다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others We also survey and discuss existing data sets that can be represented as multilayer networks We review attempts to generalize single-layer-network diagnostics to multilayer networks We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks We conclude with a summary and an outlook

Multilayer Networks

1. Overview 2. Erdos-Renyi random graphs 3. Fixed degree distributions 4. Power laws 5. Small worlds 6. Random walks 7. CHKNS model.

/pdf/random-graph-dynamics-5durp7r63x.pdf

Random graph dynamics

Diffusion processes and their sample paths

History of tuberculosis

Branching random walks on trees

I Discrete Time Markov Chains.- I.1 Three fundamental examples.- I.2 Classification of states.- I.3 Finite Markov chains.- I.4 Birth and death chains.- I.5 An example of coupling.- I.6 Time to get ruined.- I.7 Absorption probabilities for martingales.- I.8 Random walks.- I.9 The Bienayme-Galton-Watson branching process.- I.10 Proof of Theorem I.2.1.- I.11 Proof of Theorem I.2.2.- I.12 Proof of Theorem I.9.1.- II Stationary Distributions of a Markov Chain.- II. 1 Existence of stationary distributions.- II.2 Reversible measures.- II.3 Convergence to a stationary distribution.- II.4 The finite case.- II.5 Proof of Proposition II. 1.2.- II.6 Proof of Proposition II. 1.3.- II.7 Proofs of Theorems II.3.1 and II.4.2.- III Continuous Time Birth and Death Markov Chains.- III.1 The exponential distribution.- III.2 Construction and first properties.- III.3 Limiting probabilities.- III.4 Classification of states.- III.5 The Poisson process.- III.6 Passage times.- III.7 A queue which is not Markovian.- III.8 Proof of Theorem III.3.1.- III.9 Proof of Theorem III.5.1.- III.10 Proof of Theorem III.5.2.- IV Percolation.- IV.1 Percolation on Zd.- IV.2 Further properties of percolation on Zd.- IV.3 Percolation on a tree and two critical exponents.- V A Cellular Automaton.- V.1 The model.- V.2 A renormalization argument.- VI Continuous Time Branching Random Walk.- VI.1 A continuous time Bienayme-Galton-Watson process.- VI.2 A continuous time branching random walk.- VI.3 The first phase transition is continuous.- VI.4 The second phase transition is discontinuous.- VI.5 Proof of Theorem VI.2.1.- VII The Contact Process on a Homogeneous Tree.- VII.1 The two phase transitions.- VII.2 Characterization of the first phase transition.- VII.3 The graphical construction.- VII.4 Proofs.- VII.5 Open problems.- Appendix: Some Facts About Probabilities on Countable Spaces.- 1 Probability space.- 2 Independence.- 3 Discrete random variables.- References.

Classical and spatial stochastic processes

We extend certain exponential decay results of subcritical percolation to a class of locally dependent random graphs, introduced by Kuulasmaa as models for spatial epidemics on $\mathbb{Z}^d$. In these models, infected individuals eventually die (are removed) and are not replaced. We combine these results with certain continuity and rescaling arguments in order to improve our knowledge of the phase diagram of a modified epidemic model in which new susceptibles are born at some positive rate. In particular, we show that, throughout an intermediate phase where the infection rate lies between two certain critical values, no coexistence is possible for sufficiently small positive values of the recovery rate. This result provides a converse to results of Durrett and Neuhauser and Andjel and Schinazi. We show also that such an intermediate phase indeed exists for every $d \geq 1$ (i.e., that the two critical values mentioned above are distinct). An important technique is the general version of the BK inequality for disjoint occurrence, proved in 1994 by Reimer.

/pdf/dependent-random-graphs-and-spatial-epidemics-3ldkz7vqrd.pdf

Dependent random graphs and spatial epidemics

On the role of social clusters in the transmission of infectious diseases

In a poll of 100 randomly selected voters, 35 expressed support for initiative A. How does one estimate the proportion of voters in the whole population that supports initiative A based on the sample of 100? How much confidence do we have on our estimate?

Rinaldo B. Schinazi

Papers

Branching random walks on trees

Classical and spatial stochastic processes

Dependent random graphs and spatial epidemics

On the role of social clusters in the transmission of infectious diseases

Estimation and Hypothesis Testing