions on Knowledge Discovery from Data (TKDD), 2020. arXiv admin note: substantial text overlap with arXiv:1808.0937

An association of boswellia, betaine and myo-inositol (Eumastós) in the treatment of mammographic breast density. A randomized, double-blind study

Mammographic breast density is a recognized risk factor for breast cancer. The causes that lead to the proliferation of the glandular breast tissue and, therefore, to an increase of breast density are still unclear. However, a treatment strategy to reduce the mammary density may bring about very relevant clinical outcomes in breast cancer prevention. Myo-inositol is a six-fold alcohol of cyclohexane, has already been proved to modulate different pathways: inflammatory, metabolic, oxidative and endocrine processes, in a wide array of human diseases, including cancer and the genesis of mammary gland and breast diseases, like fibrosis, as well as metabolic and endocrine cues. Similarly, boswellic acid and betaine (three-methyl glycine) both inhibit inflammation and exert protective effects on breast physiology. Based on this scientific background, we hypothesized that a combination including, boswellic acid, betaine and myo-inositol would be able to reduce breast density working on different pathways.OBJECTIVE: Mammographic breast density is a recognized risk factor for breast cancer. The causes that lead to the proliferation of the glandular breast tissue and, therefore, to an increase of breast density are still unclear. However, a treatment strategy to reduce the mammary density may bring about very relevant clinical outcomes in breast cancer prevention. Myo-inositol is a six-fold alcohol of cyclohexane, has already been proved to modulate different pathways: inflammatory, metabolic, oxidative and endocrine processes, in a wide array of human diseases, including cancer and the genesis of mammary gland and breast diseases, like fibrosis, as well as metabolic and endocrine cues. Similarly, boswellic acid and betaine (threemethyl glycine) both inhibit inflammation and exert protective effects on breast physiology. Based on this scientific background, we hypothesized that a combinat ion including, boswellic acid, betaine and myo-inositol would be able to reduce breast density working on different pathways. PATIENTS AND METHODS: In this study, seventy-six premenopausal women were randomly assigned to the placebo and the experimental drug arms (Eumastós®) for six months. RESULTS: After 6 months of treatment, statistically significant difference between the two groups was recorded on the breast density reduction (60% vs. 9%), using mammographic as well as ultrasound examination. CONCLUSIONS: Preliminary data collected here with support the starting assumptions,that the association comprising boswellic acid, betaine and myo-inositol significantly reduces mammary density, providing the first evidence for a new and safe approach for the management of mammographic density treatment