Monte Carlo Simulation for Exploring Mechanical Properties of Porous Materials Based on Scaled Boundary Finite Element Method

The existence of pores is a very common feature of nature and of human life, but the existence of pores will alter the mechanical properties of the material. Therefore, it is very important to study the impact of different influencing factors on the mechanical properties of porous materials and to use the law of change in mechanical properties of porous materials for our daily lives. The SBFEM (scaled boundary finite element method) method is used in this paper to calculate a large number of random models of porous materials derived from Matlab code. Multiple influencing factors can be present in these random models. Based on the Monte Carlo simulation, after a large number of model calculations were carried out, the results of the calculations were analyzed statistically in order to determine the variation law of the mechanical properties of porous materials. Moreover, this paper gives fitting formulas for the mechanical properties of different materials. This is very useful for researchers estimating the mechanical properties of porous materials in advance.

Emergent fractal phase in energy stratified random models

We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson’s model and the celebrated Rosenzweig-Porter model (with implemented translation-invariant symmetry). In order to do this, we propose the energy-stratified spectral structure of the hopping term allowing one to decrease the range of correlations gradually. We show both analytically and numerically that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system unlike the predictions of localization of cooperative shielding. In order to describe the models with correlated kinetic terms, we develop the generalization of the Dyson Brownian motion and cavity approaches basing on stochastic matrix process with independent rank-one matrix increments and examine its applicability to the above set of models.

Randomness in classes of matroids

<p>This thesis is inspired by the observation that we have no good random model for matroids. That stands in contrast to graphs, which admit a number of elegant random models. As a result we have relatively little understanding of the properties of a "typical" matroid. Acknowledging the difficulty of the general case, we attempt to gain a grasp on randomness in some chosen classes of matroids. Firstly, we consider sparse paving matroids, which are conjectured to dominate the class of matroids (that is to say, asymptotically almost all matroids would be sparse paving). If this conjecture were true, then many results on properties of the random sparse paving matroid would also hold for the random matroid. Sparse paving matroids have limited richness of structure, making counting arguments in particular more feasible than for general matroids. This enables us to prove a number of asymptotic results, particularly with regards to minors. Secondly, we look at Graham-Sloane matroids, a special subset of sparse paving matroids with even more limited structure - in fact Graham-Sloane matroids on a labelled groundset can be randomly generated by a process as simple as independently including certain bases with probability 0.5. Notably, counting Graham-Sloane matroids has provided the best known lower bound on the total number of matroids, to log-log level. Despite the vast size of the class we are able to prove severe restrictions on what minors of Graham-Sloane matroids can look like. Finally we consider transversal matroids, which arise naturally in the context of other mathematical objects - in particular partial transversals of set systems and partial matchings in bipartite graphs. Although transversal matroids are not in one-to-one correspondence with bipartite graphs, we shall link the two closely enough to gain some useful results through exploiting the properties of random bipartite graphs. Returning to the theme of matroid minors, we prove that the class of transversal matroids of given rank is defined by finitely many excluded series-minors. Lastly we consider some other topics, including the axiomatisability of transversal matroids and related classes.</p>

Randomness in classes of matroids

<p>This thesis is inspired by the observation that we have no good random model for matroids. That stands in contrast to graphs, which admit a number of elegant random models. As a result we have relatively little understanding of the properties of a "typical" matroid. Acknowledging the difficulty of the general case, we attempt to gain a grasp on randomness in some chosen classes of matroids. Firstly, we consider sparse paving matroids, which are conjectured to dominate the class of matroids (that is to say, asymptotically almost all matroids would be sparse paving). If this conjecture were true, then many results on properties of the random sparse paving matroid would also hold for the random matroid. Sparse paving matroids have limited richness of structure, making counting arguments in particular more feasible than for general matroids. This enables us to prove a number of asymptotic results, particularly with regards to minors. Secondly, we look at Graham-Sloane matroids, a special subset of sparse paving matroids with even more limited structure - in fact Graham-Sloane matroids on a labelled groundset can be randomly generated by a process as simple as independently including certain bases with probability 0.5. Notably, counting Graham-Sloane matroids has provided the best known lower bound on the total number of matroids, to log-log level. Despite the vast size of the class we are able to prove severe restrictions on what minors of Graham-Sloane matroids can look like. Finally we consider transversal matroids, which arise naturally in the context of other mathematical objects - in particular partial transversals of set systems and partial matchings in bipartite graphs. Although transversal matroids are not in one-to-one correspondence with bipartite graphs, we shall link the two closely enough to gain some useful results through exploiting the properties of random bipartite graphs. Returning to the theme of matroid minors, we prove that the class of transversal matroids of given rank is defined by finitely many excluded series-minors. Lastly we consider some other topics, including the axiomatisability of transversal matroids and related classes.</p>

Hypertension as a Risk Factor for Contrast-Associated Acute Kidney Injury: A Meta-Analysis Including 2,830,338 Patients

<b><i>Objective:</i></b> Previous studies have shown that the relationship between hypertension (HT) and contrast-associated acute kidney injury (CA-AKI) is not clear. We apply a systematic review and meta-analysis to assess the association between HT and CA-AKI. <b><i>Methods:</i></b> We searched for articles on the study of risk factors for CA-AKI in the Embase, Medline, and Cochrane Database of Systematic Reviews (by March 25, 2021). Two authors independently performed quality assessment and extracted data such as the studies’ clinical setting, the definition of CA-AKI, and the number of patients. The CA-AKI was defined as a serum creatinine (SCr) increase ≥25% or ≥0.5 mg/dL from baseline within 72 h. We used fixed or random models to pool adjusted OR (aOR) by STATA. <b><i>Results:</i></b> A total of 45 studies (2,830,338 patients) were identified, and the average incidence of CA-AKI was 6.48%. There was an increased risk of CA-AKI associated with HT (aOR: 1.378, 95% CI: 1.211–1.567, <i>I</i>² = 67.9%). In CA-AKI with a SCr increase ≥50% or ≥0.3 mg/dL from baseline within 72 h, an increased risk of CA-AKI was associated with HT (aOR: 1.414, 95% CI: 1.152–1.736, <i>I</i>^<i>2</i> = 0%). In CA-AKI with a Scr increase ≥50% or ≥0.3 mg/dL from baseline within 7 days, HT increases the risk of CA-AKI (aOR: 1.317, 95% CI: 1.049–1.654, <i>I</i>^<i>2</i> = 51.5%). <b><i>Conclusion:</i></b> Our meta-analysis confirmed that HT is an independent risk factor for CA-AKI and can be used to identify risk stratification. Physicians should pay more attention toward prevention and treatment of patients with HT in clinical practice.

Generalized Kings and Single-Elimination Winners in Random Tournaments

Tournaments can be used to model a variety of practical scenarios including sports competitions and elections. A natural notion of strength of alternatives in a tournament is a generalized king: an alternative is said to be a k-king if it can reach every other alternative in the tournament via a directed path of length at most k. In this paper, we provide an almost complete characterization of the probability threshold such that all, a large number, or a small number of alternatives are k-kings with high probability in two random models. We show that, perhaps surprisingly, all changes in the threshold occur in the regime of constant k, with the biggest change being between k = 2 and k = 3. In addition, we establish an asymptotically tight bound on the probability threshold for which all alternatives are likely able to win a single-elimination tournament under some bracket.

Hadamard-Type Fractional Heat Equations and Ultra-Slow Diffusions

In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing the classical time derivative with the Hadamard operator. The stochastic meaning of the introduced abstract differential equation is provided, and the application to the particular case of the fractional heat equation is then discussed in detail. The ultra-slow behaviour emerges from the explicit form of the variance of the random process arising from our analysis. Finally, we obtain a particular solution for the nonlinear Hadamard-diffusive equation.

Uncertain Random Data Envelopment Analysis: Efficiency Estimation of Returns to Scale

Evaluating efficiency according to the different states of returns to scale (RTS) is crucial to resource allocation and scientific decision for decision-making units (DMUs), but this kind of evaluation will become very difficult when the DMUs are in an uncertain random environment. In this paper, we attempt to explore the uncertain random data envelopment analysis approach so as to solve the problem that the inputs and outputs of DMUs are uncertain random variables. Chance theory is applied to handling the uncertain random variables, and hence, two evaluating models, one for increasing returns to scale (IRS) and the other for decreasing returns to scale (DRS), are proposed, respectively. Along with converting the two uncertain random models into corresponding equivalent forms, we also provide a numerical example to illustrate the evaluation results of these models.

Efficient Approximation Algorithms for Minimum Dominating Sets in Social Networks

Social networks are increasingly becoming an outlet that is more and more powerful in spreading news and influence individuals. Compared with other traditional media outlets such as newspaper, radio, and television, social networks empower users to spread their ideological message and/or to deliver target advertising very efficiently in terms of both cost and time. In this article, the authors focus on efficiently finding dominating sets in social networks for the classical dominating set problem as well as for two related problems: partial dominating sets and d-hop dominating sets. They will present algorithms for determining efficiently a good approximation for the social network minimum dominating sets for each of the three variants. The authors ran an extensive suite of experiments to test the presented algorithms on several datasets that include real networks made available by the Stanford Network Analysis Project and synthetic networks that follow the power-law and random models that they generated for this work. The performed experiments show that the selection of the algorithm that performs best to determine efficiently the dominating set is dependent of network characteristics and the order of importance between the size of the dominating set and the time required to determine such a set.