Relating pp-adic eigenvalues and the local Smith normal form

Conditions are established under which the $p$-adic valuations of the invariant factors (diagonal entries of the Smith form) of an integer matrix are equal to the $p$-adic valuations of the eigenvalues. It is then shown that this correspondence is the typical case for "most" matrices; precise density bounds are given for when the property holds, as well as easy transformations to this typical case.Comment: To appear in Linear Algebra and Its Application

Parametrization of stochastic inputs using generative adversarial networks with application in geology

We investigate artificial neural networks as a parametrization tool for stochastic inputs in numerical simulations. We address parametrization from the point of view of emulating the data generating process, instead of explicitly constructing a parametric form to preserve predefined statistics of the data. This is done by training a neural network to generate samples from the data distribution using a recent deep learning technique called generative adversarial networks. By emulating the data generating process, the relevant statistics of the data are replicated. The method is assessed in subsurface flow problems, where effective parametrization of underground properties such as permeability is important due to the high dimensionality and presence of high spatial correlations. We experiment with realizations of binary channelized subsurface permeability and perform uncertainty quantification and parameter estimation. Results show that the parametrization using generative adversarial networks is very effective in preserving visual realism as well as high order statistics of the flow responses, while achieving a dimensionality reduction of two orders of magnitude

A machine learning approach for efficient uncertainty quantification using multiscale methods

Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these coarse scale basis functions. Specifically, we employ a neural network predictor fitted using a set of solution samples from which it learns to generate subsequent basis functions at a lower computational cost than solving the local problems. The computational advantage of this approach is realized for uncertainty quantification tasks where a large number of realizations has to be evaluated. We attribute the ability to learn these basis functions to the modularity of the local problems and the redundancy of the permeability patches between samples. The proposed method is evaluated on elliptic problems yielding very promising results.Comment: Journal of Computational Physics (2017

Stem cell research: a religious and ethical perspective

Stem cell research is among the most promising and controversial technological breakthroughs of our time. Stem cells are the cells from which all 210 different kinds of tissue in the human body originate. There are great potential to relieve human disease and suffering. The first studies on stem cells began in the 60s. Scientists have isolated the first human embryonic stem cell lines specifically tailored to match the nuclear DNA of patients, both male and female of various ages, suffering from disease or spinal cord injury. Because many diseases result from the death or dysfunction of a single cell type, scientists believe that the introduction of healthy cells of this type into a patient may restore lost or compromised function. Stem cells are able to divide, while maintaining their totipotent or pluripotent characteristics. Early in mammalian development, stem cells (embryonic stem cells); have the ability to differentiate into every cell of the human body (totipotent), potentially forming an entire fetus. Stem cells derived from later stages of mammalian development have the ability to differentiate into multiple cell types, but not into an entire organism. Adult stem cells are generally limited to differentiating into different cell types of their tissue of origin Most cells in the human body are differentiated and have the ability to form only cells similar to them. If one can manipulate the conditions controlling cellular differentiation, it may be possible to create replacement cells and organs, potentially curing illnesses such as diabetes, Alzheimer's disease, Parkinson's disease and other potentially serious illnesses.. Embryonic Stem cells for research are obtained from the surplus fertilized embryos in infertility management with IVF, from aborted fetuses, umbilical cord and cloning whether therapeutic or reproductive. The overwhelming objection to stem cell research is that it involves the destruction of an embryo or foetus. For many, this constitutes destruction of a potential human, and conflicts with religious and moral views held in our society. For others, the potential for this research to provide treatments and possibly cures for debilitating illnesses that have no cure and significantly impact on our way of life overrides this concern. Central to any argument on this is what actually constitutes the beginning of life for a human. Opinions on this vary from the moment of conception to a 14 day embryo and a living baby at birth. The other major ethical issue associated with stem cell research ties in with the combination of embryonic stem cell and cloning technologies. This newly emerging technology has caused a great deal of ethical, legal, and theological discussion and debate. Is IVF permitted to begin with? Are pre-embryos included in the prohibition of abortion? May a very early embryo be sacrificed for stem cells that could save lives or at least cure disease? May we fertilize ova specifically to create an embryo to be sacrificed for stem cells? With 'surplus' embryos cryopreserved in IVF clinics, is there a need to create additional embryos solely for purposes of stem cells basic research? Need we make "fences" in the form of protective laws to protect fetuses from wanton destruction? May tissue from aborted fetuses be used for research or medical treatment?. This paper discusses stem cell research in an ethical and religious perspective showing the Islamic, Catholic, Judaism and secular ethical views. it also projects possible compromises that could be utilized and urges local authorities to develop regulations for all clinical and research work that involves the human embryo

Fast Computation of Smith Forms of Sparse Matrices Over Local Rings

We present algorithms to compute the Smith Normal Form of matrices over two families of local rings. The algorithms use the \emph{black-box} model which is suitable for sparse and structured matrices. The algorithms depend on a number of tools, such as matrix rank computation over finite fields, for which the best-known time- and memory-efficient algorithms are probabilistic. For an \nxn matrix $A$ over the ring \Fzfe, where $f^e$ is a power of an irreducible polynomial f \in \Fz of degree $d$, our algorithm requires \bigO(\eta de^2n) operations in \F, where our black-box is assumed to require \bigO(\eta) operations in \F to compute a matrix-vector product by a vector over \Fzfe (and $\eta$ is assumed greater than \Pden). The algorithm only requires additional storage for \bigO(\Pden) elements of \F. In particular, if \eta=\softO(\Pden), then our algorithm requires only \softO(n^2d^2e^3) operations in \F, which is an improvement on known dense methods for small $d$ and $e$. For the ring \ZZ/p^e\ZZ, where $p$ is a prime, we give an algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small. We describe a method for dimension reduction while preserving the invariant factors. The time complexity is essentially linear in $\mu n r e \log p,$ where $\mu$ is the number of operations in \ZZ/p\ZZ to evaluate the black-box (assumed greater than $n$) and $r$ is the total number of non-zero invariant factors. To avoid the practical cost of conditioning, we give a Monte Carlo certificate, which at low cost, provides either a high probability of success or a proof of failure. The quest for a time- and memory-efficient solution without restrictions on the number of nontrivial invariant factors remains open. We offer a conjecture which may contribute toward that end.Comment: Preliminary version to appear at ISSAC 201

GIS based Traffic Accident Analysis System

In Malaysia, every year over thousands human beings die and tens of thousands are injured in road accidents. This paper focused on the goal of developing tools and methodologies to reduce accidents, and to make roadway safer, through the ability to better interpret accident records and to provide more information for individuals to evaluate accidents. It founds that the customization of GIS application for Traffic accidents analysis could be performed using Map Object and visual basic 6.0. This integration produced expert system provides wide range functions in low cost programming