Physical Sciences and Mathematics Commons^™

Keyword-Based Patent Citation Prediction Via Information Theory, Farshad Madani, Martin Zwick, Tugrul U. Daim

Engineering and Technology Management Faculty Publications and Presentations

Patent citation shows how a technology impacts other inventions, so the number of patent citations (backward citations) is used in many technology prediction studies. Current prediction methods use patent citations, but since it may take a long time till a patent is cited by other inventors, identifying impactful patents based on their citations is not an effective way. The prediction method offered in this article predicts patent citations based on the content of patents. In this research, Reconstructability Analysis (RA), which is based on information theory and graph theory, is applied to predict patent citations based on keywords extracted from …

A Spacetime Dpg Method For The Wave Equation In Multiple Dimensions, Jay Gopalakrishnan, Paulina Sepulveda

Portland Institute for Computational Science Publications

A spacetime discontinuous Petrov-Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The wellposedness of this formulation is established using a previously presented abstract framework. One of the main tasks in the verification of the conditions of this framework is proving a density result. This is done in detail for a simple domain in arbitrary dimensions. The DPG method based on the weak formulation is then studied theoretically and numerically. Error estimates and numerical results are presented for triangular, rectangular, tetrahedral, and hexahedral meshes of …

Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie

Mathematics and Statistics Faculty Publications and Presentations

The advantage of using algebraic geometry over enumeration for describing sets related to attractors in large dynamic networks from biology is advocated. Examples illustrate the gains.

Connection And Curvature In Crystals With Non-Constant Dislocation Density, Marek Z. Elźanowski, Gareth P. Parry

Mathematics and Statistics Faculty Publications and Presentations

Given a smooth defective solid crystalline structure defined by linearly independent ‘lattice’ vector fields, the Burgers vector construction characterizes some aspect of the ‘defectiveness’ of the crystal by virtue of its interpretation in terms of the closure failure of appropriately defined paths in the material and this construction partly determines the distribution of dislocations in the crystal. In the case that the topology of the body manifold M is trivial (e.g., a smooth crystal defined on an open set in R2), it would seem at first glance that there is no corresponding construction that leads to the notion of a …

Preliminary Results Of Bayesian Networks And Reconstructability Analysis Applied To The Electric Grid, Marcus Harris, Martin Zwick

Systems Science Faculty Publications and Presentations

Reconstructability Analysis (RA) is an analytical approach developed in the systems community that combines graph theory and information theory. Graph theory provides the structure of relations (model of the data) between variables and information theory characterizes the strength and the nature of the relations. RA has three primary approaches to model data: variable based (VB) models without loops (acyclic graphs), VB models with loops (cyclic graphs) and state-based models (nearly always cyclic, individual states specifying model constraints). These models can either be directed or neutral. Directed models focus on a single response variable whereas neutral models focus on all relations …

Reconstructability & Dynamics Of Elementary Cellular Automata, Martin Zwick

Systems Science Faculty Publications and Presentations

Reconstructability analysis (RA) is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss into lower ordinality relations. Set-theoretic RA (SRA) is used to characterize the mappings of elementary cellular automata. The decomposition possible for each mapping w/o loss is a better predictor than the λ parameter (Walker & Ashby, Langton) of chaos, & non-decomposable mappings tend to produce chaos. SRA yields not only the simplest lossless structure but also a vector of losses for all structures, indexed by parameter τ. These losses are analogous to transmissions in information-theoretic RA (IRA). IRA …

Introduction To Reconstructability Analysis, Martin Zwick

Systems Science Faculty Publications and Presentations

This talk will introduce Reconstructability Analysis (RA), a data modeling methodology deriving from the 1960s work of Ross Ashby and developed in the systems community in the 1980s and afterwards. RA, based on information theory and graph theory, is a member of the family of methods known as ‘graphical models,’ which also include Bayesian networks and log-linear techniques. It is designed for exploratory modeling, although it can also be used for confirmatory hypothesis testing. RA can discover high ordinality and nonlinear interactions that are not hypothesized in advance. Its conceptual framework illuminates the relationships between wholes and parts, a subject …

Beyond Spatial Autocorrelation: A Novel Approach Using Reconstructability Analysis, David Percy, Martin Zwick

Systems Science Faculty Publications and Presentations

Raster data are digital representations of spatial phenomena that are organized into rows and columns that typically have the same dimensions in each direction. They are used to represent image data at any scale. Common raster data are medical images, satellite data, and photos generated by modern smartphones.
Satellites capture reflectance data in specific bands of wavelength that correspond to red, green, blue, and often some infrared and thermal bands. These composite vectors can then be classified into actual land use categories such as forest or water using automated techniques. These classifications are verified on the ground using hand-held sensors. …

Cox Processes For Counting By Detection, Purnima Rajan, Yongming Ma, Bruno Jedynak

Portland Institute for Computational Science Publications

In this work, doubly stochastic Poisson (Cox) processes and convolutional neural net (CNN) classifiers are used to estimate the number of instances of an object in an image. Poisson processes are well suited to model events that occur randomly in space, such as the location of objects in an image or the enumeration of objects in a scene. The proposed algorithm selects a subset of bounding boxes in the image domain, then queries them for the presence of the object of interest by running a pre-trained CNN classifier. The resulting observations are then aggregated, and a posterior distribution over the …

Space-Time Discretizations Using Constrained First-Order System Least Squares (Cfosls), Kirill Voronin, Chak Shing Lee, Martin Neumüller, Paulina Sepulveda, Panayot S. Vassilevski

Portland Institute for Computational Science Publications

This paper studies finite element discretizations for three types of time-dependent PDEs, namely heat equation, scalar conservation law and wave equation, which we reformulate as first order systems in a least-squares setting subject to a space-time conservation constraint (coming from the original PDE). Available piece- wise polynomial finite element spaces in (n + 1)-dimensions for functional spaces from the (n + 1)-dimensional de Rham sequence for n = 3, 4 are used for the implementation of the method. Computational results illustrating the error behavior, iteration counts and performance of block-diagonal and monolithic geometric multi- grid preconditioners are …

Gaussian Processes With Context-Supported Priors For Active Object Localization, Bruno Jedynak

Portland Institute for Computational Science Publications

We devise an algorithm using a Bayesian optimization framework in conjunction with contextual visual data for the efficient localization of objects in still images. Recent research has demonstrated substantial progress in object localization and related tasks for computer vision. However, many current state-of-the-art object localization procedures still suffer from inaccuracy and inefficiency, in addition to failing to provide a principled and interpretable system amenable to high-level vision tasks. We address these issues with the current research.

Our method encompasses an active search procedure that uses contextual data to generate initial bounding-box proposals for a target object. We train a convolutional …

The Auxiliary Space Preconditioner For The De Rham Complex, Jay Gopalakrishnan, Martin Neumüller, Panayot S. Vassilevski

Portland Institute for Computational Science Publications

We generalize the construction and analysis of auxiliary space preconditioners to the n-dimensional finite element subcomplex of the de Rham complex. These preconditioners are based on a generalization of a decomposition of Sobolev space functions into a regular part and a potential. A discrete version is easily established using the tools of finite element exterior calculus. We then discuss the four-dimensional de Rham complex in detail. By identifying forms in four dimensions (4D) with simple proxies, form operations are written out in terms of familiar algebraic operations on matrices, vectors, and scalars. This provides the basis for our implementation of …

A New Method For Multi-Bit And Qudit Transfer Based On Commensurate Waveguide Arrays, Jovan Petrovic, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

The faithful state transfer is an important requirement in the construction of classical and quantum computers. While the high-speed transfer is realized by optical-fibre interconnects, its implementation in integrated optical circuits is affected by cross-talk. The cross-talk between densely packed optical waveguides limits the transfer fidelity and distorts the signal in each channel, thus severely impeding the parallel transfer of states such as classical registers, multiple qubits and qudits. Here, we leverage on the suitably engineered cross-talk between waveguides to achieve the parallel transfer on optical chip. Waveguide coupling coefficients are designed to yield commensurate eigenvalues of the array and …

Statistical Analysis Of Network Change, Teresa D. Schmidt, Martin Zwick

Systems Science Faculty Publications and Presentations

Networks are rarely subjected to hypothesis tests for difference, but when they are inferred from datasets of independent observations statistical testing is feasible. To demonstrate, a healthcare provider network is tested for significant change after an intervention using Medicaid claims data. First, the network is inferred for each time period with (1) partial least squares (PLS) regression and (2) reconstructability analysis (RA). Second, network distance (i.e., change between time periods) is measured as the mean absolute difference in (1) coefficient matrices for PLS and (2) calculated probability distributions for RA. Third, the network distance is compared against a reference distribution …

High-Order Method For Evaluating Derivatives Of Harmonic Functions In Planar Domains, Jeffrey S. Ovall, Samuel E. Reynolds

Mathematics and Statistics Faculty Publications and Presentations

We propose a high-order integral equation based method for evaluating interior and boundary derivatives of harmonic functions in planar domains that are specified by their Dirichlet data.

Clustering And Multifacility Location With Constraints Via Distance Function Penalty Methods And Dc Programming, Mau Nam Nguyen, Thai An Nguyen, Sam Reynolds, Tuyen Tran

Mathematics and Statistics Faculty Publications and Presentations

This paper is a continuation of our effort in using mathematical optimization involving DC programming in clustering and multifacility location. We study a penalty method based on distance functions and apply it particularly to a number of problems in clustering and multifacility location in which the centers to be found must lie in some given set constraints. We also provide different numerical examples to test our method.

On The Girth And Diameter Of Generalized Johnson Graphs, Louis Anthony Agong, Carmen Amarra, John Caughman, Ari J. Herman, Taiyo S. Terada

Mathematics and Statistics Faculty Publications and Presentations

Let v > k > i be non-negative integers. The generalized Johnson graph, J(v,k,i), is the graph whose vertices are the k-subsets of a v-set, where vertices A and B are adjacent whenever |A∩B|= i. In this article, we derive general formulas for the girth and diameter of J(v,k,i). Additionally, we provide a formula for the distance between any two vertices A and B in terms of the cardinality of their intersection.

Bootcmatch: A Software Package For Bootstrap Amg Based On Graphweighted Matching, Pasqua D'Ambra, Salvatore Filipone, Panayot S. Vassilevski

Mathematics and Statistics Faculty Publications and Presentations

This article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the …

Intensity Inhomogeneity Correction Of Sd-Oct Data Using Macular Flatspace, Andrew Lang, Aaron Carass, Bruno M. Jedynak, Sharon D. Solomon, Peter A. Calabresi, Jerry L. Prince

Mathematics and Statistics Faculty Publications and Presentations

Images of the retina acquired using optical coherence tomography (OCT) often suffer from intensity inhomogeneity problems that degrade both the quality of the images and the performance of automated algorithms utilized to measure structural changes. This intensity variation has many causes, including off-axis acquisition, signal attenuation, multi-frame averaging, and vignetting, making it difficult to correct the data in a fundamental way. This paper presents a method for inhomogeneity correction by acting to reduce the variability of intensities within each layer. In particular, the N3 algorithm, which is popular in neuroimage analysis, is adapted to work for OCT data. N3 works …

Variational Geometric Approach To Generalized Differential And Conjugate Calculi In Convex Analysis, Boris S. Mordukhovich, Nguyen Mau Nam, R. Blake Rector, T. Tran

Mathematics and Statistics Faculty Publications and Presentations

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their unified and simplified proofs based on the developed geometric variational schemes. Key words. Convex and variational analysis, Fenchel conjugates, normals and subgradients, coderivatives, convex calculus, optimal value functions.

Classification Of Minimal Separating Sets In Low Genus Surfaces, J. J. P. Veerman, William Maxwell, Victor Rielly, Austin K. Williams

Mathematics and Statistics Faculty Publications and Presentations

Consider a surface S and let M ⊂ S. If S \ M is not connected, then we say M separates S, and we refer to M as a separating set of S. If M separates S, and no proper subset of M separates S, then we say M is a minimal separating set of S. In this paper we use computational methods of combinatorial topology to classify the minimal separating sets of the orientable surfaces of genus g = 2 and g = 3. The classification for genus 0 and 1 was done …

Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe, Martin Zwick, Joshua Hughes

Systems Science Faculty Publications and Presentations

The panarchy adaptive cycle, a general model for change in natural and human systems, can be formalized by the cusp catastrophe of René Thom's topological theory. Both the adaptive cycle and the cusp catastrophe have been used to model ecological, economic, and social systems in which slow and small continuous changes in two control variables produce fast and large discontinuous changes in system behavior. The panarchy adaptive cycle, the more recent of the two models, has been used so far only for qualitative descriptions of typical dynamics of such systems. The cusp catastrophe, while also often employed qualitatively, is a …

Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe [Presentation], Martin Zwick, Joshua Hughes

Systems Science Faculty Publications and Presentations

The panarchy adaptive cycle, a general model for change in natural and human systems, can be formalized by the cusp catastrophe of René Thom's topological theory. Both the adaptive cycle and the cusp catastrophe have been used to model ecological, economic, and social systems in which slow and small continuous changes in two control variables produce fast and large discontinuous changes in system behavior. The panarchy adaptive cycle, the more recent of the two models, has been used so far only for qualitative descriptions of typical dynamics of such systems. The cusp catastrophe, while also often employed qualitatively, is a …

Ideas & Graphs, Martin Zwick

Systems Science Faculty Publications and Presentations

A graph can specify the skeletal structure of an idea, onto which meaning can be added by interpreting the structure.

This paper considers graphs (but not hypergraphs) consisting of four nodes, and suggests meanings that can be associated with several different directed and undirected graphs.

Drawing on Bennett's "systematics," specifically on the Tetrad that systematics offers as a model of 'activity,' the analysis here shows that the Tetrad is versatile model of problem-solving, regulation and control, and other processes.

Random Walks On Digraphs, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

Let V = {1, · · · n} be a vertex set and S a non-negative row-stochastic matrix (i.e. rows sum to 1). V and S define a digraph G = G(V, S) and a directed graph Laplacian L as follows. If (S)ij > 0 (in what follows we will leave out the parentheses) there is a directed edge j → i. Thus the ith row of S identifies the edges coming into vertex i and their weights. This set of vertices are collectively the neighbors of i, and is denoted by Ni . The diagonal elements Sii are chosen such …

A Weighted Möbius Function, Derek Garton

Mathematics and Statistics Faculty Publications and Presentations

Fix an odd prime ℓ and let G be the poset of isomorphism classes of finite abelian ℓ-groups, ordered by inclusion. If ξ:G→R^≥0 is a discrete probability distribution on G and A ∈ G, define the Ath moment of ξ to be . The question of determining conditions that ensure ξ is completely determined by its moments has been of recent interest in many problems of Cohen–Lenstra type. Furthermore, recovering ξ from its moments requires a new Möbius-type inversion formula on G. In this paper, we define this function, relate it to the classical Möbius …

A Finite Difference Method For Off-Fault Plasticity Throughout The Earthquake Cycle, Brittany A. Erickson, Eric M. Dunham, Arash Khosravifar

Mathematics and Statistics Faculty Publications and Presentations

We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiationdamping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor …

Dynamically Distinguishing Polynomials, Andrew Bridy, Derek Garton

Mathematics and Statistics Faculty Publications and Presentations

A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: For any prime p, reduce its coefficients mod p and consider its action on the field FpFp. We say a subset of Z[x]Z[x] is dynamically distinguishable mod p if the associated mod pdynamical systems are pairwise non-isomorphic. For any k,M∈Z>1k,M∈Z>1, we prove that there are infinitely many sets of integers MM of size M such that {xk+m∣m∈M}{xk+m∣m∈M} is dynamically distinguishable mod p for most p (in the sense of natural density). Our proof uses the Galois theory of dynatomic polynomials largely developed …

Subgradients Of Minimal Time Functions Without Calmness, Nguyen Mau Nam, Dang Van Cuong

Mathematics and Statistics Faculty Publications and Presentations

In recent years there has been great interest in variational analysis of a class of nonsmooth functions called the minimal time function. In this paper we continue this line of research by providing new results on generalized differentiation of this class of functions, relaxing assumptions imposed on the functions and sets involved for the results. In particular, we focus on the singular subdifferential and the limiting subdifferential of this class of functions.

Shift-Symmetric Configurations In Two-Dimensional Cellular Automata: Irreversibility, Insolvability, And Enumeration, Peter Banda, John S. Caughman Iv, Martin Cenek, Christof Teuscher

Mathematics and Statistics Faculty Publications and Presentations

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have been for a long time a central focus of complexity science, and physics.

Here, we introduce group-theoretic concepts to identify and enumerate the symmetric inputs, which result in irreversible system behaviors with undesired effects on many computational tasks. The concept of so-called configuration shift-symmetry is applied on two-dimensional cellular automata as an ideal model of computation. The results show the universal insolvability of “non-symmetric” tasks regardless of the transition function. By using a compact enumeration formula and bounding the number …