A Parallelizable Acceleration Framework for Packing Linear Programs

This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be used as a black box to speed up linear programming solvers dramatically, by two orders of magnitude in our experiments. We present worst-case guarantees on the quality of the solution and the speedup provided by the algorithm, showing that the framework provides an approximately optimal solution while running the original solver on a much smaller problem. The framework can be used to accelerate exact solvers, approximate solvers, and parallel/distributed solvers. Further, it can be used for both linear programs and integer linear programs

Psyche, Signals and Systems

For a century or so, the multidisciplinary nature of neuroscience has left the field fractured into distinct areas of research. In particular, the subjects of consciousness and perception present unique challenges in the attempt to build a unifying understanding bridging between the micro-, meso-, and macro-scales of the brain and psychology. This chapter outlines an integrated view of the neurophysiological systems, psychophysical signals, and theoretical considerations related to consciousness. First, we review the signals that correlate to consciousness during psychophysics experiments. We then review the underlying neural mechanisms giving rise to these signals. Finally, we discuss the computational and theoretical functions of such neural mechanisms, and begin to outline means in which these are related to ongoing theoretical research

Convex Prophet Inequalities

We introduce a new class of prophet inequalities-convex prophet inequalities-where a gambler observes a sequence of convex cost functions ci (xi ) and is required to assign some fraction 0 ≤ x_i ≤ 1 to each, such that the sum of assigned values is exactly 1. The goal of the gambler is to minimize the sum of the costs. We provide an optimal algorithm for this problem, a dynamic program, and show that it can be implemented in polynomial time when the cost functions are polynomial. We also precisely characterize the competitive ratio of the optimal algorithm in the case where the gambler has an outside option and there are polynomial costs, showing that it grows as θ(n^(p-1)/ℓ), where n is the number of stages, p is the degree of the polynomial costs and the coefficients of the cost functions are bounded by [ℓ,u]

Modeling Heat Transfer in the Eye during Cataract Surgery

Cataract surgery is one of the most commonly performed surgical procedures in the world, and it involves using a technique called phacoemulsification. With this technique, the cloudy, crystalline lens in the eye is mechanically disrupted using a probe that vibrates at an ultrasonic frequency. However, this vibrating tip mechanism leads to frictional heat generation, which can potentially cause extensive thermal damage to fragile tissue structures surrounding the lens. In order to minimize damage due to this frictional heat, a coolant is typically used while the phaco probe is in operation. In this report, our goal is to model heat transfer in the eye using COMSOL Multiphysics software in three different scenarios: (1) under normal physiological conditions, (2) considering only the frictional heat generation from the phaco probe, (3) and considering both heat generation as well as heat removal by the coolant. Using a 2-D axisymmetric geometry to model the eye structure, we determined that using the heat source by itself results in temperatures far above the threshold of 328 K for thermal wound injury. However, with the addition of the coolant for heat removal, temperatures in the iris were lowered to less than 320 K, thereby reducing any thermal burn risk to the patient. Further analysis demonstrated that decreasing the coolant temperature or decreasing the probe?s operational power can significantly improve the safety of the procedure

Spike-timing control by dendritic plateau potentials in the presence of synaptic barrages

Apical and tuft dendrites of pyramidal neurons support regenerative electrical potentials, giving rise to long-lasting (approximately hundreds of milliseconds) and strong (~50 mV from rest) depolarizations. Such plateau events rely on clustered glutamatergic input, can be mediated by calcium or by NMDA currents, and often generate somatic depolarizations that last for the time course of the dendritic plateau event. We address the computational significance of such single-neuron processing via reduced but biophysically realistic modeling. We introduce a model based on two discrete integration zones, a somatic and a dendritic one, that communicate from the dendritic to the somatic compartment via a long plateau-conductance. We show principled differences in the way dendritic vs. somatic inhibition controls spike timing, and demonstrate how this could implement a mechanism of spike time control in the face of barrages of synaptic inputs

The Physiology and Computation of Pyramidal Neurons

A variety of neural signals have been measured as correlates to consciousness. In particular, late current sinks in layer 1, distributed activity across the cortex, and feedback processing have all been implicated. What are the physiological underpinnings of these signals? What computational role do they play in the brain? Why do they correlate to consciousness? This thesis begins to answer these questions by focusing on the pyramidal neuron. As the primary communicator of long-range feedforward and feedback signals in the cortex, the pyramidal neuron is set up to play an important role in establishing distributed representations. Additionally, the dendritic extent, reaching layer 1, is well situated to receive feedback inputs and contribute to current sinks in the upper layers. An investigation of pyramidal neuron physiology is therefore necessary to understand how the brain creates, and potentially uses, the neural correlates of consciousness. An important part of this thesis will be in establishing the computational role that dendritic physiology plays. In order to do this, a combined experimental and modeling approach is used. This thesis beings with single-cell experiments in layer 5 and layer 2/3 pyramidal neurons. In both cases, dendritic nonlinearities are characterized and found to be integral regulators of neural output. Particular attention is paid to calcium spikes and NMDA spikes, which both exist in the apical dendrites, considerable distances from the spike initiation zone. These experiments are then used to create detailed multicompartmental models. These models are used to test hypothesis regarding spatial distribution of membrane channels, to quantify the effects of certain experimental manipulations, and to establish the computational properties of the single cell. We find that the pyramidal neuron physiology can carry out a coincidence detection mechanism. Further abstraction of these models reveals potential mechanisms for spike time control, frequency modulation, and tuning. Finally, a set of experiments are carried out to establish the effect of long-range feedback inputs onto the pyramidal neuron. A final discussion then explores a potential way in which the physiology of pyramidal neurons can establish distributed representations, and contribute to consciousness.</p

Distributed Optimization via Local Computation Algorithms

We propose a new approach for distributed optimization based on an emerging area of theoretical computer science -- local computation algorithms. The approach is fundamentally different from existing methodologies and provides a number of benefits, such as robustness to link failure and adaptivity in dynamic settings. Specifically, we develop an algorithm, LOCO, that given a convex optimization problem P with n variables and a "sparse" linear constraint matrix with m constraints, provably finds a solution as good as that of the best online algorithm for P using only O(log(n+m)) messages with high probability. The approach is not iterative and communication is restricted to a localized neighborhood. In addition to analytic results, we show numerically that the performance improvements over classical approaches for distributed optimization are significant, e.g., it uses orders of magnitude less communication than ADMM