Time-Shared Execution of Realtime Computer Vision Pipelines by Dynamic Partial Reconfiguration

This paper presents an FPGA runtime framework that demonstrates the feasibility of using dynamic partial reconfiguration (DPR) for time-sharing an FPGA by multiple realtime computer vision pipelines. The presented time-sharing runtime framework manages an FPGA fabric that can be round-robin time-shared by different pipelines at the time scale of individual frames. In this new use-case, the challenge is to achieve useful performance despite high reconfiguration time. The paper describes the basic runtime support as well as four optimizations necessary to achieve realtime performance given the limitations of DPR on today's FPGAs. The paper provides a characterization of a working runtime framework prototype on a Xilinx ZC706 development board. The paper also reports the performance of realtime computer vision pipelines when time-shared

Evolution equations of p-Laplace type with absorption or source terms and measure data

Let $\Omega$ be a bounded domain of $\mathbb{R}^{N}$, and $Q=\Omega \times(0,T).$ We consider problems\textit{ }of the type % \left\{ \begin{array} [c]{l}% {u_{t}}-{\Delta_{p}}u\pm\mathcal{G}(u)=\mu\qquad\text{in }Q,\\ {u}=0\qquad\text{on }\partial\Omega\times(0,T),\\ u(0)=u_{0}\qquad\text{in }\Omega, \end{array} \right. where ${\Delta_{p}}$ is the $p$-Laplacian, $\mu$ is a bounded Radon measure, $u_{0}\in L^{1}(\Omega),$ and $\pm\mathcal{G}(u)$ is an absorption or a source term$.$ In the model case $\mathcal{G}(u)=\pm\left\vert u\right\vert ^{q-1}u$ $(q>p-1),$ or $\mathcal{G}$ has an exponential type. We prove the existence of renormalized solutions for any measure $\mu$ in the subcritical case, and give sufficient conditions for existence in the general case, when $\mu$ is good in time and satisfies suitable capacitary conditions.Comment: arXiv admin note: substantial text overlap with arXiv:1310.525

Initial trace of solutions of Hamilton-Jacobi parabolic equation with absorption

Here we study the initial trace problem for the nonnegative solutions of the equation $$u\_{t}-\Delta u+|\nabla u|^{q}=0$$ in $Q\_{\Omega,T}=\Omega\times\left( 0,T\right) ,$ $T\leqq\infty,$ where $q>0,$ and $\Omega=\mathbb{R}^{N},$ or $\Omega$ is a smooth bounded domain of $\mathbb{R}^{N}$ and $u=0$ on $\partial\Omega\times\left( 0,T\right) .$ We can define the trace at $t=0$ as a nonnegative Borel measure $(\mathcal{S} ,u\_{0}),$ where $S$ is the closed set where it is infinite, and $u\_{0}$ is a Radon measure on $\Omega\backslash\mathcal{S}.$ We show that the trace is a Radon measure when $q\leqq1.$ For $q\in(1,(N+2)/(N+1)$ and any given Borel measure, we show the existence of a minimal solution, and a maximal one on conditions on $u\_{0}.$ When $\mathcal{S}$ $=\overline{\omega}\cap\Omega$ and $\omega$ is an open subset of $\Omega,$ the existence extends to any $q\leqq2$ when $u\_{0}\in L\_{loc}^{1}(\Omega)$ and any $q>1$ when $u\_{0}=0$. In particular there exists a self-similar nonradial solution with trace $(\mathbb{R}^{N+},0),$ with a growth rate of order $\left\vert x\right\vert ^{q^{\prime}}$ as $\left\vert x\right\vert \rightarrow\infty$ for fixed $t.$ Moreover we show that the solutions with trace $(\overline{\omega},0)$ in $Q\_{\mathbb{R}^{N},T}$ may present near $t=0$ a growth rate of order $t^{-1/(q-1)}$ in $\omega$ and of order $t^{-(2-q)/(q-1)}$ on $\partial \omega.

Pointwise estimates and existence of solutions of porous medium and pp-Laplace evolution equations with absorption and measure data

Let $\Omega$ be a bounded domain of $\mathbb{R}^{N}(N\geq 2)$. We obtain a necessary and a sufficient condition, expressed in terms of capacities, for existence of a solution to the porous medium equation with absorption \begin{equation*} \left\{ \begin{array}{l} {u_{t}}-{\Delta }(|u|^{m-1}u)+|u|^{q-1}u=\mu ~ \text{in }\Omega \times (0,T), \\ {u}=0~~~\text{on }\partial \Omega \times (0,T), \\ u(0)=\sigma , \end{array} \right. \end{equation*} where $\sigma$ and $\mu$ are bounded Radon measures, $q>\max (m,1)$, $m>\frac{N-2}{N}$. We also obtain a sufficient condition for existence of a solution to the $p$-Laplace evolution equation \begin{equation*} \left\{ \begin{array}{l} {u_{t}}-{\Delta _{p}}u+|u|^{q-1}u=\mu ~~\text{in }\Omega \times (0,T), \\ {u}=0 ~ \text{on }\partial \Omega \times (0,T), \\ u(0)=\sigma . \end{array} \right. \end{equation*} where $q>p-1$ and $p>2$

Stability properties for quasilinear parabolic equations with measure data

Let $\Omega$ be a bounded domain of $\mathbb{R}^{N}$, and $Q=\Omega \times(0,T).$ We study problems of the model type \left\{ \begin{array} [c]{l}% {u_{t}}-{\Delta_{p}}u=\mu\qquad\text{in }Q,\\ {u}=0\qquad\text{on }\partial\Omega\times(0,T),\\ u(0)=u_{0}\qquad\text{in }\Omega, \end{array} \right. where $p>1$, $\mu\in\mathcal{M}_{b}(Q)$ and $u_{0}\in L^{1}(\Omega).$ Our main result is a \textit{stability theorem }extending the results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case, valid for quasilinear operators $u\longmapsto\mathcal{A}(u)=$div$(A(x,t,\nabla u))$\textit{. }Comment: arXiv admin note: substantial text overlap with arXiv:1310.525

Quasilinear Lane-Emden equations with absorption and measure data

We study the existence of solutions to the equation -\Gd_pu+g(x,u)=\mu when $g(x,.)$ is a nondecreasing function and \gm a measure. We characterize the good measures, i.e. the ones for which the problem as a renormalized solution. We study particularly the cases where g(x,u)=\abs x^{\beta}\abs u^{q-1}u and g(x,u)=\abs x^{\tau}\rm{sgn}(u)(e^{\tau\abs u^\lambda}-1). The results state that a measure is good if it is absolutely continuous with respect to an appropriate Lorentz-Bessel capacities.Comment: 28 page

Custodial Parental Perceptions and Experiences of Noncustodial Parents and Child Support

Child support is a means to financially support children, yet fewer than half of children eligible for child support receive full payment, with many receiving none. Child support nonpayment is a national concern that has led to negative repercussions for non-intact families, the community, and economic system. In some cases, noncustodial parents have an inability to pay. The purpose of this descriptive, phenomenological study was to understand custodial parental perceptions and experiences of noncustodial parent\u27s inability to pay their child support. Social learning theory served as the conceptual framework for the study. In-depth interviews were conducted with a sample of 10 custodial parents ranging in age from 18 to 45 who had an active child support case enforced by a Domestic Relations Office in the northeastern United States but were not receiving payments due to the noncustodial parent\u27s inability to pay. Audiotaped interviews were manually transcribed and coded for themes using a typology organization structure. Coding was based on key terms, word repetitions, and metaphors. Member checking and audit trails were used to establish the trustworthiness of the data. The findings revealed that many custodial parents did not trust that the noncustodial parent was being truthful in their claims of having a true inability to pay. Other custodial parents believed that the noncustodial parent could make more attempts to try to assist the custodial parent in the absence of financial support. The findings of this study may contribute to social change by advancing knowledge and policies within the child support system. Likewise, findings may assist caseworkers and clinicians in better understanding their client\u27s experiences and challenges resulting in a better client service experience

Wavelet-based density estimation for noise reduction in plasma simulations using particles

For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a finite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Most importantly, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets that involve different levels of collisionality and interaction with external and self-consistent fields