Spatial and Temporal Sensing Limits of Microtubule Polarization in Neuronal Growth Cones by Intracellular Gradients and Forces

Neuronal growth cones are the most sensitive amongst eukaryotic cells in responding to directional chemical cues. Although a dynamic microtubule cytoskeleton has been shown to be essential for growth cone turning, the precise nature of coupling of the spatial cue with microtubule polarization is less understood. Here we present a computational model of microtubule polarization in a turning neuronal growth cone (GC). We explore the limits of directional cues in modifying the spatial polarization of microtubules by testing the role of microtubule dynamics, gradients of regulators and retrograde forces along filopodia. We analyze the steady state and transition behavior of microtubules on being presented with a directional stimulus. The model makes novel predictions about the minimal angular spread of the chemical signal at the growth cone and the fastest polarization times. A regulatory reaction-diffusion network based on the cyclic phosphorylation-dephosphorylation of a regulator predicts that the receptor signal magnitude can generate the maximal polarization of microtubules and not feedback loops or amplifications in the network. Using both the phenomenological and network models we have demonstrated some of the physical limits within which the MT polarization system works in turning neuron.Comment: 7 figures and supplementary materia

Algorithms for Stochastic Games on Interference Channels

We consider a wireless channel shared by multiple transmitter-receiver pairs. Their transmissions interfere with each other. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power constraint. This scenario is modeled as a stochastic game. We provide sufficient conditions for existence and uniqueness of a Nash equilibrium (NE). We then formulate the problem of finding NE as a variational inequality (VI) problem and present an algorithm to solve the VI using regularization. We also provide distributed algorithms to compute Pareto optimal solutions for the proposed game

Power Allocation Games on Interference Channels with Complete and Partial Information

We consider a wireless channel shared by multiple transmitter-receiver pairs. Their transmissions interfere with each other. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power constraint. This scenario is modeled as a stochastic game under different assumptions. We first assume that each transmitter and receiver has knowledge of all direct and cross link channel gains. We later relax the assumption to the knowledge of incident channel gains and then further relax to the knowledge of the direct link channel gains only. In all the cases, we formulate the problem of finding the Nash equilibrium as a variational inequality (VI) problem and present an algorithm to solve the VI.Comment: arXiv admin note: text overlap with arXiv:1409.755

Frequency-Doubling of Femtosecond Pulses in “Thick” Nonlinear Crystals With Different Temporal and Spatial Walk-Off Parameters

We present a comparative study on frequency-doubling characteristics of femtosecond laser pulses in thick nonlinear crystals with different temporal and spatial walk-off parameters. Using single-pass second harmonic generation (SHG) of 260 fs pulses at 1064 nm from a high-average-power femtosecond Yb-fiber laser in 5-mm-long crystals of β-BaB2O4 (BBO) and BiB3O6 (BIBO), we find that for comparable values of temporal and spatial walk-off parameters in each crystal, the optimum focusing condition for SHG is more strongly influenced by spatial walk-off than temporal walk-off. It is also observed that under such conditions, the Boyd and Kleinman theory commonly used to define the optimum focusing condition for frequency-doubling of cw and long-pulse lasers is also valid for SHG of ultrafast lasers. We also investigate the effect of focusing on the spectral, temporal, and spatial characteristics of the second harmonic (SH) radiation, as well as angular acceptance bandwidth for the SHG process, under different temporal and spatial walk-off conditions in the two crystalsPeer ReviewedPostprint (author's final draft

CONFIGR: A Vision-Based Model for Long-Range Figure Completion

CONFIGR (CONtour FIgure GRound) is a computational model based on principles of biological vision that completes sparse and noisy image figures. Within an integrated vision/recognition system, CONFIGR posits an initial recognition stage which identifies figure pixels from spatially local input information. The resulting, and typically incomplete, figure is fed back to the “early vision” stage for long-range completion via filling-in. The reconstructed image is then re-presented to the recognition system for global functions such as object recognition. In the CONFIGR algorithm, the smallest independent image unit is the visible pixel, whose size defines a computational spatial scale. Once pixel size is fixed, the entire algorithm is fully determined, with no additional parameter choices. Multi-scale simulations illustrate the vision/recognition system. Open-source CONFIGR code is available online, but all examples can be derived analytically, and the design principles applied at each step are transparent. The model balances filling-in as figure against complementary filling-in as ground, which blocks spurious figure completions. Lobe computations occur on a subpixel spatial scale. Originally designed to fill-in missing contours in an incomplete image such as a dashed line, the same CONFIGR system connects and segments sparse dots, and unifies occluded objects from pieces locally identified as figure in the initial recognition stage. The model self-scales its completion distances, filling-in across gaps of any length, where unimpeded, while limiting connections among dense image-figure pixel groups that already have intrinsic form. Long-range image completion promises to play an important role in adaptive processors that reconstruct images from highly compressed video and still camera images.Air Force Office of Scientific Research (F49620-01-1-0423); National Geospatial-Intelligence Agency (NMA 201-01-1-0216); National Science Foundation (SBE-0354378); Office of Naval Research (N000014-01-1-0624

Resource Allocation in a MAC with and without security via Game Theoretic Learning

In this paper a $K$-user fading multiple access channel with and without security constraints is studied. First we consider a F-MAC without the security constraints. Under the assumption of individual CSI of users, we propose the problem of power allocation as a stochastic game when the receiver sends an ACK or a NACK depending on whether it was able to decode the message or not. We have used Multiplicative weight no-regret algorithm to obtain a Coarse Correlated Equilibrium (CCE). Then we consider the case when the users can decode ACK/NACK of each other. In this scenario we provide an algorithm to maximize the weighted sum-utility of all the users and obtain a Pareto optimal point. PP is socially optimal but may be unfair to individual users. Next we consider the case where the users can cooperate with each other so as to disagree with the policy which will be unfair to individual user. We then obtain a Nash bargaining solution, which in addition to being Pareto optimal, is also fair to each user. Next we study a $K$-user fading multiple access wiretap Channel with CSI of Eve available to the users. We use the previous algorithms to obtain a CCE, PP and a NBS. Next we consider the case where each user does not know the CSI of Eve but only its distribution. In that case we use secrecy outage as the criterion for the receiver to send an ACK or a NACK. Here also we use the previous algorithms to obtain a CCE, PP or a NBS. Finally we show that our algorithms can be extended to the case where a user can transmit at different rates. At the end we provide a few examples to compute different solutions and compare them under different CSI scenarios.Comment: 27 pages, 12 figures. Part of the paper was presented in 2016 IEEE Information theory and applicaitons (ITA) Workshop, San Diego, USA in Feb. 2016. Submitted to journa

Krasovskii's Passivity

In this paper we introduce a new notion of passivity which we call Krasovskii's passivity and provide a sufficient condition for a system to be Krasovskii's passive. Based on this condition, we investigate classes of port-Hamiltonian and gradient systems which are Krasovskii's passive. Moreover, we provide a new interconnection based control technique based on Krasovskii's passivity. Our proposed control technique can be used even in the case when it is not clear how to construct the standard passivity based controller, which is demonstrated by examples of a Boost converter and a parallel RLC circuit