Neural Network Methods for Boundary Value Problems Defined in Arbitrarily Shaped Domains

Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the satisfaction of the boundary conditions. The method has been successfuly tested on two-dimensional and three-dimensional PDEs and has yielded accurate solutions

Piecewise Regression through the Akaike Information Criterion using Mathematical Programming

In machine learning, regression analysis is a tool for predicting the output variables from a set of known independent variables. Through regression analysis, a function that captures the relationship between the variables is fitted to the data. Many methods from literature tackle this problem with various degrees of difficulty. Some simple methods include linear regression and least squares, while some are more complicated such as support vector regression. Piecewise or segmented regression is a method of analysis that partitions the independent variables into intervals and a function is fitted to each interval. In this work, the Optimal Piecewise Linear Regression Analysis (OPLRA) model is used from literature to tackle the problem of segmented analysis. This model is a mathematical programming approach that is formulated as a mixed integer linear programming problem that optimally partitions the data into multiple regions and calculates the regression coefficients, while minimising the Mean Absolute Error of the fitting. However, the number of regions is a known priori. For this work, an extension of the model is proposed that can optimally decide on the number of regions using information criteria. Specifically, the Akaike Information Criterion is used and the objective is to minimise its value. By using the criterion, the model no longer needs a heuristic approach to decide on the number of regions and it also deals with the problem of overfitting and model complexity

Tree regression models using statistical testing and mixed integer programming

Regression analysis is a statistical procedure that fits a mathematical function to a set of data in order to capture the relationship between dependent and independent variables. In tree regression, tree structures are constructed by repeated splits of the input space into two subsets, creating if-then-else rules. Such models are popular in the literature due to their ability to be computed quickly and their simple interpretations. This work introduces a tree regression algorithm that exploits an optimisation model of an existing literature method called Mathematical Programming Tree (MPtree) to optimally split nodes into subsets and applies a statistical test to assess the quality of the partitioning. Additionally, an approach of splitting nodes using multivariate decision rules is explored in this work and compared in terms of performance and computational efficiency. Finally, a novel mathematical model is introduced that performs subset selection on each node in order to select an optimal set of variables to considered for splitting, that improves the computational performance of the proposed algorithm

A new integrable system related to the Toda lattice

A new integrable lattice system is introduced, and its integrable discretizations are obtained. A B\"acklund transformation between this new system and the Toda lattice, as well as between their discretizations, is established.Comment: LaTeX, 14 p

Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation

We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schroedinger equation, on a discrete grid. We start with a classically obtained eigenvector for a problem discretized on a coarse grid, and we efficiently construct, quantum mechanically, an approximation of the same eigenvector on a fine grid. We use this approximation as the initial state for the eigenvalue estimation algorithm, and show the relationship between its success probability and the size of the coarse grid.Comment: 4 page

Retinoic acids increase expression of GLUT4 in dedifferentiated and hypertrophied cardiac myocytes

Sufficient expression of the insulin-sensitive glucose transporter GLUT4 may be crucial for the survival of cardiac myocytes in situations of stress. Expression of GLUT4 in cardiac myocytes correlates with cell differentiation and is reduced in the hypertrophied and failing myocardium. Adult rat cardiomyocytes (ARC) in primary culture undergo dedifferentiation and reduction of GLUT4 expression. Depending on the culture condition partial redifferentiation and/or hypertrophy follows. All-trans (at) and 9-cis retinoic acids (RA) are morphogenetic agents important for cell differentiation. Both atRA and 9-cisRA restored GLUT4 expression in dedifferentiated ARC, while only 9-cisRA could increase GLUT4 expression in hypertrophic ARC. The effects of RA were associated with improved differentiation of the cardiac myocytes, as assessed from the expression of atrial natriuretic factor and the morphology of the contractile apparatus. In neonatal rat cardiomyocytes, 9-cisRA, but not atRA, stimulated transcription from the glut4 promoter. In conclusion, treatment with RA can restore the down-regulated expression of GLUT4 in cardiomyocytes in association with a partial improvement of the differentiated phenotyp

Endometriosis and Infertility: A Multi-cytokine Imbalance Versus Ovulation, Fertilization and Early Embryo Development

Endometriosis is tightly linked to infertility which is manifested at very early or more advanced stages of the gestational cycle. Alteration on the production of a great number of cytokines/growth factors can be accused for problems on ovum maturation, fertilization or implantation. Yet, macroscopically these stages are characterized by the inability of conception. A closer look of the cytokinic profile during the conceptional and early gestational cycle could, however, localize the problem and allow a therapeutic approach. In this commentary, going through the cytokine requirement during ovulation, fertilization and the early stages of pregnancy, it became possible to specifically define the harmful endometriosis-induced cytokines for each of the conceptional and early gestational stages. Thus, regulating the levels of interferon-γ and tumor necrosis-α will facilitate ovulation and fertilization, whereas adjusting the levels of interleukin-1β and colony stimulating gactor-1 will facilitate implantation

A New Era in Engineering Plastics: Compatibility and Perspectives of Sustainable Alipharomatic Poly(ethylene terephthalate)/Poly(ethylene 2,5-furandicarboxylate) Blends

The industrialisation of poly(ethylene 2,5-furandicarboxylate) for total replacement of poly(ethylene terephthalate) in the polyester market is under question. Preparation of high-performing polymer blends is a well-established strategy for tuning the properties of certain homopolymers and create tailor-made materials to meet the demands for a number of applications. In this work, the structure, thermal properties and the miscibility of a series of poly(ethylene terephthalate)/poly(ethylene 2,5-furandicarboxylate) (PET/PEF) blends have been studied. A number of thermal treatments were followed in order to examine the thermal transitions, their dynamic state and the miscibility characteristics for each blend composition. Based on their glass transition temperatures and melting behaviour the PET/PEF blends are miscible at high and low poly(ethylene terephthalate) (PET) contents, while partial miscibility was observed at intermediate compositions. The multiple melting was studied and their melting point depression was analysed with the Flory-Huggins theory. In an attempt to further improve miscibility, reactive blending was also investigated

ExoSim: the Exoplanet Observation Simulator

A new generation of exoplanet research beckons and with it the need for simulation tools that accurately predict signal and noise in transit spectroscopy observations. We developed ExoSim: an end-to-end simulator that models noise and systematics in a dynamical simulation. ExoSim improves on previous simulators in the complexity of its simulation, versatility of use and its ability to be generically applied to different instruments. It performs a dynamical simulation that can capture temporal effects such as correlated noise and systematics on the light curve. It has also been extensively validated, including against real results from the Hubble WFC3 instrument. We find ExoSim is accurate to within 5% in most comparisons. ExoSim can interact with other models which simulate specific time-dependent processes. A dedicated star spot simulator allows ExoSim to produce simulated observations that include spot and facula contamination. ExoSim has been used extensively in the Phase A and B design studies of the ARIEL mission, and has many potential applications in the field of transit spectroscopy

Solutions of Adler's lattice equation associated with 2-cycles of the Backlund transformation

The BT of Adler's lattice equation is inherent in the equation itself by virtue of its multidimensional consistency. We refer to a solution of the equation that is related to itself by the composition of two BTs (with different Backlund parameters) as a 2-cycle of the BT. In this article we will show that such solutions are associated with a commuting one-parameter family of rank-2 (i.e., 2-variable), 2-valued mappings. We will construct the explicit solution of the mappings within this family and hence give the solutions of Adler's equation that are 2-cycles of the BT.Comment: 10 pages, contribution to the NEEDS 2007 proceeding