TA Re-examination of Wagner’s Law Based on Disaggregated U.S. State-Local Government Expenditure

We used U.S. state-local data on real government expenditure and personal income over the period 1957-2006 to test the validity of Wagner’s law. Our informal analysis of level data provided prima facie evidence in favor of Wagner’s law. In particular, total expenditure and several of its sub-categories grew at rates (significantly) above the rate of growth of personal income. However, our formal analysis- based on two cointegration techniques- provided consistent evidence suggesting that, with the exception of social services and income maintenance spending to income ratio (ssim), no other spending ratio was part of a cointegrating relationship with real per capita personal income (pcpi) and, thus, error-corrected over time. Moreover, ssim was found to have an income elasticity coefficient consistent with Wagner’s law and part of a (bidirectional) causal relationship with pcpi. Our findings imply that the ability to counter cyclically adjust “public welfare” spending during the current economic downturn may be limited and federal assistance may bring a welcome relief to state and local governments.Wagner’s law; state and local governments; public expenditures; cointegration.

Passive Learning with Target Risk

In this paper we consider learning in passive setting but with a slight modification. We assume that the target expected loss, also referred to as target risk, is provided in advance for learner as prior knowledge. Unlike most studies in the learning theory that only incorporate the prior knowledge into the generalization bounds, we are able to explicitly utilize the target risk in the learning process. Our analysis reveals a surprising result on the sample complexity of learning: by exploiting the target risk in the learning algorithm, we show that when the loss function is both strongly convex and smooth, the sample complexity reduces to \O(\log (\frac{1}{\epsilon})), an exponential improvement compared to the sample complexity \O(\frac{1}{\epsilon}) for learning with strongly convex loss functions. Furthermore, our proof is constructive and is based on a computationally efficient stochastic optimization algorithm for such settings which demonstrate that the proposed algorithm is practically useful

An Evolutionary approach to microstructure optimisation of stereolithographic models.

Abstract- The aim of this work is to utilize an evolutationary algorithm to evolve the microstructure of an object created by a stereolithography machine. This should be optimised to be able to withstand loads applied to it while at the same time minimizing its overall weight. A two part algorithm is proposed which evolves the topology of the structure with a genetic algorithm, while calculating the details of the shape with a separate, deterministic, iterative process derived from standard principles of structural engineering. The division of the method into two separate processes allows both flexibility to changed design parameters without the need for re-evolution, and scalability of the microstructure to manufacture objects of increasing size. The results show that a structure was evolved that was both light and stable. The overall shape of the evolved lattice resembled a honeycomb structure that also satisfied the restrictions imposed by the stereolithography machine.

Approximate Symmetry Analysis of a Class of Perturbed Nonlinear Reaction-Diffusion Equations

In this paper, the problem of approximate symmetries of a class of non-linear reaction-diffusion equations called Kolmogorov-Petrovsky-Piskounov (KPP) equation is comprehensively analyzed. In order to compute the approximate symmetries, we have applied the method which was proposed by Fushchich and Shtelen [8] and fundamentally based on the expansion of the dependent variables in a perturbation series. Particularly, an optimal system of one dimensional subalgebras is constructed and some invariant solutions corresponding to the resulted symmetries are obtained.Comment: 14 page