Naive Extension Research Articles

Abstract variational problems with volume constraints

Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.

Optimization-based congestion control for multicast communications

This article outlines an approach for multicast congestion control based on an economic model that has been successfully applied to unicast congestion control. In this model, congestion signals are interpreted as prices and congestion-controlled sessions as utility maximizing agents. A naive extension of the unicast model fails to achieve a reasonable balance between providing the incentives necessary to promote the use of multicast and ensuring that multicast sessions do not interact too aggressively with unicast sessions. We extend the model by introducing a rational definition of multicast utility. The revised model provides a basis for multicast congestion control protocols that provide incentives to use multicast but are necessarily unfair to unicast traffic. We show, however, that the degree of unfairness can be controlled by appropriately setting a design parameter with a limiting case of strict fairness.

Improved bidirectional retrieval of sparse patterns stored by Hebbian learning

The Willshaw model is asymptotically the most efficient neural associative memory (NAM), but its finite version is hampered by high retrieval errors. Iterative retrieval has been proposed in a large number of different models to improve performance in auto-association tasks. In this paper, bidirectional retrieval for the hetero-associative memory task is considered: we define information efficiency as a general performance measure for bidirectional associative memory (BAM) and determine its asymptotic bound for the bidirectional Willshaw model. For the finite Willshaw model, an efficient new bidirectional retrieval strategy is proposed, the appropriate combinatorial model analysis is derived, and implications of the proposed sparse BAM for applications and brain theory are discussed. The distribution of the dendritic sum in the finite Willshaw model given by Buckingham and Willshaw [Buckingham, J., & Willshaw, D. (1992). Performance characteristics of associative nets. Network, 3, 407–414] allows no fast numerical evaluation. We derive a combinatorial formula with a highly reduced evaluation time that is used in the improved error analysis of the basic model and for estimation of the retrieval error in the naive model extension, where bidirectional retrieval is employed in the hetero-associative Willshaw model. The analysis rules out the naive BAM extension as a promising improvement. A new bidirectional retrieval algorithm — called crosswise bidirectional (CB) retrieval — is presented. The cross talk error is significantly reduced without employing more complex learning procedures or dummy augmentation in the pattern coding, as proposed in other refined BAM models [Wang, Y. F., Cruz, J. B., & Mulligan, J. H. (1990). Two coding strategies for bidirectional associative memory. IEEE Trans. Neural Networks, 1(1), 81–92; Leung, C.-S., Chan, L.-W., & Lai, E. (1995). Stability, capacity and statistical dynamics of second-order bidirectional associative memory. IEEE Trans. Syst. Man Cybern., 25(10), 1414–1424]. The improved performance of CB retrieval is shown by a combinatorial analysis of the first step and by simulation experiments: it allows very efficient hetero-associative mapping, as well as auto-associative completion for sparse patterns — the experimentally achieved information efficiency is close to the asymptotic bound. The different retrieval methods in the hetero-associative Willshaw matrix are discussed as Boolean linear optimization problems. The improved BAM model opens interesting new perspectives, for instance, in information retrieval it allows efficient data access providing segmentation of ambiguous user input, relevance feedback and relevance ranking. Finally, we discuss BAM models as functional models for reciprocal cortico–cortical pathways, and the implication of this for a more flexible version of Hebbian cell-assemblies.

Bayesian analysis of censored data

We consider consistency of the posterior in the context of right censored data. We establish posterior consistency when the distribution of the lifetime has a Dirichlet distribution and also investigate the case when the prior is generated through a prior for the distribution of the observable ( Z, Δ). We also show that a naive extension of these methods to interval censored data leads to peculiar estimates.

Existence of long-range order in the steady state of a two-dimensional, two-temperature XY model.

Monte Carlo simulations are used to show that the steady state of the d=2, two-temperature, diffusive XY model displays a continuous phase transition from a homogeneous disordered phase to a phase with long-range order. The long-range order exists although both the dynamics and the interactions are local, thus indicating the failure of a naive extension of the Mermin-Wagner theorem to nonequilibrium steady states. It is argued that the ordering is due to effective dipole interactions generated by the nonequilibrium dynamics.

Observation of the Aharonov-Bohm effect at finite frequency in mesoscopic Ag rings

We have measured the complex magnetoconductance of disordered mesoscopic Ag rings at frequencies from 250 Hz to 1.2 GHz. The data show conductance oscillations of flux period h/ e which persist to our highest measurement frequency with nearly constant average amplitude. From physical considerations and from a naive extension of dc transport theory, an exponential decay of the oscillations is expected at these frequencies. Our results are in conflict with this expectation.

String Order Parameters in the Haldane Gap Phase of the Spin-1/2 Alternating Heisenberg Chain –Numerical Diagonalization and Variational Study–

Two possible extensions of the string order parameter originally defined for the spin-1 Heisenberg chain to the spin-1/2 alternating Heisenberg chain are examined by comparing the numerical diagonalization results of finite size systems and the variational results. It is suggested that the naive extension in which the spin-1 operator is simply replaced by the sum of two spin-1/2 operators can be regarded as the valence bond solid (VBS) order parameter while another extension proposed by Hida corresponds to the measure of the strength of the localized singlet taking the full value for the completely localized singlet state.

Match algorithms for generalized Rete networks

We present a match algorithm which operates correctly on generalized Rete networks that allow arbitrary association of patterns. The original OPS5 Rete algorithm implements matching for left-associative joins; later work generalized this algorithm to support arbitrary join association. However, the naive extension of the OPS5 Rete algorithm to support arbitrary join associations has some subtle flaws (sometimes not all matches are produced with no duplicates) when processing networks having reconvergent (or self-joined) nodes. As a pedagogical means, we first describe an abstract match algorithm for an abstract Rete network having additional edge memories, which provides a useful model for general Rete operations. We then develop two practical specializations of the abstract algorithm, and prove their correctness. The first specialization corresponds to traditional Rete match implementation techniques that are guaranteed to operate correctly for generalized Rete networks. The second specialization is formulated in a general way that allows for delaying match processing at arbitrary stop points within the Rete, with correct match results available on demand at a later time. One current system uses a derivative of this algorithm to support Rete-based matching on demand, complementing the normal match computations done on data-change.

Operator content and modular properties of higher-dimensional conformal field theories

Possible generalizations of the principle of modular invariance to conformal field theories in dimensions d>2 are considered. It is shown that the partition function in a geometry with the topology of S d−1 ×S 1 encodes the operator content of the theory, and that this result implies that the asymptotic behavior of the density of scaling dimensions is determined by the universal coefficient of the Casimir term. These relations are verified for the case of a free massless scalar field, and it shon that, if the field is conformally coupled, the above partition functions enjoy modular properties which generalize those of the case d=2. A naive extension to the continuum limit of the three-dimensional Ising model fails, however.

Color singlet projection in the Nambu-Jona-Lasinio model at finite temperature

We study the baryon number susceptibility in the Nambu-Jona-Lasinio (NJL) model within the mean field approximation. We find that the naive extension of the NJL model to the finite temperature situation cannot reproduce the correct low temperature behavior of the baryon number susceptibility. We propose the color singlet projection in order to remove the colored quark states from the thermodynamic potential. We find that the color singlet projection considerably improves the low temperature behavior of the susceptibility.

Determination of Fusion Rule for E8-Type Conformal Field Theory

We show that the fusion rule for a modular invariant E8-type conformal field theory, which is constructed from the one for the A1(1) Kac-Moody algebra by naive extension, is not associative. Then by imposing further restrictions to this naive fusion rule, we obtain 10 associative fusion rules for the left-right symmetric E8-type conformal field theory. We also discuss the factorization property of the fusion rule into left and right sectors.

Determination of Fusion Rule for E7-Type Conformal Field Theory

We show that the fusion rule for a modular invariant E 7 -type conformal field theory, which is constructed from the one for the A 1 (1) Kac-Moody algebra by naive extension, is not associative. Then by imposing further restrictions to this naive fusion rule, we obtain associative fusion rules for the E 7 -type conformal field theory. Unlike the case of an E 6 -type conformal field theory, these fusion rules cannot be factorized into left and right sectors

Determination of Fusion Rule for E7-Type Conformal Field Theory

We show that the fusion rule for a modular invariant E7-type conformal field theory, which is constructed from the one for the A1(1) Kac-Moody algebra by naive extension, is not associative. Then by imposing further restrictions to this naive fusion rule, we obtain associative fusion rules for the E7-type conformal field theory. Unlike the case of an E6-type conformal field theory, these fusion rules cannot be factorized into left and right sectors.

Determination of fusion rule for E 6-type conformal field theory

We show that the fusion rule for the E 6 model, which is constructed from the one for the A (1) 1 Kač-Moody algebra by naive extension, is not associative. Then by using the associativity as a guiding principle, we obtain two types of fusion rules: one is left-right symmetric and the other asymmetric. The latter contains parameters and can not be factorized into left and right sectors except one special case. A l and D l models are briefly discussed.

Fourth-generation effect on anticharm-charm asymmetry in B0 inclusive decays.

Dunietz and Sachs calculated the CP asymmetry A(c,c\ifmmode\bar\else\textasciimacron\fi{}) between inclusive charmed and anticharmed modes in ${B}^{0}$,B\ifmmode\bar\else\textasciimacron\fi{} $^{0}$ decay in the standard Kobayashi-Masakawa model. We calculate the same asymmetry in the four-generation model by using a naive extension of the Dunietz-Sachs scheme. It is shown that \ensuremath{\Vert}A(c,c\ifmmode\bar\else\textasciimacron\fi{})\ensuremath{\Vert}0.015 for the ${B}_{d}$ meson and \ensuremath{\Vert}A(c,c\ifmmode\bar\else\textasciimacron\fi{})\ensuremath{\Vert}0.017 for the ${B}_{s}$ meson, which are almost the same as in the three-generation model. The reason for this small effect of the fourth generation is investigated. Some comments are also given for the case of the two-Higgs-doublet and left-right-symmetric models.

Polyakov's fermion-boson transmutation in 3+1 dimensions.

It is shown how a naive extension of Polyakov's construction to the (3+1)-dimensional case leads to transmutation between bosonic and fermionic one-dimensional structures.

A remark on K0 of crystallographic groups

F. Quinn recently proved a conjecture of Farrell and Hsiang giving a calculation of the projective class group of the rational group ring of a crystallographic group. This paper contains a counterexample to a naive extension of this conjecture for the integral group ring.

Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river

Rivers are capable of transporting their own bed material without altering their width. However, a naive extension of the threshold theory of canals in coarse alluvium to straight reaches of gravel rivers leads to the stable-channel paradox: transport of bed material is incompatible with a stable width. In this paper singular perturbation techniques are used to obtain a bed stress distribution which allows a mobile bed but immobile banks at bankfull or dominant discharge. This result is used to obtain regime relations for straight rivers with bed and banks composed of coarse gravel.The analysis, although dependent on a series of approximate assumptions for Reynolds-stress closure and sediment transport, provides reasonable agreement with data.