Abstract: The typical fraction of the space of interactions between each pair of N Ising spins which solve the problem of storing a given set of p random patterns as N-bit spin configurations is considered. The volume is calculated explicitly as a function of the storage ratio, alpha =p/N, of the value kappa (>0) of the product of the spin and the magnetic field at each site and of the magnetisation, m. Here m may vary between 0 (no correlation) and 1 (completely correlated). The capacity increases with the correlation between patterns from alpha =2 for correlated patterns with kappa =0 and tends to infinity as m tends to 1. The calculations use a saddle-point method and the order parameters at the saddle point are assumed to be replica symmetric. This solution is shown to be locally stable. A local iterative learning algorithm for updating the interactions is given which will converge to a solution of given kappa provided such solutions exist.

Abstract: Laboratory studies of consumer demand theory require assumptions regarding the definition of price in the absence of a medium of exchange (money). In this study we test the proposition that the fundamental dimension of price is a cost-benefit ratio expressed as the effort expended per unit of food value consumed. Using rats as subjects, we tested the generality of this "unit price" concept by varying four dimensions of price: fixed-ratio schedule, number of food pellets per fixed-ratio completion, probability of reinforcement, and response lever weight or effort. Two levels of the last three factors were combined in a 2 x 2 x 2 design giving eight groups. Each group was studied under a series of six FR schedules. Using the nominal values of all factors to determine unit price, we found that grams of food consumed plotted as a function of unit price followed a single demand curve. Similarly, total work output (responses x effort) conformed to a single function when plotted in terms of unit price. These observations provided a template for interpreting the effects of biological factors, such as brain lesions or drugs, that might alter the cost-benefit ratio.

Abstract: An important optimization problem that arises in control is to minimize $\varphi ( x )$, the largest eigenvalue (in magnitude) of a symmetric matrix function of x. If the matrix function is affine,...

Abstract: WHEN DISTINCT OUTPUTS OF AN ADAPTIVE SYSTEM HAVE EQUIVALENT EFFECTS ON THE ENVIRONMENT, THE PROBLEM OF FINDING APPROPRIATE ACTIONS GIVEN DESIRED RESULTS IS ILL-POSED. FOR SUPERVISED LEARNING ALGORITHMS, THE ILL-POSEDNESS OF SUCH "INVERSE LEARNING PROBLEMS" IMPLIES A CERTAIN FLEXIBILITY---DURING TRAINING, THERE ARE IN GENERAL MANY POSSIBLE TARGET VECTORS CORRESPONDING TO EACH INPUT VECTOR. TO ALLOW SUPERVISED LEARNING ALGORITHMS TO MAKE USE OF THIS FLEXIBILITY, THE CURRENT PAPER CONSIDERS HOW TO SPECIFY TARGETS BY SETS OF CONSTRAINTS, RATHER THAN AS PARTICULAR VECTORS. TWO CLASSES OF CONSTRAINTS ARE DISTINGUISHED---`CONFIGURATIONAL'' CONSTRAINTS, WHICH DEFINE REGIONS OF OUTPUT SPACE IN WHICH AN OUTPUT VECTOR MUST LIE, AND `TEMPORAL'' CONSTRAINTS, WHICH DEFINE RELATIONSHIPS BETWEEN OUTPUTS PRODUCED AT DIFFER- ENT POINTS IN TIME. LEARNING ALGORITHMS MINIMIZE A COST FUNCTION THAT CON- TAINS TERMS FOR BOTH KINDS OF CONSTRAINTS. THIS APPROACH TO INVERSE LEARN- ING IS ILLUSTRATED BY A ROBOTICS APPLICATION IN WHICH A NETWORK FINDS TRA- JECTORIES OF INVERSE KINEMATIC SOLUTIONS FOR MANIPULATORS WITH EXCESS DEGREES OF FREEDOM.

Abstract: We introduce a two‐point cluster function C2(r1,r2) which reflects information about clustering in general continuum–percolation models. Specifically, for any two‐phase disordered medium, C2(r1,r2) gives the probability of finding both points r1 and r2 in the same cluster of one of the phases. For distributions of identical inclusions whose coordiantes are fully specified by center‐of‐mass positions (e.g., disks, spheres, oriented squares, cubes, ellipses, or ellipsoids, etc.), we obtain a series representation of C2 which enables one to compute the two‐point cluster function. Some general asymptotic properties of C2 for such models are discussed. The two‐point cluster function is then computed for the adhesive‐sphere model of Baxter. The two‐point cluster function for arbitrary media provides a better signature of the microstructure than does a commonly employed two‐point correlation function defined in the text.

Abstract: Let be a positive definite binary quadratic form with real coefficients and discriminant b2 − 4ac = −1.Among such forms, let . The Epstein zeta function of f is denned to beRankin [7], Cassels [1], Ennola [5], and Diananda [4] between them proved that for every real s > 0,We prove a corresponding result for theta functions. For real α > 0, letThis function satisfies the functional equation(This may be proved by using the formula (4) below, and then twice applying the identity (8).)

Abstract: Contents: General Qualitative Dynamics of Some Nonlinear Systems. Choice of a Recursive Core Equation. A Recursive Loop System Using . A Subjective Weber Function and Output Uncertainty. A Generic Dynamic Mapping of Environment onto . Further Variants on Mapping of Inputs. Cascading of the Loop. Elementary Identification of Variants and Parameters. Matching Data Patterns and Theory Patterns. Metric or Nonmetric Scaling: Properties of Outputs. Analogues of SDT and Isocriterion Plots. Range and Transposition Effects. Mixing and Attenuation. R sum .

Abstract: Automating proofs of properties of functions defined on inductively constructed data structures is important in many computer science and artificial intelligence applications, in particular in program verification and specification systems. A new induction principle based on a constructor model of a data structure is developed. This principle along with a given function definition as a set of equations is used to construct automatically an induction scheme suitable for proving inductive properties of the function. The proposed induction principle thus gives different induction schema for different function definitions, just as Boyer and Moore's prover does. A novel feature of this approach is that it can also be used for proving properties by induction for data structures such as integers, finite sets, whose values cannot be freely constructed, i.e., constructors for such data structures are related to each other. This method has been implemented in RRL, a rewrite-rule based theorem prover. More than a hundred theorems in number theory including the unique prime factorization theorem, have been proved using the method.

Abstract: 4 = c2u, f(u, x)7 (1.1) is studied, where f is of bistable type for each x. Here “bistable” means that f vanishes for exactly three values of U, and fU is negative at the two outer ones; the prototype is f = u u3. When f is independent of x, the equation has a dynamical theory which is pretty well understood. Its most striking feature in that-case is the existence of travelling wave solutions, which are globally stable. This is also true for the heterogeneous equation (1. l), although such travelling wave solutions have up to now only been studied by formal asymptotics. They are not travelling waves in the strictest sense, but are rather frontal structures (confined to thin zones of width O(E)) which move with variable velocity. Starting with smooth arbitrary initial data Us which do not depend on E, the formation of these fronts at certain locations can be predicted, and their approximate subsequent motion can be determined by solving an ordinary differential equation. This heuristic analysis is explained in Section 2. The purpose of this paper is to provide the heuristics with a rigorous footing. In fact, we obtain detailed estimates for the error made by approximating the exact solution by the function constructed in Section 2. For simplicity, we treat the case when there is only a single front, although multiple fronts may clearly occur. The process under consideration consists of two parts, proceeding under two different time scales: which are the initial generation of a layer, followed by its propagation. The analysis describing the first part is the more involved. (If comparison functions based on the ordinary differential equation in Section 2 are used, the analysis simplifies, but weaker results are obtained.)

Abstract: The binding energy, lateral and vertical extension, dimensionality, and lifetime of excitons in quantum wells are calculated as a function of well width. A novel variational approach including an elliptically symmetric wave function, finite barriers, and different masses in the well and the barrier is used. Thus, for the first time the geometrical anisotropy and the anisotropy of the physical properties of the quantum well are fully considered. Numerical results are presented for ${\mathrm{Al}}_{0.40}$${\mathrm{Ga}}_{0.60}$As/GaAs and ${\mathrm{In}}_{0.53}$${\mathrm{Ga}}_{0.47}$As/InP.

Abstract: We make use of a recently developed diagrammatic theory to calculate correlation functions for interacting fermions of Hubbard-type models in terms of the Gutzwiller wave function. Of the eleven nontrivial correlation functions involving the spin, density, empty and doubly occupied sites, and local Cooper pairs, four are shown to be independent. They are expressed as a power series in a suitably chosen correlation parameter, whose terms are represented diagrammatically. In one dimension these terms may be evaluated to arbitrary order by employing symmetry relations. This allows for an analytic, approximation-free calculation of the correlation functions for arbitrary momentum, particle density, and interaction strength. In the atomic limit the momentum-dependent spin-correlation function shows an antiferromagnetic divergence at half filling in all dimensions. In one dimension the behavior is in very good agreement with all exact analytic and numerical results for the antiferromagnetic Heisenberg chain. Hole-hole correlations also compare very well with exact results. However, correlations between holes and doubly occupied sites appear insufficient. Superconducting correlations involving on-site, singlet Cooper pairs are suppressed. The results allow for an analytic evaluation of the ground-state energy of a large class of extended Hubbard models in terms of the Gutzwiller wave function. Thus they provide exact upper bounds for their ground-state energies.

Abstract: A portable radio apparatus includes a receiving section capable of being tuned to one of a plurality of channels, a switch circuit for controlling the supply of power from a battery to the receiving section, a detector circuit for detecting the strength of an electric field which is developed on a channel, and a control section connected to the receiving section and the switch circuit whereby, in response to an output from the detector circuit, the control section scans the channels for tuning the receiving section sequentially to the channels while, at the same time, controlling the switch circuit to feed power continuously to the receiving section and, in the absence of data on a channel within a first predetermined period of time during the channel scanning, executes a saving scan ning step for repeating a cycle in which the channels are sequentially scanned once prior to interrupting the scanning for a second predetermined period of time while controlling the switch circuit to feed power to the receiving section in synchronism with the saving scanning step.

Abstract: This paper is the second in a two-part series which studies the efficiency of several algorithms for solving the problem of multicomponent mass transport with equilibrium chemical reactions. In particular, the relative efficiency of competing algorithms is evaluated as a function of the nature of the chemistry. The first, formulation A, introduces the total soluble concentration of each component as the primary dependent variable. The second, with variants B and C, introduces the total component concentration, aqueous plus all solid forms, as the primary dependent variable. Finite element discretization in space and a single-step, implicit time marching scheme reduces the problem to a set of nonlinear algebraic equations in each time step. Several versions of Newton-Raphson iteration and Picard iteration are evaluated for the basic formulations by studying a set of single- and three-component problems. The specific cases studied are each designed in order to emphasize a particular aspect of the equilibrium chemical reactions. Results indicate that overall, a modified Newton-Raphson iteration is the most efficient solution strategy for the range of problems considered.

Abstract: The exact Hausdorff dimension function is determined for sets in Rm constructed by using a recursion that is governed by some given law of randomness.

Abstract: A software package based on a modification of the Weeks' method is presented for calculating function values f(t) of the inverse Laplace transform This method requires transform values F(z) at arbitrary points in the complex plane, and is suitable when f(t) has continuous derivatives of all orders; it is especially attractive when f(t) is required at a number of different abscissas t

Abstract: A system and method is disclosed for generating a synthetic netlist which mimics the size and complexity of a specified target circuit. The first step of synthetic netlist generation is to generate an abstract of the netlist of a known circuit of the same type as the specified target circuit. Information in the abstract specifies the relative usage rates of the circuit elements in the known circuit and the complexity of the interconnections between circuit elements and circuit signals. The second step is to generate a synthetic netlist, scaled to include a specified number of circuit elements. The circuit elements in the synthetic netlist are interconnected in a sequential process so as to have the interconnection complexity specified by the abstract of the known circuit. While the circuit represented by the resulting synthetic netlist would not perform any useful circuit function, the layout of the synthetic netlist will accurately represent the size and interconnection complexity of the specified target circuit. The synthetic netlist generated by the present invention is suitable for use with a silicon complier so as to generate a circuit layout representative of the specified target circuit.

Abstract: How well can a polytope with n vertices approximate the unit ball Bd of the d-dimensional Euclidean space? The answer is quite well known when d is fixed and n tends to infinity. In this paper the same question is answered when n is a function of d (a polynomial in d, say) and d tends to infinity. Some applications of the results are also indicated.

Abstract: We show that the throughput of a single-class closed queueing network CQN of Jackson type, as a function of the job population, is nondecreasing concave [respectively, convex, anti-starshaped, starshaped, subadditive or superadditive] if the service rate at each node, as a function of the local queue length, has the same property. The key to the proofs is the concept of “equilibrium rate.” For a discrete positive random variable Y the equilibrium rate is defined as a function: r0 = 0, rn = P[Y = n-1]/P[Y = n], n ≥ 1. It turns out that the equilibrium rate rn is nondecreasing in n if and only if the pmf of Y is a Polya frequency function of order two; and it is known that the said property hence, the nondecreasing property of equilibrium rates is preserved under convolution. Here, we represent the CQN throughput function as the equilibrium rate of a sum of independent random variables, each corresponding to a node in the network, with the service rate of the node as its equilibrium rate. The second order properties of the CQN throughput are then established by proving that the second-order properties of equilibrium rates are also preserved under convolution.

Abstract: The authors present a multilayer feedforward network, called the Gaussian potential function network (GPFN), performing association or classification based on a set of potentially fields synthesized over the domain of input space by a number of Gaussian potential function units (GPFUs). A GPFU as a basic component of the GPFN is designed to generate a Gaussian form of a potential field. A weighted summation of Gaussian potential fields generated by a suitable number of GPFUs provides an arbitrary shape of a potential field over the domain of input space. The authors also present a detailed learning algorithm for the GPFN. Learning consists of the determination of the minimally necessary number of GPFUs and the adjustment of the locations and shapes of the individual Gaussian potential fields defined by GPFUs as well as the summation weights. The learning of the minimally necessary number of GPFUs is based on the control of the effective radius of GPFUs, while the parameter learning is based on the gradient descent procedure. >

Abstract: Disclosed is a method of locking the functions of a mobile telephone system. At least two lock codes are stored in a memory together with the functions to be kept locked or actuated when the locked state of the mobile system is released. The locked state of the automobile is not released unless a registered lock code is input. When the locked state is released by inputting one of the registered lock codes, some functions remain in the locked state in accordance with the input lock code, while other functions are actuated. Thus it is possible to limit the use of the mobile telephone system depending upon who drives the car.

Abstract: SUMMARY Estimators are proposed of the underlying distribution function of independent bivariate random vectors which are subject to random right censorship in each coordinate. The estimators satisfy the monotonicity requirements of a distribution function, are uniformly strongly consistent at a rate equal to that of the empirical distribution function and are fairly simple to compute.

Abstract: Stochastic linear programs require the evaluation of an integral in which the integrand is itself the value of a linear program. This integration is often approximated by discrete distributions that bound the integral from above or below. A difficulty with previous upper bounds is that they generally require a number of function evaluations that grows exponentially in the number of variables. We give a new upper bound that requires operations that only grow polynomially in the number of random variables. We show that this bound is sharp if the function is linear and give computational results to illustrate its performance.