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2015

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Full-Text Articles in Physical Sciences and Mathematics

A Data Science Course For Undergraduates: Thinking With Data, Benjamin Baumer Dec 2015

A Data Science Course For Undergraduates: Thinking With Data, Benjamin Baumer

Mathematics Sciences: Faculty Publications

Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the increasingly sophisticated array of data available in many settings. These data tend to be nontraditional, in the sense that they are often live, large, complex, and/or messy. A first course in statistics at the undergraduate level typically introduces students to a variety of techniques to analyze small, neat, and clean datasets. However, whether they pursue more formal training in statistics or not, many of these students will end up …

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Geometric Auxetics, Ciprian Borcea, Ileana Streinu Dec 2015

Geometric Auxetics, Ciprian Borcea, Ileana Streinu

Computer Science: Faculty Publications

We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We demonstrate its usefulness by predicting or recognizing, without experiment, computer simulations or numerical approximations, the auxetic capabilities of several well-known structures available in the literature. We propose new principles of auxetic design and rely on the stronger notion of expansive behavior to provide an infinite supply of planar auxetic mechanisms and several new three-dimensional structures.

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Hypercube Unfoldings That Tile R3 And R2, Giovanna Diaz, Joseph O'Rourke Dec 2015

Hypercube Unfoldings That Tile R3 And R2, Giovanna Diaz, Joseph O'Rourke

Computer Science: Faculty Publications

We show that the hypercube has a face-unfolding that tiles space, and that unfolding has an edge-unfolding that tiles the plane. So the hypercube is a "dimension-descending tiler." We also show that the hypercube cross unfolding made famous by Dali tiles space, but we leave open the question of whether or not it has an edge-unfolding that tiles the plane.

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Narrow Na And K Absorption Lines Toward T Tauri Stars: Tracing The Atomic Envelope Of Molecular Clouds, I. Pascucci, Suzan Edwards, M Heyer, E. Rigliaco, L. Hillenbrand, U. Gorti, D. Hollenbach, M. N. Simon Nov 2015

Narrow Na And K Absorption Lines Toward T Tauri Stars: Tracing The Atomic Envelope Of Molecular Clouds, I. Pascucci, Suzan Edwards, M Heyer, E. Rigliaco, L. Hillenbrand, U. Gorti, D. Hollenbach, M. N. Simon

Astronomy: Faculty Publications

We present a detailed analysis of narrow Na I and K I absorption resonance lines toward nearly 40 T Tauri stars in Taurus with the goal of clarifying their origin. The Na I λ5889.95 line is detected toward all but one source, while the weaker K I λ7698.96 line is detected in about two-thirds of the sample. The similarity in their peak centroids and the significant positive correlation between their equivalent widths demonstrate that these transitions trace the same atomic gas. The absorption lines are present toward both disk and diskless young stellar objects, which excludes cold gas within the …

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Regularity Of Mean Curvature Flow Of Graphs On Lie Groups Free Up To Step 2, Luca Capogna, Giovanna Citti, Maria Manfredini Oct 2015

Regularity Of Mean Curvature Flow Of Graphs On Lie Groups Free Up To Step 2, Luca Capogna, Giovanna Citti, Maria Manfredini

Mathematics Sciences: Faculty Publications

We consider (smooth) solutions of the mean curvature flow of graphs over bounded domains in a Lie group free up to step two (and not necessarily nilpotent), endowed with a one parameter family of Riemannian metrics σ ε collapsing to a subRiemannian metric σ0 as ε → 0. We establish Ckα estimates for this flow, that are uniform as ε → 0 and as a consequence prove long time existence for the subRiemannian mean curvature flow of the graph. Our proof extend to the setting of every step two Carnot group (not necessarily free) and can be adapted following …

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Spiral Unfoldings Of Convex Polyhedra, Joseph O'Rourke Oct 2015

Spiral Unfoldings Of Convex Polyhedra, Joseph O'Rourke

Computer Science: Faculty Publications

The notion of a spiral unfolding of a convex polyhedron, resulting by flattening a special type of Hamiltonian cut-path, is explored. The Platonic and Archimedian solids all have nonoverlapping spiral unfoldings, although among generic polyhedra, overlap is more the rule than the exception. The structure of spiral unfoldings is investigated, primarily by analyzing one particular class, the polyhedra of revolution.

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Data Science In Statistics Curricula: Preparing Students To “Think With Data”, J. Hardin, R. Hoerl, Nicholas J. Horton, D. Nolan, B. Baumer, O. Hall-Holt, P. Murrell, R. Peng, P. Roback, D. Temple Lang, M. D. Ward Oct 2015

Data Science In Statistics Curricula: Preparing Students To “Think With Data”, J. Hardin, R. Hoerl, Nicholas J. Horton, D. Nolan, B. Baumer, O. Hall-Holt, P. Murrell, R. Peng, P. Roback, D. Temple Lang, M. D. Ward

Statistical and Data Sciences: Faculty Publications

A growing number of students are completing undergraduate degrees in statistics and entering the workforce as data analysts. In these positions, they are expected to understand how to use databases and other data warehouses, scrape data from Internet sources, program solutions to complex problems in multiple languages, and think algorithmically as well as statistically. These data science topics have not traditionally been a major component of undergraduate programs in statistics. Consequently, a curricular shift is needed to address additional learning outcomes. The goal of this article is to motivate the importance of data science proficiency and to provide examples and …

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Can The Wave Function In Configuration Space Be Replaced By Single-Particle Wave Functions In Physical Space?, Travis Norsen, Damiano Marian, Xavier Oriols Oct 2015

Can The Wave Function In Configuration Space Be Replaced By Single-Particle Wave Functions In Physical Space?, Travis Norsen, Damiano Marian, Xavier Oriols

Physics: Faculty Publications

The ontology of Bohmian mechanics includes both the universal wave function (living in 3N-dimensional configuration space) and particles (living in ordinary 3-dimensional physical space). Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated – replaced by a set of single-particle pilot-wave fields living in ordinary physical space. Such a re-formulation …

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Set It And Forget It: Approximating The Set Once Strip Cover Problem, Amotz Bar-Noy, Benjamin Baumer, Dror Rawitz Aug 2015

Set It And Forget It: Approximating The Set Once Strip Cover Problem, Amotz Bar-Noy, Benjamin Baumer, Dror Rawitz

Mathematics Sciences: Faculty Publications

We consider the Set Once Strip Cover problem, in which n wireless sensors are deployed over a one-dimensional region. Each sensor has a fixed battery that drains in inverse proportion to a radius that can be set just once, but activated at any time. The problem is to find an assignment of radii and activation times that maximizes the length of time during which the entire region is covered. We show that this problem is NP-hard and that RoundRobin, the algorithm in which the sensors take turns covering the entire region, has a tight approximation guarantee of 3. Moreover, we …

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Quantum Mechanical Derivation Of The Wallis Formula For Π, Tamar Friedmann, C. R. Hagen Aug 2015

Quantum Mechanical Derivation Of The Wallis Formula For Π, Tamar Friedmann, C. R. Hagen

Mathematics Sciences: Faculty Publications

A famous pre-Newtonian formula for π is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.

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The Robinson-Schensted Correspondence And A2-Web Bases, Matthew Housley, Heather M. Russell, Julianna Tymoczko Aug 2015

The Robinson-Schensted Correspondence And A2-Web Bases, Matthew Housley, Heather M. Russell, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to [n, n, n]: the reduced web basis associated to Kuperberg’s combinatorial description of the spider category; and the left cell basis for the left cell construction of Kazhdan and Lusztig. In the case of [n, n], the spider category is the Temperley-Lieb category; reduced webs correspond to planar matchings, which are equivalent to left cell bases. This paper compares the image of these bases under classical maps: the Robinson–Schensted algorithm between permutations and Young tableaux and Khovanov–Kuperberg’s bijection between Young tableaux and reduced …

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Upper Plate Reverse Fault Reactivation And The Unclamping Of The Megathrust During The 2014 Northern Chile Earthquake Sequence, Gabriel González, Pablo Salazar, John P. Loveless, Richard W. Allmendinger, Felipe Aron, Mahesh Shrivastava Aug 2015

Upper Plate Reverse Fault Reactivation And The Unclamping Of The Megathrust During The 2014 Northern Chile Earthquake Sequence, Gabriel González, Pablo Salazar, John P. Loveless, Richard W. Allmendinger, Felipe Aron, Mahesh Shrivastava

Geosciences: Faculty Publications

After 137 years without a great earthquake, the Mw 8.1 Pisagua event of 1 April 2014 occurred in the central portion of the southern Peru–northern Chile subduction zone. This megathrust earthquake was preceded by more than 2 weeks of foreshock activity migrating ∼3.5 km/day toward the mainshock hypocenter. This foreshock sequence was triggered by an Mw 6.7 earthquake on a reverse fault in the upper plate that strikes at a high angle to the trench, similar to well-documented reverse faults onshore. These margin-oblique reverse faults accommodate north-south shortening resulting from subduction across a plate boundary that is curved in map …

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A Character Style Library For Syriac Manuscripts, Nicholas Howe, Alice Yang, Michael Penn Aug 2015

A Character Style Library For Syriac Manuscripts, Nicholas Howe, Alice Yang, Michael Penn

Computer Science: Faculty Publications

Paleographers study ancient and historical handwriting in order to learn more about documents of significant interest and their creators. Computational tools and methods can aid this task in numerous ways, particularly for languages and scripts that are not widely known today. One project currently underway seeks to gather a collection of securely dated letter samples from Syriac documents dating between 500 and 1100 CE. The set comprises over 60,000 human selected character samples. This paper gives details on the collection and describes the automatic techniques used to process the initial human input so as to produce high-quality segmented character samples …

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Inkball Models For Character Localization And Out-Of-Vocabulary Word Spotting, Nicholas Howe Aug 2015

Inkball Models For Character Localization And Out-Of-Vocabulary Word Spotting, Nicholas Howe

Computer Science: Faculty Publications

Inkball models have previously been used for keyword spotting under the whole word query-by-image paradigm. This paper applies inkball methods to string-based queries for the first time, using synthetic models composed from individual characters. A hybrid system using both query-by-string for unknown words and query-by-example for known words outperforms either approach by itself on the George Washington and Parzival test sets. In addition, inkball character models offer an explanatory tool for understanding handwritten markings. In combination with a transcript they can help to to attribute each ink pixel of a word image to specific letters, resulting in highquality character segmentations.

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Lang’S Universal Molecule Algorithm, John C. Bowers, Ileana Streinu Aug 2015

Lang’S Universal Molecule Algorithm, John C. Bowers, Ileana Streinu

Computer Science: Faculty Publications

Robert Lang’s Universal Molecule algorithm, a landmark in modern computational origami, is the main component of his widely used Tree Maker program for origami design. It computes a crease pattern of a convex polygonal region, starting with a compatible metric tree. Although it has been informally described in several publications, neither the full power nor the inherent limitations of the method are well understood. In this paper we introduce a rigorous mathematical formalism to relate the input metric tree, the output crease pattern and the folded uniaxial origami base produced by the Universal Molecule algorithm. We characterize the family of …

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Modular Classes Of Lie Groupoid Representations Up To Homotopy, Rajan Amit Mehta Jul 2015

Modular Classes Of Lie Groupoid Representations Up To Homotopy, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein’s “The volume of a differentiable stack”.

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Horticultural Escape And Naturalization Of Magnolia Tripetala In Western Massachusetts: Biogeographic Context And Possible Relationship To Recent Climate Change, Jesse Bellemare, Claudia Deeg Jul 2015

Horticultural Escape And Naturalization Of Magnolia Tripetala In Western Massachusetts: Biogeographic Context And Possible Relationship To Recent Climate Change, Jesse Bellemare, Claudia Deeg

Biological Sciences: Faculty Publications

No abstract provided.

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Aerobic Copper-Catalyzed O-Methylation With Methylboronic Acid, Clare E. Jacobson, Noella Martinez-Muñoz, David J. Gorin Jun 2015

Aerobic Copper-Catalyzed O-Methylation With Methylboronic Acid, Clare E. Jacobson, Noella Martinez-Muñoz, David J. Gorin

Chemistry: Faculty Publications

The oxidative coupling of alkylboronic acids with oxygen nucleophiles offers a strategy for replacing toxic, electrophilic alkylating reagents. Although the Chan–Lam reaction has been widely applied in the arylation of heteroatom nucleophiles, O-alkylation with boronic acids is rare. We report a Cu-catalyzed nondecarboxylative methylation of carboxylic acids with methylboronic acid that proceeds in air with no additional oxidant. An isotope-labeling study supports an oxidative cross-coupling mechanism, in analogy to that proposed for Chan–Lam arylation.

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Liftings And Stresses For Planar Periodic Frameworks, Ciprian Borcea, Ileana Streinu Jun 2015

Liftings And Stresses For Planar Periodic Frameworks, Ciprian Borcea, Ileana Streinu

Computer Science: Faculty Publications

We formulate and prove a periodic analog of Maxwell’s theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing their finite counterparts. These properties are then applied to questions originating in mathematical crystallography and materials science, concerning planar periodic auxetic structures and ultrarigid periodic frameworks.

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Energy, Contact, And Density Profiles Of One-Dimensional Fermions In A Harmonic Trap Via Nonuniform-Lattice Monte Carlo Calculations, Casey E. Berger, E. R. Anderson, J. E. Drut May 2015

Energy, Contact, And Density Profiles Of One-Dimensional Fermions In A Harmonic Trap Via Nonuniform-Lattice Monte Carlo Calculations, Casey E. Berger, E. R. Anderson, J. E. Drut

Physics: Faculty Publications

We determine the ground-state energy and Tan's contact of attractively interacting few-fermion systems in a one-dimensional harmonic trap, for a range of couplings and particle numbers. Complementing those results, we show the corresponding density profiles. The calculations were performed with a lattice Monte Carlo approach based on a nonuniform discretization of space, defined via Gauss-Hermite quadrature points and weights. This particular coordinate basis is natural for systems in harmonic traps, and can be generalized to traps of other shapes. In all cases, it yields a position-dependent coupling and a corresponding nonuniform Hubbard-Stratonovich transformation. The resulting path integral is performed with …

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Average Case Network Lifetime On An Interval With Adjustable Sensing Ranges, Amotz Bar-Noy, Benjamin Baumer May 2015

Average Case Network Lifetime On An Interval With Adjustable Sensing Ranges, Amotz Bar-Noy, Benjamin Baumer

Mathematics Sciences: Faculty Publications

Given n sensors on an interval, each of which is equipped with an adjustable sensing radius and a unit battery charge that drains in inverse linear proportion to its radius, what schedule will maximize the lifetime of a network that covers the entire interval? Trivially, any reasonable algorithm is at least a 2-approximation for this Sensor Strip Cover problem, so we focus on developing an efficient algorithm that maximizes the expected network lifetime under a random uniform model of sensor distribution. We demonstrate one such algorithm that achieves an expected network lifetime within 12 % of the theoretical maximum. Most …

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Global Pattern Search At Scale, R. Jordan Crouser, Matthew C. Schmidt, Stephen Kelley, Benjamin Miller, Daniel Hook, Lauren Edwards, Maja Milosavljevic, Elizabeth Michel, Elizabeth Ferme, Robert Carrington, Albert I. Reuther Apr 2015

Global Pattern Search At Scale, R. Jordan Crouser, Matthew C. Schmidt, Stephen Kelley, Benjamin Miller, Daniel Hook, Lauren Edwards, Maja Milosavljevic, Elizabeth Michel, Elizabeth Ferme, Robert Carrington, Albert I. Reuther

Computer Science: Faculty Publications

In recent years, data collection has far outpaced the tools for data analysis in the area of non-traditional GEOINT analysis. Traditional tools are designed to analyze small-scale numerical data, but there are few good interactive tools for processing large amounts of unstructured data such as raw text. In addition to the complexities of data processing, presenting the data in a way that is meaningful to the end user poses another challenge. In our work, we focused on analyzing a corpus of 35,000 news articles and creating an interactive geovisualization tool to reveal patterns to human analysts. Our comprehensive tool, Global …

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The Atiyah Class Of A Dg-Vector Bundle, Rajan Amit Mehta, Mathieu Stiénon, Ping Xu Apr 2015

The Atiyah Class Of A Dg-Vector Bundle, Rajan Amit Mehta, Mathieu Stiénon, Ping Xu

Mathematics Sciences: Faculty Publications

We introduce the notions of Atiyah class and Todd class of a differential graded vector bundle with respect to a differential graded Lie algebroid. We prove that the space of vector fields X(M) on a dg-manifold M with homological vector field Q admits a structure of L∞[1]-algebra with the Lie derivative LQ as unary bracket λ1, and the Atiyah cocycle AtM corresponding to a torsion-free affine connection as binary bracket λ2.

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Are There Really Two Different Bell’S Theorems?, Travis Norsen Mar 2015

Are There Really Two Different Bell’S Theorems?, Travis Norsen

Physics: Faculty Publications

This is a polemical response to Howard Wiseman’s recent paper, “The two Bell’s theorems of John Bell”. Wiseman argues that, in 1964, Bell established a conflict between the quantum mechanical predictions and the joint assumptions of determinism and (what is now usually known as) “parameter independence”. Only later, in 1976, did Bell, according to Wiseman, first establish a conflict between the quantum mechanical predictions and locality alone (in the specific form that Bell would sometimes call “local causality”). Thus, according to Wiseman, the long-standing disagreements about what, exactly, Bell’s theorem does and does not prove can be understood largely as …

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Fossils Of Putative Marine Algae From The Cryogenian Glacial Interlude Of Mongolia, Phoebe A. Cohen, Francis A. Macdonald, Sara Pruss, Emily Matys, Tanja Bosak Mar 2015

Fossils Of Putative Marine Algae From The Cryogenian Glacial Interlude Of Mongolia, Phoebe A. Cohen, Francis A. Macdonald, Sara Pruss, Emily Matys, Tanja Bosak

Geosciences: Faculty Publications

Neoproterozoic carbonate successions provide a new taphonomic window into the diversification of eukaryotes. We report recently discovered macroscopic organic warty sheets (MOWS) in macerates of limestone from the ca. 662-635 Ma Taishir Formation (Tsagaan Olom Group, Mongolia). Sheets are applanate. One surface contains raised ridges and conspicuous, ∼ 100-μm-tall warty protuberances with depressed tops that enclose internal cavities containing cellular structures. The Taishir MOWS may be the remains of unusual bacterial, protistan, or fungal biofilms, or a previously undocumented, extinct taxon. However, multiple lines of evidence including the morphology of warty protuberances and the presence of cellular architecture within protuberances …

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Probing Stellar Accretion With Mid-Infrared Hydrogen Lines, Elisabetta Rigliaco, Ilaria Pascucci, Gaspard Duchene, Suzan Edwards, D. R. Ardila, C. Grady, Ignacio Mendigutía, Benjamín Montesinos, Gijs D. Mulders, Joan R. Najita, J. Carpenter, Elise Furlan, Uma Gorti, Rowin Meijerink, M. R. Meyer Feb 2015

Probing Stellar Accretion With Mid-Infrared Hydrogen Lines, Elisabetta Rigliaco, Ilaria Pascucci, Gaspard Duchene, Suzan Edwards, D. R. Ardila, C. Grady, Ignacio Mendigutía, Benjamín Montesinos, Gijs D. Mulders, Joan R. Najita, J. Carpenter, Elise Furlan, Uma Gorti, Rowin Meijerink, M. R. Meyer

Astronomy: Faculty Publications

In this paper we investigate the origin of the mid-infrared (IR) hydrogen recombination lines for a sample of 114 disks in different evolutionary stages (full, transitional, and debris disks) collected from the Spitzer archive. We focus on the two brighter H I lines observed in the Spitzer spectra, the H I (7-6) at 12.37 μm and the H I (9-7) at 11.32 μm. We detect the H I (7-6) line in 46 objects, and the H I (9-7) in 11. We compare these lines with the other most common gas line detected in Spitzer spectra, the [Ne II] at 12.81 …

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Periodic Body-And-Bar Frameworks, Ciprian Borcea, Ileana Streinu, Shin-Ichi Tanigawa Jan 2015

Periodic Body-And-Bar Frameworks, Ciprian Borcea, Ileana Streinu, Shin-Ichi Tanigawa

Computer Science: Faculty Publications

Periodic body-and-bar frameworks are abstractions of crystalline structures made of rigid bodies connected by fixed-length bars and subject to the action of a lattice of translations. We give a Maxwell–Laman characterization for minimally rigid periodic body-and-bar frameworks in terms of their quotient graphs. As a consequence we obtain efficient polynomial time algorithms for their recognition based on matroid partition and pebble games.

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Taphonomic Bias Of Selective Silicification Revealed By Paired Petrographic And Insoluble Residue Analysis, Sara B. Pruss, Jonathan L. Payne, Sophie Westacott Jan 2015

Taphonomic Bias Of Selective Silicification Revealed By Paired Petrographic And Insoluble Residue Analysis, Sara B. Pruss, Jonathan L. Payne, Sophie Westacott

Geosciences: Faculty Publications

Silicification is an important mode of fossil preservation but the extent to which silicified material represents an unbiased sampling of the total fossil assemblage within a given rock sample remains poorly quantified. Here, we use paired analyses of thin sections and acid-extracted silicified specimens from the same samples to examine the biases introduced during silicification of Lower Triassic Virgin Limestone carbonates preserved in the Muddy Mountains of southern Nevada. Bivalves dominate most thin sections in the point count data, but rarely silicify completely enough to be recognized in residue. Echinoderms and gastropods are less abundant in thin section but dominate …

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Deforming Diamond, Ciprian Borcea, Ileana Streinu Jan 2015

Deforming Diamond, Ciprian Borcea, Ileana Streinu

Computer Science: Faculty Publications

For materials science, diamond crystals are almost unrivaled for hardness and a range of other properties. Yet, when simply abstracting the carbon bonding structure as a geometric bar-and-joint periodic framework, it is far from rigid. We study the geometric deformations of this type of framework in arbitrary dimension d, with particular regard to the volume variation of a unit cell.

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Expansive Periodic Mechanisms, Ciprian Borcea, Ileana Streinu Jan 2015

Expansive Periodic Mechanisms, Ciprian Borcea, Ileana Streinu

Computer Science: Faculty Publications

A one-parameter deformation of a periodic bar-and-joint framework is expansive when all distances between joints increase or stay the same. In dimension two, expansive behavior can be fully explained through our theory of periodic pseudo-triangulations. However, higher dimensions present new challenges. In this paper we study a number of periodic frameworks with expansive capabilities in dimension d ≥ 3 and register both similarities and contrasts with the two-dimensional case.

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