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Friday, February 26th, 2016

Andrea Halpern – Halpern, Andrea; Golden, Hannah L.; Magdalinou, Nadia; Witoonpanich, Pirada; and Warren, Jason D. “Musical Tasks Targeting Preserved and Impaired Functions in Two Dementias.” Annals of the New York Academy of Sciences 1337, no. 1 (2015) : 241-248.

Andrea Halpern, Professor of Psychology

Studies of musical abilities in dementia have for the most part been rather general assessments of abilities, for instance, assessing retention of music learned premorbidly. Here, we studied patients with dementias with contrasting cognitive profiles to explore specific aspects of music cognition under challenge. Patients suffered from Alzheimer’s disease (AD), in which a primary impairment is in forming new declarative memories, or Lewy body disease (PD/LBD), a type of parkinsonism in which executive impairments are prominent. In the AD patients, we examined musical imagery. Behavioral and neural evidence confirms involvement of perceptual networks in imagery, and these are relatively spared in early stages of the illness. Thus, we expected patients to have relatively intact imagery in a mental pitch comparison task. For the LBD patients, we tested whether executive dysfunction would extend to music. We probed inhibitory skills by asking for a speeded pitch or timbre judgment when the irrelevant dimension was held constant or also changed. Preliminary results show that AD patients score similarly to controls in the imagery tasks, but PD/LBD patients are impaired relative to controls in suppressing some irrelevant musical dimensions, particularly when the required judgment varies from trial to trial.

2014 The Authors. Annals of the New York Academy of Sciences published by Wiley Periodicals Inc. on behalf of The New York Academy of Sciences.

Halpern, Andrea; Golden, Hannah L.; Magdalinou, Nadia; Witoonpanich, Pirada; and Warren, Jason D. “Musical Tasks Targeting Preserved and Impaired Functions in Two Dementias.” Annals of the New York Academy of Sciences 1337, no. 1 (2015) : 241-248.

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Friday, February 26th, 2016

Thomas H. Solomon – Gowen, Savannah and Solomon, Thomas H. “Experimental Studies of Coherent Structures in an Advection-Reaction-Diffusion System.” Chaos (Woodbury, N.Y.) 25, no. 8 (2015) : 087403.

Thomas H. Solomon, Professor of Physics

We present experimental studies of reaction front propagation in a single vortex flow with an imposed external wind. The fronts are produced by the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. The flow is generated using an electromagnetic forcing technique: an almost-radial electrical current interacts with a magnetic field from a magnet below the fluid layer to produce the vortex. The magnet is mounted on crossed translation stages allowing for movement of the vortex through the flow. Reaction fronts triggered in or in front of the moving vortex form persistent structures that are seen experimentally for time-independent (constant motion), time-periodic, and time-aperiodic flows. These results are examined with the use of burning invariant manifolds that act as one-way barriers to front motion in the flows. We also explore the usefulness of finite-time Lyapunov exponent fields as an instrument for analyzing front propagation behavior in a fluid flow.

Gowen, Savannah and Solomon, Thomas H. “Experimental Studies of Coherent Structures in an Advection-Reaction-Diffusion System.” Chaos (Woodbury, N.Y.) 25, no. 8 (2015) : 087403.

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Friday, February 26th, 2016

Andrea Halpern – Schaal, Nora K.; Javadi, Amir-Homayoun; Halpern, Andrea; Pollok, Bettina; and Banissy, Michael J. “Right Parietal Cortex Mediates Recognition Memory for Melodies.” European Journal of Neuroscience 42, no. 1 (2015) : 1660-1666.

Andrea Halpern, Professor of Psychology

Functional brain imaging studies have highlighted the significance of right-lateralized temporal, frontal and parietal brain areas for memory for melodies. The present study investigated the involvement of bilateral posterior parietal cortices (PPCs) for the recognition memory of melodies using transcranial direct current stimulation (tDCS). Participants performed a recognition task before and after tDCS. The task included an encoding phase (12 melodies), a retention period, as well as a recognition phase (24 melodies). Experiment 1 revealed that anodal tDCS over the right PPC led to a deterioration of overall memory performance compared with sham. Experiment 2 confirmed the results of Experiment 1 and further showed that anodal tDCS over the left PPC did not show a modulatory effect on memory task performance, indicating a right lateralization for musical memory. Furthermore, both experiments revealed that the decline in memory for melodies can be traced back to an interference of anodal stimulation on the recollection process (remember judgements) rather than to familiarity judgements. Taken together, this study revealed a causal involvement of the right PPC for memory for melodies and demonstrated a key role for this brain region in the recollection process of the memory task.

Schaal, Nora K.; Javadi, Amir-Homayoun; Halpern, Andrea; Pollok, Bettina; and Banissy, Michael J. “Right Parietal Cortex Mediates Recognition Memory for Melodies.” European Journal of Neuroscience 42, no. 1 (2015) : 1660-1666.

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Friday, February 26th, 2016

Thomas H. Solomon – Mahoney, John R.; Li, John; Boyer, Carleen; and Solomon, Thomas H. “Frozen Reaction Fronts in Steady Flows: A Burning-Invariant-Manifold Perspective.” Physical Review E 92, no. 6 (2015) : 063005.

Thomas H. Solomon, Professor of Physics

The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the reacted domain is static, and the front appears “frozen.” Our central result is that these frozen fronts in the two-dimensional fluid are composed of segments of burning invariant manifolds, invariant manifolds of front-element dynamics in xy theta space, where theta is the front orientation. Burning invariant manifolds (BIMs) have been identified previously as important local barriers to front propagation in fluid flows. The relevance of BIMs for frozen fronts rests in their ability, under appropriate conditions, to form global barriers, separating reacted domains from nonreacted domains for all time. The second main result of this paper is an understanding of bifurcations that lead from a nonfrozen state to a frozen state, as well as bifurcations that change the topological structure of the frozen front. Although the primary results of this study apply to general fluid flows, our analysis focuses on a chain of vortices in a channel flow with an imposed wind. For this system, we present both experimental and numerical studies that support the theoretical analysis developed here.

Mahoney, John R.; Li, John; Boyer, Carleen; and Solomon, Thomas H. “Frozen Reaction Fronts in Steady Flows: A Burning-Invariant-Manifold Perspective.” Physical Review E 92, no. 6 (2015) : 063005.

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Friday, February 26th, 2016

Thomas H. Solomon – Megson, P. W.; Najarian, M. L.; Lilienthal, Katie; and Solomon, Thomas H. “Pinning of Reaction Fronts by Burning Invariant Manifolds in Extended Flows.” Physics of Fluids 27, no. 2 (2015) : 023601.

Thomas H. Solomon, Professor of Physics

We present experiments on the behavior of reaction fronts in extended, vortex-dominated flows in the presence of an imposed wind. We use the ferroin-catalyzed, excitable Belousov-Zhabotinsky chemical reaction, which produces pulse-like reaction fronts. Two time-independent flows are studied: an ordered (square) array of vortices and a spatially disordered flow. The flows are generated with a magneto-hydrodynamic forcing technique, with a pattern of magnets underneath the fluid cell. The magnets are mounted on a translation stage which moves with a constant speed V-d under the fluid, resulting in motion of the vortices within the flow. In a reference frame moving with magnets, the flow is equivalent to one with stationary vortices and a uniform wind with speed W = V-d. For a wide range of wind speeds, reaction fronts pin to the vortices (in a co-moving reference frame), propagating neither forward against the wind nor being blown backward. We analyze this pinning phenomenon and the resulting front shapes using a burning invariant manifold (BIM) formalism. The BIMs are one-way barriers to reaction fronts in the advection-reaction-diffusion process. Pinning occurs when several BIMs overlap to form a complete barrier that spans the width of the system. In that case, the shape of the front is determined by the shape of the BIMs. For the ordered array flow, we predict the locations of the BIMs numerically using a simplified model of the velocity field for the ordered vortex array and compare the BIM shapes to the pinned reaction fronts. We also explore transient behavior of the fronts (before reaching their steady state) to highlight the one-way nature of the BIMs. (C) 2015 Author(s).

Megson, P. W.; Najarian, M. L.; Lilienthal, Katie; and Solomon, Thomas H. “Pinning of Reaction Fronts by Burning Invariant Manifolds in Extended Flows.” Physics of Fluids 27, no. 2 (2015) : 023601.

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Friday, February 26th, 2016

Katharina Vollmayr-Lee – Helfferich, Julian; Vollmayr-Lee, Katharina; Ziebert, Falko; Meyer, Hendrik; and Baschnagel, Joerg. “Glass Formers Display Universal Non-Equilibrium Dynamics on the Level of Single-Particle Jumps.” European Physical Letters 109, (2015) : 36004-p1-36004-p9.

Katharina Vollmayr-Lee, Professor of Physics

Glasses are inherently out-of-equilibrium systems evolving slowly toward their equilibrium state in a process called physical aging. During aging, dynamic observables depend on the history of the system, hampering comparative studies of dynamics in different glass formers. Here, we demonstrate how glass formers can be directly compared on the level of single-particle jumps, i.e. the structural relaxation events underlying the alpha-process. Describing the dynamics in terms of a continuous-time random walk, an analytic prediction for the jump rate is derived. The result is subsequently compared to molecular-dynamics simulations of amorphous silica and a polymer melt as two generic representatives of strong and fragile glass formers, and good agreement is found.

Helfferich, Julian; Vollmayr-Lee, Katharina; Ziebert, Falko; Meyer, Hendrik; and Baschnagel, Joerg. “Glass Formers Display Universal Non-Equilibrium Dynamics on the Level of Single-Particle Jumps.” European Physical Letters 109, (2015) : 36004-p1-36004-p9.

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Friday, February 26th, 2016

Katharina Vollmayr-Lee – Helfferich, J.; Vollmayr-Lee, Katharina; Ziebert, F.; Meyer, H.; and Baschnagel, J. “Glass Formers Display Universal Non-Equilibrium Dynamics on the Level of Single-Particle Jumps.” EPL 109, no. 3 (2015) : 36004.

Katharina Vollmayr-Lee, Professor of Physics

Glasses are inherently out-of-equilibrium systems evolving slowly toward their equilibrium state in a process called physical aging. During aging, dynamic observables depend on the history of the system, hampering comparative studies of dynamics in different glass formers. Here, we demonstrate how glass formers can be directly compared on the level of single-particle jumps, i. e. the structural relaxation events underlying the a-process. Describing the dynamics in terms of a continuous-time random walk, an analytic prediction for the jump rate is derived. The result is subsequently compared to molecular-dynamics simulations of amorphous silica and a polymer melt as two generic representatives of strong and fragile glass formers, and good agreement is found. Copyright (C) EPLA, 2015

Helfferich, J.; Vollmayr-Lee, Katharina; Ziebert, F.; Meyer, H.; and Baschnagel, J. “Glass Formers Display Universal Non-Equilibrium Dynamics on the Level of Single-Particle Jumps.” EPL 109, no. 3 (2015) : 36004.

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Friday, February 26th, 2016

John A. Doces – Magee, Christopher S. and Doces, John A. “Reconsidering Regime Type and Growth: Lies, Dictatorships, and Statistics.” International Studies Quarterly 59, no. 2 (2015) : 223-237.

John A. Doces, Associate Professor of Political Science

Some recent papers have concluded that authoritarian regimes have faster economic growth than democracies. These supposed growth benefits of autocracies are estimated using data sets in which growth rates rely heavily on data reported by each government. Governments have incentives to exaggerate their economic growth figures, however, and authoritarian regimes may have fewer limitations than democracies on their ability to do so. This paper argues that growth data submitted to international agencies are overstated by authoritarian regimes compared to democracies. If true, it calls into question the estimated relationship between government type and economic growth found in the literature. To measure the degree to which each government’s official growth statistics are overstated, the economic growth rates reported in the World Bank’s World Development Indicators are compared to a new measure of economic growth based on satellite imaging of nighttime lights. This comparison reveals whether or not dictators exaggerate their true growth rates and by how much. Annual GDP growth rates are estimated to be overstated by 0.5-1.5 percentage points in the statistics that dictatorships report to the World Bank.

Magee, Christopher S. and Doces, John A. “Reconsidering Regime Type and Growth: Lies, Dictatorships, and Statistics.” International Studies Quarterly 59, no. 2 (2015) : 223-237.

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Friday, February 26th, 2016

John A. Doces – Doces, John A. and Magee, Christopher S. “Trade and Democracy: A Factor-Based Approach.” International Interactions 41, no. 2 (2015) : 407-425.

John A. Doces, Associate Professor of Political Science

We study the relationship between trade openness and democracy using a data set with capital-labor ratios, trade flows, and regime type for 142 countries between 1960 and 2007. We are among the first to test a prediction that emerges from the model of Acemoglu and Robinson (2006): Relative factor endowments determine whether trade promotes democracy or not. The statistical results from two-stage least squares estimation indicate that trade is positively associated with democracy among labor-abundant countries but that trade has a negative effect on democracy in capital-abundant countries. The results are not robust, however, and thus we conclude that the evidence in support of their argument is relatively weak.

Doces, John A. and Magee, Christopher S. “Trade and Democracy: A Factor-Based Approach.” International Interactions 41, no. 2 (2015) : 407-425.

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Friday, February 26th, 2016

Karen M. Morin – Morin, Karen M. “Carceral Space: Prisoners and Animals.” Antipode: A Radical Journal of Geography (2016).

Karen M. Morin, Associate Provost

This paper develops a framework for exploring resonances across human and nonhuman carceral geographies. I illustrate the close linkages across prisoner and animal carcerality and captivity focusing on three types of sites and institutions: the prison execution chamber and the animal slaughterhouse; sites of medical (and other) laboratory testing of pharmaceutical and other products on incarcerated humans and captive animals; and sites and institutions of exploited prisoner and animal labor. The main themes that call for a ‘carceral comparison’ among these sites include the emotional and psychological strain and violence enacted on bodies that is interwoven into their day-to-day operations; their geographies (locations, design and layout) and the carefully choreographed and regulated movements within them that speak to regimes of surveillance, power, and control; and the ethical questions that arise when we consider the potential for these sites to become locations of genocide and extinction of particular populations.

Morin, Karen M. “Carceral Space: Prisoners and Animals.” Antipode: A Radical Journal of Geography (2016).

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Friday, February 26th, 2016

Michael James – James, Michael. “Constituency Deliberation.” Political Research Quarterly 68, no. 3 (2015) : 552-563.

Michael James, Associate Professor of Political Science

How do we distinguish legitimate, democratic representation from illegitimate, undemocratic elite rule? Empirical scholars of representation typically rely on the “bedrock norm” that democratic representatives must respond to the antecedent interests of their constituents, but empirical studies of public opinion suggest that constituents’ interests emerge following engagement with their representatives. The result is the “constituency paradox”: representatives are supposed to respond to constituent interests, interests that representatives themselves help to create. Deliberative democratic theories seek to circumvent this paradox by distinguishing between representatives who communicatively educate their constituents from those who strategically manipulate them, but it is empirically impossible to distinguish legitimate education from illegitimate manipulation. Nondeliberative criteria requiring elite competition and popular contestation also fail to ground legitimate democratic representation. In response, I develop a model of constituency deliberation that does not rely on the bedrock norm, accepts strategic as well as communicative action, acknowledges the asymmetric but reciprocal relationship between constituents and representatives, and uses a systemic approach to assess democratic representation. This deliberative model leads to institutional reforms that avoid the bedrock norm and seek to mitigate representative manipulation by creating space for constituents to respond to representatives’ claims to represent their interests.

James, Michael. “Constituency Deliberation.” Political Research Quarterly 68, no. 3 (2015) : 552-563.

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Friday, February 26th, 2016

Karen M. Morin – Morin, Karen M. “The Late-Modern American Jail: Epistemologies of Space and Violence.” The Geographical Journal forthcoming (2015).

Karen M. Morin, Associate Provost

One of the most troubling aspects of current trends in American mass incarceration is the extent to which ‘criminality’ is produced within prison walls, primarily in the form of inmate–inmate or inmate–staff assaults. Most methods of prison or jail control have the adverse, and perverse, effect of increasing inmates’ levels of fear, terror, and ultimately violence – with stabbings, beatings, and other types of assaults common occurrences. The design of podular ‘direct supervision’ jails and their accompanying philosophies of punishment aspire to change these conditions. Direct supervision features correctional officers inside each housing unit with no physical barriers impeding supervision, and is intended to create a safe, more humane, stress-free environment for both inmates and staff. This study draws on ethnographic evidence of inmate experiences with direct supervision at Douglas County Department of Corrections in Omaha, Nebraska (USA). The respondents generally do feel safe in this jail environment, for a combination of reasons, some of which are related to spatial design. Inmates identified a number of implications – gains and losses – of this more ‘humane’ form of incarceration in terms of power and empowerment. The study also documents the potential for inmate activism on their own behalf through this design.

Morin, Karen M. “The Late-Modern American Jail: Epistemologies of Space and Violence.” The Geographical Journal forthcoming (2015).

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Friday, February 26th, 2016

Michael James – James, Michael Rabinder. “Two Concepts of Constituency.” Journal of Politics 77, no. 2 (2015) : 381-393.

Michael James, Associate Professor of Political Science

In this essay, I challenge the conceptual and normative arguments of Andrew Rehfeld’s The Concept of Constituency. I argue that Rehfeld conflates two distinct concepts of constituency as a result of errors in his normative argument for random, permanent constituencies. In response, I carefully distinguish the two concepts of objective constituency (the grouping of citizens into geographic or other electoral rolls through parametric action) and subjective constituency (the formation of cohesive voting blocs to elect a representative through strategic and communicative action between constituents and candidates). Distinguishing between objective and subjective constituency allows me to identify the shortcomings in the normative analyses of democratic constituencies proffered by Lisa Disch and Thomas Pogge. I then propose the use of random, permanent constituencies, each of which elects five representatives through the single transferable vote. This facilitates the representation of racial and ethnic minorities, while encouraging constituency deliberation aimed at the national interest.

James, Michael Rabinder. “Two Concepts of Constituency.” Journal of Politics 77, no. 2 (2015) : 381-393.

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Friday, February 26th, 2016

Chris Boyatzis – Cook, Kaye V.; Kimball, Cynthia; Boyatzis, Chris; and Leonard, Kathleen C. “Religiousness and Spirituality Among Highly Religious Emerging Adults.” Journal of Psychology and Christianity 34, no. 3 (2015) : 252-265.

Chris Boyatzis, Professor of Psychology

Three mixed-methods studies assessed whether students at Christian colleges maintain a traditional faith over time. For a population of recent, two-year, and four-year alumni at two Christian colleges (Study 1), as well as first-year and senior undergraduate students at one of the two Christian colleges (Studies 2 and 3), we measured changes in denominational commitments, religious attitudes and behavior, and descriptions of changing points in faith. We analyzed the interview data (faith changing points) for instances of moralistic therapeutic deism (MTD), which Smith and his colleagues (Smith & Denton, 2005; Smith & Snell, 2009) have identified as characteristic of emerging adults’ religiousness. MTD is described as a watered-down faith in which God is understood as a personal helper who sets moral standards but places little demand on the believer. Our findings indicate that undergraduates and alumni from Christian college contexts maintain solid faith commitments that are not consistent with MTD. Instead they hold a robust, traditional faith marked by trust in God, ownership of their own faith, and an embrace of historically central religious constructs, consistent with the traditionalists (Smith & Snell, 2009) and conservative believers (Arnett, 2014). In their traditionalism, the undergraduates in Study 3 experience themselves as having greater concern for spirituality (or faith) than when they entered college, but no greater concern for religiousness (or institutional commitment), describing themselves as “more spiritual but less religious.”

Cook, Kaye V.; Kimball, Cynthia; Boyatzis, Chris; and Leonard, Kathleen C. “Religiousness and Spirituality Among Highly Religious Emerging Adults.” Journal of Psychology and Christianity 34, no. 3 (2015) : 252-265.

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Friday, February 26th, 2016

Pamela Gorkin – Gorkin, Pamela and Akeroyd, John. “Uniform Approximation by Indestructible Blaschke Products.” Journal of Mathematical Analysis and its Applications 434, no. 2 (2016) : 1419-1434.

Pamela Gorkin, Professor of Mathematics

We address the question: Are the inner functions in the uniform closure in the algebra of bounded analytic functions of the indestructible Blaschke products? We show, in particular, that every inner function with countable spectrum is in the closure of the indestructible Blaschke products, that every Blaschke product is a product of two indestructible Blaschke products and we study approximation in modulus.

Gorkin, Pamela and Akeroyd, John. “Uniform Approximation by Indestructible Blaschke Products.” Journal of Mathematical Analysis and its Applications 434, no. 2 (2016) : 1419-1434.

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Friday, February 26th, 2016

Jeffrey J. Langford – Langford, Jeffrey J. “Neumann Comparison Theorems in Elliptic PDEs.” Potential Analysis 43, no. 3 (2015) : 415-459.

Jeffrey J. Langford, Assistant Professor of Mathematics

In this paper we prove a spherical comparison result for the (k,n)-spherical rearrangement using the spherical Green’s function and a rearrangement inequality of A. Baernstein. We next use a simple reflection argument to obtain a Neumann comparison result on a hemisphere for the (k,n)-hemispherical rearrangement. Using the Lambert equal-area projection and stereographic projection, we obtain Neumann comparison results in Euclidean space. We end with a discussion of open problems in the unit disk involving heat flow.

Langford, Jeffrey J. “Neumann Comparison Theorems in Elliptic PDEs.” Potential Analysis 43, no. 3 (2015) : 415-459.

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Friday, February 26th, 2016

Peter A. Brooksbank – Brooksbank, Peter A. and Wilson, James B. “The Module Isomorphism Problem Reconsidered.”Journal of Algebra 421, no. SI (2015) : 541-559.

Peter A. Brooksbank, Professor of Mathematics

Algorithms to decide isomorphism of modules have been honed continually over the last 30 years, and their range of applicability has been extended to include modules over a wide range of rings. Highly efficient computer implementations of these algorithms form the bedrock of systems such as GAP and MAGMA, at least in regard to computations with groups and algebras. By contrast, the fundamental problem of testing for isomorphism between other types of algebraic structures – such as groups, and almost any type of algebra – seems today as intractable as ever. What explains the vastly different complexity status of the module isomorphism problem? This paper argues that the apparent discrepancy is explained by nomenclature. Current algorithms to solve module isomorphism, while efficient and immensely useful, are actually solving a highly constrained version of the problem. We report that module isomorphism in its general form is as hard as algebra isomorphism and graph isomorphism, both well-studied problems that are widely regarded as difficult. On a more positive note, for cyclic rings we describe a polynomial-time algorithm for the general module isomorphism problem. We also report on a MAGMA implementation of our algorithm. (C) 2014 Elsevier Inc. All rights reserved.

Brooksbank, Peter A. and Wilson, James B. “The Module Isomorphism Problem Reconsidered.”Journal of Algebra 421, no. SI (2015) : 541-559.

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Friday, February 26th, 2016

Peter R.W. McNamara – McNamara, Peter R. W. and Steingrímsson, Einar. “On the Topology of the Permutation Pattern Poset.” Journal of Combinatorial Theory, Series A 134, (2015) : 1-35.

Peter R.W. McNamara, Associate Professor of Mathematics

The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a disconnected subinterval and are thus not shellable. Nevertheless, there seem to be large classes of intervals that are shellable and thus have the homotopy type of a wedge of spheres. We prove this to be the case for all intervals of layered permutations that have no disconnected subintervals of rank 3 or more. We also characterize in a simple way those intervals of layered permutations that are disconnected. These results carry over to the poset of generalized subword order when the ordering on the underlying alphabet is a rooted forest. We conjecture that the same applies to intervals of separable permutations, that is, that such an interval is shellable if and only if it has no disconnected subinterval of rank 3 or more. We also present a simplified version of the recursive formula for the Möbius function of decomposable permutations given by Burstein et al.

McNamara, Peter R. W. and Steingrímsson, Einar. “On the Topology of the Permutation Pattern Poset.” Journal of Combinatorial Theory, Series A 134, (2015) : 1-35.

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Friday, February 26th, 2016

Peter A. Brooksbank – Brooksbank, Peter A. “The Module Isomorphism Problem Reconsidered.” Journal of Algebra 421, (2015) : 541-559.

Peter A. Brooksbank, Professor of Mathematics

Algorithms to decide isomorphism of modules have been honed continually over the last 30 years, and their range of applicability has been extended to include modules over a wide range of rings. Highly efficient computer implementations of these algorithms form the bedrock of systems such as GAP and MAGMA, at least in regard to computations with groups and algebras. By contrast, the fundamental problem of testing for isomorphism between other types of algebraic structures — such as groups, and almost any type of algebra — seems today as intractable as ever. What explains the vastly different complexity status of the module isomorphism problem?

This paper argues that the apparent discrepancy is explained by nomenclature. Current algorithms to solve module isomorphism, while efficient and immensely useful, are actually solving a highly constrained version of the problem. We report that module isomorphism in its general form is as hard as algebra isomorphism and graph isomorphism, both well-studied problems that are widely regarded as difficult. On a more positive note, for cyclic rings we describe a polynomial-time algorithm for the general module isomorphism problem. We also report on a MAGMA implementation of our algorithm.

Brooksbank, Peter A. “The Module Isomorphism Problem Reconsidered.” Journal of Algebra 421, (2015) : 541-559.

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