Search results for "generalization"
showing 10 items of 250 documents
Exact affine counter automata
2017
We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las Vegas affine finite automata. Lastly, we show that how a counter helps for affine finite automata by showing that the language MANYTWINS, which is conjectured not to be recognized by affin…
Surrogate outcomes and transportability
2019
Identification of causal effects is one of the most fundamental tasks of causal inference. We consider an identifiability problem where some experimental and observational data are available but neither data alone is sufficient for the identification of the causal effect of interest. Instead of the outcome of interest, surrogate outcomes are measured in the experiments. This problem is a generalization of identifiability using surrogate experiments and we label it as surrogate outcome identifiability. We show that the concept of transportability provides a sufficient criteria for determining surrogate outcome identifiability for a large class of queries.
The General Routing Problem polyhedron: Facets from the RPP and GTSP polyhedra
1998
[EN] In this paper we study the polyhedron associated with the General Routing Problem (GRP). This problem, first introduced by Orloff in 1974, is a generalization of both the Rural Postman Problem (RPP) and the Graphical Traveling Salesman Problem (GTSP) and, thus, is NP -hard. We describe a formulation of the problem such that from every non-trivial facet-inducing inequality for the RPP and GTSP polyhedra, we obtain facet-inducing inequalities for the GRP polyhedron, We describe a new family of facet-inducing inequalities for the GRP, the honeycomb constraints, which seem to be very useful for solving GRP and RPP instances. Finally, new classes of facets obtained by composition of facet-i…
Using the Hermite Regression Formula to Design a Neural Architecture with Automatic Learning of the “Hidden” Activation Functions
2000
The value of the output function gradient of a neural network, calculated in the training points, plays an essential role for its generalization capability. In this paper a feed forward neural architecture (αNet) that can learn the activation function of its hidden units during the training phase is presented. The automatic learning is obtained through the joint use of the Hermite regression formula and the CGD optimization algorithm with the Powell restart conditions. This technique leads to a smooth output function of αNet in the nearby of the training points, achieving an improvement of the generalization capability and the flexibility of the neural architecture. Experimental results, ob…
Eigenfunction expansions for time dependent hamiltonians
2008
We describe a generalization of Floquet theory for non periodic time dependent Hamiltonians. It allows to express the time evolution in terms of an expansion in eigenfunctions of a generalized quasienergy operator. We discuss a conjecture on the extension of the adiabatic theorem to this type of systems, which gives a procedure for the physical preparation of Floquet states. *** DIRECT SUPPORT *** A3418380 00004
Efficient finite-difference scheme for solving some heat transfer problems with convection in multilayer media
2000
Abstract An efficient finite-difference method for solving the heat transfer equation with piecewise discontinuous coefficients in a multilayer domain is developed. The method may be considered as a generalization of the finite-volumes method for the layered systems. We apply this method with the aim to reduce the 3D or 2D problem to the corresponding series of 2D or 1D problems. In the case of constant piecewise coefficients, we obtain the exact discrete approximation of the steady-state 1D boundary-value problem.
Heat and mass flows coupled with stress in a continuous medium
1996
Abstract The present paper is concerned with the formulation of the generalization of theories describing heat and mass flows in a continuous medium. The considerations are based on the non-equilibrium thermodynamics. As a result the fundamental equations for the mass and heat fluxes and for the thermodynamic and mechanical fields, are obtained and the corresponding set of differential equations is formulated. Certain differences are pointed out between the general theories presented here and the thermodiffusion theory and the theory of mixtures. A thermodynamic variational principle is constructed. All the investigations concern only flows with a single temperature field. Copyright © 1996 …
Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics
2006
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type.
Functional principal component analysis for multivariate multidimensional environmental data
2015
Data with spatio-temporal structure can arise in many contexts, therefore a considerable interest in modelling these data has been generated, but the complexity of spatio-temporal models, together with the size of the dataset, results in a challenging task. The modelization is even more complex in presence of multivariate data. Since some modelling problems are more natural to think through in functional terms, even if only a finite number of observations is available, treating the data as functional can be useful (Berrendero et al. in Comput Stat Data Anal 55:2619–2634, 2011). Although in Ramsay and Silverman (Functional data analysis, 2nd edn. Springer, New York, 2005) the case of multiva…
A Widrow–Hoff Learning Rule for a Generalization of the Linear Auto-associator
1996
Abstract A generalization of the linear auto-associator that allows for differential importance and nonindependence of both the stimuli and the units has been described previously by Abdi (1988). This model was shown to implement the general linear model of multivariate statistics. In this note, a proof is given that the Widrow–Hoff learning rule can be similarly generalized and that the weight matrix will converge to a generalized pseudo-inverse when the learning parameter is properly chosen. The value of the learning parameter is shown to be dependent only upon the (generalized) eigenvalues of the weight matrix and not upon the eigenvectors themselves. This proof provides a unified framew…