Abstract: This paper describes the correlations between inequality and the growth rates in cross-country data. Using non-parametric methods, we show that the growth rate is an inverted U-shaped function of net changes in inequality: changes in inequality (in any direction) are associated with reduced growth in the next period. The estimated relationship is robust to variations in control variables and estimation methods. This inverted U-curve is consistent with a simple political economy model but it could also reflect the nature of measurement errors, and, in general, efforts to interpret this evidence causally run into difficult identification problems. We show that this non-linearity is sufficient to explain why previous estimates of the relationship between the level of inequality and growth are so different from one another.

Abstract: The power function is treated as the law relating response time to practice trials. However, the evidence for a power law is flawed, because it is based on averaged data. We report a survey that assessed the form of the practice function for individual learners and learning conditions in paradigms that have shaped theories of skill acquisition. We fit power and exponential functions to 40 sets of data representing 7,910 learning series from 475 subjects in 24 experiments. The exponential function fit better than the power function in all the unaveraged data sets. Averaging produced a bias in favor of the power function. A new practice function based on the exponential, the APEX function, fit better than a power function with an extra, preexperimental practice parameter. Clearly, the best candidate for the law of practice is the exponential or APEX function, not the generally accepted power function. The theoretical implications are discussed.

Abstract: In this paper, we develop a thermodynamic approach for modeling a class of viscoelastic fluids based on the notion of an `evolving natural configuration'. The material has a family of elastic (or non-dissipative) responses governed by a stored energy function that is parametrized by the `natural configurations'. Changes in the current natural configuration result in dissipative behavior that is determined by a rate of dissipation function. Specifically, we assume that the material possesses an infinity of possible natural (or stress-free) configurations. The way in which the current natural configuration changes is determined by a `maximum rate of dissipation' criterion subject to the constraint that the difference between the stress power and the rate of change of the stored energy is equal to the rate of dissipation. By choosing different forms for the stored energy function ψ and the rate of dissipation function ξ, a whole plethora of energetically consistent rate type models can be developed. We show that the choice of a neo-Hookean type stored energy function and a rate of dissipation function that is quadratic, leads to a Maxwell-like fluid response. By using this procedure with a different choice for the rate of dissipation, we also derive a model that is similar to the Oldroyd-B model. We also discuss several limiting cases, including the limit of small elastic strains, but arbitrarily large total strains, which leads to the classical upper convected Maxwell model as well as the Oldroyd-B model.

Abstract: We present calculations for the nonbonded interactions in the dimeric complexes: methane dimer, ammonia dimer, water dimer, H2O·(NH3), CH4·(NH3), and (FHF)- as a function of theory level (HF, DFT(B3LYP), MP2, LMP2, MP3, MP4, CCSD(T), and others) and basis set (6-31G**, cc-pVXZ, X = D, T, Q, 5). Dimer minimum energy structures are determined at the MP2 theory level for the cc-pVTZ basis set employing analytical second derivatives. For HF and DFT levels of theory, methane dimer and one structure of CH4·(NH3) are not bound. The basis set superposition error (BSSE) begins to converge (becomes systematically small) for basis sets larger than cc-pVTZ. For hydrogen-bonded systems, most levels of theory seem to give reasonable estimates of the experimentally known binding energies, but here, too, the BSSE overwhelms the reliability of the binding energies for the smaller basis sets. The CH4·(NH3) dimer has two minimum energy conformations with similar binding energies, but very different BSSE values especially f...

Abstract: Motivated by questions about secure multi-party computation, we introduce and study a new natural representation of functions by polynomials, which we term randomizing polynomials. "Standard" low-degree polynomials over a finite field are easy to compute with a small number of communication rounds in virtually any setting for secure computation. However, most Boolean functions cannot be evaluated by a polynomial whose degree is smaller than their input size. We get around this barrier by relaxing the requirement of evaluating f into a weaker requirement of randomizing f: mapping the inputs of f along with independent random inputs into a vector of outputs, whose distribution depends only on the value of f. We show that degree-3 polynomials are sufficient to randomize any function f, relating the efficiency of such a randomization to the branching program size of f. On the other hand, by characterizing the exact class of Boolean functions which can be randomized by degree-2 polynomials, we show that 3 is the minimal randomization degree of most functions. As an application, randomizing polynomials provide a powerful, general, and conceptually simple tool for the design of round-efficient secure protocols. Specifically, the secure evaluation of any function can be reduced to a secure evaluation of degree-3 polynomials. One corollary of this reduction is that two (respectively, three) communication rounds are sufficient for k parties to compute any Boolean function f of their inputs, with perfect information-theoretic [k-1/3]-privacy (resp., [k-1/2]-privacy), and communication complexity which is at most quadratic in the branching program size of f (with a small probability of one-sided error).

Abstract: Let $X$ be the interior of a compact manifold $\overline X$ of dimension $n+1$ with boundary $M=\partial X$, and $g_+$ be a conformally compact metric on $X$, namely $\overline g\equiv r^2g_+$ extends continuously (or with some degree of smoothness) as a metric to $X$, where $r$ denotes a defining function for $M$, i.e. $r>0$ on $X$ and $r=0$, $dr e 0$ on $M$. The restrction of $\overline g$ to $TM$ rescales upon changing $r$, so defines invariantly a conformal class of metrics on $M$, which is called the conformal infinity of $g_+$. In the present paper, the author considers conformally compact metrics satisfying the Einstein condition Ric$(g_+)=-ng_+$, which are called conformally compact Einstein metrics on $X$, and their extensions to $X$ together with the restrictions of $\overline g$ to the boundary $M=\partial X$. First, the author notes that a representative metric $g$ on $M$ for the conformal infinity of a conformally compact Einstein metric

Abstract: The first example of a simultaneous inductive-recursive definition in intuitionistic type theory is Martin-Lofs universe a la Tarski. A set U0 of codes for small sets is generated inductively at the same time as a function T0, which maps a code to the corresponding small set, is defined by recursion on the way the elements of U0 are generated.In this paper we argue that there is an underlying general notion of simultaneous inductive-recursive definition which is implicit in Martin-Lof's intuitionistic type theory. We extend previously given schematic formulations of inductive definitions in type theory to encompass a general notion of simultaneous induction-recursion. This enables us to give a unified treatment of several interesting constructions including various universe constructions by Palmgren, Griffor, Rathjen, and Setzer and a constructive version of Aczel's Frege structures. Consistency of a restricted version of the extension is shown by constructing a realisability model in the style of Allen.

Abstract: We consider the problem of estimating parameters of a model described by an equation of special form. Specific models arise in the analysis of a wide class of computer vision problems, including conic fitting and estimation of the fundamental matrix. We assume that noisy data are accompanied by (known) covariance matrices characterizing the uncertainty of the measurements. A cost function is first obtained by considering a maximum-likelihood formulation and applying certain necessary approximations that render the problem tractable. A Newton-like iterative scheme is then generated for determining a minimizer of the cost function. Unlike alternative approaches such as Sampson's method or the renormalization technique, the new scheme has as its theoretical limit the minimizer of the cost function. Furthermore, the scheme is simply expressed, efficient, and unsurpassed as a general technique in our testing. An important feature of the method is that it can serve as a basis for conducting theoretical comparison of various estimation approaches.

Abstract: Linear projections for dimensionality reduction, computed using linear discriminant analysis (LDA), are commonly based on optimization of certain separability criteria in the output space. The resulting optimization problem is linear, but these separability criteria are not directly related to the classification accuracy in the output space. Consequently, a trial and error procedure has to be invoked, experimenting with different separability criteria that differ in the weighting function used and selecting the one that performed best on the training set. Often, even the best weighting function among the trial choices results in poor classification of data in the subspace. In this short paper, we introduce the concept of fractional dimensionality and develop an incremental procedure, called the fractional-step LDA (F-LDA) to reduce the dimensionality in fractional steps. The F-LDA algorithm is more robust to the selection of weighting function and for any given weighting function, it finds a subspace in which the classification accuracy is higher than that obtained using LDA.

Abstract: Motivated by questions about secure multi-party computation, we introduce and study a new natural representation offunctions by polynomials, which we term randomizing polynomials. “Standard” low-degree polynomials over ajnitejeldare easy to compute witha small numberof communication rounds in virtually any setting for secure computation. Howevel; most Boolean functions cannot be evaluated by a polynomial whose degree is smaller than their input size. We get around this barrier by relaxing the requirement of evaluating f into a weaker requirement of randomizing f: mapping the inputs off along with independent random inputs into a vector of outputs, whose distribution depends only on the value off. We show that degree-3 polynomials are sufficient to randomize any function f, relating the efficiency of such a randomization to the branching program size of f. On the other hand, by characterizing the exact class of Boolean functions which can be randomized by degree-2 polynomials, we show that 3 is the minimal randomization degree of most functions. As an application, randomizing polynomials provide a powerjiul, general, and conceptually simple tool for the design of round-efficient secure protocols. Specifically, the secure evaluation of any function can be reduced to a secure evaluation of degree-3 polynomials. One corollary of this reduction is that two (respectively, three) communication rounds are sufficient for k parties to compute any Boolean function f of their inputs, with perfect information-theoretic ly J -privacy (resp., [YJ -privacy), and communication complexity which is at most quadratic in the branchingpmgram size off (with a small probability of one-sided error).

Abstract: The results of an optimization of a folding potential are reported The complete energy function is modeled as a sum of pairwise interactions with a flexible functional form The relevant distance between two amino acids (2 − 9 A) is divided into 13 intervals, and the energy of each interval is optimized independently We show, in accord with a previous publication (Tobi et al, Proteins 2000;40:71–85) that it is impossible to find a pair potential with the above flexible form that recognizes all native folds Nevertheless, a potential that rates correctly a subset of the decoy structures was constructed and optimized The resulting potential is compared with a distance-dependent statistical potential of Bahar and Jernigan It is further tested against decoy structures that were created in the Levitt's group On average, the new potential places native shapes lower in energy and provides higher Z scores than other potentials Proteins 2000;41:40–46 © 2000 Wiley-Liss, Inc

Abstract: We suggest a candidate one-way function using combinatorial constructs such as expander graphs. These graphs are used to determine a sequence of small overlapping subsets of input bits, to which a hard-wired random predicate is applied. Thus, the function is extremely easy to evaluate: All that is needed is to take multiple projections of the input bits, and to use these as entries to a look-up table. It is feasible for the adversary to scan the look-up table, but we believe it would be infeasible to find an input that fits a given sequence of values obtained for these overlapping projections. The conjectured difficulty of inverting the suggested function does not seem to follow from any well-known assumption. Instead, we propose the study of the complexity of inverting this function as an interesting open problem, with the hope that further research will provide evidence to our belief that the inversion task is intractable.

Abstract: In terms of the Hadmard product (or convolution), define the operator by , where the function f is analytic in the unit disk. The classes of k-uniformly convex and k-starlike functions , denoted by , respectively, were introduced recently (cf.[3] and [5]). The object of the present paper is to find conditions on the papameters a,b,c, and k, for which the linear operator maps the classes of starlike and univalent functions onto .

Abstract: Different approach to both Gautschi’s inequalities (1) and (2) is given. This results in obtaining the best upper bound in (1) and the best lower bound in (2). The main result is the proof of the convexity of the function [Γ(x+t)/Γ(x+s)]1/(t−s) for |t−s| < 1 . Several new very simple inequalities for digamma function, like ψ ′(x) < exp(−ψ(x)) or ψ(x + 1) < log(x + e−γ ) are also proved. Mathematics subject classification (1991): 33B15, 26D07.

Abstract: This paper presents the first combinatorial polynomial-time algorithm for minimizing submodular set functions, answering an open question posed in 1981 by Grotschel, Lovasz, and Schrijver. The algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter. The resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the largest length of the function value. The paper also presents a strongly polynomial-time version that runs in time bounded by a polynomial in the size of the underlying set independent of the function value.

Abstract: In this research, artificial neural networks were employed to model corn yield. The overall objective was to test two hypotheses, i.e.: (1) That an artificial neural network (ANN) can be trained to approximate the nonlinear function relating corn yield to the factors that influence yield, and (2) That an ANN trained for one field can be retrained for a different field with a much sparser data set. The specific research objectives were: (1) To train an ANN using corn yield and input factor data from the Morrow Plots, (2) To evaluate the performance of the trained ANN, and (3) To retrain the ANN using data from the Dudley Smith Farm. First, the factors affected corn yields were analyzed. The corn yield was expressed as function of soil factors, weather factors, and management factors. 15 influencing factors were fed into input layer of the neural network. The neural network structure was designed with 15 input factors, one output, corn yield, and one hidden layer with 20 nodes. The network topology and parameters were set by trial and error. The Morrow Plots data was used to train the neural network. The data set was divided to training set and test set. After training with 5,000 epochs, the test set was used to verify this network. The RMS error was about 20%. Then, the network performance was evaluated in four aspects: for prediction yield trend with each influencing factor, the network gave realistic prediction trend with each factor; for interaction between nitrogen fertilizer and late July rainfall, the network captured the interaction between the two factors; for the influencing factors combination searching to get maximized yield using genetic algorithm, the network predicted a yield 75% larger than the maximum observed yield in the training set; for the influencing factors sensitivity analyzing, the calculated yields were most sensitive to the corn growing season rainfall, especially late July rain, then nitrogen fertilizer. The network was retrained with the Dudley Smith Farm data. The network topology was changed accordingly. The verification of the retraining model, the RMS error, was about 17%. Several training and retraining strategies were discussed.

Abstract: We show that any global nonnegative and bounded solution to the degenerate parabolic problemut-Δum+f(u)=0 qquad {\rm on} quad Ώ⊂ RN,u|{∂Ώ}=0converges to a single stationary state as time goes to infinity. Here m>0, f is a restriction of a real analytic function defined on a sector containing the half-line [0, ∞), and f(u1/m) is a continuously differentiable function of u.

Abstract: We define a system of ‘dynamical’ differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the ‘dual’ variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions.

Abstract: Recent developments in the econometric estimation of multi-output, multi-input distance functions have provided a promising new solution to the single-output restriction implicit in the standard production function. However, a suspicion that regressor endogeneity may introduce possible simultaneous equations bias has concerned some econometricians. In this paper we show that, under profit maximising behaviour, distance functions face no greater danger from such bias than their production function cousins. Furthermore, we prove that ordinary least squares (OLS) provides consistent estimates of an input distance function under an assumption of cost minimising behaviour. We also prove that OLS provides consistent estimates of an output distance function under an assumption of revenue maximising behaviour. These results are established for the Cobb-Douglas and translog functional forms, which are the two most commonly used functional forms in applied analyses. Our results provide strong support for the direct estimation of distance functions, and indicate that the instrumental variables (IV) methods, proposed by some authors, may not be required in many cases.

Abstract: We present some nonlinear characterizations of the automorphisms of the operator algebra $B(H)$ and the function algebra $C(X)$ by means of their spectrum preserving properties.

Abstract: We critique a Pad\'e analytic continuation method whereby a rational polynomial function is fit to a set of input points by means of a single matrix inversion. This procedure is accomplished to an extremely high accuracy using a symbolic computation algorithm. As an example of this method in action, it is applied to the problem of determining the spectral function of a single-particle thermal Green's function known only at a finite number of Matsubara frequencies with two example self energies drawn from the T-matrix theory of the Hubbard model. We present a systematic analysis of the effects of error in the input points on the analytic continuation, and this leads us to propose a procedure to test quantitatively the reliability of the resulting continuation, thus eliminating the black-magic label frequently attached to this procedure.

Abstract: This paper presents a sliding-mode controller for a class of nonlinear discrete-time systems. The proposed controller uses a modified switching function that produces a low-chattering control signal. In order to improve the controller performance, an adaptive term is added to the original sliding-mode algorithm. This new feature uses an artificial neural network for online identification of the modeling error. Simulations and experimental results illustrate the main characteristics and performance of this approach,.

Abstract: We consider the El Farol bar problem, also known as the minority game (W. B. Arthur, The American Economic Review, 84 (1994) 406; D. Challet and Y. C. Zhang, Physica A, 256 (1998) 514). We view it as an instance of the general problem of how to configure the nodal elements of a distributed dynamical system so that they do not work at cross purposes, in that their collective dynamics avoids frustration and thereby achieves a provided global goal. We summarize a mathematical theory for such configuration applicable when (as in the bar problem) the global goal can be expressed as minimizing a global energy function and the nodes can be expressed as minimizers of local free energy functions. We show that a system designed with that theory performs nearly optimally for the bar problem.

Abstract: We give sufficient conditions for translates and modulates of a function g in L^2(R) to be a frame for its closed linear span. Even in the case where this family spans all of L^2(R), wou conditions are significantly weaker than the previous known conditions.

Abstract: Let A be the class of analytic functions in the open unit disk U. Given 0 ≤ λ < 1, let Ωλ be the operator defined on A by (ωλf)(z)=Γ(2-λ)zλDλzf(z) , where Dλzf is the fractional derivative of f of order λ. A function f in A is said to be in the class SPλ if Ωλf is a parabolic starlike function. In this paper, several basic properties and characteristics of the class SPλ are investigated. These include subordination, inclusion, and growth theorems, class-preserving operators, Fekete-Szegő problems, and sharp estimates for the first few coefficients of the inverse function.

Abstract: A method for configuring a telecommunications system including a plurality of entities communicating data via a plurality of transport channels. The entities inlclude at least one sending entity and receiving entity. The communication includes a plurality of processing procedures specific to the plurality of transport channels. Each processing procedure includes a rate matching step including a transformation of an input block of an initial size into an output block of a final size by puncturing and/or repetition. The method includes transmitting a parameter representative of a maximum puncture rate. The method also includes calculating by the sending entity, for each processing procedure, the final size of the output block as a function of the initial size of the input block based on the parameter transmitted. Some input block bits are punctured or repeated based on a variation between a final size and an initial size in the rate matching step.

Abstract: The Landau Zener method allows to measure very small tunnel splittings \Delta in molecular clusters Fe_8. The observed oscillations of \Delta as a function of the magnetic field applied along the hard anisotropy axis are explained in terms of topological quantum interference of two tunnel paths of opposite windings. Studies of the temperature dependence of the Landau Zener transition rate P gives access to the topological quantum interference between exited spin levels. The influence of nuclear spins is demonstrated by comparing P of the standard Fe_8 sample with two isotopically substituted samples. The need of a generalized Landau Zener transition rate theory is shown.