Dynamic remapping of parallel computations with varying resource demands

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity

Statistical methodologies for the control of dynamic remapping

Following an initial mapping of a problem onto a multiprocessor machine or computer network, system performance often deteriorates with time. In order to maintain high performance, it may be necessary to remap the problem. The decision to remap must take into account measurements of performance deterioration, the cost of remapping, and the estimated benefits achieved by remapping. We examine the tradeoff between the costs and the benefits of remapping two qualitatively different kinds of problems. One problem assumes that performance deteriorates gradually, the other assumes that performance deteriorates suddenly. We consider a variety of policies for governing when to remap. In order to evaluate these policies, statistical models of problem behaviors are developed. Simulation results are presented which compare simple policies with computationally expensive optimal decision policies; these results demonstrate that for each problem type, the proposed simple policies are effective and robust

Signatures of superconducting gap inhomogeneities in optical properties

Scanning tunneling spectroscopy applied to the high-$T_{c}$ cuprates has revealed significant spatial inhomogeneity on the nanoscale. Regions on the order of a coherence length in size show variations of the magnitude of the superconducting gap of order $\pm20$ or more. An important unresolved question is whether or not these variations are also present in the bulk, and how they influence superconducting properties. As many theories and data analyses for high-$T_{c}$ superconductivity assume spatial homogeneity of the gap magnitude, this is a pressing question. We consider the far-infrared optical conductivity and evaluate, within an effective medium approximation, what signatures of spatial variations in gap magnitude are present in various optical quantities. In addition to the case of d-wave superconductivity, relevant to the high-$T_c$ cuprates, we have also considered s-wave gap symmetry in order to provide expected signatures of inhomogeneities for superconductors in general. While signatures of gap inhomogeneities can be strongly manifested in s-wave superconductors, we find that the far-infrared optical conductivity in d-wave is robust against such inhomogeneity.Comment: 8 pages, 7 figure

Nonlinear current response of one- and two-band superconductors

We have calculated the nonlinear current of a number of single band s-wave electron-phonon superconductors. Among issues considered were those of dimensionality, strong electron-phonon coupling, impurities, and comparison with BCS. For the case of two bands, particular attention is paid to the role of anisotropy, the integration effects of the off-diagonal electron-phonon interaction, as well as inter- and intraband impurities. For the specific case of MgB2, we present results based on the known microscopic parameters of band theory.Comment: 10 pages, 6 figure

The unusual thickness dependence of superconductivity in α\alpha-MoGe thin films

Thin films of $\alpha$-MoGe show progressively reduced $T_{c}$'s as the thickness is decreased below 30 nm and the sheet resistance exceeds 100 $\Omega/\Box$. We have performed far-infrared transmission and reflection measurements for a set of $\alpha$-MoGe films to characterize this weakened superconducting state. Our results show the presence of an energy gap with ratio $2\Delta_0/k_BT_{c} = 3.8 \pm 0.1$ in all films studied, slightly higher than the BCS value, even though the transition temperatures decrease significantly as film thickness is reduced. The material properties follow BCS-Eliashberg theory with a large residual scattering rate except that the coherence peak seen in the optical scattering rate is found to be strongly smeared out in the thinner superconducting samples. A peak in the optical mass renormalization at $2\Delta_0$ is predicted and observed for the first time

Considering the impact of situation-specific motivations and constraints in the design of naturally ventilated and hybrid buildings

A simple logical model of the interaction between a building and its occupants is presented based on the principle that if free to do so, people will adjust their posture, clothing or available building controls (windows, blinds, doors, fans, and thermostats) with the aim of achieving or restoring comfort and reducing discomfort. These adjustments are related to building design in two ways: first the freedom to adjust depends on the availability and ease-of-use of control options; second the use of controls affects building comfort and energy performance. Hence it is essential that these interactions are considered in the design process. The model captures occupant use of controls in response to thermal stimuli (too warm, too cold etc.) and non-thermal stimuli (e.g. desire for fresh air). The situation-specific motivations and constraints on control use are represented through trigger temperatures at which control actions occur, motivations are included as negative constraints and incorporated into a single constraint value describing the specifics of each situation. The values of constraints are quantified for a range of existing buildings in Europe and Pakistan. The integration of the model within a design flow is proposed and the impact of different levels of constraints demonstrated. It is proposed that to minimise energy use and maximise comfort in naturally ventilated and hybrid buildings the designer should take the following steps: 1. Provide unconstrained low energy adaptive control options where possible, 2. Avoid problems with indoor air quality which provide motivations for excessive ventilation rates, 3. Incorporate situation-specific adaptive behaviour of occupants in design simulations, 4. Analyse the robustness of designs against variations in patterns of use and climate, and 5. Incorporate appropriate comfort standards into the operational building controls (e.g. BEMS)