ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. Although there exist sophisticated algorithms to determine the dynamics of discrete models, their implementations usually require labor-intensive formatting of the model formulation, and they are oftentimes not accessible to users without programming skills. Efficient analysis methods are needed that are accessible to modelers and easy to use. Method: By converting discrete models into algebraic models, tools from computational algebra can be used to analyze their dynamics. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Results: A method for efficiently identifying attractors, and the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness, i.e., while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes, and robustness, i.e., small number of attractors

Memory-Efficient Topic Modeling

As one of the simplest probabilistic topic modeling techniques, latent Dirichlet allocation (LDA) has found many important applications in text mining, computer vision and computational biology. Recent training algorithms for LDA can be interpreted within a unified message passing framework. However, message passing requires storing previous messages with a large amount of memory space, increasing linearly with the number of documents or the number of topics. Therefore, the high memory usage is often a major problem for topic modeling of massive corpora containing a large number of topics. To reduce the space complexity, we propose a novel algorithm without storing previous messages for training LDA: tiny belief propagation (TBP). The basic idea of TBP relates the message passing algorithms with the non-negative matrix factorization (NMF) algorithms, which absorb the message updating into the message passing process, and thus avoid storing previous messages. Experimental results on four large data sets confirm that TBP performs comparably well or even better than current state-of-the-art training algorithms for LDA but with a much less memory consumption. TBP can do topic modeling when massive corpora cannot fit in the computer memory, for example, extracting thematic topics from 7 GB PUBMED corpora on a common desktop computer with 2GB memory.Comment: 20 pages, 7 figure

Distributed Time-Sensitive Task Selection in Mobile Crowdsensing

With the rich set of embedded sensors installed in smartphones and the large number of mobile users, we witness the emergence of many innovative commercial mobile crowdsensing applications that combine the power of mobile technology with crowdsourcing to deliver time-sensitive and location-dependent information to their customers. Motivated by these real-world applications, we consider the task selection problem for heterogeneous users with different initial locations, movement costs, movement speeds, and reputation levels. Computing the social surplus maximization task allocation turns out to be an NP-hard problem. Hence we focus on the distributed case, and propose an asynchronous and distributed task selection (ADTS) algorithm to help the users plan their task selections on their own. We prove the convergence of the algorithm, and further characterize the computation time for users' updates in the algorithm. Simulation results suggest that the ADTS scheme achieves the highest Jain's fairness index and coverage comparing with several benchmark algorithms, while yielding similar user payoff to a greedy centralized benchmark. Finally, we illustrate how mobile users coordinate under the ADTS scheme based on some practical movement time data derived from Google Maps

Time Versus Cost Tradeoffs for Deterministic Rendezvous in Networks

Two mobile agents, starting from different nodes of a network at possibly different times, have to meet at the same node. This problem is known as $\mathit{rendezvous}$. Agents move in synchronous rounds. Each agent has a distinct integer label from the set $\{1,\dots,L\}$. Two main efficiency measures of rendezvous are its $\mathit{time}$ (the number of rounds until the meeting) and its $\mathit{cost}$ (the total number of edge traversals). We investigate tradeoffs between these two measures. A natural benchmark for both time and cost of rendezvous in a network is the number of edge traversals needed for visiting all nodes of the network, called the exploration time. Hence we express the time and cost of rendezvous as functions of an upper bound $E$ on the time of exploration (where $E$ and a corresponding exploration procedure are known to both agents) and of the size $L$ of the label space. We present two natural rendezvous algorithms. Algorithm $\mathtt{Cheap}$ has cost $O(E)$ (and, in fact, a version of this algorithm for the model where the agents start simultaneously has cost exactly $E$) and time $O(EL)$. Algorithm $\mathtt{Fast}$ has both time and cost $O(E\log L)$. Our main contributions are lower bounds showing that, perhaps surprisingly, these two algorithms capture the tradeoffs between time and cost of rendezvous almost tightly. We show that any deterministic rendezvous algorithm of cost asymptotically $E$ (i.e., of cost $E+o(E)$) must have time $\Omega(EL)$. On the other hand, we show that any deterministic rendezvous algorithm with time complexity $O(E\log L)$ must have cost $\Omega (E\log L)$

A Distributed algorithm to find Hamiltonian cycles in Gnp random graphs

In this paper, we present a distributed algorithm to find Hamiltonian cycles in random binomial graphs Gnp. The algorithm works on a synchronous distributed setting by first creating a small cycle, then covering almost all vertices in the graph with several disjoint paths, and finally patching these paths and the uncovered vertices to the cycle. Our analysis shows that, with high probability, our algorithm is able to find a Hamiltonian cycle in Gnp when p_n=omega(sqrt{log n}/n^{1/4}). Moreover, we conduct an average case complexity analysis that shows that our algorithm terminates in expected sub-linear time, namely in O(n^{3/4+epsilon}) pulses.Postprint (published version