Social Enterprise and Public Procurement Opportunities

These slides are from our 2016 national conference, A Nation That Works: What's It Going to Take? Many social enterprises earn revenue through contracts with state and local governments. Those contracts can be very competitive, and governments' selection processes typically don't account for the ways in which hiring social enterprises can produce additional public benefits. This session will explore the policy opportunities to position social enterprises as qualified competitive bidders for public procurement and contracts and offer two successful models of working with State and local government. Attendees will also learn about the future of California's SB 1219 Employment Social Enterprise, the first statewide piece of legislation certifying social enterprise and granting public procurement and contract preferences similar to those of small business and disabled veteran business enterprises. SB1219 passed the California state Senate and Assembly without opposition, and is currently awaiting the Governor's signature

Survival of a Diffusing Particle in a Transverse Shear Flow: A First-Passage Problem with Continuously Varying Persistence Exponent

We consider a particle diffusing in the y-direction, dy/dt=\eta(t), subject to a transverse shear flow in the x-direction, dx/dt=f(y), where x \ge 0 and x=0 is an absorbing boundary. We treat the class of models defined by f(y) = \pm v_{\pm}(\pm y)^\alpha where the upper (lower) sign refers to y>0 (y<0). We show that the particle survives with probability Q(t) \sim t^{-\theta} with \theta = 1/4, independent of \alpha, if v_{+}=v_{-}. If v_{+} \ne v_{-}, however, we show that \theta depends on both \alpha and the ratio v_{+}/v_{-}, and we determine this dependence.Comment: 4 page

The role of landscape and history on the genetic structure of peripheral populations of the Near Eastern fire salamander, Salamandra infraimmaculata, in Northern Israel

Genetic studies on core versus peripheral populations have yielded many patterns. This diversity in genetic patterns may reflect diversity in the meaning of peripheral populations as defined by geography, gene flow patterns, historical effects, and ecological conditions. Populations at the lower latitude periphery of a species' range are of particular concern because they may be at increased risk for extinction due to global climate change. In this work we aim to understand the impact of landscape and ecological factors on different geographical types of peripheral populations with respect to levels of genetic diversity and patterns of local population differentiation. We examined three geographical types of peripheral populations of the endangered salamander, Salamandra infraimmaculata, in Northern Israel, in the southernmost periphery of the genus Salamandra, by analyzing the variability in 15 microsatellite loci from 32 sites. Our results showed that: (1) genetic diversity decreases towards the geographical periphery of the species' range; (2) genetic diversity in geographically disjunct peripheral areas is low compared to the core or peripheral populations that are contiguous to the core and most likely affected by a founder effect; (3) ecologically marginal conditions enhance population subdivision. The patterns we found lead to the conclusion that genetic diversity is influenced by a combination of geographical, historical, and ecological factors. These complex patterns should be addressed when prioritizing areas for conservation.Peer reviewe

Series Expansion Calculation of Persistence Exponents

We consider an arbitrary Gaussian Stationary Process X(T) with known correlator C(T), sampled at discrete times T_n = n \Delta T. The probability that (n+1) consecutive values of X have the same sign decays as P_n \sim \exp(-\theta_D T_n). We calculate the discrete persistence exponent \theta_D as a series expansion in the correlator C(\Delta T) up to 14th order, and extrapolate to \Delta T = 0 using constrained Pad\'e approximants to obtain the continuum persistence exponent \theta. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.Comment: 5 pages; 5 page appendix containing series coefficient

Nontrivial Exponent for Simple Diffusion

The diffusion equation \partial_t\phi = \nabla^2\phi is considered, with initial condition \phi( _x_ ,0) a gaussian random variable with zero mean. Using a simple approximate theory we show that the probability p_n(t_1,t_2) that \phi( _x_ ,t) [for a given space point _x_ ] changes sign n times between t_1 and t_2 has the asymptotic form p_n(t_1,t_2) \sim [\ln(t_2/t_1)]^n(t_1/t_2)^{-\theta}. The exponent \theta has predicted values 0.1203, 0.1862, 0.2358 in dimensions d=1,2,3, in remarkably good agreement with simulation results.Comment: Minor typos corrected, affecting table of exponents. 4 pages, REVTEX, 1 eps figure. Uses epsf.sty and multicol.st

Inelastic collapse of a randomly forced particle

We consider a randomly forced particle moving in a finite region, which rebounds inelastically with coefficient of restitution r on collision with the boundaries. We show that there is a transition at a critical value of r, r_c\equiv e^{-\pi/\sqrt{3}}, above which the dynamics is ergodic but beneath which the particle undergoes inelastic collapse, coming to rest after an infinite number of collisions in a finite time. The value of r_c is argued to be independent of the size of the region or the presence of a viscous damping term in the equation of motion.Comment: 4 pages, REVTEX, 2 EPS figures, uses multicol.sty and epsf.st

Spatial Persistence of Fluctuating Interfaces

We show that the probability, P_0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P_0(l) \sim l^(-\theta). Here \theta is a `spatial' persistence exponent, and takes different values, \theta_s or \theta_0, depending on how the point from which l is measured is specified. While \theta_s is related to fractional Brownian motion, and can be determined exactly, \theta_0 is non-trivial even for Gaussian interfaces.Comment: 5 pages, new material adde

Persistence with Partial Survival

We introduce a parameter $p$, called partial survival, in the persistence of stochastic processes and show that for smooth processes the persistence exponent $\theta(p)$ changes continuously with $p$, $\theta(0)$ being the usual persistence exponent. We compute $\theta(p)$ exactly for a one-dimensional deterministic coarsening model, and approximately for the diffusion equation. Finally we develop an exact, systematic series expansion for $\theta(p)$, in powers of $\epsilon=1-p$, for a general Gaussian process with finite density of zero crossings.Comment: 5 pages, 2 figures, references added, to appear in Phys.Rev.Let

Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes

We consider the problem of `discrete-time persistence', which deals with the zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no crossing) probability decays as exp(-\theta_D T) = [\rho(a)]^n for large n, where a = \exp[-(\Delta T)/2], and the discrete persistence exponent, \theta_D, is given by \theta_D = \ln(\rho)/2\ln(a). Using the `Independent Interval Approximation', we show how \theta_D varies with (\Delta T) for small (\Delta T) and conclude that experimental measurements of persistence for smooth processes, such as diffusion, are less sensitive to the effects of discrete sampling than measurements of a randomly accelerated particle or random walker. We extend the matrix method developed by us previously [Phys. Rev. E 64, 015151(R) (2001)] to determine \rho(a) for a two-dimensional random walk and the one-dimensional random acceleration problem. We also consider `alternating persistence', which corresponds to a < 0, and calculate \rho(a) for this case.Comment: 14 pages plus 8 figure