Philadelphia's Workforce Development Challenge: Serving Employers, Helping Jobseekers and Fixing the System

Over the last four years, half a billion dollars in public funds were spent in Philadelphia in the name of workforce development -- helping residents get jobs or skills and employers find workers to sustain or expand their businesses.These services, which include training for workers and recruiting for employers, were funded largely by federal and state dollars at an annual cost that ranged from $118 million to$134 million. All of these services were free of charge to workers; most were free to employers. Had these efforts been part of city government last year, and they were not, they would have constituted its fifth biggest department, surpassed only by police, fire, prisons, and human services. Roughly 1 in 10 workingage Philadelphians have sought help at a workforce development center on an annual basis. Behind this system have been two nonprofit organizations, the Philadelphia Workforce Development Corporation, which allocates most of the money, and the Philadelphia Workforce Investment Board Inc., which sets general strategy. Both are led by city appointees and are accountable to state funding agencies. For years, the performance of the two organizations received little attention from local elected officials, and their complicated division of roles sometimes led to confusion and impasses. In recent years, unpublicized state audits have found isolated problems with their financial controls.That structure is now being changed, and a new strategy is being implemented. The development corporation and most functions of the investment board are to be combined under a single agency, Philadelphia Works Inc., which will formally take over by June 2012. This report examines the workforce development system's performance, operations and challenges over the past several years -- hard economic times in which increasing numbers of Philadelphians were looking for work. It is based on extensive interviews, a review of internal audits and reports, and a statistical comparison of the system's performance with that of similar, federally mandated programs in other region

Energy statistics in disordered systems: The local REM conjecture and beyond

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. Here we give necessary conditions for this hypothesis to be true, which we show to hold in wide classes of examples: short range spin glasses and mean field spin glasses of the SK type. We also show that, under certain conditions, the conjecture holds even if energy levels that grow moderately with the volume of the system are considered. In the case of the Generalised Random energy model, we give a complete analysis for the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture holds exactly up to energies E_N<\b_c N, where \b_c is the critical temperature. We also explain the more complex behaviour that sets in at higher energies.Comment: to appear in Proceedings of Applications of random matrices to economics and other complex system

A Kohn-Sham system at zero temperature

An one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor {nano}structures and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schr\"odinger operator with effective Kohn-Sham potential and obtain $W^{1,2}$-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow to apply Schauder's fixed point theorem. In case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.Comment: 27 page

An optimal stopping problem in a diffusion-type model with delay

We present an explicit solution to an optimal stopping problem in a model described by a stochastic delay differential equation with an exponential delay measure. The method of proof is based on reducing the initial problem to a free-boundary problem and solving the latter by means of the smooth-fit condition. The problem can be interpreted as pricing special perpetual average American put options in a diffusion-type model with delay.Optimal stopping, stochastic delay differential equation, diffusion process, sufficient statistic, free-boundary problem, smooth fit, Girsanov’s theorem, Ito’s formula

Sensitivities for Bermudan Options by Regression Methods

In this article we propose several pathwise and finite difference based methods for calculating sensitivities of Bermudan options using regression methods and Monte Carlo simulation. These methods rely on conditional probabilistic representations which allow, in combination with a regression approach, for efficient simultaneous computation of sensitivities at many initial positions. Assuming that the price of a Bermudan option can be evaluated sufficiently accurate, we develop a method for constructing deltas based on least squares. We finally propose a testing procedure for assessing the performance of the developed methods.American and Bermudan options, Optimal stopping times, Monte Carlo simulation, Deltas, Conditional probabilistic representations, Regression methods

Metastability and small eigenvalues in Markov chains

In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.Comment: 5pp, AMSTe

Remarks on the operator-norm convergence of the Trotter product formula

We revise the operator-norm convergence of the Trotter product formula for a pair {A,B} of generators of semigroups on a Banach space. Operator-norm convergence holds true if the dominating operator A generates a holomorphic contraction semigroup and B is a A-infinitesimally small generator of a contraction semigroup, in particular, if B is a bounded operator. Inspired by studies of evolution semigroups it is shown in the present paper that the operator-norm convergence generally fails even for bounded operators B if A is not a holomorphic generator. Moreover, it is shown that operator norm convergence of the Trotter product formula can be arbitrary slow.Comment: 12 page

Classical solutions of drift-diffusion equations for semiconductor devices: the 2d case

We regard drift-diffusion equations for semiconductor devices in Lebesgue spaces. To that end we reformulate the (generalized) van Roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of electrons and holes. This evolution equation falls into a class of quasi-linear parabolic systems which allow unique, local in time solution in certain Lebesgue spaces. In particular, it turns out that the divergence of the electron and hole current is an integrable function. Hence, Gauss' theorem applies, and gives the foundation for space discretization of the equations by means of finite volume schemes. Moreover, the strong differentiability of the electron and hole density in time is constitutive for the implicit time discretization scheme. Finite volume discretization of space, and implicit time discretization are accepted custom in engineering and scientific computing.--This investigation puts special emphasis on non-smooth spatial domains, mixed boundary conditions, and heterogeneous material compositions, as required in electronic device simulation

Adaptive Smoothing of Digital Images: The R Package adimpro

Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used non-adaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here we present a new package adimpro for R, which implements the propagationseparation approach by (Polzehl and Spokoiny 2006) for smoothing digital images. This method naturally adapts to different structures of different size in the image and thus avoids oversmoothing edges and fine structures. We extend the method for imaging data with spatial correlation. Furthermore we show how the estimation of the dependence between variance and mean value can be included. We illustrate the use of the package through some examples.

Regression methods in pricing American and Bermudan options using consumption processes

Here we develop methods for e±cient pricing multidimensional discrete-time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying the sample space with payoffs at the optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach admits constructing both low and upper bounds for the price by Monte Carlo simulations. The methods are illustrated by pricing Bermudan swaptions and snowballs in the Libor market model.American and Bermudan options, Low and Upper bounds, Monte Carlo simulations, Consumption process, Regression methods, Optimal stopping times