Interpreting Social Accounting Matrix (SAM) as an Information Channel

Information theory, and the concept of information channel, allows us to calculate the mutual information between the source (input) and the receiver (output), both represented by probability distributions over their possible states. In this paper, we use the theory behind the information channel to provide an enhanced interpretation to a Social Accounting Matrix (SAM), a square matrix whose columns and rows present the expenditure and receipt accounts of economic actors. Under our interpretation, the SAM’s coefficients, which, conceptually, can be viewed as a Markov chain, can be interpreted as an information channel, allowing us to optimize the desired level of aggregation within the SAM. In addition, the developed information measures can describe accurately the evolution of a SAM over time. Interpreting the SAM matrix as an ergodic chain could show the effect of a shock on the economy after several periods or economic cycles. Under our new framework, finding the power limit of the matrix allows one to check (and confirm) whether the matrix is well-constructed (irreducible and aperiodic), and obtain new optimization functions to balance the SAM matrix. In addition to the theory, we also provide two empirical examples that support our channel concept and help to understand the associated measures.     

Tight compactly supported wavelet frames of arbitrarily high smoothness

Based on Ron and Shen's new method for constructing tight wave-let frames, we show that one can construct, for any dilation matrix, and in any spatial dimension, tight wavelet frames generated by compactly supported functions with arbitrarily high smoothness.

     

Coarse-grained model of proteins incorporating atomistic detail of the active site

We present a novel approach to explore the conformational space of globular proteins near their native state. It combines the advantages of coarse-grained models with those of all-atoms simulations, required to treat molecular recognition processes. The comparison between calculated structural properties with those obtained with all-atoms molecular dynamics simulations establishes the accuracy of the model. Our method has the potential to be extended to molecular recognition processes in systems whose characteristic size and time scale prevent an analysis based on all-atoms molecular dynamics.     

Role of the Pauli principle in collective-model coupled-channel calculations

A multichannel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. By tracking the results in the zero coupling limit, a correct interpretation of the subthreshold and resonant spectra of the compound system can be made. As an example, the neutron-12C system is studied defining properties of 13C to 10 MeV excitation. Accounting for the Pauli principle in collective coupled-channels models is crucial to the outcome.     

Generalized Shift-Invariant Systems

A countable collection $X$ of functions in $L_2(\mbox{\footnotesize\bf R})$ is said to be a Bessel system if the associated analysis operator $$ \txs{X}:L_2(\mbox{\smallbf R}^d)\to \ell_2(X) : f\mapsto (\inpro{f,x})_{x\in X} $$ is well-defined and bounded. A Bessel system is a fundamental frame if $\txs{X}$ is injective and its range is closed. This paper considers the above two properties for a generalized shift-invariant system $X$. By definition, such a system has the form $$ X=\bigcup_{j\in J} Y_j, $$ where each $Y_j$ is a shift-invariant system (i.e., is comprised of lattice translates of some function(s)) and $J$ is a countable (or finite) index set. The definition is general enough to include wavelet systems, shift-invariant systems, Gabor systems, and many variations of wavelet systems such as quasi-affine ones and nonstationary ones. The main theme of this paper is the fiberization of $\txs{X}$, which allows one to study the frame and Bessel properties of $X$ via the spectral properties of a collection of finite-order Hermitian nonnegative matrices.     

A Coaccelerated Observer

We analyze the situation of an observer coaccelerated relative to a linearly accelerated charge, in order to find whether he can observe the radiation emitted from the accelerated charge. It is found that the seemingly special situation of the coaccelerated observer relative to any other observer, is deduced from a wrong use of the retarded coordinate system, when such a system is inadmissible. It is also found that the coaccelerated observer has no special position other than any other observer, and hence, he can observe any physical events as any other observer.     

Polynomial Interpolation to Data on Flats in

Stimulated by recent work of Hakopian and Sahakian, polynomial interpolation to data at all the s-dimensional intersections of an arbitrary sequence of hyperplanes in ^d is considered, and reduced, by the adjunction of an additional s hyperplanes in general position with respect to the given sequence, to the case s=0 solved much earlier by two of the present authors. In particular, interpolation is from the very same polynomial spaces already used earlier. The difficult question of multiplicity and corresponding matching of derivative information is completely solved, with the number of independent derivative conditions at an intersection exactly equal to that intersection's multiplicity. Also, the consistency requirements placed on the data are minimal in the sense that they need to be checked only at the finitely many 0-dimensional intersections of the hyperplanes involved. The arguments used provide, incidentally, further insights into the two polynomial spaces, (Ξ) and (Ξ), of basic interest in box spline theory.     

Probing Balitsky-Fadin-Kuraev-Lipatov dynamics in the dijet cross section at large rapidity intervals in pp collisions at sqrt[s]=1800 and 630 GeV

Inclusive dijet production at large pseudorapidity intervals (Deltaeta) between the two jets has been suggested as a regime for observing Balitsky-Fadin-Kuraev-Lipatov (BFKL) dynamics. We have measured the dijet cross section for large Deltaeta in pp collisions at sqrt[s]=1800 and 630 GeV using the D0 detector. The partonic cross section increases strongly with the size of Deltaeta. The observed growth is even stronger than expected on the basis of BFKL resummation in the leading logarithmic approximation. The growth of the partonic cross section can be accommodated with an effective BFKL intercept of alphaBFKL(20 GeV)=1.65+/-0.07.     

Measurement of the W-->taunu production cross section in pp collisions at square root s=1.8 TeV

We report on a measurement of sigma(pp-->W+X)B(W-->taunu) in pp collisions at sqrt[s]=1.8 TeV at the Fermilab Tevatron. The measurement is based on an integrated luminosity (lum) of 18 pb-1 of data collected with the D0 detector during 1994-1995. We find that sigma(pp-->W+X)B(W-->taunu)=2.22+/-0.09 (stat)+/-0. 10 (syst)+/-0.10 (lum) nb. Lepton universality predicts that the ratio of the tau and electron electroweak charged current couplings to the W boson, gWtau/gWe, be unity. We find gWtau/gWe=0.980+/-0.031, in agreement with lepton universality.     

Valence-doorway model for radiative capture

A model of radiative capture is presented in which the T-matrix for valence capture is expressed as the sum of three terms, viz., a direct capture term, a term that describes the coupling between a single-particle resonance and the many possible continuum channels, and a pure single-particle resonance term. Expressions for the target excitations are not explicitly included, and projection operators are used to break up the single-particle space into resonant and nonresonant parts. The spreading of single-particle resonances is described through the coupling to particle-vibration doorways. The model is applied to the cases of ⁹⁸Mo(n, γ) ⁹⁹Mo and ⁹²Mo(n, γ) ⁹³Mo for an energy range of 0–3 MeV. In these cases the single-particle resonance amplitude is overwhelmingly dominant, and doorway effects are found to be relatively unimportant. Radiative widths obtained from our calculated average cross sections are compared to the corresponding widths obtained by averaging over the detailed fine structure measurements of Chrien et al. for ⁹⁹Mo. Good agreement is obtained. The valence capture cross section in ⁹³Mo is considerably smaller than in ⁹⁹Mo. This is consistent with the measurements of Chrien et al. and in good agreement with a recent analysis by Soloviev and Voronov.