抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Journal of the ACM

Introduction. 1. Mathematical Preliminaries. Submodular Systems and Base Polyhedra. 2. From Matroids to Submodular Systems. Matroids. Polymatroids. Submodular Systems. 3. Submodular Systems and Base Polyhedra. Fundamental Operations on Submodular Systems. Greedy Algorithm. Structures of Base Polyhedra. Intersecting- and Crossing-Submodular Functions. Related Polyhedra. Submodular Systems of Network Type. Neoflows. 4. The Intersection Problem. The Intersection Theorem. The Discrete Separation Theorem. The Common Base Problem. 5. Neoflows. The Equivalence of the Neoflow Problems. Feasibility for Submodular Flows. Optimality for Submodular Flows. Algorithms for Neoflows. Matroid Optimization. Submodular Analysis. 6. Submodular Functions and Convexity. Conjugate Functions and a Fenchel-Type Min-Max Theorem for Submodular and Supermodular Functions. Subgradients of Submodular Functions. The Lovasz Extensions of Submodular Functions. 7. Submodular Programs. Submodular Programs - Unconstrained Optimization. Submodular Programs - Constrained Optimization. Nonlinear Optimization with Submodular Constraints. 8. Separable Convex Optimization. Optimality Conditions. A Decomposition Algorithm. Discrete Optimization. 9. The Lexicographically Optimal Base Problem. Nonlinear Weight Functions. Linear Weight Functions. 10. The Weighted Max-Min and Min-Max Problems. Continuous Variables. Discrete Variables. 11. The Fair Resource Allocation Problem. Continuous Variables. Discrete Variables. 12. The Neoflow Problem with a Separable Convex Cost Function. References. Index.

Submodular functions and optimization

The deferred acceptance algorithm proposed by Gale and Shapley (1962) has had a profound influence on market design, both directly, by being adapted into practical matching mechanisms, and, indirectly, by raising new theoretical questions. Deferred acceptance algorithms are at the basis of a number of labor market clearinghouses around the world, and have recently been implemented in school choice systems in Boston and New York City. In addition, the study of markets that have failed in ways that can be fixed with centralized mechanisms has led to a deeper understanding of some of the tasks a marketplace needs to accomplish to perform well. In particular, marketplaces work well when they provide thickness to the market, help it deal with the congestion that thickness can bring, and make it safe for participants to act effectively on their preferences. Centralized clearinghouses organized around the deferred acceptance algorithm can have these properties, and this has sometimes allowed failed markets to be reorganized.

Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions

Identifying community structure in networks is an issue of particular interest in network science. The modularity introduced by Newman and Girvan is the most popular quality function for community detection in networks. In this study, we identify a problem in the concept of modularity and suggest a solution to overcome this problem. Specifically, we obtain a new quality function for community detection. We refer to the function as Z-modularity because it measures the Z-score of a given partition with respect to the fraction of the number of edges within communities. Our theoretical analysis shows that Z-modularity mitigates the resolution limit of the original modularity in certain cases. Computational experiments using both artificial networks and well-known real-world networks demonstrate the validity and reliability of the proposed quality function.

/pdf/z-score-based-modularity-for-community-detection-in-networks-4x1rlonmpy.pdf

Z-score-based modularity for community detection in networks

Randomized algorithms for online knapsack problems

In this paper, we study the online unweighted knapsack problem with removal cost. The input is a sequence of items u 1,u 2,?,u n , each of which has a size and a value, where the value of each item is assumed to be equal to the size. Given the ith item u i , we either put u i into the knapsack or reject it with no cost. When u i is put into the knapsack, some items in the knapsack are removed with removal cost if the sum of the size of u i and the total size in the current knapsack exceeds the capacity of the knapsack. Here the removal cost means a cancellation charge or disposal fee. Our goal is to maximize the profit, i.e., the sum of the values of items in the last knapsack minus the total removal cost occurred.

In this paper, we consider two kinds of removal cost: unit and proportional cost. For both models, we provide their competitive ratios. Namely, we construct optimal online algorithms and prove that they are best possible.

Online Unweighted Knapsack Problem with Removal Cost

In the densest subgraph problem, given an edge-weighted undirected graph $$G=(V,E,w)$$
 , we are asked to find $$S\subseteq V$$
 that maximizes the density, i.e., w(S) / |S|, where w(S) is the sum of weights of the edges in the subgraph induced by S. This problem has often been employed in a wide variety of graph mining applications. However, the problem has a drawback; it may happen that the obtained subset is too large or too small in comparison with the size desired in the application at hand. In this study, we address the size issue of the densest subgraph problem by generalizing the density of $$S\subseteq V$$
 . Specifically, we introduce the f-density of $$S\subseteq V$$
 , which is defined as w(S) / f(|S|), where $$f:\mathbb {Z}_{\ge 0}\rightarrow \mathbb {R}_{\ge 0}$$
 is a monotonically non-decreasing function. In the f-densest subgraph problem (f-DS), we aim to find $$S\subseteq V$$
 that maximizes the f-density w(S) / f(|S|). Although f-DS does not explicitly specify the size of the output subset of vertices, we can handle the above size issue using a convex/concave size function f appropriately. For f-DS with convex function f, we propose a nearly-linear-time algorithm with a provable approximation guarantee. On the other hand, for f-DS with concave function f, we propose an LP-based exact algorithm, a flow-based $$O(|V|^3)$$
 -time exact algorithm for unweighted graphs, and a nearly-linear-time approximation algorithm.

/pdf/the-densest-subgraph-problem-with-a-convex-concave-size-u26ds6c440.pdf

The Densest Subgraph Problem with a Convex/Concave Size Function

In this paper, we study online knapsack problems. The input is a sequence of items e 1 , e 2 , ? , e n , each of which has a size and a value. Given the ith item e i , we either put e i into the knapsack or reject it. In the removable setting, when e i is put into the knapsack, some items in the knapsack are removed with no cost if the sum of the size of e i and the total size in the current knapsack exceeds the capacity of the knapsack. Our goal is to maximize the profit, i.e., the sum of the values of items in the last knapsack.We present a simple randomized 2-competitive algorithm for the unweighted non-removable case and show that it is the best possible, where knapsack problem is called unweighted if the value of each item is equal to its size.For the removable case, we propose a randomized 2-competitive algorithm despite there is no constant competitive deterministic algorithm. We also provide a lower bound 1 + 1 / e ? 1.368 for the competitive ratio. For the unweighted removable case, we propose a 10/7-competitive algorithm and provide a lower bound 1.25 for the competitive ratio.

Yasushi Kawase

Papers

Z-score-based modularity for community detection in networks

Randomized algorithms for online knapsack problems

Online Unweighted Knapsack Problem with Removal Cost

The Densest Subgraph Problem with a Convex/Concave Size Function

Randomized Algorithms for Online Knapsack Problems (回路とシステム)