Kinematic Basis of Emergent Energetics of Complex Dynamics

Stochastic kinematic description of a complex dynamics is shown to dictate an energetic and thermodynamic structure. An energy function $\varphi(x)$ emerges as the limit of the generalized, nonequilibrium free energy of a Markovian dynamics with vanishing fluctuations. In terms of the $\nabla\varphi$ and its orthogonal field $\gamma(x)\perp\nabla\varphi$, a general vector field $b(x)$ can be decomposed into $-D(x)\nabla\varphi+\gamma$, where $\nabla\cdot\big(\omega(x)\gamma(x)\big)=$ $-\nabla\omega D(x)\nabla\varphi$. The matrix $D(x)$ and scalar $\omega(x)$, two additional characteristics to the $b(x)$ alone, represent the local geometry and density of states intrinsic to the statistical motion in the state space at $x$. $\varphi(x)$ and $\omega(x)$ are interpreted as the emergent energy and degeneracy of the motion, with an energy balance equation $d\varphi(x(t))/dt=\gamma D^{-1}\gamma-bD^{-1}b$, reflecting the geometrical $\|D\nabla\varphi\|^2+\|\gamma\|^2=\|b\|^2$. The partition function employed in statistical mechanics and J. W. Gibbs' method of ensemble change naturally arise; a fluctuation-dissipation theorem is established via the two leading-order asymptotics of entropy production as $\epsilon\to 0$. The present theory provides a mathematical basis for P. W. Anderson's emergent behavior in the hierarchical structure of complexity science.Comment: 7 page

High Performance Biological Pairwise Sequence Alignment: FPGA versus GPU versus Cell BE versus GPP

This paper explores the pros and cons of reconfigurable computing in the form of FPGAs for high performance efficient computing. In particular, the paper presents the results of a comparative study between three different acceleration technologies, namely, Field Programmable Gate Arrays (FPGAs), Graphics Processor Units (GPUs), and IBM’s Cell Broadband Engine (Cell BE), in the design and implementation of the widely-used Smith-Waterman pairwise sequence alignment algorithm, with general purpose processors as a base reference implementation. Comparison criteria include speed, energy consumption, and purchase and development costs. The study shows that FPGAs largely outperform all other implementation platforms on performance per watt criterion and perform better than all other platforms on performance per dollar criterion, although by a much smaller margin. Cell BE and GPU come second and third, respectively, on both performance per watt and performance per dollar criteria. In general, in order to outperform other technologies on performance per dollar criterion (using currently available hardware and development tools), FPGAs need to achieve at least two orders of magnitude speed-up compared to general-purpose processors and one order of magnitude speed-up compared to domain-specific technologies such as GPUs