Term Structure Equations Under Benchmark Framework

This paper makes use of an integrated benchmark modeling framework that allows us to derive term structure equations for bond and forward prices. The benchmark or numeraire is chosen to be the growth optimal portfolio (GOP). For deterministic short rate the solution of the bond term structure equation coincides with the explicit formula obtained in Platen(2005). The resulting term structure equations are used to explain moves in bond and forward prices by introducing GOP as a factor and therefore constructing a hedge portfolio for bond consisting of units of the GOP and the saving account. The paper also derives an affine term structure equation for forward price in term of the GOP factor. In the case of stochastic short rate we restrict our selves to give only a term structure equation for the bond price.Term structure, Benchmark approach, GOP, Forward price, bond.

A framework for the construction of generative models for mesoscale structure in multilayer networks

Multilayer networks allow one to represent diverse and coupled connectivity patterns—such as time-dependence, multiple subsystems, or both—that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical networks make it crucial to develop generative models that can produce the features that one encounters in empirical networks. Key purposes of such models include generating synthetic networks with empirical properties of interest, benchmarking mesoscale-detection methods and algorithms, and inferring structure in empirical multilayer networks. In this paper, we introduce a framework for the construction of generative models for mesoscale structures in multilayer networks. Our framework provides a standardized set of generative models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. It unifies and generalizes many existing models for mesoscale structures in fully ordered (e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can also use it to construct generative models for mesoscale structures in partially ordered multilayer networks (e.g., networks that are both temporal and multiplex). Our framework has the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers. We discuss the parameters and properties of our framework, and we illustrate examples of its use with benchmark models for community-detection methods and algorithms in multilayer networks

Optimized Synthesis and Structural Characterization of the Borosilicate MCM-70

A structure analysis of the borosilicate zeolite MCM-70, whose synthesis had been patented in 2003, was reported in 2005. Unfortunately, that structure analysis was somewhat ambiguous. Anisotropic line broadening made it difficult to model the peak shape, some peaks in the electron density map could not be interpreted satisfactorily, the framework geometry was distorted, and MAS NMR results were partially contradictory. In an attempt to resolve some of these points, an optimization of the synthesis was undertaken, and the structure was reinvestigated. The structure was solved from synchrotron powder diffraction data collected on an as-synthesized sample (Pmn2_1, a = 13.3167(1) Å, b = 4.6604(1) Å, c = 8.7000(1) Å) using a powder charge-flipping algorithm. The framework topology, with a 1-dimensional, 10-ring channel system, is identical to the one previously reported. However, the B in this new sample was found to be ordered in the framework, fully occupying one of the four tetrahedral sites. Two extra-framework K^+ ion positions, each coordinated to five framework O atoms and one water molecule, were also found. The solid state ^(29)Si, ^(11)B and ^1H NMR results are fully consistent with this ordered structure

Framework for Understanding the Legal Structure of Texas Public Schools

Texas public school stakeholders consist primarily of students, parents, faculty and staff, administrators, school board members, business leaders, community members, and taxpayers. While each of these stakeholders has a vested interest in the local school district, many fail to understand how public schools came into existence and the legal rationale upon which they operate. The problem lies in the structural complexity of schools, which is prohibitive to a complete understanding by its entire constituency. While the multiple layers of politics and numerous laws and policies that define the Texas public school structure may be necessary for proper operation, the intricacy further exacerbates the ability of many to fully comprehend it. The purpose of this study was to create a framework for understanding the legal structure of Texas public schools to facilitate a more complete understanding by all constituents

Extension of SBL Algorithms for the Recovery of Block Sparse Signals with Intra-Block Correlation

We examine the recovery of block sparse signals and extend the framework in two important directions; one by exploiting signals' intra-block correlation and the other by generalizing signals' block structure. We propose two families of algorithms based on the framework of block sparse Bayesian learning (BSBL). One family, directly derived from the BSBL framework, requires knowledge of the block structure. Another family, derived from an expanded BSBL framework, is based on a weaker assumption on the block structure, and can be used when the block structure is completely unknown. Using these algorithms we show that exploiting intra-block correlation is very helpful in improving recovery performance. These algorithms also shed light on how to modify existing algorithms or design new ones to exploit such correlation and improve performance.Comment: Matlab codes can be downloaded at: https://sites.google.com/site/researchbyzhang/bsbl, or http://dsp.ucsd.edu/~zhilin/BSBL.htm

Deformed Base Antisymmetrized Molecular Dynamics and its Application to ^{20}Ne

A new theoretical framework named as deformed base antisymmetrized molecular dynamics that uses the localized triaxially deformed Gaussian as the single particle wave packet is presented. The model space enables us to describe sufficiently well the deformed mean-field structure as well as the cluster structure and their mixed structure within the same framework. The improvement over the original version of the antisymmetrized molecular dynamics which uses the spherical Gaussian is verified by the application to $^{20}{\rm Ne}$ nucleus. The almost pure $\alpha + ^{16}{\rm O_{g.s}}$ cluster structure of the $K^\pi$=$0^-$ band, the distortion of the cluster structure in the $K^\pi$=$0^+_1$ band and the dominance of the deformed mean-field structure of the $K^\pi$=$2^-$ band are confirmed and their observed properties are reproduced. Especially, the intra-band E2 transition probabilities in $K^\pi$=$0^+_1$ and $2^-$ bands are reproduced without any effective charge. Since it has been long known that the pure $\alpha + ^{16}{\rm O}_{g.s.}$ cluster model underestimates the intra-band $E2$ transitions in the $K^\pi$=$0^+_1$ band by about 30%, we consider that this success is due to the sufficient description of the deformed mean-field structure in addition to the cluster structure by the present framework. From the successful description of $^{20}{\rm Ne}$, we expect that the present framework presents us with a powerful approach for the study of the coexistence and interplay of the mean-field structure and the cluster structure