Digital Commons at Loyola Marymount University and Loyola Law SchoolCopyright (c) 2016 Loyola Marymount University and Loyola Law School All rights reserved.
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Recent documents in Digital Commons at Loyola Marymount University and Loyola Law Schoolen-usFri, 02 Dec 2016 01:38:25 PST3600Our L.A.?: Korean Americans in the 'New' Los Angeles
http://digitalcommons.lmu.edu/aaas_fac/9
http://digitalcommons.lmu.edu/aaas_fac/9Thu, 01 Dec 2016 17:14:52 PSTEdward J.W. ParkThe Impact of Mainstream Political Mobilization on Asian American Communities: The Case of Korean Americans in Los Angeles, 1992-1998
http://digitalcommons.lmu.edu/aaas_fac/8
http://digitalcommons.lmu.edu/aaas_fac/8Thu, 01 Dec 2016 17:14:46 PSTEdward J.W. ParkCommunity Divided: Korean American Politics in Post-Civil Unrest Los Angeles
http://digitalcommons.lmu.edu/aaas_fac/7
http://digitalcommons.lmu.edu/aaas_fac/7Thu, 01 Dec 2016 17:14:41 PSTEdward J.W. ParkAsian Pacific Americans and Urban Politics
http://digitalcommons.lmu.edu/aaas_fac/6
http://digitalcommons.lmu.edu/aaas_fac/6Thu, 01 Dec 2016 17:14:35 PSTEdward J.W. ParkProbationary Americans: Contemporary Immigration Policies and the Shaping of Asian American Communities
http://digitalcommons.lmu.edu/aaas_fac/5
http://digitalcommons.lmu.edu/aaas_fac/5Thu, 01 Dec 2016 17:14:30 PSTEdward J.W. Park et al.Asian Americans in Silicon Valley: High Technology Industrial Development and Community Transformation
http://digitalcommons.lmu.edu/aaas_fac/4
http://digitalcommons.lmu.edu/aaas_fac/4Thu, 01 Dec 2016 17:14:25 PSTEdward J.W. Park et al.Asians Matter: Asian Americans and the High Technology Industry in Silicon Valley
http://digitalcommons.lmu.edu/aaas_fac/3
http://digitalcommons.lmu.edu/aaas_fac/3Thu, 01 Dec 2016 17:14:20 PSTEdward J.W. ParkKorean Americans and the Crisis of the Liberal Coalition: Immigrants and Politics in Los Angeles
http://digitalcommons.lmu.edu/aaas_fac/2
http://digitalcommons.lmu.edu/aaas_fac/2Thu, 01 Dec 2016 17:14:14 PSTEdward J.W. Park et al.Political Formation of Korean Americans in Los Angeles: Visions of Political Power, 1992-1996
http://digitalcommons.lmu.edu/aaas_fac/1
http://digitalcommons.lmu.edu/aaas_fac/1Thu, 01 Dec 2016 17:14:09 PST
Since the Los Angeles Civil Unrest of 1992, Korean Americans have taken their first steps toward mainstream political participation and inclusion. From its initial stages, their struggle for political empowerment has been marked by profound partisan divisions. These divisions implicate a range of issues and point to pivotal concerns that organize and divide the political formation of the Korean American community. As the Korean American community is being transformed by its political engagement, mainstream politics in Los Angeles is also undergoing change as it confronts the new issues and complexities Korean Americans have brought to the city's political agenda.
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Edward J.W. ParkThe Fourier-Analytic Proof of Quadratic Reciprocity
http://digitalcommons.lmu.edu/math_fac/56
http://digitalcommons.lmu.edu/math_fac/56Thu, 01 Dec 2016 15:35:50 PSTMichael BergEpimorphisms and boundary slopes of 2–bridge knots
http://digitalcommons.lmu.edu/math_fac/55
http://digitalcommons.lmu.edu/math_fac/55Thu, 01 Dec 2016 12:17:34 PST
In this article we study a partial ordering on knots in S^{3} where K_{1}≥K_{2} if there is an epimorphism from the knot group of K_{1} onto the knot group of K_{2} which preserves peripheral structure. If K_{1} is a 2–bridge knot and K_{1}≥K_{2}, then it is known that K_{2} must also be 2–bridge. Furthermore, Ohtsuki, Riley and Sakuma give a construction which, for a given 2–bridge knot K_{p∕q}, produces infinitely many 2–bridge knots K_{p′/q′} with K_{p′∕q′}≥K_{p∕q}. After characterizing all 2–bridge knots with 4 or less distinct boundary slopes, we use this to prove that in any such pair, K_{p′∕q′} is either a torus knot or has 5 or more distinct boundary slopes. We also prove that 2–bridge knots with exactly 3 distinct boundary slopes are minimal with respect to the partial ordering. This result provides some evidence for the conjecture that all pairs of 2–bridge knots with K_{p′/q′}≥K_{p∕q} arise from the Ohtsuki–Riley–Sakuma construction.
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Jim Hoste et al.Links with finite n-quandles
http://digitalcommons.lmu.edu/math_fac/54
http://digitalcommons.lmu.edu/math_fac/54Thu, 01 Dec 2016 12:17:27 PST
We prove a conjecture of Przytycki which asserts that the n-quandle of a link L in the 3-sphere is finite if and only if the fundamental group of the n-fold cyclic branched cover of the 3-sphere, branched over L, is finite.
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Jim Hoste et al.Involutory quandles of (2,2,r)-Montesinos links
http://digitalcommons.lmu.edu/math_fac/53
http://digitalcommons.lmu.edu/math_fac/53Thu, 01 Dec 2016 12:17:21 PST
In this paper we show that Montesinos links of the form L(1/2, 1/2, p/q;e), which we call (2,2,r)-Montesinos links, have finite involutory quandles. This generalizes an observation of Winker regarding the (2, 2, q)-pretzel links. We also describe some properties of these quandles.
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Jim Hoste et al.Twisted Alexander polynomials of 2-bridge knots
http://digitalcommons.lmu.edu/math_fac/52
http://digitalcommons.lmu.edu/math_fac/52Thu, 01 Dec 2016 12:17:13 PST
We investigate the twisted Alexander polynomial of a 2-bridge knot associated to a Fox coloring. For several families of 2-bridge knots, including but not limited to, torus knots and genus-one knots, we derive formulae for these twisted Alexander polynomials. We use these formulae to confirm a conjecture of Hirasawa and Murasugi for these knots.
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Jim Hoste et al.Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots
http://digitalcommons.lmu.edu/math_fac/51
http://digitalcommons.lmu.edu/math_fac/51Thu, 01 Dec 2016 12:17:04 PST
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} has an upper bound. As an application we answer a question of Suzuki, showing that there is no upper bound for the set consisting of the trefoil and figure-eight knots.
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Scott M. Garrabrant et al.Commensurability classes of twist knots
http://digitalcommons.lmu.edu/math_fac/50
http://digitalcommons.lmu.edu/math_fac/50Thu, 01 Dec 2016 12:16:57 PST
In this paper we prove that if M_{K} is the complement of a non-fibered twist knot K in S^{3}, then M_{K} is not commensurable to a fibered knot complement in a Z/2Z-homology sphere. To prove this result we derive a recursive description of the character variety of twist knots and then prove that a commensurability criterion developed by D. Calegari and N. Dunfield is satisfied for these varieties. In addition, we partially extend our results to a second infinite family of 2-bridge knots.
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Jim Hoste et al.Consistency of Cheeger and Ratio Graph Cuts
http://digitalcommons.lmu.edu/math_fac/49
http://digitalcommons.lmu.edu/math_fac/49Wed, 30 Nov 2016 17:59:54 PST
This paper establishes the consistency of a family of graph-cut- based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based on graph cuts like the Cheeger and ratio cuts. We show that minimizers of these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut (which partitions the ground truth measure). Moreover, we obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for the consistency to hold. We provide results for two-way and for multiway cuts. Furthermore we provide numerical experiments that illustrate the results and explore the optimality of scaling in dimension two.
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Nicolas Garcia Trillos et al.A New Topological Perspective on Quantization in Physics
http://digitalcommons.lmu.edu/math_fac/48
http://digitalcommons.lmu.edu/math_fac/48Wed, 30 Nov 2016 17:59:49 PST
We propose a new characterization of classical quantization in physics in terms of sheaf cohomology on the site of spacetime as a smooth 4-manifold. The perspective of sheaf cohomology is motivated by a presentation of the Aharonov-Bohm effect in terms of the integration of differential forms.
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Hooman Rahimizadeh et al.Derived Categories and the Analytic Approach to General Reciprocity Laws. Part III
http://digitalcommons.lmu.edu/math_fac/47
http://digitalcommons.lmu.edu/math_fac/47Wed, 30 Nov 2016 17:59:45 PST
Building on the scaffolding constructed in the first two articles in this series, we now proceed to the geometric phase of our sheaf (-complex) theoretic quasidualization of Kubota's formalism for n-Hilbert reciprocity. Employing recent work by Bridgeland on stability conditions, we extend our yoga of t-structures situated above diagrams of specifically designed derived categories to arrangements of metric spaces or complex manifolds. This prepares the way for proving n-Hilbert reciprocity by means of singularity analysis.
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Michael BergDerived Categories and the Analytic Approach to General Reciprocity Laws. Part II
http://digitalcommons.lmu.edu/math_fac/46
http://digitalcommons.lmu.edu/math_fac/46Wed, 30 Nov 2016 17:59:41 PST
Building on the topological foundations constructed in Part I, we now go on to address the homological algebra preparatory to the projected final arithmetical phase of our attack on the analytic proof of general reciprocity for a number field. In the present work, we develop two algebraic frameworks corresponding to two interpretations of Kubota's n-Hilbert reciprocity formalism, presented in a quasi-dualized topological form in Part I, delineating two sheaf-theoretic routes toward resolving the aforementioned (open) problem. The first approach centers on factoring sheaf morphisms eventually to yield a splitting homomorphism for Kubota's n-fold cover of the adelized special linear group over the base field. The second approach employs linked exact triples of derived sheaf categories and the yoga of gluing t-structures to evolve a means of establishing the vacuity of certain vertices in diagrams of underlying topological spaces from Part I. Upon assigning properly designed t-structures to three of seven specially chosen derived categories, the collapse just mentioned is enough to yield n-Hilbert reciprocity.
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Michael BergDerived Categories and the Analytic Approach to General Reciprocity Laws. Part I
http://digitalcommons.lmu.edu/math_fac/45
http://digitalcommons.lmu.edu/math_fac/45Wed, 30 Nov 2016 17:59:37 PST
We reformulate Hecke's open problem of 1923, regarding the Fourier-analytic proof of higher reciprocity laws, as a theorem about morphisms involving stratified topological spaces. We achieve this by placing Kubota's formulations of n-Hilbert reciprocity in a new topological context, suited to the introduction of derived categories of sheaf complexes. Subsequently, we begin to investigate conditions on associated sheaves and a derived category of sheaf complexes specifically designed for an attack on Hecke's eighty-year-old challenge.
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Michael BergThe Double Cover of the Real Symplectic Group and a Theme from Feynman’s Quantum Mechanics
http://digitalcommons.lmu.edu/math_fac/44
http://digitalcommons.lmu.edu/math_fac/44Wed, 30 Nov 2016 17:59:33 PST
We present a direct connection between the 2-cocycle defining the double cover of the real symplectic group and a Feynman path integral describing the time evolution of a quantum mechanical system.
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Michael BergVirtual Spatial Graphs
http://digitalcommons.lmu.edu/math_fac/43
http://digitalcommons.lmu.edu/math_fac/43Wed, 30 Nov 2016 11:57:05 PST
Two natural generalizations of knot theory are t he study of spatially embedded graphs, and Kauffman's theory of virtual knots. In this paper we combine these approaches to begin the study of virtual spat ial graphs.
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Thomas Fleming et al.Intrinsic Linking and Knotting in Virtual Spatial Graphs
http://digitalcommons.lmu.edu/math_fac/42
http://digitalcommons.lmu.edu/math_fac/42Wed, 30 Nov 2016 11:56:58 PST
We introduce a notion of intrinsic linking and knotting for virtual spatial graphs. Our theory gives two filtrations of the set of all graphs, allowing us to measure, in a sense, how intrinsically linked or knotted a graph is; we show that these filtrations are descending and nonterminating. We also provide several examples of intrinsically virtually linked and knotted graphs. As a byproduct, we introduce the virtual unknotting number of a knot, and show that any knot with nontrivial Jones polynomial has virtual unknotting number at least 2.
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Thomas Fleming et al.Intrinsic linking and knotting of graphs in arbitrary 3–manifolds
http://digitalcommons.lmu.edu/math_fac/41
http://digitalcommons.lmu.edu/math_fac/41Wed, 30 Nov 2016 11:56:49 PST
We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is intrinsically linked in S^{3}. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S^{3}.
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Erica Flapan et al.A Geometric Interpretation of Milnor's Triple Invariants
http://digitalcommons.lmu.edu/math_fac/40
http://digitalcommons.lmu.edu/math_fac/40Wed, 30 Nov 2016 11:56:42 PST
Milnor's triple linking numbers of a link in the 3-sphere are interpreted geometrically in terms of the pattern of intersections of the Seifert surfaces of the components of the link. This generalizes the well known formula as an algebraic count of triple points when the pairwise linking numbers vanish.
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Blake Mellor et al.Complete graphs whose topological symmetry groups are polyhedral
http://digitalcommons.lmu.edu/math_fac/39
http://digitalcommons.lmu.edu/math_fac/39Wed, 30 Nov 2016 11:56:36 PST
We determine for which m the complete graph K_{m} has an embedding in S^{3} whose topological symmetry group is isomorphic to one of the polyhedral groups A_{4}, A_{5} or S_{4}.
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Eric Flapan et al.A Few Weight Systems Arising from Intersection Graphs
http://digitalcommons.lmu.edu/math_fac/38
http://digitalcommons.lmu.edu/math_fac/38Mon, 28 Nov 2016 17:35:18 PSTBlake Mellor