Sampling Algorithms for Butterfly Counting on Temporal Bipartite Graphs

Temporal bipartite graphs are widely used to denote time-evolving relationships between two disjoint sets of nodes, such as customer-product interactions in E-commerce and user-group memberships in social networks. Temporal butterflies, $(2,2)$-bicliques that occur within a short period and in a prescribed order, are essential in modeling the structural and sequential patterns of such graphs. Counting the number of temporal butterflies is thus a fundamental task in analyzing temporal bipartite graphs. However, existing algorithms for butterfly counting on static bipartite graphs and motif counting on temporal unipartite graphs are inefficient for this purpose. In this paper, we present a general framework with three sampling strategies for temporal butterfly counting. Since exact counting can be time-consuming on large graphs, our approach alternatively computes approximate estimates accurately and efficiently. We also provide analytical bounds on the number of samples each strategy requires to obtain estimates with small relative errors and high probability. We finally evaluate our framework on six real-world datasets and demonstrate its superior accuracy and efficiency compared to several baselines. Overall, our proposed framework and sampling strategies provide efficient and accurate approaches to approximating temporal butterfly counts on large-scale temporal bipartite graphs.Comment: 10 pages, 10 figures; under revie

Protective effect of salvianolic acid B against intestinal ischemia reperfusion-induced injury in a rat model

Purpose: To evaluate the gastro-protective efficacy of salvianolic acid B (SAB)  against intestinal ischemic-reperfusion injury (IIRI) in a rat model.Methods: Forty-eight healthy male rats were randomly choosen and divided into 4 groups of 12 rats each. Control group rats underwent laparotomy without occlusion; IIRI group rats underwent laparotomy with occlusion for 60 min, followed by 24 h of reperfusion; SAB + IIRI group received 7 days of pretreatment with 40 mg/kg of SAB + IIRI; while the fourth group received only SAB. The antioxidant, inflammatory markers, intestinal permeability marker, as well as intestinal histopathological changes were assessed.Results: The activities of antioxidants including reduced glutathione (GSH),  catalase (CAT) and superoxide dismutase (SOD) were significantly ameliorated (p < 0.01) in SAB-supplemented group (SAB + IIRI). The concentration of inflammatory markers, including interleukin-1β (IL-1β), interleukin-6 (IL-6), tumor necrosis factor alpha (TNF-α) and nuclear factor p65 (NF-p65) as well as small intestinal permeability marker (FITC-Dextran), were significantly reduced (p < 0.01) following administration of SAB for 7 days. In addition, pretreatment with SAB reverted intestinal (ileum) histopathological changes to almost normal architecture with significant reduction in Chiu score.Conclusion: The results of this study demonstrate that SAB may protect the intestine by attenuating oxidative stress and inflammatory response and hence, may be potentially for treating IIRI.Keywords: Salvianolic acid B, Intestinal Ischemia-reperfusion, Antioxidants,  Inflammation, Intestinal permeabilit

Efficient and Scalable Parametric High-Order Portfolios Design via the Skew-t Distribution

Since Markowitz's mean-variance framework, optimizing a portfolio that maximizes the profit and minimizes the risk has been ubiquitous in the financial industry. Initially, profit and risk were measured by the first two moments of the portfolio's return, a.k.a. the mean and variance, which are sufficient to characterize a Gaussian distribution. However, it is broadly believed that the first two moments are not enough to capture the characteristics of the returns' behavior, which have been recognized to be asymmetric and heavy-tailed. Although there is ample evidence that portfolio designs involving the third and fourth moments, i.e., skewness and kurtosis, will outperform the conventional mean-variance framework, they are non-trivial. Specifically, in the classical framework, the memory and computational cost of computing the skewness and kurtosis grow sharply with the number of assets. To alleviate the difficulty in high-dimensional problems, we consider an alternative expression for high-order moments based on parametric representations via a generalized hyperbolic skew-t distribution. Then, we reformulate the high-order portfolio optimization problem as a fixed-point problem and propose a robust fixed-point acceleration algorithm that solves the problem in an efficient and scalable manner. Empirical experiments also demonstrate that our proposed high-order portfolio optimization framework is of low complexity and significantly outperforms the state-of-the-art methods by 2 to 4 orders of magnitude

Network Topology Inference with Sparsity and Laplacian Constraints

We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex} has uncovered the limitations of the widely used $\ell_1$-norm in learning sparse graphs under this model: empirically, the number of nonzero entries in the solution grows with the regularization parameter of the $\ell_1$-norm; theoretically, a large regularization parameter leads to a fully connected (densest) graph. To overcome these challenges, we propose a graph Laplacian estimation method incorporating the $\ell_0$-norm constraint. An efficient gradient projection algorithm is developed to solve the resulting optimization problem, characterized by sparsity and Laplacian constraints. Through numerical experiments with synthetic and financial time-series datasets, we demonstrate the effectiveness of the proposed method in network topology inference

Self‐Healable and Recyclable Tactile Force Sensors with Post‐Tunable Sensitivity

It is challenging to post‐tune the sensitivity of a tactile force sensor. Herein, a facile method is reported to tailor the sensing properties of conductive polymer composites by utilizing the liquid‐like property of dynamic polymer matrix at low strain rates. The idea is demonstrated using dynamic polymer composites (CB/dPDMS) made via evaporation‐induced gelation of the suspending toluene solution of carbon black (CB) and acid‐catalyzed dynamic polydimethylsiloxane (dPDMS). The dPDMS matrices allow CB to redistribute to change the sensitivity of materials at the liquid‐like state, but exhibit typical solid‐like behavior and thus can be used as strain sensors at normal strain rates. It is shown that the gauge factor of the polymer composites can be easily post‐tuned from 1.4 to 51.5. In addition, the dynamic polymer matrices also endow the composites with interesting self‐healing ability and recyclability. Therefore, it is envisioned that this method can be useful in the design of various novel tactile sensing materials for many applications

Revealing Hidden Vibration Polariton Interactions by 2D IR Spectroscopy

We report the first experimental two-dimensional infrared (2D IR) spectra of novel molecular photonic excitations - vibrational-polaritons. The application of advanced 2D IR spectroscopy onto novel vibrational-polariton challenges and advances our understanding in both fields. From spectroscopy aspect, 2D IR spectra of polaritons differ drastically from free uncoupled molecules; from vibrational-polariton aspects, 2D IR uniquely resolves hybrid light-matter polariton excitations and unexpected dark states in a state-selective manner and revealed hidden interactions between them. Moreover, 2D IR signals highlight the role of vibrational anharmonicities in generating non-linear signals. To further advance our knowledge on 2D IR of vibrational polaritons, we develop a new quantum-mechanical model incorporating the effects of both nuclear and electrical anharmonicities on vibrational-polaritons and their 2D IR signals. This work reveals polariton physics that is difficult or impossible to probe with traditional linear spectroscopy and lays the foundation for investigating new non-linear optics and chemistry of molecular vibrational-polaritons