A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

Statistical theory of finite Fermi systems with chaotic excited eigenstates

A theory of strongly interacting Fermi systems of a few particles is developed. At high excit at ion energies (a few times the single-parti cle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-part icle basis st at es by the residual two- body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-part icle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variable s such as t emperature in an isolated microscopic Fermi system of a few particles.

Scattering theory of multilevel atoms interacting with arbitrary radiation fields

We present a generic transfer matrix approach for the description of the interaction of atoms possessing multiple ground state and excited state sublevels with light fields. This model allows us to treat multi-level atoms as classical scatterers in light fields modified by, in principle, arbitrarily complex optical components such as mirrors, resonators, dispersive or dichroic elements, or filters. We verify our formalism for two prototypical sub-Doppler cooling mechanisms and show that it agrees with the standard literature.

Construction of Drug–Polymer Thermodynamic Phase Diagrams Using Flory–Huggins Interaction Theory: Identifying the Relevance of Temperature and Drug Weight Fraction to Phase Separation within Solid Dispersions

Amorphous drug-polymer solid dispersions have the potential to enhance the dissolution performance and thus bioavailability of BCS class II drug compounds. The principle drawback of this approach is the limited physical stability of amorphous drug within the dispersion. Accurate determination of the solubility and miscibility of drug in the polymer matrix is the key to the successful design and development of such systems. In this paper, we propose a novel method, based on Flory-Huggins theory, to predict and compare the solubility and miscibility of drug in polymeric systems. The systems chosen for this study are (1) hydroxypropyl methylcellulose acetate succinate HF grade (HPMCAS-HF)-felodipine (FD) and (2) Soluplus (a graft copolymer of polyvinyl caprolactam-polyvinyl acetate-polyethylene glycol)-FD. Samples containing different drug compositions were mixed, ball milled, and then analyzed by differential scanning calorimetry (DSC). The value of the drug-polymer interaction parameter ? was calculated from the crystalline drug melting depression data and extrapolated to lower temperatures. The interaction parameter ? was also calculated at 25 °C for both systems using the van Krevelen solubility parameter method. The rank order of interaction parameters of the two systems obtained at this temperature was comparable. Diagrams of drug-polymer temperature-composition and free energy of mixing (?G mix) were constructed for both systems. The maximum crystalline drug solubility and amorphous drug miscibility may be predicted based on the phase diagrams. Hyper-DSC was used to assess the validity of constructed phase diagrams by annealing solid dispersions at specific drug loadings. Three different samples for each polymer were selected to represent different regions within the phase diagram

A multi-fibre multi-layer representative volume element (M2RVE) for prediction of matrix and interfacial damage in composite laminates

Multiscale micro-mechanics theory is extensively used for the prediction of the material response and damage analysis of unidirectional lamina using a representative volume element (RVE). Th is paper presents a RVE-based approach to characterize the materi al response of a multi-fibre cross-ply laminate considering the effect of matrix damage and fibre-matrix interfacial strength. The framework of the homogenization theory for periodic media has been used for the analysis of a 'multi-fibre multi-layer representative volume element' (M2 RVE) representing cross-ply laminate. The non-homogeneous stress-strain fields within the M2RVE are related to the average stresses and strains by using Gauss theorem and the Hill-Mandal strain energy equivalence principle. The interfacial bonding strength affects the in-plane shear stress-strain response significantl y. The material response predicted by M2 RVE is in good agreement with the experimental results available in the literature. The maximum difference between the shear stress predicted using M2 RVE and the experimental results is ~15% for the bonding strength of 30MPa at the strain value of 1.1%

Disturbance, neutral theory and patterns of beta diversity in soil communities

Beta diversity describes how local communities within an area or region differ in species composition/abundance. There have been attempts to use changes in beta diversity as a biotic indicator of disturbance, but lack of theory and methodological caveats have hampered progress. We here propose that the neutral theory of biodiversity plus the definition of beta diversity as the total variance of a community matrix provide a suitable, novel, starting point for ecological applications. Observed levels of beta diversity (BD) can be compared to neutral predictions with three possible outcomes: Observed BD equals neutral prediction or is larger (divergence) or smaller (convergence) than the neutral prediction. Disturbance might lead to either divergence or convergence, depending on type and strength. We here apply these ideas to datasets collected on oribatid mites (a key, very diverse soil taxon) under several regimes of disturbances. When disturbance is expected to increase the heterogeneity of soil spatial properties or the sampling strategy encompassed a range of diverging environmental conditions, we observed diverging assemblages. On the contrary, we observed patterns consistent with neutrality when disturbance could determine homogenization of soil properties in space or the sampling strategy encompassed fairly homogeneous areas. With our method, spatial and temporal changes in beta diversity can be directly and easily monitored to detect significant changes in community dynamics, although the method itself cannot inform on underlying mechanisms. However, human-driven disturbances and the spatial scales at which they operate are usually known. In this case, our approach allows the formulation of testable predictions in terms of expected changes in beta diversity, thereby offering a promising monitoring tool.

Single-photon single ionization of W+ ions: experiment and theory

Experimental and theoretical results are reported for photoionization of Ta-like (W+) tungsten ions. Absolute cross sections were measured in the energy range 16–245 eV employing the photon–ion merged-beam setup at the advanced light source in Berkeley. Detailed photon-energy scans at 100 meV bandwidth were performed in the 16–108 eV range. In addition, the cross section was scanned at 50 meV resolution in regions where fine resonance structures could be observed. Theoretical results were obtained from a Dirac–Coulomb R-matrix approach. Photoionization cross section calculations were performed for singly ionized atomic tungsten ions in their 5s²5p⁶5d⁴(⁵D)6s ⁶Dj.  J = 1/2, ground level and the associated excited metastable levels with J = 3/2, 5/2, 7/2 and 9/2. Since the ion beams used in the experiments must be expected to contain long-lived excited states also from excited configurations, additional cross-section calculations were performed for the second-lowest term, 5d⁵⁶Sj, J = 5/2, and for the 4F term, 5d³6s^{2 4}Fj, with J = 3/2, 5/2, 7/2 and 9/2. Given the complexity of the electronic structure of W+ the calculations reproduce the main features of the experimental cross section quite well.

High-resolution photoionization of Xe + ions: Experiment and theory

High-resolution photoionization measurements of Xe + ions have been performed at the Advanced Light Source in Berkeley, California, USA. The experimental cross sections are compared with results from Dirac-Coulomb R-matrix calculations.

Higher order derivatives and norms of certain matrix functions

Tese de doutoramento, Matemática (Álgebra Lógica e Fundamentos), Universidade de Lisboa, Faculdade de Ciências, 2014

Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

The mean-field theory of a spin glass with a specific form of nearest- and next-nearest-neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we find either the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one-step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

Queueing Theory And Other Applications Of Stochastic Processes Queueing And Inventory Models With Rest Periods

In this thesis we study the effect of rest periods in queueing systems without exhaustive service and inventory systems with rest to the server. Most of the works in the vacation models deal with exhaustive service. Recently some results have appeared for the systems without exhaustive service.

Semiclassical evaluation of average nuclear one- and two-body matrix elements

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results, and it is demonstrated that the semiclassical matrix elements, as function of energy, well pass through the average of the scattered quantum values. For the one-body matrix elements it is shown how the Thomas-Fermi approach can be projected on good parity and also on good angular momentum. For the two-body case, the pairing matrix elements are considered explicitly.

Reconciling internalization theory and the eclectic paradigm

The eclectic paradigm of Dunning (1980) (with its OLI and four motives for FDI framework) can be reconciled with the firm and country matrix of Rugman (1981). However, the fit is not perfect. The main reason for misalignment is that Dunning is focused upon outward FDI into host economies, whereas Rugman’s matrix is for firm-level strategy covering MNE activity in both home and host countries.