Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms have an on-line complexity of $\mathcal{O}(k^{p+1})$, where $k$ is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once the POD basis dimension $k$ is increased. Numerical experiments are carried out with a two dimensional shallow water equation (SWE) test problem to compare the performance of tensorial POD, standard POD, and POD/Discrete Empirical Interpolation Method (DEIM). Numerical results show that tensorial POD decreases by $76\times$ times the computational cost of the on-line stage of standard POD for configurations using more than $300,000$ model variables. The tensorial POD SWE model was only $2-8\times$ slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM shallow water equation model to compute its off-line stage faster than the standard and tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table

Budgetary Dynamics in The Local Authorities in Israel

This study examines the short-run effects and dynamics of exogenous shocks to the regular budgets of the local authorities in Israel with emphasis on the reduction in government participation and taking into account the heterogeneity of the local authorities. To accomplish this, the study uses a panel of 193 local authorities for the years 1996–2002 and estimates a dynamic model for the components of the regular budget. This makes it possible to examine the dynamics of fiscal adjustment in response to changes in the size of the deficit and in the components of the budget. The changes in revenue from municipal taxes and other independent revenues, expenditure and participation and equalization grants were estimated by means of a Vector Error Correction model. The main findings are as follows: (a) Exogenous changes in the components of the budget, such as a reduction in government grants, affect the level of the per capita deficit in the short run but following that the deficit converges to its original level. (b) A reduction in government grants leads to an immediate cutback in services to residents and increased deficits. (c) The process of adjustment in the non-Jewish local authorities is twice as long as that in the Jewish ones. Therefore, the reduction in grants leads to an increase in deficits for a longer period in non-Jewish local authorities. (d) The process of budgetary adjustment differs among local authorities according to socioeconomic ranking. The weakest local authorities (clusters 1-3) and the strongest local authorities (clusters 8-10) respond to a change in the deficit primarily by reducing labor costs while the development town local authorities cut back their services to residents.local authorities, local government, localities, israel, government, guy, navon

Human Capital Spillovers in the Workplace: Labor Diversity and Productivity

The paper studies the relationship between human capital spillovers and productivity using a unique longitudinal matched employer–employee dataset of Israeli manufacturing plants that contains individual records on all plant employees. I focus on the within-plant diversity of employees’ higher-education diplomas (university degrees). The variance decomposition shows that most knowledge diversity takes place within the industries. Using a semi-parametric approach, the study finds that hiring workers who are diversified in their specific knowledge is beneficial for plants’ productivity—the knowledge-diversity elasticity is about 0.2–0.25 and is robust—and that the benefit of knowledge diversity increase with the size of the plant. This suggests that for each allocation of labor in the production process it is beneficial for plants to diversify their skilled labor. The findings also suggest that the conventional way of estimating plant-level production function using Ordinary Least Squares or Fixed-Effects method is biased upward due to simultaneity of the inputs and the unobserved productivity shock.human capital, spillovers, within, firm, plant, guy, navon, pakes, levinsohn, petrin, poi, olley

Geochemical Consequences of Melt Percolation: The Upper Mantle as a Chromatographic Column

As magmas rise toward the surface, they traverse regions of the mantle and crust with which they are not in equilibrium; to the extent that time and the intimacy of their physical contact permit, the melts and country rocks will interact chemically. We have modeled aspects of these chemical interactions in terms of ion-exchange processes similar to those operating in simple chromatographic columns. The implications for trace element systematics are straightforward: the composition of melt emerging from the top of the column evolves from close to that of the incipient melt of the column matrix toward that of the melt introduced into the base of the column. The rate of evolution is faster in the incompatible than the compatible elements and, as a result, the abundance ratios of elements of different compatibilities can vary considerably with time. If diffusion and other dispersive processes in the melt are negligible and if exchange between melt and solid rock is rapid, extreme fractionations may occur, and the change from initial to final concentration for each element can be through an abrupt concentration front. Integration and mixing of the column output in a magma chamber or dispersive processes within the column, in particular the incomplete equilibration between matrix and fluid due to the slow diffusion in the solid phases, may lead to diffuse fronts and smooth trace element abundance patterns in the column output. If the matrix material is not replenished, the chromatographic process is a transient phenomenon. In some geological situations (e.g., under island arcs and oceanic islands), fresh matrix may be fed continuously into the column, leading to the evolution of a steady state. Aspects of the geochemistry of ultramafic rocks, island arc lavas, and comagmatic alkaline and tholeiitic magmas may be explained by the operation of chromatographic columns

Exploring the Kibble-Zurek mechanism with homogeneous Bose gases

Out-of-equilibrium phenomena is a subject of considerable interest in many fields of physics. Ultracold quantum gases, which are extremely clean, well-isolated and highly controllable systems, offer ideal platforms to investigate this topic. The recent progress in tailoring trapping potentials now allows the experimental production of homogeneous samples in custom geometries, which is a key advance for studies of the emergence of coherence in interacting quantum systems. Here we review recent experiments in which temperature quenches have been performed across the Bose-Einstein condensation (BEC) phase transition in an annular geometry and in homogeneous 3D and quasi-2D gases. Combined, these experiments give a comprehensive picture of the Kibble-Zurek (KZ) scenario through complementary measurements of correlation functions and topological defects density. They also allow the measurement of KZ scaling laws, the direct confirmation of the "freeze-out" hypothesis that underlies the KZ theory, and the extraction of critical exponents of the Bose-Einstein condensation transition.Comment: 11 pages, 6 figures; topical revie

Parameterized Complexity of Critical Node Cuts

We consider the following natural graph cut problem called Critical Node Cut (CNC): Given a graph $G$ on $n$ vertices, and two positive integers $k$ and $x$, determine whether $G$ has a set of $k$ vertices whose removal leaves $G$ with at most $x$ connected pairs of vertices. We analyze this problem in the framework of parameterized complexity. That is, we are interested in whether or not this problem is solvable in $f(\kappa) \cdot n^{O(1)}$ time (i.e., whether or not it is fixed-parameter tractable), for various natural parameters $\kappa$. We consider four such parameters: - The size $k$ of the required cut. - The upper bound $x$ on the number of remaining connected pairs. - The lower bound $y$ on the number of connected pairs to be removed. - The treewidth $w$ of $G$. We determine whether or not CNC is fixed-parameter tractable for each of these parameters. We determine this also for all possible aggregations of these four parameters, apart from $w+k$. Moreover, we also determine whether or not CNC admits a polynomial kernel for all these parameterizations. That is, whether or not there is an algorithm that reduces each instance of CNC in polynomial time to an equivalent instance of size $\kappa^{O(1)}$, where $\kappa$ is the given parameter