Gunrock: A High-Performance Graph Processing Library on the GPU

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs have been two significant challenges for developing a programmable high-performance graph library. "Gunrock", our graph-processing system designed specifically for the GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high performance GPU computing primitives and optimization strategies with a high-level programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. We evaluate Gunrock on five key graph primitives and show that Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives, and better performance than any other GPU high-level graph library.Comment: 14 pages, accepted by PPoPP'16 (removed the text repetition in the previous version v5

Dynamics of polymer chain collapse into compact states

Molecular dynamics simulation methods are used to study the folding of polymer chains into packed cubic states. The polymer model, based on a chain of linked sites moving in the continuum, includes both excluded volume and torsional interactions. Different native-state packing arrangements and chain lengths are explored; the organization of the native state is found to affect both the ability of the chain to fold successfully and the nature of the folding pathway as the system is gradually cooled. An order parameter based on contact counts is used to provide information about the folding process, with contacts additionally classified according to criteria such as core and surface sites or local and distant site pairs. Fully detailed contact maps and their evolution are also examined.Comment: 11 pages, 11 figures (some low resolution

Effect of Collagen type-I on the rate of osseointegration of Ca-containing biodegradable Mg-Zr based alloys

Mg-Zr based biodegradable implants alloyed with Ca were investigated to assess their biocompatibility and efficacy in bone formation and osseointegration. Bare alloys, containing Ca, exhibited low surface energy, poor corrosion-resistance, reduced osteoinduction and bone integration activity. Upon coating with Collagen type-I, these alloys demonstrated enhanced performance as an implant material that are suitable for rapid and efficient new bone tissue induction with optimal mineral content and cellular properties

THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge between the moments of jump of the random walk and interpreted as an energy function over the bridge connfiguration; the random walk acts as the random environment. This model provides a continuum version of a model with some relevance to protein conformation. The thermodynamic limit of the specific free energy is shown to exist and to be self-averaging, i.e. it is equal to a trivial --- explicitly computed --- random variable. An estimate of the asymptotic behaviour of the ground state energy is also obtained.Comment: 20 pages, uuencoded postscrip

Molecular dynamics simulation of polymer helix formation using rigid-link methods

Molecular dynamics simulations are used to study structure formation in simple model polymer chains that are subject to excluded volume and torsional interactions. The changing conformations exhibited by chains of different lengths under gradual cooling are followed until each reaches a state from which no further change is possible. The interactions are chosen so that the true ground state is a helix, and a high proportion of simulation runs succeed in reaching this state; the fraction that manage to form defect-free helices is a function of both chain length and cooling rate. In order to demonstrate behavior analogous to the formation of protein tertiary structure, additional attractive interactions are introduced into the model, leading to the appearance of aligned, antiparallel helix pairs. The simulations employ a computational approach that deals directly with the internal coordinates in a recursive manner; this representation is able to maintain constant bond lengths and angles without the necessity of treating them as an algebraic constraint problem supplementary to the equations of motion.Comment: 15 pages, 14 figure

Ground States of Two-Dimensional Polyampholytes

We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers $\pm q_0$, restricted to a 2-dimensional square lattice. Monomers interact via a logarithmic (Coulomb) interaction. We study the ground state properties of the polymers as a function of their excess charge $Q$ for all possible charge sequences up to a polymer length N=18. We find that the ground state of the neutral ensemble is compact and its energy extensive and self-averaging. The addition of small excess charge causes an expansion of the ground state with the monomer density depending only on $Q$. In an annealed ensemble the ground state is fully stretched for any excess charge $Q>0$.Comment: 6 pages, 6 eps figures, RevTex, Submitted to Phys. Rev.

Fluctuating Filaments I: Statistical Mechanics of Helices

We examine the effects of thermal fluctuations on thin elastic filaments with non-circular cross-section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies non-monotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix ``melts'' and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross--section leads to resonant dependence of the persistence length on the twist rate.Comment: 5 figure

Two-Dimensional Polymers with Random Short-Range Interactions

We use complete enumeration and Monte Carlo techniques to study two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$. The interaction of charges at neighboring lattice sites is described by $q_i q_j$. We find that a polymer undergoes a collapse transition at a temperature $T_{\theta}$, which decreases with increasing imbalance between charges. At the transition point, the dependence of the radius of gyration of the polymer on the number of monomers is characterized by an exponent $\nu_{\theta} = 0.60 \pm 0.02$, which is slightly larger than the similar exponent for homopolymers. We find no evidence of freezing at low temperatures.Comment: 4 two-column pages, 6 eps figures, RevTex, Submitted to Phys. Rev.

Embedding a Native State into a Random Heteropolymer Model: The Dynamic Approach

We study a random heteropolymer model with Langevin dynamics, in the supersymmetric formulation. Employing a procedure similar to one that has been used in static calculations, we construct an ensemble in which the affinity of the system for a native state is controlled by a "selection temperature" T0. In the limit of high T0, the model reduces to a random heteropolymer, while for T0-->0 the system is forced into the native state. Within the Gaussian variational approach that we employed previously for the random heteropolymer, we explore the phases of the system for large and small T0. For large T0, the system exhibits a (dynamical) spin glass phase, like that found for the random heteropolymer, below a temperature Tg. For small T0, we find an ordered phase, characterized by a nonzero overlap with the native state, below a temperature Tn \propto 1/T0 > Tg. However, the random-globule phase remains locally stable below Tn, down to the dynamical glass transition at Tg. Thus, in this model, folding is rapid for temperatures between Tg and Tn, but below Tg the system can get trapped in conformations uncorrelated with the native state. At a lower temperature, the ordered phase can also undergo a dynamical glass transition, splitting into substates separated by large barriers.Comment: 19 pages, revtex, 6 figure