Algorithmic challenges in green data centers

With data centers being the supporting infrastructure for a wide range of IT services, their efficiency has become a big concern to operators, as well as to society, for both economic and environmental reasons. The goal of this thesis is to design energy-efficient algorithms that reduce energy cost while minimizing compromise to service. We focus on the algorithmic challenges at different levels of energy optimization across the data center stack. The algorithmic challenge at the device level is to improve the energy efficiency of a single computational device via techniques such as job scheduling and speed scaling. We analyze the common speed scaling algorithms in both the worst-case model and stochastic model to answer some fundamental issues in the design of speed scaling algorithms. The algorithmic challenge at the local data center level is to dynamically allocate resources (e.g., servers) and to dispatch the workload in a data center. We develop an online algorithm to make a data center more power-proportional by dynamically adapting the number of active servers. The algorithmic challenge at the global data center level is to dispatch the workload across multiple data centers, considering the geographical diversity of electricity price, availability of renewable energy, and network propagation delay. We propose algorithms to jointly optimize routing and provisioning in an online manner. Motivated by the above online decision problems, we move on to study a general class of online problem named "smoothed online convex optimization", which seeks to minimize the sum of a sequence of convex functions when "smooth" solutions are preferred. This model allows us to bridge different research communities and help us get a more fundamental understanding of general online decision problems.

Expression of eph-family receptor tyrosine kinases and ephrins in the tadpole of the frog Xenopus laevis, and possible roles in the development of retinotectal topography

Assembling a nervous system requires exquisite specificity in the construction of neuronal connectivity. One method by which such specificity is implemented is the presence of chemical cues within the tissues, differentiating one region from another, and the presence of receptors for those cues on the surface of neurons and their axons that are navigating within this cellular environment.

Connections from one part of the nervous system to another often take the form of a topographic mapping. One widely studied model system that involves such a mapping is the vertebrate retinotectal projection-the set of connections between the eye and the optic tectum of the midbrain, which is the primary visual center in non-mammals and is homologous to the superior colliculus in mammals. In this projection the two-dimensional surface of the retina is mapped smoothly onto the two-dimensional surface of the tectum, such that light from neighboring points in visual space excites neighboring cells in the brain. This mapping is implemented at least in part via differential chemical cues in different regions of the tectum.

The Eph family of receptor tyrosine kinases and their cell-surface ligands, the ephrins, have been implicated in a wide variety of processes, generally involving cellular movement in response to extracellular cues. In particular, they possess expression patterns-i.e., complementary gradients of receptor in retina and ligand in tectum- and in vitro and in vivo activities and phenotypes-i.e., repulsive guidance of axons and defective mapping in mutants, respectively-consistent with the long-sought retinotectal chemical mapping cues.

The tadpole of Xenopus laevis, the South African clawed frog, is advantageous for in vivo retinotectal studies because of its transparency and manipulability. However, neither the expression patterns nor the retinotectal roles of these proteins have been well characterized in this system. We report here comprehensive descriptions in swimming stage tadpoles of the messenger RNA expression patterns of eleven known Xenopus Eph and ephrin genes, including xephrin-A3, which is novel, and xEphB2, whose expression pattern has not previously been published in detail. We also report the results of in vivo protein injection perturbation studies on Xenopus retinotectal topography, which were negative, and of in vitro axonal guidance assays, which suggest a previously unrecognized attractive activity of ephrins at low concentrations on retinal ganglion cell axons. This raises the possibility that these axons find their correct targets in part by seeking out a preferred concentration of ligands appropriate to their individual receptor expression levels, rather than by being repelled to greater or lesser degrees by the ephrins but attracted by some as-yet-unknown cue(s).

On concentrated loads and Green's functions in elastostatics

This investigation is concerned with the notion of concentrated loads in classical elastostatics and related issues. Following a limit treatment of problems involving concentrated internal and surface loads, the orders of the ensuing displacements and stress singularities, as well as the stress resultants of the latter, are determined. These conclusions are taken as a basis for an alternative direct formulation of concentrated-load problems, the completeness of which is established through an appropriate uniqueness theorem. In addition, the present work supplies a reciprocal theorem and an integral representation-theorem applicable to singular problems of the type under consideration. Finally, in the course of the analysis presented here, the theory of Green's functions in elastostatics is extended.

Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains

In this thesis, a collection of novel numerical techniques culminating in a fast, parallel method for the direct numerical simulation of incompressible viscous flows around surfaces immersed in unbounded fluid domains is presented. At the core of all these techniques is the use of the fundamental solutions, or lattice Green’s functions, of discrete operators to solve inhomogeneous elliptic difference equations arising in the discretization of the three-dimensional incompressible Navier-Stokes equations on unbounded regular grids. In addition to automatically enforcing the natural free-space boundary conditions, these new lattice Green’s function techniques facilitate the implementation of robust staggered-Cartesian-grid flow solvers with efficient nodal distributions and fast multipole methods. The provable conservation and stability properties of the appropriately combined discretization and solution techniques ensure robust numerical solutions. Numerical experiments on thin vortex rings, low-aspect-ratio flat plates, and spheres are used verify the accuracy, physical fidelity, and computational efficiency of the present formulations.