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Recent ucdavismath_faculty items
https://escholarship.org/uc/ucdavismath_faculty/rss
Recent eScholarship items from Faculty
Sun, 1 Aug 2021 02:31:40 +0000

Polymer stress growth in viscoelastic fluids in oscillating extensional flows with applications to microorganism locomotion
https://escholarship.org/uc/item/7r57q2kp
Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers. We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocity are found from numerical simulations in an oscillating 4roll mill geometry. The stress from these simulations is compared with the theoretical calculation of stress in the decoupled (given flow) case, and similar stress behavior is observed. The flow around tips of a timereversible flexing filament in a viscoelastic fluid is shown to exhibit an oscillating extension along particle trajectories,...
https://escholarship.org/uc/item/7r57q2kp
Thu, 13 Jun 2019 00:00:00 +0000

Lectures on quasiisometric rigidity
https://escholarship.org/uc/item/6674s3b3
Lectures on quasiisometric rigidity
https://escholarship.org/uc/item/6674s3b3
Thu, 13 Jun 2019 00:00:00 +0000

Structural stability of meanderinghyperbolic group actions
https://escholarship.org/uc/item/5mr0v8z2
In his 1985 paper Sullivan sketched a proof of his structural stability
theorem for group actions satisfying certain expansionhyperbolicity axioms. In
this paper we relax Sullivan's axioms and introduce a notion of meandering
hyperbolicity for group actions on general metric spaces. This generalization
is substantial enough to encompass actions of certain nonhyperbolic groups,
such as actions of uniform lattices in semisimple Lie groups on flag manifolds.
At the same time, our notion is sufficiently robust and we prove that
meanderinghyperbolic actions are still structurally stable. We also prove some
basic results on meanderinghyperbolic actions and give other examples of such
actions.
https://escholarship.org/uc/item/5mr0v8z2
Thu, 13 Jun 2019 00:00:00 +0000

Novel genetic loci underlying human intracranial volume identified through genomewide association.
https://escholarship.org/uc/item/5mc3m2mn
Intracranial volume reflects the maximally attained brain size during development, and remains stable with loss of tissue in late life. It is highly heritable, but the underlying genes remain largely undetermined. In a genomewide association study of 32,438 adults, we discovered five previously unknown loci for intracranial volume and confirmed two known signals. Four of the loci were also associated with adult human stature, but these remained associated with intracranial volume after adjusting for height. We found a high genetic correlation with child head circumference (ρ<sub>genetic</sub> = 0.748), which indicates a similar genetic background and allowed us to identify four additional loci through metaanalysis (N<sub>combined</sub> = 37,345). Variants for intracranial volume were also related to childhood and adult cognitive function, and Parkinson's disease, and were enriched near genes involved in growth pathways, including PI3KAKT signaling. These findings identify the...
https://escholarship.org/uc/item/5mc3m2mn
Thu, 13 Jun 2019 00:00:00 +0000

A morse lemma for quasigeodesics in symmetric spaces and euclidean buildings
https://escholarship.org/uc/item/5js648vn
We prove a Morse lemma for regular quasigeodesics in nonpositively curved symmetric spaces and euclidean buildings. We apply it to give a new coarse geometric characterization of Anosov subgroups of the isometry groups of such spaces simply as undistorted subgroups which are uniformly regular.
https://escholarship.org/uc/item/5js648vn
Thu, 13 Jun 2019 00:00:00 +0000

Hierarchical graph Laplacian eigen transforms
https://escholarship.org/uc/item/5j79p8ng
Hierarchical graph Laplacian eigen transforms
https://escholarship.org/uc/item/5j79p8ng
Thu, 13 Jun 2019 00:00:00 +0000

Common genetic variants influence human subcortical brain structures.
https://escholarship.org/uc/item/5cp2c1bd
The highly complex structure of the human brain is strongly shaped by genetic influences. Subcortical brain regions form circuits with cortical areas to coordinate movement, learning, memory and motivation, and altered circuits can lead to abnormal behaviour and disease. To investigate how common genetic variants affect the structure of these brain regions, here we conduct genomewide association studies of the volumes of seven subcortical regions and the intracranial volume derived from magnetic resonance images of 30,717 individuals from 50 cohorts. We identify five novel genetic variants influencing the volumes of the putamen and caudate nucleus. We also find stronger evidence for three loci with previously established influences on hippocampal volume and intracranial volume. These variants show specific volumetric effects on brain structures rather than global effects across structures. The strongest effects were found for the putamen, where a novel intergenic locus with replicable...
https://escholarship.org/uc/item/5cp2c1bd
Thu, 13 Jun 2019 00:00:00 +0000

Combinatorial Markov chains on linear extensions
https://escholarship.org/uc/item/5b83d5dn
We consider generalizations of Schuetzenberger's promotion operator on the
set L of linear extensions of a finite poset of size n. This gives rise to a
strongly connected graph on L. By assigning weights to the edges of the graph
in two different ways, we study two Markov chains, both of which are
irreducible. The stationary state of one gives rise to the uniform
distribution, whereas the weights of the stationary state of the other has a
nice product formula. This generalizes results by Hendricks on the Tsetlin
library, which corresponds to the case when the poset is the antichain and
hence L=S_n is the full symmetric group. We also provide explicit eigenvalues
of the transition matrix in general when the poset is a rooted forest. This is
shown by proving that the associated monoid is Rtrivial and then using
Steinberg's extension of Brown's theory for Markov chains on left regular bands
to Rtrivial monoids.
https://escholarship.org/uc/item/5b83d5dn
Thu, 13 Jun 2019 00:00:00 +0000

Multiplescale analysis on the radiation within the coupled KdV equations
https://escholarship.org/uc/item/57t0f8cm
A multiple scale model of the nonlinearly coupled KdV equations is
established to predict mechanism of interaction of equatorial Rossby waves and
barotropic waves in certain case. Analytically, predicted precursor radiation
is a centrosymmetric object and is shown in excellent quantitative agreement
with numerical simulations; furthermore, the multiple scale model elucidates
the salient mechanisms of the interaction of solitary waves and the mechanism
for radiation. While the atmosphereocean science community is very interested
in theoretical studies of tropical wave interactions and in developing reduced
dynamical models that can explain some key features of equatorial phenomena,
our analytic predictions quantitively explain formation of radiation during
interaction in Biello's model beyond qualitative level.
https://escholarship.org/uc/item/57t0f8cm
Thu, 13 Jun 2019 00:00:00 +0000

Analysis of peristaltic waves and their role in migrating Physarum plasmodia
https://escholarship.org/uc/item/4s0047d7
The true slime mold Physarum polycephalum exhibits a vast array of sophisticated manipulations of its intracellular cytoplasm. Growing microplasmodia of Physarum have been observed to adopt an elongated tadpole shape, then contract in a rhythmic, traveling wave pattern that resembles peristaltic pumping. This contraction drives a fast flow of nongelated cytoplasm along the cell longitudinal axis. It has been hypothesized that this flow of cytoplasm is a driving factor in generating motility of the plasmodium. In this work, we use two different mathematical models to investigate how peristaltic pumping within Physarum may be used to drive cellular motility. We compare the relative phase of flow and deformation waves predicted by both models to similar phase data collected from in vivo experiments using Physarum plasmodia. The first is a PDE model based on a dimensional reduction of peristaltic pumping within a finite length chamber. The second is a more sophisticated computational...
https://escholarship.org/uc/item/4s0047d7
Thu, 13 Jun 2019 00:00:00 +0000

The support of integer optimal solutions
https://escholarship.org/uc/item/4f58m5rx
The support of a vector is the number of nonzero components. We show that given anintegral m×n matrix A, the integer linear optimization problem maxfcT x: Ax = b; x = 0; x 2 Znghas an optimal solution whose support is bounded by 2m log(2pmkAk1), where kAk1 is the largestabsolute value of an entry of A. Compared to previous bounds, the one presented here is independentof the objective function. We furthermore provide a nearly matching asymptotic lower bound on thesupport of optimal solutions.
https://escholarship.org/uc/item/4f58m5rx
Thu, 13 Jun 2019 00:00:00 +0000

PattersonSullivan theory for Anosov subgroups
https://escholarship.org/uc/item/3tn924mz
We extend several notions and results from the classical PattersonSullivan
theory to the setting of Anosov subgroups of higher rank semisimple Lie groups,
working primarily with invariant Finsler metrics on associated symmetric
spaces. In particular, we prove the equality between the Hausdorff dimensions
of flag limit sets, computed with respect to a suitable Gromov (pre)metric on
the flag manifold, and the Finsler critical exponents of Anosov subgroups.
https://escholarship.org/uc/item/3tn924mz
Thu, 13 Jun 2019 00:00:00 +0000

Morse actions of discrete groups on symmetric space
https://escholarship.org/uc/item/3kc4r7t6
We study the geometry and dynamics of discrete infinite covolume subgroups of
higher rank semisimple Lie groups. We introduce and prove the equivalence of
several conditions, capturing "rank one behavior'' of discrete subgroups of
higher rank Lie groups. They are direct generalizations of rank one equivalents
to convex cocompactness. We also prove that our notions are equivalent to the
notion of Anosov subgroup, for which we provide a closely related, but
simplified and more accessible reformulation, avoiding the geodesic flow of the
group. We show moreover that the Anosov condition can be relaxed further by
requiring only nonuniform unbounded expansion along the (quasi)geodesics in
the group.
A substantial part of the paper is devoted to the coarse geometry of these
discrete subgroups. A key concept which emerges from our analysis is that of
Morse quasigeodesics in higher rank symmetric spaces, generalizing the Morse
property for quasigeodesics in Gromov hyperbolic spaces....
https://escholarship.org/uc/item/3kc4r7t6
Thu, 13 Jun 2019 00:00:00 +0000

Mechanosensitive Adhesion Explains Stepping Motility in Amoeboid Cells
https://escholarship.org/uc/item/31k9s95q
© 2017 Biophysical Society Cells employing amoeboid motility exhibit repetitive cycles of rapid expansion and contraction and apply coordinated traction forces to their environment. Although aspects of this process are well studied, it is unclear how the cell controls the coordination of cell length changes with adhesion to the surface. Here, we develop a simple model to mechanistically explain the emergence of periodic changes in length and spatiotemporal dynamics of traction forces measured in chemotaxing unicellular amoeba, Dictyostelium discoideum. In contrast to the biochemical mechanisms that have been implicated in the coordination of some cellular processes, we show that many features of amoeboid locomotion emerge from a simple mechanochemical model. The mechanism for interaction with the environment in Dictyostelium is unknown and thus, we explore different cellenvironment interaction models to reveal that mechanosensitive adhesions are necessary to reproduce the spatiotemporal...
https://escholarship.org/uc/item/31k9s95q
Thu, 13 Jun 2019 00:00:00 +0000

Unified theory for finite Markov chains
https://escholarship.org/uc/item/30d0p416
We provide a unified framework to compute the stationary distribution of any finite irreducible Markov chain or equivalently of any irreducible random walk on a finite semigroup S. Our methods use geometric finite semigroup theory via the Karnofsky–Rhodes and the McCammond expansions of finite semigroups with specified generators; this does not involve any linear algebra. The original Tsetlin library is obtained by applying the expansions to P(n), the set of all subsets of an n element set. Our setup generalizes previous groundbreaking work involving leftregular bands (or Rtrivial bands) by Brown and Diaconis, extensions to Rtrivial semigroups by Ayyer, Steinberg, Thiéry and the second author, and important recent work by Chung and Graham. The Karnofsky–Rhodes expansion of the right Cayley graph of S in terms of generators yields again a right Cayley graph. The McCammond expansion provides normal forms for elements in the expanded S. Using our previous results with Silva based...
https://escholarship.org/uc/item/30d0p416
Thu, 13 Jun 2019 00:00:00 +0000

Noncoherence of some lattices in Isom(Hn)
https://escholarship.org/uc/item/2wv4q3j1
We prove noncoherence of certain families of lattices in the isometry group
of the hyperbolic nspace for n greater than 3. For instance, every nonuniform
arithmetic lattice in SO(n,1) is noncoherent, provided that n is at least 6.
https://escholarship.org/uc/item/2wv4q3j1
Thu, 13 Jun 2019 00:00:00 +0000

The influence of soluble fragments of extracellular matrix (ECM) on tumor growth and morphology.
https://escholarship.org/uc/item/2qz417kk
A major challenge in matrixmetalloproteinase (MMP) target validation and MMPinhibitordrug development for anticancer clinical trials is to better understand their complex roles (often competing with each other) in tumor progression. While there is extensive research on the growthpromoting effects of MMPs, the growthinhibiting effects of MMPs has not been investigated thoroughly. So we develop a continuum model of tumor growth and invasion including chemotaxis and haptotaxis in order to examine the complex interaction between the tumor and its host microenvironment and to explore the inhibiting influence of the gradients of soluble fragments of extracellular matrix (ECM) density on tumor growth and morphology. Previously, it was shown both computationally (in one spatial dimension) and experimentally that the chemotactic pull due to soluble ECM gradients is antiinvasive, contrary to the traditional view of the role of chemotaxis in malignant invasion [1]. With twodimensional...
https://escholarship.org/uc/item/2qz417kk
Thu, 13 Jun 2019 00:00:00 +0000

Pingpong in Hadamard manifolds
https://escholarship.org/uc/item/1x84j5s5
In this paper, we prove a quantitative version of the Tits alternative for
negatively pinched manifolds $X$. Precisely, we prove that a nonelementary
discrete isometry subgroup of $\mathrm{Isom}(X)$ generated by two nonelliptic
isometries $g$, $f$ contains a free subgroup of rank $2$ generated by
isometries $f^N , h$ of uniformly bounded word length. Furthermore, we show
that this free subgroup is convexcocompact when $f$ is hyperbolic.
https://escholarship.org/uc/item/1x84j5s5
Thu, 13 Jun 2019 00:00:00 +0000

On quasihomomorphisms with noncommutative targets
https://escholarship.org/uc/item/1tw883m1
We describe structure of quasihomomorphisms from arbitrary groups to discrete groups. We show that all quasihomomorphisms are “constructible”, i.e., are obtained via certain natural operations from homomorphisms to some groups and quasihomomorphisms to abelian groups. We illustrate this theorem by describing quasihomomorphisms to certain classes of groups. For instance, every unbounded quasihomomorphism to a torsionfree hyperbolic group H is either a homomorphism to a subgroup of H or is a quasihomomorphism to an infinite cyclic subgroup of H.
https://escholarship.org/uc/item/1tw883m1
Thu, 13 Jun 2019 00:00:00 +0000

Erratum: Spontaneous S U 2 (C) symmetry breaking in the ground states of quantum spin chain (Journal of Mathematical Physics (2018) 59 (111701) DOI: 10.1063/1.5078597)
https://escholarship.org/uc/item/01c0p4jn
The reviewers contacted by the editors to evaluate this work have been unable to confirm that the main results are correct. Flaws that were identified by the reviewers in earlier versions of the paper have been addressed by the author. Although it is possible that future research will uncover a significant mistake in this paper or show that the conclusions are in error, I believe that publishing it may benefit the readership of the Journal and stimulate further work in mathematical physics on an important topic.
https://escholarship.org/uc/item/01c0p4jn
Thu, 13 Jun 2019 00:00:00 +0000

Relativizing characterizations of Anosov subgroups, I
https://escholarship.org/uc/item/95j4s9r6
We propose several common extensions of the classes of Anosov subgroups and
geometrically finite Kleinian groups among discrete subgroups of semisimple Lie
groups. We relativize various dynamical and coarse geometric characterizations
of Anosov subgroups given in our earlier work, extending the class from
intrinsically hyperbolic to relatively hyperbolic subgroups. We prove
implications and equivalences between the various relativizations.
https://escholarship.org/uc/item/95j4s9r6
Fri, 14 Sep 2018 00:00:00 +0000

Lectures on the Topological Recursion for Higgs Bundles and Quantum Curves
https://escholarship.org/uc/item/858382hb
© 2018 World Scientific Publishing Co. Pte. Ltd. This chapter aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the new discovery of the relation between the following two disparate subjects: one is the topological recursion, that has its origin in random matrix theory and has been effectively applied to many enumerative geometry problems; and the other is the quantization of Hitchin spectral curves associated with Higgs bundles. Our emphasis is on explaining the motivation and examples. Concrete examples of the direct relation between Hitchin spectral curves and enumeration problems are given. A general geometric framework of quantum curves is also discussed.
https://escholarship.org/uc/item/858382hb
Fri, 14 Sep 2018 00:00:00 +0000

A note on Selberg's Lemma and negatively curved Hadamard manifolds
https://escholarship.org/uc/item/80w4w0h3
Answering a question by Margulis we prove that the conclusion of Selberg's
Lemma fails for discrete isometry groups of negatively curved Hadamard
manifolds.
https://escholarship.org/uc/item/80w4w0h3
Fri, 14 Sep 2018 00:00:00 +0000

Unlinking chromosome catenanes in vivo by sitespecific recombination.
https://escholarship.org/uc/item/67f779w5
A challenge for chromosome segregation in all domains of life is the formation of catenated progeny chromosomes, which arise during replication as a consequence of the interwound strands of the DNA double helix. Topoisomerases play a key role in DNA unlinking both during and at the completion of replication. Here we report that chromosome unlinking can instead be accomplished by multiple rounds of sitespecific recombination. We show that stepwise, sitespecific recombination by XerCDdif or CreloxP can unlink bacterial chromosomes in vivo, in reactions that require KOPSguided DNA translocation by FtsK. Furthermore, we show that overexpression of a cytoplasmic FtsK derivative is sufficient to allow chromosome unlinking by XerCDdif recombination when either subunit of TopoIV is inactivated. We conclude that FtsK acts in vivo to simplify chromosomal topology as Xer recombination interconverts monomeric and dimeric chromosomes.
https://escholarship.org/uc/item/67f779w5
Fri, 14 Sep 2018 00:00:00 +0000

A porous viscoelastic model for the cell cytoskeleton
https://escholarship.org/uc/item/52m5t4gs
The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In this work, we consider a poroelastic immersed boundary method in which a fluid permeates a porous, elastic structure of negligible volume fraction, and extend this method to include stress relaxation of the material. The porous viscoelastic method presented here is validated for a prescribed oscillatory shear and for an expansion driven by the motion at the boundary of a circular material by comparing numerical solutions to an analytical solution of the Maxwell model for viscoelasticity. Finally, an application of the modelling framework to cell biology is provided: passage of a cell through a microfluidic channel. We demonstrate that the rheology of the cell cytoplasm is important for capturing the transit time through a narrow channel in the presence of a pressure drop in the extracellular fluid.
https://escholarship.org/uc/item/52m5t4gs
Fri, 14 Sep 2018 00:00:00 +0000

Determining the topology of stable proteinDNA complexes.
https://escholarship.org/uc/item/51f0d82j
Difference topology is an experimental technique that can be used to unveil the topological structure adopted by two or more DNA segments in a stable proteinDNA complex. Difference topology has also been used to detect intermediates in a reaction pathway and to investigate the role of DNA supercoiling. In the present article, we review difference topology as applied to the Mu transpososome. The tools discussed can be applied to any stable nucleoprotein complex.
https://escholarship.org/uc/item/51f0d82j
Fri, 14 Sep 2018 00:00:00 +0000

LiebRobinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems
https://escholarship.org/uc/item/29b5v2hp
We prove LiebRobinson bounds for a general class of lattice fermion systems.
By making use of a suitable conditional expectation onto subalgebras of the CAR
algebra, we can apply the LiebRobinson bounds much in the same way as for
quantum spin systems. We preview how to obtain the spectral flow automorphisms
and to prove stability of the spectral gap for frustrationfree gapped systems
satisfying a Local Topological Quantum Order condition.
https://escholarship.org/uc/item/29b5v2hp
Fri, 14 Sep 2018 00:00:00 +0000

A combination theorem for Anosov subgroups
https://escholarship.org/uc/item/1px69959
We prove an analogue of Klein combination theorem for Anosov subgroups by using a localtoglobal principle for Morse quasigeodesics.
https://escholarship.org/uc/item/1px69959
Fri, 14 Sep 2018 00:00:00 +0000

On gapped phases with a continuous symmetry and boundary operators
https://escholarship.org/uc/item/0mt6k7m9
We discuss the role of compact symmetry groups, G, in the classification of
gapped ground state phases of quantum spin systems. We consider two
representations of G on infinite subsystems. First, in arbitrary dimensions, we
show that the ground state spaces of models within the same Gsymmetric phase
carry equivalent representations of the group for each finite or infinite
sublattice on which they can be defined and on which they remain gapped. This
includes infinite systems with boundaries or with nontrivial topologies.
Second, for two classes of onedimensional models, by two different methods,
for G=SU(2) in one, and G\subset SU(d), in the other we construct explicitly an
`excess spin' operator that implements rotations of half of the infinite chain
on the GNS Hilbert space of the ground state of the full chain. Since this
operator is constructed as the limit of a sequence of observables, the
representation itself is, in principle, experimentally observable. We claim
that...
https://escholarship.org/uc/item/0mt6k7m9
Fri, 14 Sep 2018 00:00:00 +0000

Finsler bordifications of symmetric and certain locally symmetric spaces
https://escholarship.org/uc/item/0j98n6t5
© 2018, Mathematical Sciences Publishers. All Rights reserved. We give a geometric interpretation of the maximal Satake compactification of symmetric spaces X=G/K of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable Ginvariant Finsler metric on X. As an application, we establish the existence of natural bordifications, as orbifoldswithcorners, of locally symmetric spaces X/Γ for arbitrary discrete subgroups Γ
https://escholarship.org/uc/item/0j98n6t5
Fri, 14 Sep 2018 00:00:00 +0000

Efficient approximation and denoising of graph signals using the multiscale basis dictionaries
https://escholarship.org/uc/item/0bv9t4c8
We propose methods to efficiently approximate and denoise signals sampled on the nodes of graphs using our overcomplete multiscale transforms/basis dictionaries for such graph signals: the hierarchical graph Laplacian eigen transform (HGLET) and the generalized HaarWalsh transform (GHWT). These can be viewed as generalizations of the hierarchical discrete cosine transform and the HaarWalsh wavelet packet transform, respectively, from regularly sampled signals to graph signals. Both of these transforms generate dictionaries containing an immense number of choosable bases, and in order to select a particular basis most suitable for a given task, we have generalized the best basis algorithm from classical signal processing. After briefly reviewing these transforms and the best basis algorithm, we precisely prove their efficiency in approximating graph signals belonging to discrete analogs of the space of Hölder continuous functions and the Besov spaces. Then, we validate their...
https://escholarship.org/uc/item/0bv9t4c8
Fri, 14 Sep 2018 00:00:00 +0000

How Can We Naturally Order and Organize Graph Laplacian Eigenvectors?
https://escholarship.org/uc/item/062077zh
When attempting to develop wavelet transforms for graphs and networks, some researchers have used graph Laplacian eigenvalues and eigenvectors in place of the frequencies and complex exponentials in the Fourier theory for regular lattices in the Euclidean domains. This viewpoint, however, has a fundamental flaw: on a general graph, the Laplacian eigenvalues cannot be interpreted as the frequencies of the corresponding eigenvectors. In this paper, we discuss this important problem further and propose a new method to organize those eigenvectors by defining and measuring 'natural' distances between eigenvectors using the Ramified Optimal Transport Theory followedby embedding them into a lowdimensional Euclidean domain. We demonstrate its effectiveness using a synthetic graph as well as a dendritic tree of a retinal ganglioncell of a mouse.
https://escholarship.org/uc/item/062077zh
Fri, 14 Sep 2018 00:00:00 +0000

Quantum Curves for Hitchin Fibrations and the EynardOrantin Theory
https://escholarship.org/uc/item/9w04t1t0
We generalize the topological recursion of EynardOrantin (JHEP 0612:053, 2006; Commun Number Theory Phys 1:347452, 2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle T*C of an arbitrary smooth base curve C. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal h{stroke}deformation family of D modules over an arbitrary projective algebraic curve C of genus greater than 1, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the SL(2, ℂ)character variety of the fundamental group π1(C). We show that the semiclassical limit through the WKB approximation of these h{stroke}deformed D modules recovers the initial family of Hitchin spectral curves. © 2014 Springer Science+Business Media Dordrecht.
https://escholarship.org/uc/item/9w04t1t0
Mon, 14 May 2018 00:00:00 +0000

Product Vacua and Boundary State Models in Dimensions
https://escholarship.org/uc/item/9k771949
Product Vacua and Boundary State Models in Dimensions
https://escholarship.org/uc/item/9k771949
Mon, 14 May 2018 00:00:00 +0000

On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties
https://escholarship.org/uc/item/9d327011
We prove that for any affine variety S defined over Q there exist Shephard and Artin groups G such that a Zariski open subset U of S is biregular isomorphic to a Zariski open subset of the character variety X(G, PO(3)) = Hom(G, PO(3))//PO(3). The subset U contains all real points of S. As an application we construct new examples of finitelypresented groups which are not fundamental groups of smooth complex algebraic varieties. © 1998 Publications mathématiques de l'I.H.É.S.
https://escholarship.org/uc/item/9d327011
Mon, 14 May 2018 00:00:00 +0000

Phase response properties of halfcenter oscillators.
https://escholarship.org/uc/item/9cb006k5
We examine the phase response properties of halfcenter oscillators (HCOs) that are modeled by a pair of MorrisLecartype neurons connected by strong fast inhibitory synapses. We find that the two basic mechanisms for halfcenter oscillations, "release" and "escape", give rise to strikingly different phase response curves (PRCs). Releasetype HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the active to the suppressed state, and PRCs are dominated by a large negative peak (phase delays) at corresponding phases. On the other hand, escapetype HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the suppressed to the active state, and PRCs are dominated by a large positive peak (phase advances) at corresponding phases. By analyzing the phase space structure of MorrisLecartype HCO models with fast synaptic dynamics, we identify the dynamical mechanisms underlying...
https://escholarship.org/uc/item/9cb006k5
Mon, 14 May 2018 00:00:00 +0000

Parameterization for InSilico Modeling of Ion Channel Interactions with Drugs.
https://escholarship.org/uc/item/98k4c5zk
Since the first Hodgkin and Huxley ion channel model was described in the 1950s, there has been an explosion in mathematical models to describe ion channel function. As experimental data has become richer, models have concomitantly been improved to better represent ion channel kinetic processes, although these improvements have generally resulted in more model complexity and an increase in the number of parameters necessary to populate the models. Models have also been developed to explicitly model drug interactions with ion channels. Recent models of drugchannel interactions account for the discrete kinetics of drug interaction with distinct ion channel state conformations, as it has become clear that such interactions underlie complex emergent kinetics such as usedependent block. Here, we describe an approach for developing a model for ion channel drug interactions. The method describes the process of extracting rate constants from experimental electrophysiological function...
https://escholarship.org/uc/item/98k4c5zk
Mon, 14 May 2018 00:00:00 +0000

On augmentation algorithms for linear and integerlinear programming: From EdmondsKarp to Bland and beyond
https://escholarship.org/uc/item/95m842mb
Motivated by Bland's linear programming (LP) generalization of the renowned EdmondsKarp efficient refinement of the FordFulkerson maximum flow algorithm, we analyze three closely related natural augmentation rules for LP and integerlinear programming (ILP) augmentation algorithms. For all three rules and in both contexts, LP and ILP, we bound the number of augmentations. Extending Bland's "discrete steepestdescent" augmentation rule (i.e., choosing directions with the best ratio of cost improvement per unit 1norm length, and then making maximal augmentations in such directions) from LP to ILP, we (i) show that the number of discrete steepestdescent augmentations is bounded by the number of elements in the Graver basis of the problem matrix and (ii) give the first strongly polynomialtime algorithm for Nfold ILP. For LP, two of the rules can suffer from a "zigzagging" phenomenon, and so in those cases we apply the rules more subtly to achieve good bounds. Our results improve...
https://escholarship.org/uc/item/95m842mb
Mon, 14 May 2018 00:00:00 +0000

Local limit of the fixed point forest
https://escholarship.org/uc/item/95d5t7zz
Consider the following partial “sorting algorithm” on permutations: take the first entry of the permutation in oneline notation and insert it into the position of its own value. Continue until the first entry is 1. This process imposes a forest structure on the set of all permutations of size n, where the roots are the permutations starting with 1 and the leaves are derangements. Viewing the process in the opposite direction towards the leaves, one picks a fixed point and moves it to the beginning. Despite its simplicity, this “fixed point forest” exhibits a rich structure. In this paper, we consider the fixed point forest in the limit n → ∞ and show using Stein’s method that at a random permutation the local structure weakly converges to a tree defined in terms of independent Poisson point processes. We also show that the distribution of the length of the longest path from a random permutation to a leaf converges to the geometric distribution with mean e − 1, and the length...
https://escholarship.org/uc/item/95d5t7zz
Mon, 14 May 2018 00:00:00 +0000

Type Dn(1) rigged configuration bijection
https://escholarship.org/uc/item/9535d55z
© 2017, Springer Science+Business Media New York. We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov–Reshetikhin crystals of type Dn(1) in full generality. We prove the invariance of rigged configurations under the action of the combinatorial Rmatrix on tensor products and show that the bijection preserves certain statistics (cocharge and energy). As a result, we establish the fermionic formula for type Dn(1). In addition, we establish that the bijection is a classical crystal isomorphism.
https://escholarship.org/uc/item/9535d55z
Mon, 14 May 2018 00:00:00 +0000

Twooscillator model of ventilatory rhythmogenesis in the frog
https://escholarship.org/uc/item/92p61887
Frogs produce two distinct yet highly coordinated ventilatory behaviors, buccal and lung. Lung ventilation occurs in short episodes, interspersed with periods of buccal ventilation. Recent data suggests that two brainstem oscillators are involved in generating these behaviors, one primarily responsible for buccal ventilation, the other for lung. Here we use a modeling approach to demonstrate that the episodic pattern of lung ventilation might be an emergent property of the coupling between the oscillators, and may not require a perturbing input from another, as yet unidentified but previously postulated, neuronal oscillator. © 2004 Elsevier B.V. All rights reserved.
https://escholarship.org/uc/item/92p61887
Mon, 14 May 2018 00:00:00 +0000

Phlst with adaptive tiling and its application to antarctic remote sensing image approximation
https://escholarship.org/uc/item/8t4175pw
We propose an efficient nonlinear approximation scheme using the Polyharmonic Local Sine Transform (PHLST) of Saito and Remy combined with an algorithm to tile a given image automatically and adaptively according to its local smoothness and singularities. To measure such local smoothness, we introduce the socalled local Besov indices of an image, which is based on the pointwise modulus of smoothness of the image. Such an adaptive tiling of an image is important for image approximation using PHLST because PHLST stores the corner and boundary information of each tile and consequently it is wasteful to divide a smooth region of a given image into a set of smaller tiles. We demonstrate the superiority of the proposed algorithm using Antarctic remote sensing images over the PHLST using the uniform tiling. Analysis of such images including their efficient approximation and compression has gained its importance due to the global climate change. © 2014 American Institute of Mathematical...
https://escholarship.org/uc/item/8t4175pw
Mon, 14 May 2018 00:00:00 +0000

Quantum spectral curve for the GromovWitten theory of the complex projective line
https://escholarship.org/uc/item/8rq33480
We construct the quantum curve for the GromovWitten theory of the complex projective line.
https://escholarship.org/uc/item/8rq33480
Mon, 14 May 2018 00:00:00 +0000

Markov chains, Rtrivial monoids and representation theory
https://escholarship.org/uc/item/8b53k9s2
© 2015 World Scientific Publishing Company. We develop a general theory of Markov chains realizable as random walks on Rtrivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Möbius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as ToomTsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.
https://escholarship.org/uc/item/8b53k9s2
Mon, 14 May 2018 00:00:00 +0000

Discreteness is undecidable
https://escholarship.org/uc/item/8784b7nr
We prove that the discreteness problem for twogenerated nonelementary subgroups of SL(2, C) is undecidable in the BlumShubSmale (BSS) computability model.
https://escholarship.org/uc/item/8784b7nr
Mon, 14 May 2018 00:00:00 +0000

Crystal structure on rigged configurations and the filling map
https://escholarship.org/uc/item/86v883p8
© 2015, Australian National University. All rights reserved. In this paper, we extend work of the first author on a crystal structure on rigged con_gurations of simplylaced type to all nonexceptional affine types using the technology of virtual rigged con_gurations and crystals. Under the bijection between rigged configurations and tensor products of KirillovReshetikhin crystals specialized to a single tensor factor, we obtain a new tableaux model for KirillovReshetikhin crystals. This is related to the model in terms of KashiwaraNakashima tableaux via a filling map, generalizing the recently discovered filling map in typeD(1)n
https://escholarship.org/uc/item/86v883p8
Mon, 14 May 2018 00:00:00 +0000

Current theoretical models fail to predict the topological complexity of the human genome.
https://escholarship.org/uc/item/81g179cj
Understanding the folding of the human genome is a key challenge of modern structural biology. The emergence of chromatin conformation capture assays (e.g., HiC) has revolutionized chromosome biology and provided new insights into the three dimensional structure of the genome. The experimental data are highly complex and need to be analyzed with quantitative tools. It has been argued that the data obtained from HiC assays are consistent with a fractal organization of the genome. A key characteristic of the fractal globule is the lack of topological complexity (knotting or interlinking). However, the absence of topological complexity contradicts results from polymer physics showing that the entanglement of long linear polymers in a confined volume increases rapidly with the length and with decreasing volume. In vivo and in vitro assays support this claim in some biological systems. We simulate knotted lattice polygons confined inside a sphere and demonstrate that their contact...
https://escholarship.org/uc/item/81g179cj
Mon, 14 May 2018 00:00:00 +0000

Equilibrium circulation and stress distribution in viscoelastic creeping flow
https://escholarship.org/uc/item/7z04t51g
An analytic, asymptotic approximation of the nonlinear steadystate equations for viscoelastic creeping flow, modeled by the OldroydB equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stressisland, or birefringent strand. The polymer stress diffusion coefficient is used, both as an asymptotic parameter and a regularization parameter. The structure of the singular part of the polymer stress tensor is a Gaussian aligned with the incoming streamline of the stagnation point a smoothed δdistribution whose width is proportional to the squareroot of the diffusion coefficient. The amplitude of the stress island scales with the Wiessenberg number, and although singular in the limit of vanishing diffusion, it is integrable in the cross stream direction due to its vanishing width; this yields a convergent secondary flow. The leading order...
https://escholarship.org/uc/item/7z04t51g
Mon, 14 May 2018 00:00:00 +0000

Dynamics on flag manifolds: Domains of proper discontinuity and cocompactness
https://escholarship.org/uc/item/79b5x84m
© 2018, Mathematical Sciences Publishers. All rights reserved. For noncompact semisimple Lie groups G with finite center, we study the dynamics of the actions of their discrete subgroups Γ < G on the associated partial flag manifolds G/P. Our study is based on the observation, already made in the deep work of Benoist, that they exhibit also in higher rank a certain form of convergencetype dynamics. We identify geometrically domains of proper discontinuity in all partial flag manifolds. Under certain dynamical assumptions equivalent to the Anosov subgroup condition, we establish the cocompactness of the Taction on various domains of proper discontinuity, in particular on domains in the full flag manifold G/B. In the regular case (eg of BAnosov subgroups), we prove the nonemptiness of such domains if G has (locally) at least one noncompact simple factor not of the type A1, B2or G2by showing the nonexistence of certain ball packings of the visual boundary.
https://escholarship.org/uc/item/79b5x84m
Mon, 14 May 2018 00:00:00 +0000

Mirror symmetry for orbifold hurwitz numbers
https://escholarship.org/uc/item/715632rq
We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion, which is then proved to be equivalent to the integral recursion of Eynard and Orantin with spectral curve given by the rLambert curve. We argue that the rLambert curve also arises in the infinite framing limit of orbifold GromovWitten theory of [C3/(Z/rZ)]. Finally, we prove that the mirror model to orbifold Hurwitz numbers admits a quantum curve. © 2014 Lehigh University.
https://escholarship.org/uc/item/715632rq
Mon, 14 May 2018 00:00:00 +0000

Geometric infiniteness in negatively pinched Hadamard manifolds
https://escholarship.org/uc/item/6zg865h3
We generalize Bonahon's characterization of geometrically infinite
torsionfree discrete subgroups of PSL(2, $\mathbb{C}$) to geometrically
infinite discrete isometry subgroups in the case of rank 1 symmetric spaces,
and, under the assumption of bounded torsion, to the case of negatively pinched
Hadamard manifolds. Every such geometrically infinite isometry subgroup
$\Gamma$ has a set of nonconical limit points with cardinality of continuum.
https://escholarship.org/uc/item/6zg865h3
Mon, 14 May 2018 00:00:00 +0000

Braid moves in commutation classes of the symmetric group
https://escholarship.org/uc/item/6vm3n48c
Braid moves in commutation classes of the symmetric group
https://escholarship.org/uc/item/6vm3n48c
Mon, 14 May 2018 00:00:00 +0000

Universality theorems for configuration spaces of planar linkages
https://escholarship.org/uc/item/6t79m3nh
We prove realizability theorems for vectorvalued polynomial mappings, realalgebraic sets and compact smooth manifolds by moduli spaces of planar linkages. We also establish a relation between universality theorems for moduli spaces of mechanical linkages and projective arrangements. © 2002 Elsevier Science Ltd. All rights reserved.
https://escholarship.org/uc/item/6t79m3nh
Mon, 14 May 2018 00:00:00 +0000

Noncoherence of arithmetic hyperbolic lattices
https://escholarship.org/uc/item/6r46c4sg
We prove that all arithmetic lattices in O (n, 1), n≥ 4, n ≠ 7, are noncoherent. We lso establish noncoherence of uniform arithmetic lattices of the simplest type in SU (2, 1), n ≥ 2, and of uniform lattices in SU(2, 1) which have infinite abelianization.
https://escholarship.org/uc/item/6r46c4sg
Mon, 14 May 2018 00:00:00 +0000

Neural mechanism of optimal limb coordination in crustacean swimming.
https://escholarship.org/uc/item/6qc6j30v
A fundamental challenge in neuroscience is to understand how biologically salient motor behaviors emerge from properties of the underlying neural circuits. Crayfish, krill, prawns, lobsters, and other longtailed crustaceans swim by rhythmically moving limbs called swimmerets. Over the entire biological range of animal size and paddling frequency, movements of adjacent swimmerets maintain an approximate quarterperiod phase difference with the more posterior limbs leading the cycle. We use a computational fluid dynamics model to show that this frequencyinvariant stroke pattern is the most effective and mechanically efficient paddling rhythm across the full range of biologically relevant Reynolds numbers in crustacean swimming. We then show that the organization of the neural circuit underlying swimmeret coordination provides a robust mechanism for generating this stroke pattern. Specifically, the wavelike limb coordination emerges robustly from a combination of the halfcenter...
https://escholarship.org/uc/item/6qc6j30v
Mon, 14 May 2018 00:00:00 +0000

A generating function for all semimagic squares and the volume of the Birkhoff polytope
https://escholarship.org/uc/item/6bs706xg
We present a multivariate generating function for all n×n nonnegative integral matrices with all row and column sums equal to a positive integer t, the so called semimagic squares. As a consequence we obtain formulas for all coefficients of the Ehrhart polynomial of the polytope B n of n×n doublystochastic matrices, also known as the Birkhoff polytope. In particular we derive formulas for the volumes of B n and any of its faces. © 2008 Springer Science+Business Media, LLC.
https://escholarship.org/uc/item/6bs706xg
Mon, 14 May 2018 00:00:00 +0000

SOME RECENT RESULTS ON ANOSOV REPRESENTATIONS
https://escholarship.org/uc/item/69p8q00w
© 2016, Springer Science+Business Media New York. In this note we give an overview of some of our recent work on Anosov representations of discrete groups into higher rank semisimple Lie groups.
https://escholarship.org/uc/item/69p8q00w
Mon, 14 May 2018 00:00:00 +0000

Algebraic unimodular counting
https://escholarship.org/uc/item/666982kh
We study algebraic algorithms for expressing the number of nonnegative integer solutions to a unimodular system of linear equations as a function of the right hand side. Our methods include Todd classes of toric varieties via Gröbner bases, and rational generating functions as in Barvinok's algorithm. We report polyhedral and computational results for two special cases: counting contingency tables and Kostant's partition function.
https://escholarship.org/uc/item/666982kh
Mon, 14 May 2018 00:00:00 +0000

The monodromy groups of Schwarzian equations on closed Riemann surfaces
https://escholarship.org/uc/item/641060t5
Let θ : π1(R) → PSL(2, ℂ) be a homomorphism of the fundamental group of an oriented, closed surface R of genus exceeding one. We will establish the following theorem. THEOREM. Necessary and sufficient for θ to be the monodromy representation associated with a complex projective stucture on R, either unbranched or with a single branch point of order 2, is that θ(π1(R)) be nonelementary. A branch point is required if and only if the representation θ does not lift to SL(2, ℂ).
https://escholarship.org/uc/item/641060t5
Mon, 14 May 2018 00:00:00 +0000

A uniform model for KirillovReshetikhin crystals I: Lifting the parabolic quantum bruhat graph
https://escholarship.org/uc/item/5xk368c6
© 2014 © The Author(s) 2014. Published by Oxford University Press. All rights reserved. We lift the parabolic quantum Bruhat graph (QBG) into the Bruhat order on the affine Weyl group and into Littelmann's poset on levelzero weights. We establish a quantum analog of Deodhar's Bruhatminimum lift from a parabolic quotient of the Weyl group. This result asserts a remarkable compatibility of the QBG on the Weyl group, with the cosets for every parabolic subgroup. Also, we generalize Postnikov's lemma from the QBG to the parabolic one; this lemma compares paths between two vertices in the former graph. The results in this paper will be applied in a second paper to establish a uniform construction of tensor products of onecolumn KirillovReshetikhin (KR) crystals, and the equality, for untwisted affine root systems, between the Macdonald polynomial with t set to zero and the graded character of tensor products of onecolumn KR modules.
https://escholarship.org/uc/item/5xk368c6
Mon, 14 May 2018 00:00:00 +0000

Kschur functions and affine schubert calculus
https://escholarship.org/uc/item/5v8503xj
This book is an exposition of the current state of research of affine
Schubert calculus and $k$Schur functions. This text is based on a series of
lectures given at a workshop titled "Affine Schubert Calculus" that took place
in July 2010 at the Fields Institute in Toronto, Ontario. The story of this
research is told in three parts: 1. Primer on $k$Schur Functions 2. Stanley
symmetric functions and Peterson algebras 3. Affine Schubert calculus
https://escholarship.org/uc/item/5v8503xj
Mon, 14 May 2018 00:00:00 +0000

Computing fundamental matrix decompositions accurately via the matrix sign function in two iterations: The power of Zolotarev's functions
https://escholarship.org/uc/item/5qs3v0rs
The symmetric eigenvalue decomposition and the singular value decomposition (SVD) are fundamental matrix decompositions with many applications. Conventional algorithms for computing these decompositions are suboptimal in view of recent trends in computer architectures which require minimizing communication together with arithmetic costs. Spectral divideandconquer algorithms, which recursively decouple the problem into two smaller subproblems, can achieve both requirements. Such algorithms can be constructed with the polar decomposition playing two key roles: it forms a bridge between the symmetric eigendecomposition and the SVD, and its connection to the matrix sign function naturally leads to spectraldecoupling. For computing the polar decomposition, the scaled Newton and QDWH iterations are two of the most popular algorithms, as they are backward stable and converge in at most nine and six iterations, respectively. Following this framework, we develop a higherorder variant...
https://escholarship.org/uc/item/5qs3v0rs
Mon, 14 May 2018 00:00:00 +0000

Short rational functions for toric algebra and applications
https://escholarship.org/uc/item/5d18n90g
We encode the binomials belonging to the toric ideal IAassociated with an integral d×n matrix A using a short sum of rational functions as introduced by Barvinok (Math. Operations Research 19 (1994) 769) and Barvinok and Woods (J. Amer. Math. Soc. 16 (2003) 957). Under the assumption that d and n are fixed, this representation allows us to compute a universal Gröbner basis and the reduced Gröbner basis of the ideal IA, with respect to any term order, in time polynomial in the size of the input. We also derive a polynomial time algorithm for normal form computations which replaces in this new encoding the usual reductions typical of the division algorithm. We describe other applications, such as the computation of Hilbert series of normal semigroup rings, and we indicate applications to enumerative combinatorics, integer programming, and statistics. © 2004 Elsevier Ltd. All rights reserved.
https://escholarship.org/uc/item/5d18n90g
Mon, 14 May 2018 00:00:00 +0000

Directed Nonabelian Sandpile Models on Trees
https://escholarship.org/uc/item/5c82z72n
We define two general classes of nonabelian sandpile models on directed trees
(or arborescences) as models of nonequilibrium statistical phenomena. These
models have the property that sand grains can enter only through specified
reservoirs, unlike the wellknown abelian sandpile model.
In the Trickledown sandpile model, sand grains are allowed to move one at a
time. For this model, we show that the stationary distribution is of product
form. In the Landslide sandpile model, all the grains at a vertex topple at
once, and here we prove formulas for all eigenvalues, their multiplicities, and
the rate of convergence to stationarity. The proofs use wreath products and the
representation theory of monoids.
https://escholarship.org/uc/item/5c82z72n
Mon, 14 May 2018 00:00:00 +0000

Quantitative Combinatorial Geometry for Continuous Parameters
https://escholarship.org/uc/item/5bv869t1
We prove variations of Carathéodory’s, Helly’s and Tverberg’s theorems where the sets involved are measured according to continuous functions such as the volume or diameter. Among our results, we present continuous quantitative versions of Lovász’s colorful Helly’s theorem, Bárány’s colorful Carathéodory’s theorem, and the colorful Tverberg’s theorem.
https://escholarship.org/uc/item/5bv869t1
Mon, 14 May 2018 00:00:00 +0000

Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves
https://escholarship.org/uc/item/50x6b862
We analyze Weierstrass cycles and tautological rings in moduli spaces of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus less than or equal to 6. In particular, we show that our general formula gives a good estimate for the dimension of Weierstrass cycles for low genera.
https://escholarship.org/uc/item/50x6b862
Mon, 14 May 2018 00:00:00 +0000

The Central Curve in Linear Programming
https://escholarship.org/uc/item/4xp7v6zj
The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime ideal of the central curve, thereby answering a question of Bayer and Lagarias. These invariants, along with the degree of the Gauss image of the curve, are expressed in terms of the matroid of the input matrix. Extending work of Dedieu, Malajovich and Shub, this yields an instancespecific bound on the total curvature of the central path, a quantity relevant for interiorpoint methods. The global geometry of central curves is studied in detail. © 2012 SFoCM.
https://escholarship.org/uc/item/4xp7v6zj
Mon, 14 May 2018 00:00:00 +0000

Reproducibility of 3D chromatin configuration reconstructions.
https://escholarship.org/uc/item/4vv4w2pc
It is widely recognized that the threedimensional (3D) architecture of eukaryotic chromatin plays an important role in processes such as gene regulation and cancerdriving gene fusions. Observing or inferring this 3D structure at even modest resolutions had been problematic, since genomes are highly condensed and traditional assays are coarse. However, recently devised highthroughput molecular techniques have changed this situation. Notably, the development of a suite of chromatin conformation capture (CCC) assays has enabled elicitation of contactsspatially close chromosomal lociwhich have provided insights into chromatin architecture. Most analysis of CCC data has focused on the contact level, with less effort directed toward obtaining 3D reconstructions and evaluating the accuracy and reproducibility thereof. While questions of accuracy must be addressed experimentally, questions of reproducibility can be addressed statisticallythe purpose of this paper. We use a constrained...
https://escholarship.org/uc/item/4vv4w2pc
Mon, 14 May 2018 00:00:00 +0000

Energy of harmonic functions and Gromov's proof of Stallings' theorem
https://escholarship.org/uc/item/4vb7215r
© 2014 by De Gruyter 2014. We provide details for Gromov's proof of Stallings' theorem on groups with infinitely many ends using harmonic functions. The main technical result of the paper is a compactness theorem for a certain family of harmonic functions.
https://escholarship.org/uc/item/4vb7215r
Mon, 14 May 2018 00:00:00 +0000

Edge contraction on dual ribbon graphs and 2D TQFT
https://escholarship.org/uc/item/4d28920b
We present a new set of axioms for 2D TQFT formulated on the category of cell graphs with edgecontraction operations as morphisms. We construct a functor from this category to the endofunctor category consisting of Frobenius algebras. Edgecontraction operations correspond to natural transformations of endofunctors, which are compatible with the Frobenius algebra structure. Given a Frobenius algebra A, every cell graph determines an element of the symmetric tensor algebra defined over the dual space A⁎. We show that the edgecontraction axioms make this assignment depending only on the topological type of the cell graph, but not on the graph itself. Thus the functor generates the TQFT corresponding to A.
https://escholarship.org/uc/item/4d28920b
Mon, 14 May 2018 00:00:00 +0000

A rainbow Ramsey analogue of Rado's theorem
https://escholarship.org/uc/item/48r5h3gd
We present a Rainbow Ramsey version of the wellknown Ramseytype theorem of Richard Rado. We use new techniques from the Geometry of Numbers. We also disprove two conjectures proposed in the literature.
https://escholarship.org/uc/item/48r5h3gd
Mon, 14 May 2018 00:00:00 +0000

Weak orientability of matroids and polynomial equations
https://escholarship.org/uc/item/4827g1tw
© 2015 Elsevier Ltd. This paper studies systems of polynomial equations that provide information about orientability of matroids.First, we study systems of linear equations over F2, originally alluded to by Bland and Jensen in their seminal paper on weak orientability. The BlandJensen linear equations for a matroid M have a solution if and only if M is weakly orientable. We use the BlandJensen system to determine weak orientability for all matroids on at most nine elements and all matroids between ten and twelve elements having rank three. Our experiments indicate that for small rank, about half the time, when a simple matroid is not orientable, it is already nonweakly orientable, and further this may happen more often as the rank increases. Thus, about half of the small simple nonorientable matroids of rank three are not representable over fields having order congruent to three modulo four. For binary matroids, the BlandJensen linear systems provide a practical way to check...
https://escholarship.org/uc/item/4827g1tw
Mon, 14 May 2018 00:00:00 +0000

Edges versus circuits: A hierarchy of diameters in polyhedra
https://escholarship.org/uc/item/47t065k4
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [5] by introducing a vast hierarchy of generalizations to the notion of graph diameter. This hierarchy provides some interesting lower bounds for the usual graph diameter. After explaining the structure of the hierarchy and discussing these bounds, we focus on clearly explaining the differences and similarities among the many diameter notions of our hierarchy. Finally, we fully characterize the hierarchy in dimension two. It collapses into fewer categories, for which we exhibit the ranges of values that can be realized as diameters.
https://escholarship.org/uc/item/47t065k4
Mon, 14 May 2018 00:00:00 +0000

Blocks in the asymmetric simple exclusion process
https://escholarship.org/uc/item/44c3g3xm
In earlier work, the authors obtained formulas for the probability in the asymmetric simple exclusion process that the mth particle from the left is at site x at time t. They were expressed in general as sums of multiple integrals and, for the case of step initial condition, as an integral involving a Fredholm determinant. In the present work, these results are generalized to the case where the mth particle is the leftmost one in a contiguous block of L particles. The earlier work depended in a crucial way on two combinatorial identities, and the present work begins with a generalization of these identities to general L.
https://escholarship.org/uc/item/44c3g3xm
Mon, 14 May 2018 00:00:00 +0000

Geometric finiteness in negatively pinched Hadamard manifolds
https://escholarship.org/uc/item/3xs9z3m3
In this paper, we generalize Bonahon's characterization of geometrically infinite torsionfree discrete subgroups of PSL(2,C) to geometrically infinite discrete subgroups Γ of isometries of negatively pinched Hadamard manifolds X. We then generalize a theorem of Bishop to prove that every discrete geometrically infinite isometry subgroup Γ has a set of nonconical limit points with the cardinality of the continuum.
https://escholarship.org/uc/item/3xs9z3m3
Mon, 14 May 2018 00:00:00 +0000

Synaptic basis for intense thalamocortical activation of feedforward inhibitory cells in neocortex
https://escholarship.org/uc/item/3t23p33z
The thalamus provides fundamental input to the neocortex. This input activates inhibitory interneurons more strongly than excitatory neurons, triggering powerful feedforward inhibition. We studied the mechanisms of this selective neuronal activation using a mouse somatosensory thalamocortical preparation. Notably, the greater responsiveness of inhibitory interneurons was not caused by their distinctive intrinsic properties but was instead produced by synaptic mechanisms. Axons from the thalamus made stronger and more frequent excitatory connections onto inhibitory interneurons than onto excitatory cells. Furthermore, circuit dynamics allowed feedforward inhibition to suppress responses in excitatory cells more effectively than in interneurons. Thalamocortical excitatory currents rose quickly in interneurons, allowing them to fire action potentials before significant feedforward inhibition emerged. In contrast, thalamocortical excitatory currents rose slowly in excitatory cells,...
https://escholarship.org/uc/item/3t23p33z
Mon, 14 May 2018 00:00:00 +0000

Bistability in a leaky integrateandfire neuron with a passive dendrite
https://escholarship.org/uc/item/3hw5g673
We examine the influence of dendritic load on the firing dynamics of a spatially extended leaky integrateandfire (LIF) neuron that explicitly includes spiking dynamics. We obtain an exact analytical solution for this model and use it to derive a return map that completely captures the dynamics of the system. Using the map, we find that dendritic properties can significantly change the firing dynamics of the system. Under certain conditions, the addition of the dendrite can change the LIF model from type 1 excitability to type 2 excitability and induce bistability between periodic firing and the quiescent state. We identify the mechanism that causes the periodic behavior in the bistable regime as somatodendritic pingpong. Furthermore, we use the return map to fully explore the model parameter space in order to find regions where this bistable behavior occurs. We then give physical interpretations of the dependence of the bistable behavior on model parameters. Finally, we demonstrate...
https://escholarship.org/uc/item/3hw5g673
Mon, 14 May 2018 00:00:00 +0000

On Rayleightype formulas for a nonlocal boundary value problem associated with an integral operator commuting with the Laplacian
https://escholarship.org/uc/item/3447s8vt
© 2016 Elsevier Inc. In this article we prove the existence, uniqueness, and simplicity of a negative eigenvalue for a class of integral operators whose kernel is of the form x−yρ, 0<ρ≤1, x,y∈[−a,a]. We also provide two different ways of producing recursive formulas for the Rayleigh functions (i.e., recursion formulas for power sums) of the eigenvalues of this integral operator when ρ=1, providing means of approximating this negative eigenvalue. These methods offer recursive procedures for dealing with the eigenvalues of a onedimensional Laplacian with nonlocal boundary conditions which commutes with an integral operator having a harmonic kernel. The problem emerged in recent work by one of the authors [48]. We also discuss extensions in higher dimensions and links with distance matrices.
https://escholarship.org/uc/item/3447s8vt
Mon, 14 May 2018 00:00:00 +0000

The spectral curve and the Schrödinger equation of double Hurwitz numbers and higher spin structures
https://escholarship.org/uc/item/33h6h6cc
We derive the spectral curves for qpart double Hurwitz numbers, rspin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0, 1)geometry. We quantize this family of spectral curves and obtain the Schrödinger equations for the partition function of the corresponding Hurwitz problems. We thus confirm the conjecture for the existence of quantum curves in these generalized Hurwitz number cases.
https://escholarship.org/uc/item/33h6h6cc
Mon, 14 May 2018 00:00:00 +0000

Saturation and Irredundancy for Spin(8)
https://escholarship.org/uc/item/30j0s5fh
We explicitly calculate the triangle inequalities for the group PSO(8).
Therefore we explicitly solve the eigenvalues of sum problem for this group
(equivalently describing the sidelengths of geodesic triangles in the
corresponding symmetric space for the Weyl chambervalued metric). We then
apply some computer programs to verify two basic questions/conjectures. First,
we verify that the above system of inequalities is irredundant. Then, we verify
the ``saturation conjecture'' for the decomposition of tensor products of
finitedimensional irreducible representations of Spin(8). Namely, we show that
for any triple of dominant weights a, b, c such that a+b+c is in the root
lattice, and any positive integer N, the tensor product of the irreducible
representations V(a) and V(b) contains V(c) if and only if the tensor product
of V(Na) and V(Nb) contains V(Nc).
https://escholarship.org/uc/item/30j0s5fh
Mon, 14 May 2018 00:00:00 +0000

FtsKdependent XerCDdif recombination unlinks replication catenanes in a stepwise manner.
https://escholarship.org/uc/item/3079k8f5
In Escherichia coli, complete unlinking of newly replicated sister chromosomes is required to ensure their proper segregation at cell division. Whereas replication links are removed primarily by topoisomerase IV, XerC/XerDdif sitespecific recombination can mediate sister chromosome unlinking in Topoisomerase IVdeficient cells. This reaction is activated at the division septum by the DNA translocase FtsK, which coordinates the last stages of chromosome segregation with cell division. It has been proposed that, after being activated by FtsK, XerC/XerDdif recombination removes DNA links in a stepwise manner. Here, we provide a mathematically rigorous characterization of this topological mechanism of DNA unlinking. We show that stepwise unlinking is the only possible pathway that strictly reduces the complexity of the substrates at each step. Finally, we propose a topological mechanism for this unlinking reaction.
https://escholarship.org/uc/item/3079k8f5
Mon, 14 May 2018 00:00:00 +0000

Intermediate sums on polyhedra II: bidegree and poisson formula
https://escholarship.org/uc/item/2vc4921t
Copyright © 2016 University College London. We continue our study of intermediate sums over polyhedra, interpolating between integrals and discrete sums, which were introduced by Barvinok [Computing the Ehrhart quasipolynomial of a rational simplex. Math. Comp. 75 (2006), 14491466]. By wellknown decompositions, it is sufficient to consider the case of affine cones s+c, where is an arbitrary real vertex and is a rational polyhedral cone. For a given rational subspace L, we define the intermediate generating functions SL(s+c)(ξ) by integrating an exponential function over all lattice slices of the affine cone s+c parallel to the subspace L and summing up the integrals. We expose the bidegree structure in parameters and ξ, which was implicitly used in the algorithms in our papers [Computation of the highest coefficients of weighted Ehrhart quasipolynomials of rational polyhedra. Found. Comput. Math. 12 (2012), 435469] and [Intermediate sums on polyhedra: computation and real...
https://escholarship.org/uc/item/2vc4921t
Mon, 14 May 2018 00:00:00 +0000

The hierarchy of circuit diameters and transportation polytopes
https://escholarship.org/uc/item/2mb049gn
The study of the diameter of the graph of polyhedra is a classical problem in the theory of linear programming. While transportation polytopes are at the core of operations research and statistics it is still unknown whether the Hirsch conjecture is true for general m×ntransportation polytopes. In earlier work the first three authors introduced a hierarchy of variations to the notion of graph diameter in polyhedra. This hierarchy provides some interesting lower bounds for the usual graph diameter. This paper has three contributions: First, we compare the hierarchy of diameters for the m×ntransportation polytopes. We show that the Hirsch conjecture bound of m+n−1 is actually valid in most of these diameter notions. Second, we prove that for 3×ntransportation polytopes the Hirsch conjecture holds in the classical graph diameter. Third, we show for 2×ntransportation polytopes that the stronger monotone Hirsch conjecture holds and improve earlier bounds on the graph diameter.
https://escholarship.org/uc/item/2mb049gn
Mon, 14 May 2018 00:00:00 +0000

On representation varieties of 3manifold groups
https://escholarship.org/uc/item/2f1562bj
© 2017, Mathematical Sciences Publishers. All rights reserved. We prove universality theorems (“Murphy’s laws”) for representation varieties of fundamental groups of closed 3dimensional manifolds. We show that germs of SL(2) representation schemes of such groups are essentially the same as germs of schemes over ℚ of finite type.
https://escholarship.org/uc/item/2f1562bj
Mon, 14 May 2018 00:00:00 +0000

Tree simplification and the 'plateaux' phenomenon of graph Laplacian eigenvalues
https://escholarship.org/uc/item/2bj3g2sz
© 2015 Elsevier Inc. All rights reserved. We developed a procedure of reducing the number of vertices and edges of a given tree, which we call the "tree simplification procedure," without changing its topological information. Our motivation for developing this procedure was to reduce computational costs of graph Laplacian eigenvalues of such trees. When we applied this procedure to a set of trees representing dendritic structures of retinal ganglion cells of a mouse and computed their graph Laplacian eigenvalues, we observed two "plateaux" (i.e., two sets of multiple eigenvalues) in the eigenvalue distribution of each such simplified tree. In this article, after describing our tree simplification procedure, we analyze why such eigenvalue plateaux occur in a simplified tree; explain such plateaux can occur in a more general graph if it satisfies a certain condition; and identify these two eigenvalues specifically as well as the lower bound to their multiplicity.
https://escholarship.org/uc/item/2bj3g2sz
Mon, 14 May 2018 00:00:00 +0000

The biHecke monoid of a finite coxeter group and its representations
https://escholarship.org/uc/item/29h0171c
For any finite Coxeter group W, we introduce two new objects: its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matrices, almost forms a lattice on W. The construction of the biHecke monoid relies on the usual combinatorial model for the 0Hecke algebra H0(W), that is, for the symmetric group, the algebra (or monoid) generated by the elementary bubble sort operators. The authors previously introduced the Hecke group algebra, constructed as the algebra generated simultaneously by the bubble sort and antisort operators, and described its representation theory. In this paper, we consider instead the monoid generated by these operators. We prove that it admits W simple and projective modules. In order to construct the simple modules, we introduce for each w ∈ W a combinatorial module Tw whose support is the interval [1,w]R in right weak order. This module yields an algebra, whose representation...
https://escholarship.org/uc/item/29h0171c
Mon, 14 May 2018 00:00:00 +0000

A global bifurcation and the appearance of a onedimensional spiral wave in excitable media
https://escholarship.org/uc/item/28m357wt
It is well known that excitable media can sustain "fast" stable traveling pulses of excitation. In models for which analysis is tractable, the fast pulse solution is known to appear through a saddlenode bifurcation accompanied by a "slow" unstable traveling pulse. Furthermore, the uniform rest state is also a stable solution. It is generally assumed that the boundary between the basins of attractions of the rest state and fast pulse (i.e., threshold) consists of the stable manifold of the slow pulse. We use numerical experiments to explore this issue. Our results indicate that, near the saddlenode bifurcation, the stable manifold of the slow pulse does indeed act as the threshold between the rest state and fast pulse. However, further away from the saddlenode bifurcation, a global bifurcation involving the heteroclinic connections between slow and fast pulses occurs. This bifurcation gives rise to an unstable periodic solution that has been referred to as a onedimensional spiral...
https://escholarship.org/uc/item/28m357wt
Mon, 14 May 2018 00:00:00 +0000

Spectral Gap for RandomtoRandom Shuffling on Linear Extensions
https://escholarship.org/uc/item/2849t7dv
In this paper, we propose a new Markov chain which generalizes
randomtorandom shuffling on permutations to randomtorandom shuffling on
linear extensions of a finite poset of size $n$. We conjecture that the second
largest eigenvalue of the transition matrix is bounded above by
$(1+1/n)(12/n)$ with equality when the poset is disconnected. This Markov
chain provides a way to sample the linear extensions of the poset with a
relaxation time bounded above by $n^2/(n+2)$ and a mixing time of $O(n^2 \log
n)$. We conjecture that the mixing time is in fact $O(n \log n)$ as for the
usual randomtorandom shuffling.
https://escholarship.org/uc/item/2849t7dv
Mon, 14 May 2018 00:00:00 +0000

Dirichlet fundamental domains and topology of projective varieties
https://escholarship.org/uc/item/27w4s14f
We prove that for every finitelypresented group G there exists a 2dimensional irreducible complexprojective variety W with the fundamental group G, so that all singularities of W are normal crossings and Whitney umbrellas. © 2013 SpringerVerlag Berlin Heidelberg.
https://escholarship.org/uc/item/27w4s14f
Mon, 14 May 2018 00:00:00 +0000

Immersed boundary smooth extension: A highorder method for solving PDE on arbitrary smooth domains using Fourier spectral methods
https://escholarship.org/uc/item/27n8r19q
© 2015 Elsevier Inc. The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves firstorder spatial accuracy near embedded boundaries. In this paper, we introduce a new highorder numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves highorder accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesiangrid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized deltafunctions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple,...
https://escholarship.org/uc/item/27n8r19q
Mon, 14 May 2018 00:00:00 +0000

Effects of dendritic load on the firing frequency of oscillating neurons.
https://escholarship.org/uc/item/22f42910
We study the effects of passive dendritic properties on the dynamics of neuronal oscillators. We find that the addition of a passive dendrite can sometimes have counterintuitive effects on firing frequency. Specifically, the addition of a hyperpolarized passive dendritic load can either increase, decrease, or have negligible effects on firing frequency. We use the theory of weak coupling to derive phase equations for "ballandstick" model neurons and twocompartment model neurons. We then develop a framework for understanding how the addition of passive dendrites modulates the frequency of neuronal oscillators. We show that the average value of the neuronal oscillator's phase response curves measures the sensitivity of the neuron's firing rate to the dendritic load, including whether the addition of the dendrite causes an increase or decrease in firing frequency. We interpret this finding in terms of to the slope of the neuronal oscillator's frequencyapplied current curve. We...
https://escholarship.org/uc/item/22f42910
Mon, 14 May 2018 00:00:00 +0000

Quantitative Tverberg Theorems Over Lattices and Other Discrete Sets
https://escholarship.org/uc/item/2037z49w
This paper presents a new variation of Tverberg’s theorem. Given a discrete set S of Rd, we study the number of points of S needed to guarantee the existence of an mpartition of the points such that the intersection of the m convex hulls of the parts contains at least k points of S. The proofs of the main results require new quantitative versions of Helly’s and Carathéodory’s theorems.
https://escholarship.org/uc/item/2037z49w
Mon, 14 May 2018 00:00:00 +0000

RAAGs in Ham
https://escholarship.org/uc/item/1zw9r8c7
We prove that every RAAG (Right Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of every symplectic manifold. © 2012 Springer Basel AG.
https://escholarship.org/uc/item/1zw9r8c7
Mon, 14 May 2018 00:00:00 +0000

Homological indices of collections of 1forms
https://escholarship.org/uc/item/1x30s3zh
Homological index of a holomorphic 1form on a complexanalytic variety with an isolated singular point is an analogue of the usual index of a 1form on a nonsingular manifold. One can say that it corresponds to the top Chern number of a manifold. We offer a definition of homological indices for collections of 1forms on a (purely dimensional) complexanalytic variety with an isolated singular point corresponding to other Chern numbers. We also define new invariants of germs of complexanalytic varieties with isolated singular points related to ‘vanishing Chern numbers’ at them.
https://escholarship.org/uc/item/1x30s3zh
Mon, 14 May 2018 00:00:00 +0000

Hyperbolic groups with lowdimensional boundary
https://escholarship.org/uc/item/1wc1h3wq
If a torsionfree hyperbolic group G has 1dimensional boundary ∂∞G, then ∂∞G is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When ∂∞G is a Sierpinski carpet we show that G is a quasiconvex subgroup of a 3dimensional hyperbolic Poincaré duality group. We also construct a "topologically rigid" hyperbolic group G: any homeomorphism of ∂∞G is induced by an element of G. © 2000 Éditions scientifiques et médicales Elsevier SAS.
https://escholarship.org/uc/item/1wc1h3wq
Mon, 14 May 2018 00:00:00 +0000

A UNIFORM MODEL FOR KIRILLOV–RESHETIKHIN CRYSTALS III: NONSYMMETRICMACDONALD POLYNOMIALS AT t = 0 AND DEMAZURE CHARACTERS
https://escholarship.org/uc/item/1v05d417
© 2017, Springer Science+Business Media New York. We establish the equality of the specialization Ewλ(x ; q; 0) of the nonsymmetric Macdonald polynomial Ewλ(x ; q; t) at t = 0 with the graded character gch Uw+(λ) of a certain Demazuretype submodule Uw+(λ) of a tensor product of “singlecolumn” Kirillov–Reshetikhin modules for an untwisted affine Lie algebra, where λ is a dominant integral weight and w is a (finite) Weyl group element; this generalizes our previous result, that is, the equality between the specialization Pλ(x ; q; 0) of the symmetric Macdonald polynomial Pλ(x ; q; t) at t = 0 and the graded character of a tensor product of singlecolumn Kirillov–Reshetikhin modules. We also give two combinatorial formulas for the mentioned specialization of nonsymmetric Macdonald polynomials: one in terms of quantum Lakshmibai–Seshadri paths and the other in terms of the quantum alcove model.
https://escholarship.org/uc/item/1v05d417
Mon, 14 May 2018 00:00:00 +0000

The semaphore codes attached to a Turing machine via resets and their various limits
https://escholarship.org/uc/item/1s69r185
© 2016 World Scientific Publishing Company. We introduce semaphore codes associated to a Turing machine via resets. Semaphore codes provide an approximation theory for resets. In this paper, we generalize the setup of our previous paper "Random walks on semaphore codes and delay de Bruijn semigroups" to the infinite case by taking the profinite limit of kresets to obtain (ω)resets. We mention how this opens new avenues to attack the vs. NP problem.
https://escholarship.org/uc/item/1s69r185
Mon, 14 May 2018 00:00:00 +0000

Random sampling in computational algebra: Helly numbers and violator spaces
https://escholarship.org/uc/item/1s132759
This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving largescale polynomial systems and finding small generating sets of graded ideals. The cornerstone of our work is showing that the theory of violator spaces of Gärtner et al. applies to polynomial ideal problems. To show this, one utilizes a Hellytype result for algebraic varieties. The resulting algorithms have expected runtime linear in the number of input polynomials, making the ideas interesting for handling systems with very large numbers of polynomials, but whose rank in the vector space of polynomials is small (e.g., when the number of variables and degree is constant).
https://escholarship.org/uc/item/1s132759
Mon, 14 May 2018 00:00:00 +0000

A quantitative DoignonBellScarf theorem
https://escholarship.org/uc/item/1rk725c0
The famous DoignonBellScarf theorem is a Hellytype result about the existence of integer solutions to systems of linear inequalities. The purpose of this paper is to present the following quantitative generalization: Given an integer k, we prove that there exists a constant c(n,k), depending only on the dimension n and k, such that if a polyhedron {x∈Rn: Ax≤b} contains exactly k integer points, then there exists a subset of the rows, of cardinality no more than c(n,k), defining a polyhedron that contains exactly the same k integer points. In this case c(n,0)=2n as in the original case of DoignonBellScarf for infeasible systems of inequalities. We work on both upper and lower bounds for the constant c(n,k) and discuss some consequences, including a Clarksonstyle algorithm to find the lth best solution of an integer program with respect to the ordering induced by the objective function.
https://escholarship.org/uc/item/1rk725c0
Mon, 14 May 2018 00:00:00 +0000

Effects of correlated input and electrical coupling on synchrony in fastspiking cell networks
https://escholarship.org/uc/item/1947n9cf
Fastspiking (FS) cells in layer IV of the somatosensory cortex receive direct thalamocortical (TC) input and provide feedforward inhibition onto layer IV excitatory cells. The level of synchronous firing of FS cells will affect the shape of this feedforward output. Two factors that contribute to the synchrony are correlated TC input and electrical coupling between FS cells. Using a cellpair model, we show that these two factors act synergistically to increase synchrony, and we examine the underlying mechanism. © 2006 Elsevier B.V. All rights reserved.
https://escholarship.org/uc/item/1947n9cf
Mon, 14 May 2018 00:00:00 +0000