Shared Rough and Quasi-Isometries of Groups

We present a variation of quasi-isometry to approach the problem of defining a geometric notion equivalent to commensurability. In short, this variation can be summarized as "quasi-isometry with uniform parameters for a large enough family of generating systems". Two similar notions (using isometries and rough isometries instead, respectively) are presented alongside. This article is based mainly on a chapter of the author's doctoral thesis (\cite{Lochmann_dissertation}).Comment: 16 page

An Analysis of the Transition Zone Between the Various Scaling Regimes in the Small-World Model

We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution equations containing more of the previously neglected (possibly relevant) non-linear terms. As an exact solution of this entangled system of equations is out of question we develop a (as we think, promising) method of enclosing the ``exact'' solutions for the expected quantities by upper and lower bounds, which represent solutions of a slightly simpler system of differential equation. Furthermore we discuss the relation between difference and differential equations and scrutinize the limits of the spreading idea for random graphs. We then show that there exists in fact a ``broad'' (with respect to scaling exponents) crossover zone, smoothly interpolating between linear and logarithmic scaling of the diameter or average distance. We are able to corroborate earlier findings in certain regions of phase or parameter space (as e.g. the finite size scaling ansatz) but find also deviations for other choices of the parameters. Our analysis is supplemented by a variety of numerical calculations, which, among other things, quantify the effect of various approximations being made. With the help of our analytical results we manage to calculate another important network characteristic, the (fractal) dimension, and provide numerical values for the case of the small-world network. Catchwords: Small-World Networks, Non-linear Difference EquationsComment: Latex, 21 pages, 3 figures, identical to journal versio

Construction of direction selectivity in V1: from simple to complex cells

Despite detailed knowledge about the anatomy and physiology of the primary visual cortex (V1), the immense number of feed-forward and recurrent connections onto a given V1 neuron make it difficult to understand how the physiological details relate to a given neuron’s functional properties. Here, we focus on a well-known functional property of many V1 complex cells: phase-invariant direction selectivity (DS). While the energy model explains its construction at the conceptual level, it remains unclear how the mathematical operations described in this model are implemented by cortical circuits. To understand how DS of complex cells is constructed in cortex, we apply a nonlinear modeling framework to extracellular data from macaque V1. We use a modification of spike-triggered covariance (STC) analysis to identify multiple biologically plausible "spatiotemporal features" that either excite or suppress a cell. We demonstrate that these features represent the true inputs to the neuron more accurately, and the resulting nonlinear model compactly describes how these inputs are combined to result in the functional properties of the cell. In a population of 59 neurons, we find that both simple and complex V1 cells are selective to combinations of excitatory and suppressive motion features. Because the strength of DS and simple/complex classification is well predicted by our models, we can use simulations with inputs matching thalamic and simple cells to assess how individual model components contribute to these measures. Our results unify experimental observations regarding the construction of DS from thalamic feed-forward inputs to V1: based on the differences between excitatory and inhibitory inputs, they suggest a connectivity diagram for simple and complex cells that sheds light on the mechanism underlying the DS of cortical cells. More generally, they illustrate how stage-wise nonlinear combination of multiple features gives rise to the processing of more abstract visual information

The Effect of Language Training on Immigrants' Economic Integration - Empirical Evidence from France

We examine the impact of language training on the economic integration of immigrants in France. The assignment to this training, offered by the French Ministry of the Interior, depends mainly on a precise rule: the training is available when the test score of an initial language exam is below a certain threshold. This eligibility rule creates a discontinuity in the relation between the test result and the variables of interest, which is used to estimate the causal effect of this training, through the method of Regression Discontinuity Design. We find that the number of assigned hours of training significantly increases labor force participation of the treated individuals. The language classes appear to have a larger effect for labor migrants and refugees relative to family migrants, for men and individuals below the median age, and for individuals with higher levels of education. Our estimates suggest that the main channel for the improved labor market participation is the information on job search strategies that immigrants derive from the interaction with their classmates and teachers during classes

Potential, Implications and Solutions Regarding the Use of Rendered Animal Fats in Aquafeeds

Problem statement: In the past, aquafeeds were comprised largely of fish meal and fish oil derived from marine reduction fisheries. In addition to being highly palatable and readily digested by cultured fishes, these feedstuffs were historically inexpensive sources of protein, energy and essential nutrients. However, increasing cost and concerns over safety and sustainability have greatly incentivized the transition from fish meal and oil to alternative sources of protein and lipid for aquafeed formulation. Fish oil replacement is proving more difficult than originally anticipated, particularly for marine carnivorous species. Approach: If complete fish oil replacement is not a viable goal for fish nutritionists and aquafeed manufacturers, at a minimum, we must strive for judicious use of limited marine-derived resources. In the present review, we explore the opportunities of using rendered fats as alternatives to marine-derived fish oils in aquaculture feeds, beginning with a discussion of the products themselves before reviewing the most recent literature and concluding with a discussion of the future of these products in aquafeed formulations. Results: Rendered fats have not been as intensively evaluated in aquaculture nutrition as grain and oilseed-derived lipids, although a number of recent publications on the subject suggest increasing interest in the use of rendered products in aquafeeds. Conclusion: Poultry fat, beef tallow, pork lard and to a lesser extent, yellow/restaurant grease and catfish oil, have been investigated individually or in combination with other lipids in feeds for a broad range of cultured taxa with generally acceptable results

Decomposition of optical MIMO systems using polynomial matrix factorization

Within the last years the multiple-input multiple-output (MIMO) technology has revolutionized the optical fiber community. Theoretically, the concept of MIMO is well understood and shows some similarities to wireless MIMO systems. The interference in broadband MIMO systems can be removed by applying a spatio-temporal vector coding (STVC) channel description and using singular value decomposition (SVD) in combination with signal pre- and post-processing. In this contribution a newly developed SVD algorithm for polynomial matrices (PMSVD) is analyzed and compared to the commonly used SVD-based STVC. The PMSVD is implemented by an iterative polynomial matrix eigenvalue decomposition (PEVD) algorithm, namely the second order sequential best rotation algorithm (SBR2). The bit-error rate (BER) performance is evaluated and optimized by applying bit and power allocation schemes. For our simulations, the specific impulse responses of the (2 × 2) MIMO channel, including a 1.4 km multi-mode fiber and optical couplers at both ends, are measured for the operating wavelength of 1576 nm. The computer simulation results show that the PMSVD could be an alternative signal processing approach compared to conventional SVD-based MIMO approaches in frequency-selective MIMO channels