Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

In this paper, we consider the question of determining whether a function f has property P or is e-far from any function with property P. A property testing algorithm is given a sample of the value of f on instances drawn according to some distribution. In some cases, it is also allowed to query f on instances of its choice. We study this question for different properties and establish some connections to problems in learning theory and approximation.In particular, we focus our attention on testing graph properties. Given access to a graph G in the form of being able to query whether an edge exists or not between a pair of vertices, we devise algorithms to test whether the underlying graph has properties such as being bipartite, k-Colorable, or having a p-Clique (clique of density p with respect to the vertex set). Our graph property testing algorithms are probabilistic and make assertions that are correct with high probability, while making a number of queries that is independent of the size of the graph. Moreover, the property testing algorithms can be used to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph that correspond to the property being tested, if it holds for the input graph.

Property Testing and its connection to Learning and Approximation

Workbook of atmospheric dispersion estimates

Preface 1. Introduction and background 2. Linear algebra and the Dirac notation 3. Qubits and the framework of quantum mechanics 4. A quantum model of computation 5. Superdense coding and quantum teleportation 6. Introductory quantum algorithms 7. Algorithms with super-polynomial speed-up 8. Algorithms based on amplitude amplification 9. Quantum computational complexity theory and lower bounds 10. Quantum error correction Appendices Bibliography Index

An introduction to quantum computing

Cooperativity in Noncovalent Interactions.

An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In the first result of this paper we prove that computing rc(G) is NP-Hard solving an open problem from Caro et al. (Electron. J. Comb. 15, 2008, Paper R57). In fact, we prove that it is already NP-Complete to decide if rc(G)=2, and also that it is NP-Complete to decide whether a given edge-colored (with an unbounded number of colors) graph is rainbow connected. On the positive side, we prove that for every ?>0, a connected graph with minimum degree at least ? n has bounded rainbow connection, where the bound depends only on ?, and a corresponding coloring can be constructed in polynomial time. Additional non-trivial upper bounds, as well as open problems and conjectures are also presented.

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Hardness and algorithms for rainbow connection

An edge-colored graph $G$ is {\em rainbow connected} if any two vertices are connected by a path whose edges have distinct colors. The {\em rainbow connection} of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected. In the first result of this paper we prove that computing $rc(G)$ is NP-Hard solving an open problem from \cite{Ca-Yu}. In fact, we prove that it is already NP-Complete to decide if $rc(G)=2$, and also that it is NP-Complete to decide whether a given edge-colored (with an unbounded number of colors) graph is rainbow connected. On the positive side, we prove that for every $\epsilon >0$, a connected graph with minimum degree at least $\epsilon n$ has {\em bounded} rainbow connection, where the bound depends only on $\epsilon$, and a corresponding coloring can be constructed in polynomial time. Additional non-trivial upper bounds, as well as open problems and conjectures are also presented.

Hardness and Algorithms for Rainbow Connection

An edge-colored graph $G$ is {\em rainbow connected} if any two vertices are connected by a path whose edges have distinct colors. The {\em rainbow connectivity} of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected. In addition to being a natural combinatorial problem, the rainbow connectivity problem is motivated by applications in cellular networks. In this paper we give the first proof that computing $rc(G)$ is NP-Hard. In fact, we prove that it is already NP-Complete to decide if $rc(G)=2$, and also that it is NP-Complete to decide whether a given edge-colored (with an unbounded number of colors) graph is rainbow connected. On the positive side, we prove that for every $\epsilon >0$, a connected graph with minimum degree at least $\epsilon n$ has bounded rainbow connectivity, where the bound depends only on $\epsilon$, and the corresponding coloring can be constructed in polynomial time. Additional non-trivial upper bounds, as well as open problems and conjectures are also presented.

Hardness and Algorithms for Rainbow Connectivity

AbstractWe study the problem of monotonicity testing over the hypercube. As previously observed in several works, a positive answer to a natural question about routing properties of the hypercube network would imply the existence of efficient monotonicity testers. In particular, if any set of source-sink pairs on the directed hypercube (with all sources and all sinks distinct) can be connected with edge-disjoint paths, then monotonicity of functions $$f:\\{ 0,1\\} ^n \\to \\mathcal{R}$$ can be tested with O(n/∈) queries, for any totally ordered range $$\\mathcal{R}$$. More generally, if at least a µ(n) fraction of the pairs can always be connected with edge-disjoint paths then the query complexity is O(n/(∈µ(n))).We construct a family of instances of Ω(2n) pairs in n-dimensional hypercubes such that no more than roughly a $$\\frac{1}\n{{\\sqrt n }}$$ fraction of the pairs can be simultaneously connected with edge-disjoint paths. This answers an open question of Lehman and Ron [16], and suggests that the aforementioned appealing combinatorial approach for deriving query-complexity upper bounds from routing properties cannot yield, by itself, query-complexity bounds better than ≈ n3/2. Additionally, our construction can also be used to obtain a strong counterexample to Szymanski’s conjecture about routing on the hypercube. In particular, we show that for any δ > 0, the n-dimensional hypercube is not $$n^{\\tfrac{1}\n{2} - \\delta }$$-realizable with shortest paths, while previously it was only known that hypercubes are not 1-realizable with shortest paths.We also prove a lower bound of Ω(n/∈) queries for one-sided non-adaptive testing of monotonicity over the n-dimensional hypercube, as well as additional bounds for specific classes of functions and testers.

Monotonicity Testing and Shortest-Path Routing on the Cube.

Fireworks display during festive celebrations can cause acute short term air pollution. Deepawali –the festival of light– is celebrated in India, every year during October or November with great fireworks display. Concentration of air pollutants such as SPM (suspended particulate matter), PM10, PM2.5, SO2 y NO2 were monitored for six consecutive days during Deepawali in Salkia, a densely populated residential area near Kolkata, India, for assessing the impacts of fireworks on ambient air quality. The pollutant concentrations as recorded on Deepawali were found to be several times higher (6.44 times for SPM, 7.16 times for PM10, 5.35 times for PM2.5, 1.73 times for SO2 and 1.27 times for NO2) compared to a typical winter day value. The results indicated the huge contribution of fireworks on the pollutant levels. The particulate concentrations on Deepawali exceeded its respective 24 hour residential standards by several times (11.6 times for SPM, 22.3 times for PM10, and 34.3 times for PM2.5). Concentrations of metals like Ba, Cu, Cd, Pb, Hg, Al in collected PMPM2.5 were found to be increased by many times on Deepawali (56.72, 79.00, 16.67, 14.86, 12.00 and 6.26 times, respectively) compared to the previous day. The probable health impact of this huge though short-lived deterioration of the ambient air quality is estimated through Monte Carlo's simulation in terms of increase in relative risk of mortality and morbidity in exposed individuals and found to be extremely high. It suggests some controls on fireworks during festive celebrations.

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Sourav Chakraborty

Papers

Hardness and algorithms for rainbow connection

Hardness and Algorithms for Rainbow Connection

Hardness and Algorithms for Rainbow Connectivity

Monotonicity Testing and Shortest-Path Routing on the Cube.

Air pollution from fireworks during festival of lights (Deepawali) in Howrah, India - a case study