Exogenous and Endogenous Spatial Growth Models

In this paper, we investigate the impact on aggregate regional utility as a result of both exogenous growth and endogenous growth in a spatial system. We will first analyze the case of two closed regions, followed by the case of two open regions. The main instrument used in our approach to study the changes in collective regional welfare is Dynamic Programming. The traditional exogenous Solow growth model forms the basis of our paper. The analysis of this model will be extended to a comparison of two closed regions with exogenous growth. By introducing a case of a common labour market, we are able to investigate exogenous growth between two open regions. For the analysis of endogenous growth, we adopt the same structure as the one used for the investigation of exogenous growth models. In this framework, an investment in knowledge is considered as the endogenous driving force. Finally, we take a closer look at the timing of cost-reducing investments. In total, seven related but distinct cases are identified and studied in more detail

Inverse Scattering and Acousto-Optic Imaging

We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes use of the principle of interior control of boundary measurements by an external wave field.Comment: 10 page

Phase Space Models for Stochastic Nonlinear Parabolic Waves: Wave Spread and Singularity

We derive several kinetic equations to model the large scale, low Fresnel number behavior of the nonlinear Schrodinger (NLS) equation with a rapidly fluctuating random potential. There are three types of kinetic equations the longitudinal, the transverse and the longitudinal with friction. For these nonlinear kinetic equations we address two problems: the rate of dispersion and the singularity formation. For the problem of dispersion, we show that the kinetic equations of the longitudinal type produce the cubic-in-time law, that the transverse type produce the quadratic-in-time law and that the one with friction produces the linear-in-time law for the variance prior to any singularity. For the problem of singularity, we show that the singularity and blow-up conditions in the transverse case remain the same as those for the homogeneous NLS equation with critical or supercritical self-focusing nonlinearity, but they have changed in the longitudinal case and in the frictional case due to the evolution of the Hamiltonian

The Cop Number of the One-Cop-Moves Game on Planar Graphs

Cops and robbers is a vertex-pursuit game played on graphs. In the classical cops-and-robbers game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph's edges with perfect information about each other's positions. If a cop eventually occupies the same vertex as the robber, then the cops win; the robber wins if she can indefinitely evade capture. Aigner and Frommer established that in every connected planar graph, three cops are sufficient to capture a single robber. In this paper, we consider a recently studied variant of the cops-and-robbers game, alternately called the one-active-cop game, one-cop-moves game or the lazy-cops-and-robbers game, where at most one cop can move during any round. We show that Aigner and Frommer's result does not generalise to this game variant by constructing a connected planar graph on which a robber can indefinitely evade three cops in the one-cop-moves game. This answers a question recently raised by Sullivan, Townsend and Werzanski.Comment: 32 page

Core and penumbra estimation using deep learning-based AIF in association with clinical measures in computed tomography perfusion

Objectives: To investigate whether utilizing a convolutional neural network (CNN)-based arterial input function (AIF) improves the volumetric estimation of core and penumbra in association with clinical measures in stroke patients. Methods: The study included 160 acute ischemic stroke patients (male = 87, female = 73, median age = 73 years) with approval from the institutional review board. The patients had undergone CTP imaging, NIHSS and ASPECTS grading. convolutional neural network (CNN) model was trained to fit a raw AIF curve to a gamma variate function. CNN AIF was utilized to estimate the core and penumbra volumes which were further validated with clinical scores. Results: Penumbra estimated by CNN AIF correlated positively with the NIHSS score (r = 0.69; p  20) and lower ASPECT score ( 10 s, Tmax > 10 s volumes were statistically significantly higher (p < .05). Conclusions: With inclusion of the CNN AIF in perfusion imaging pipeline, penumbra and core estimations are more reliable as they correlate with scores representing neurological deficits in stroke. Critical relevance statement: With CNN AIF perfusion imaging pipeline, penumbra and core estimations are more reliable as they correlate with scores representing neurological deficits in stroke

Kinetic Limit for Wave Propagation in a Random Medium

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order epsilon^(1/2). The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit epsilon to 0 the disorder averaged Wigner function on the kinetic scale, time and space of order epsilon^(-1), is governed by a linear Boltzmann equation.Comment: 71 pages, 3 figure