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Recent ucdavismath_rw items
https://escholarship.org/uc/ucdavismath_rw/rss
Recent eScholarship items from Recent Work
Tue, 19 Jan 2021 12:59:35 +0000

Quantitative Study of the Chiral Organization of the Phage Genome Induced by the Packaging Motor.
https://escholarship.org/uc/item/53z4f791
Molecular motors that translocate DNA are ubiquitous in nature. During morphogenesis of doublestranded DNA bacteriophages, a molecular motor drives the viral genome inside a protein capsid. Several models have been proposed for the threedimensional geometry of the packaged genome, but very little is known of the signature of the molecular packaging motor. For instance, biophysical experiments show that in some systems, DNA rotates during the packaging reaction, but most current biophysical models fail to incorporate this property. Furthermore, studies including rotation mechanisms have reached contradictory conclusions. In this study, we compare the geometrical signatures imposed by different possible mechanisms for the packaging motors: rotation, revolution, and rotation with revolution. We used a previously proposed kinetic Monte Carlo model of the motor, combined with Brownian dynamics simulations of DNA to simulate deterministic and stochastic motor models. We find that...
https://escholarship.org/uc/item/53z4f791
Tue, 5 Jan 2021 00:00:00 +0000

Fine structure of viral dsDNA encapsidation.
https://escholarship.org/uc/item/9rj6g2gn
Unraveling the mechanisms of packing of DNA inside viral capsids is of fundamental importance to understanding the spread of viruses. It could also help develop new applications to targeted drug delivery devices for a large range of therapies. In this article, we present a robust, predictive mathematical model and its numerical implementation to aid the study and design of bacteriophage viruses for application purposes. Exploiting the analogies between the columnar hexagonal chromonic phases of encapsidated viral DNA and chromonic aggregates formed by plankshaped molecular compounds, we develop a firstprinciples effective mechanical model of DNA packing in a viral capsid. The proposed expression of the packing energy, which combines relevant aspects of the liquid crystal theory, is developed from the model of hexagonal columnar phases, together with that describing configurations of polymeric liquid crystals. The method also outlines a parameter selection strategy that uses...
https://escholarship.org/uc/item/9rj6g2gn
Tue, 4 Aug 2020 00:00:00 +0000

A Liquid Crystal Model of Viral DNA Encapsidation
https://escholarship.org/uc/item/80p154v2
A liquid crystal continuum modeling framework for icosahedra bacteriophage
viruses is developed and tested. The main assumptions of the model are the
chromonic columnar hexagonal structure of confined DNA, the high resistance to
bending and the phase transition from solid to fluidlike states as the
concentration of DNA in the capsid decreases during infection. The model
predicts osmotic pressure inside the capsid and the ejection force of the DNA
as well as the size of the isotropic volume at the center of the capsid.
Extensions of the model are discussed.
https://escholarship.org/uc/item/80p154v2
Tue, 4 Aug 2020 00:00:00 +0000

Holonomy theorem for finite semigroups
https://escholarship.org/uc/item/0sm4c2dz
We provide a simple proof of the Holonomy Theorem using a new LyndonChiswell
length function on the KarnofskyRhodes expansion of a semigroup. Unexpectedly,
we have both a left and a right action on the Chiswell tree by elliptic maps.
https://escholarship.org/uc/item/0sm4c2dz
Tue, 4 Aug 2020 00:00:00 +0000

A uniform model for KirillovReshetikhin crystals. Extended abstract
https://escholarship.org/uc/item/9vv27295
We present a uniform construction of tensor products of onecolumn
KirillovReshetikhin (KR) crystals in all untwisted affine types, which uses a
generalization of the LakshmibaiSeshadri paths (in the theory of the
Littelmann path model). This generalization is based on the graph on parabolic
cosets of a Weyl group known as the parabolic quantum Bruhat graph. A related
model is the socalled quantum alcove model. The proof is based on two lifts of
the parabolic quantum Bruhat graph: to the Bruhat order on the affine Weyl
group and to Littelmann's poset on levelzero weights. Our construction leads
to a simple calculation of the energy function. It also implies the equality
between a Macdonald polynomial specialized at t=0 and the graded character of a
tensor product of KR modules.
https://escholarship.org/uc/item/9vv27295
Tue, 7 Jul 2020 00:00:00 +0000

Explicit description of the degree function in terms of quantum LakshmibaiSeshadri paths
https://escholarship.org/uc/item/98n3n97g
We give an explicit and computable description, in terms of the parabolic
quantum Bruhat graph, of the degree function defined for quantum
LakshmibaiSeshadri paths, or equivalently, for "projected" (affine) levelzero
LakshmibaiSeshadri paths. This, in turn, gives an explicit and computable
description of the global energy function on tensor products of
KirillovReshetikhin crystals of onecolumn type, and also of (classically
restricted) onedimensional sums.
https://escholarship.org/uc/item/98n3n97g
Tue, 7 Jul 2020 00:00:00 +0000

An insertion algorithm on multiset partitions with applications to diagram algebras
https://escholarship.org/uc/item/91g365wv
© 2020 Elsevier Inc. We generalize the Robinson–Schensted–Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer algebras and the spaces they act on. In addition, restrictions on the multisets lead to further identities and representation theory analogues. For instance, we obtain a bijection between words of length k with entries in [n] and pairs of tableaux of the same shape with one being a standard Young tableau of size n and the other being a standard multiset tableau of content [k]. We also obtain an algorithm from partition diagrams to pairs of a standard tableau and a standard multiset tableau of the same shape, which has the remarkable property that it is wellbehaved with respect to restricting a representation to a subalgebra. This insertion algorithm matches recent representationtheoretic results of Halverson and Jacobson [15].
https://escholarship.org/uc/item/91g365wv
Tue, 7 Jul 2020 00:00:00 +0000

Markov chains through semigroup graph expansions (a survey)
https://escholarship.org/uc/item/8230v82t
We review the recent approach to Markov chains using the KarnofksyRhodes and
McCammond expansions in semigroup theory by the authors and illustrate them by
two examples.
https://escholarship.org/uc/item/8230v82t
Tue, 7 Jul 2020 00:00:00 +0000

A minimajpreserving crystal on ordered multiset partitions
https://escholarship.org/uc/item/6st9h2k4
© 2017 Elsevier Inc. We provide a crystal structure on the set of ordered multiset partitions, which recently arose in the pursuit of the Delta Conjecture. This conjecture was stated by Haglund, Remmel and Wilson as a generalization of the Shuffle Conjecture. Various statistics on ordered multiset partitions arise in the combinatorial analysis of the Delta Conjecture, one of them being the minimaj statistic, which is a variant of the major index statistic on words. Our crystal has the property that the minimaj statistic is constant on connected components of the crystal. In particular, this yields another proof of the Schur positivity of the graded Frobenius series of the generalization Rn,k due to Haglund, Rhoades and Shimozono of the coinvariant algebra Rn. The crystal structure also enables us to demonstrate the equidistributivity of the minimaj statistic with the major index statistic on ordered multiset partitions.
https://escholarship.org/uc/item/6st9h2k4
Tue, 7 Jul 2020 00:00:00 +0000

Markov Chains for Promotion Operators
https://escholarship.org/uc/item/66j441v6
We consider generalizations of Schuetzenberger's promotion operator on the
set L of linear extensions of a finite poset. This gives rise to a strongly
connected graph on L. In earlier work (arXiv:1205.7074), we studied
promotionbased Markov chains on these linear extensions which generalizes
results on the Tsetlin library. We used the theory of Rtrivial monoids in an
essential way to obtain explicitly the eigenvalues of the transition matrix in
general when the poset is a rooted forest. We first survey these results and
then present explicit bounds on the mixing time and conjecture eigenvalue
formulas for more general posets. We also present a generalization of promotion
to arbitrary subsets of the symmetric group.
https://escholarship.org/uc/item/66j441v6
Tue, 7 Jul 2020 00:00:00 +0000

Rigged configuration bijection and proof of the X = M conjecture for nonexceptional affine types
https://escholarship.org/uc/item/5nm9w7ts
© 2018 Elsevier Inc. We establish a bijection between rigged configurations and highest weight elements of a tensor product of Kirillov–Reshetikhin crystals for all nonexceptional types. A key idea for the proof is to embed both objects into bigger sets for simplylaced types An(1) or Dn(1), whose bijections have already been established. As a consequence we settle the X=M conjecture in full generality for nonexceptional types. Furthermore, the bijection extends to a classical crystal isomorphism and sends the combinatorial Rmatrix to the identity map on rigged configurations.
https://escholarship.org/uc/item/5nm9w7ts
Tue, 7 Jul 2020 00:00:00 +0000

Characterization of queer supercrystals
https://escholarship.org/uc/item/5006m8mn
© 2020 Elsevier Inc. We provide a characterization of the crystal bases for the quantum queer superalgebra recently introduced by Grantcharov et al. This characterization is a combination of local queer axioms generalizing Stembridge's local axioms for crystal bases for simplylaced root systems, which were recently introduced by Assaf and Oguz, with further axioms and a new graph G characterizing the relations of the type A components of the queer supercrystal. We provide a counterexample to Assaf's and Oguz' conjecture that the local queer axioms uniquely characterize the queer supercrystal. We obtain a combinatorial description of the graph G on the type A components by providing explicit combinatorial rules for the odd queer operators on certain highest weight elements. This also yields a new combinatorial description of the Schur expansion of the Schur Ppolynomials.
https://escholarship.org/uc/item/5006m8mn
Tue, 7 Jul 2020 00:00:00 +0000

Normal distributions of finite Markov chains
https://escholarship.org/uc/item/4t66s6hm
© 2019 World Scientific Publishing Company. We show that the stationary distribution of a finite Markov chain can be expressed as the sum of certain normal distributions. These normal distributions are associated to planar graphs consisting of a straight line with attached loops. The loops touch only at one vertex either of the straight line or of another attached loop. Our analysis is based on our previous work, which derives the stationary distribution of a finite Markov chain using semaphore codes on the KarnofskyRhodes and McCammond expansion of the right Cayley graph of the finite semigroup underlying the Markov chain.
https://escholarship.org/uc/item/4t66s6hm
Tue, 7 Jul 2020 00:00:00 +0000

Demazure crystals, KirillovReshetikhin crystals, and the energy function
https://escholarship.org/uc/item/35d851r4
It has previously been shown that, at least for nonexceptional KacMoody Lie
algebras, there is a close connection between Demazure crystals and tensor
products of KirillovReshetikhin crystals. In particular, certain Demazure
crystals are isomorphic as classical crystals to tensor products of
KirillovReshetikhin crystals via a canonically chosen isomorphism. Here we
show that this isomorphism intertwines the natural affine grading on Demazure
crystals with a combinatorially defined energy function. As a consequence, we
obtain a formula of the Demazure character in terms of the energy function,
which has applications to Macdonald polynomials and qdeformed Whittaker
functions.
https://escholarship.org/uc/item/35d851r4
Tue, 7 Jul 2020 00:00:00 +0000

The forgotten monoid
https://escholarship.org/uc/item/2bm3t312
We study properties of the forgotten monoid which appeared in work of Lascoux
and Schutzenberger and recently resurfaced in the construction of dual
equivalence graphs by Assaf. In particular, we provide an explicit
characterization of the forgotten classes in terms of inversion numbers and
show that there are n^23n+4 forgotten classes in the symmetric group S_n. Each
forgotten class contains a canonical element that can be characterized by
pattern avoidance. We also show that the sum of Gessel's quasisymmetric
functions over a forgotten class is a 01 sum of ribbonSchur functions.
https://escholarship.org/uc/item/2bm3t312
Tue, 7 Jul 2020 00:00:00 +0000

A Demazure crystal construction for Schubert polynomials
https://escholarship.org/uc/item/29x2x292
Stanley symmetric functions are the stable limits of Schubert polynomials. In
this paper, we show that, conversely, Schubert polynomials are Demazure
truncations of Stanley symmetric functions. This parallels the relationship
between Schur functions and Demazure characters for the general linear group.
We establish this connection by imposing a Demazure crystal structure on key
tableaux, recently introduced by the first author in connection with Demazure
characters and Schubert polynomials, and linking this to the type A crystal
structure on reduced word factorizations, recently introduced by Morse and the
second author in connection with Stanley symmetric functions.
https://escholarship.org/uc/item/29x2x292
Tue, 7 Jul 2020 00:00:00 +0000

A crystal on decreasing factorizations in the 0hecke monoid
https://escholarship.org/uc/item/13x7k80f
© The authors. We introduce a type A crystal structure on decreasing factorizations of fullycommutative elements in the 0Hecke monoid which we call ⋆crystal. This crystal is a Ktheoretic generalization of the crystal on decreasing factorizations in the symmetric group of the first and last author. We prove that under the residue map the ⋆crystal intertwines with the crystal on setvalued tableaux recently introduced by Monical, Pechenik and Scrimshaw. We also define a new insertion from decreasing factorization to pairs of semistandard Young tableaux and prove several properties, such as its relation to the Hecke insertion and the uncrowding algorithm. The new insertion also intertwines with the crystal operators.
https://escholarship.org/uc/item/13x7k80f
Tue, 7 Jul 2020 00:00:00 +0000

Quantum LakshmibaiSeshadri paths and root operators
https://escholarship.org/uc/item/0qm8t8ps
We give an explicit description of the image of a quantum LS path, regarded
as a rational path, under the action of root operators, and show that the set
of quantum LS paths is stable under the action of the root operators. As a
byproduct, we obtain a new proof of the fact that a projected levelzero LS
path is just a quantum LS path.
https://escholarship.org/uc/item/0qm8t8ps
Tue, 7 Jul 2020 00:00:00 +0000

Convergent solutions of Stokes OldroydB boundary value problems using the Immersed Boundary Smooth Extension (IBSE) method
https://escholarship.org/uc/item/7ps6t1t6
© 2019 Elsevier B.V. The Immersed Boundary (IB) method has been widely used to solve fluidstructure interaction problems, including those where the structure interacts with polymeric fluids. In this paper, we examine the convergence of one such scheme for a well known twodimensional benchmark flow for the OldroydB constitutive model, and we show that the traditional IBbased scheme fails to adequately capture the polymeric stress near to embedded boundaries. We analyze the reason for such failure, and we argue that this feature is not specific to the case study chosen, but a general feature of such methods due to lack of convergence in velocity gradients near interfaces. In order to remedy this problem, we build a different scheme for the OldroydB system using the Immersed Boundary Smooth Extension (IBSE) scheme, which provides convergent viscous stresses near boundaries. We show that this modified scheme produces convergent polymeric stresses through the whole domain, including...
https://escholarship.org/uc/item/7ps6t1t6
Tue, 23 Jun 2020 00:00:00 +0000

A numerical study of metachronal propulsion at low to intermediate reynolds numbers
https://escholarship.org/uc/item/5921171j
© 2020 by the authors. Inspired by the forward swimming of longtailed crustaceans, we study an underwater propulsion mechanism for a swimming body with multiple rigid paddles attached underneath undergoing cycles of power and return strokes with a constant phasedifference between neighboring paddles, a phenomenon known as metachronal propulsion. To study how interpaddle phasedifference affects flux production, we develop a computational fluid dynamics model and a numerical algorithm based on the immersed boundary method, which allows us to simulate metachronal propulsion at Reynolds numbers (RE) ranging from close to 0 to about 100. Our main finding is that the highest average flux is generated when nearestneighbor paddles maintain an approximate 20%25% phasedifference with the more posterior paddle leading the cycle; this result is independent of stroke frequency across the full range of RE considered here. We also find that the optimal paddle spacing and the number of...
https://escholarship.org/uc/item/5921171j
Tue, 23 Jun 2020 00:00:00 +0000

Identification of Copy Number Aberrations in Breast Cancer Subtypes Using Persistence Topology.
https://escholarship.org/uc/item/6rq2j8rt
DNA copy number aberrations (CNAs) are of biological and medical interest because they help identify regulatory mechanisms underlying tumor initiation and evolution. Identification of tumordriving CNAs (driver CNAs) however remains a challenging task, because they are frequently hidden by CNAs that are the product of random events that take place during tumor evolution. Experimental detection of CNAs is commonly accomplished through array comparative genomic hybridization (aCGH) assays followed by supervised and/or unsupervised statistical methods that combine the segmented profiles of all patients to identify driver CNAs. Here, we extend a previouslypresented supervised algorithm for the identification of CNAs that is based on a topological representation of the data. Our method associates a twodimensional (2D) point cloud with each aCGH profile and generates a sequence of simplicial complexes, mathematical objects that generalize the concept of a graph. This representation...
https://escholarship.org/uc/item/6rq2j8rt
Tue, 19 May 2020 00:00:00 +0000

Automatic design of synthetic gene circuits through mixed integer nonlinear programming.
https://escholarship.org/uc/item/5jz8t8b7
Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver suboptimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer nonlinear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and userdefined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective...
https://escholarship.org/uc/item/5jz8t8b7
Tue, 19 May 2020 00:00:00 +0000

Pathways of DNA unlinking: A story of stepwise simplification.
https://escholarship.org/uc/item/3rt3b7bk
In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the sitespecific recombination complex XerCD difFtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies,...
https://escholarship.org/uc/item/3rt3b7bk
Tue, 19 May 2020 00:00:00 +0000

A Computational Modeling and Simulation Approach to Investigate Mechanisms of Subcellular cAMP Compartmentation.
https://escholarship.org/uc/item/10x3x8xb
Subcellular compartmentation of the ubiquitous second messenger cAMP has been widely proposed as a mechanism to explain unique receptordependent functional responses. How exactly compartmentation is achieved, however, has remained a mystery for more than 40 years. In this study, we developed computational and mathematical models to represent a subcellular sarcomeric space in a cardiac myocyte with varying detail. We then used these models to predict the contributions of various mechanisms that establish subcellular cAMP microdomains. We used the models to test the hypothesis that phosphodiesterases act as functional barriers to diffusion, creating discrete cAMP signaling domains. We also used the models to predict the effect of a range of experimentally measured diffusion rates on cAMP compartmentation. Finally, we modeled the anatomical structures in a cardiac myocyte diad, to predict the effects of anatomical diffusion barriers on cAMP compartmentation. When we incorporated...
https://escholarship.org/uc/item/10x3x8xb
Tue, 19 May 2020 00:00:00 +0000

iGTP: a software package for largescale gene tree parsimony analysis.
https://escholarship.org/uc/item/0t30p5hk
<h4>Background</h4>The everincreasing wealth of genomic sequence information provides an unprecedented opportunity for largescale phylogenetic analysis. However, species phylogeny inference is obfuscated by incongruence among gene trees due to evolutionary events such as gene duplication and loss, incomplete lineage sorting (deep coalescence), and horizontal gene transfer. Gene tree parsimony (GTP) addresses this issue by seeking a species tree that requires the minimum number of evolutionary events to reconcile a given set of incongruent gene trees. Despite its promise, the use of gene tree parsimony has been limited by the fact that existing software is either not fast enough to tackle large data sets or is restricted in the range of evolutionary events it can handle.<h4>Results</h4>We introduce iGTP, a platformindependent software program that implements stateoftheart algorithms that greatly speed up species tree inference under the duplication, duplicationloss, and...
https://escholarship.org/uc/item/0t30p5hk
Tue, 19 May 2020 00:00:00 +0000

How round is a protein? Exploring protein structures for globularity using conformal mapping.
https://escholarship.org/uc/item/06f3k947
We present a new algorithm that automatically computes a measure of the geometric difference between the surface of a protein and a round sphere. The algorithm takes as input two triangulated genus zero surfaces representing the protein and the round sphere, respectively, and constructs a discrete conformal map f between these surfaces. The conformal map is chosen to minimize a symmetric elastic energy E S (f) that measures the distance of f from an isometry. We illustrate our approach on a set of basic sample problems and then on a dataset of diverse protein structures. We show first that E S (f) is able to quantify the roundness of the Platonic solids and that for these surfaces it replicates well traditional measures of roundness such as the sphericity. We then demonstrate that the symmetric elastic energy E S (f) captures both global and local differences between two surfaces, showing that our method identifies the presence of protruding regions in protein structures and quantifies...
https://escholarship.org/uc/item/06f3k947
Tue, 19 May 2020 00:00:00 +0000

The Rabl configuration limits topological entanglement of chromosomes in budding yeast.
https://escholarship.org/uc/item/7vr0x0rm
The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions....
https://escholarship.org/uc/item/7vr0x0rm
Sun, 17 May 2020 00:00:00 +0000

Chromosomes are predominantly located randomly with respect to each other in interphase human cells.
https://escholarship.org/uc/item/0hw7r55m
To test quantitatively whether there are systematic chromosomechromosome associations within human interphase nuclei, interchanges between all possible heterologous pairs of chromosomes were measured with 24color wholechromosome painting (multiplex FISH), after damage to interphase lymphocytes by sparsely ionizing radiation in vitro. An excess of interchanges for a specific chromosome pair would indicate spatial proximity between the chromosomes comprising that pair. The experimental design was such that quite small deviations from randomness (extra pairwise interchanges within a group of chromosomes) would be detectable. The only statistically significant chromosome cluster was a group of five chromosomes previously observed to be preferentially located near the center of the nucleus. However, quantitatively, the overall deviation from randomness within the whole genome was small. Thus, whereas some chromosomechromosome associations are clearly present, at the wholechromosomal...
https://escholarship.org/uc/item/0hw7r55m
Fri, 15 May 2020 00:00:00 +0000

Al'brekht's Method in Infinite Dimensions
https://escholarship.org/uc/item/93s7s0x6
In 1961 E. G. Albrekht presented a method for the optimal stabilization of
smooth, nonlinear, finite dimensional, continuous time control systems. This
method has been extended to similar systems in discrete time and to some
stochastic systems in continuous and discrete time. In this paper we extend
Albrekht's method to the optimal stabilization of some smooth, nonlinear,
infinite dimensional, continuous time control systems whose nonlinearities are
described by Fredholm integral operators.
https://escholarship.org/uc/item/93s7s0x6
Wed, 18 Mar 2020 00:00:00 +0000

Hilbert schemes and $y$ification of KhovanovRozansky homology
https://escholarship.org/uc/item/9vq7313z
We define a deformation of the triply graded KhovanovRozansky homology of a
link $L$ depending on a choice of parameters $y_c$ for each component of $L$,
which satisfies linksplitting properties similar to the BatsonSeed invariant.
Keeping the $y_c$ as formal variables yields a link homology valued in triply
graded modules over $\mathbb{Q}[x_c,y_c]_{c\in \pi_0(L)}$. We conjecture that
this invariant restores the missing $Q\leftrightarrow TQ^{1}$ symmetry of the
triply graded KhovanovRozansky homology, and in addition satisfies a number of
predictions coming from a conjectural connection with Hilbert schemes of points
in the plane. We compute this invariant for all positive powers of the full
twist and match it to the family of ideals appearing in Haiman's description of
the isospectral Hilbert scheme.
https://escholarship.org/uc/item/9vq7313z
Tue, 17 Mar 2020 00:00:00 +0000

On stable Khovanov homology of torus knots
https://escholarship.org/uc/item/9sg0d7mb
We conjecture that the stable Khovanov homology of torus knots can be described as the Koszul homology of an explicit irregular sequence of quadratic polynomials. The corresponding Poincaré series turns out to be related to the RogersRamanujan identity. © Taylor & Francis Group, LLC.
https://escholarship.org/uc/item/9sg0d7mb
Tue, 17 Mar 2020 00:00:00 +0000

Torus knots and the rational DAHA
https://escholarship.org/uc/item/8v74w5ct
© 2014. We conjecturally extract the triply graded KhovanovRozansky homology of the (m;n) torus knot from the unique finitedimensional simple representation of the rational DAHA of type A, rank n  1, and central character m/n. The conjectural differentials of Gukov, Dunfield, and the third author receive an explicit algebraic expression in this picture, yielding a prescription for the doubly graded KhovanovRozansky homologies. We match our conjecture to previous conjectures of the first author relating knot homology to q; tCatalan numbers and to previous conjectures of the last three authors relating knot homology to Hilbert schemes on singular curves.
https://escholarship.org/uc/item/8v74w5ct
Tue, 17 Mar 2020 00:00:00 +0000

Immersed Concordances of Links and Heegaard Floer Homology
https://escholarship.org/uc/item/8t5744gd
An immersed concordance between two links is a concordance with possible
selfintersections. Given an immersed concordance we construct a smooth
fourdimensional cobordism between surgeries on links. By applying
$d$invariant inequalities for this cobordism we obtain inequalities between
the $H$functions of links, which can be extracted from the link Floer homology
package. As an application we show a Heegaard Floer theoretical criterion for
bounding the splitting number of links. The criterion is especially effective
for Lspace links, and we present an infinite family of Lspace links with
vanishing linking numbers and arbitrary large splitting numbers. We also show a
semicontinuity of the $H$function under $\delta$constant deformations of
singularities with many branches.
https://escholarship.org/uc/item/8t5744gd
Tue, 17 Mar 2020 00:00:00 +0000

Quadratic ideals and Rogers–Ramanujan recursions
https://escholarship.org/uc/item/8r4727pj
© 2019, Springer Science+Business Media, LLC, part of Springer Nature. We give an explicit recursive description of the Hilbert series and Gröbner bases for the family of quadratic ideals defining the jet schemes of a double point. We relate these recursions to the Rogers–Ramanujan identity and prove a conjecture of the second author, Oblomkov and Rasmussen.
https://escholarship.org/uc/item/8r4727pj
Tue, 17 Mar 2020 00:00:00 +0000

Serre duality for Khovanov–Rozansky homology
https://escholarship.org/uc/item/8p62j3db
© 2019, Springer Nature Switzerland AG. We prove that the full twist is a Serre functor in the homotopy category of type A Soergel bimodules. As a consequence, we relate the top and bottom Hochschild degrees in Khovanov–Rozansky homology, categorifying a theorem of Kálmán.
https://escholarship.org/uc/item/8p62j3db
Tue, 17 Mar 2020 00:00:00 +0000

Evaluations of annular KhovanovRozansky homology
https://escholarship.org/uc/item/74n254xw
We describe the universal target of annular KhovanovRozansky link homology
functors as the homotopy category of a free symmetric monoidal category
generated by one object and one endomorphism. This categorifies the ring of
symmetric functions and admits categorical analogues of plethystic
transformations, which we use to characterize the annular invariants of Coxeter
braids. Further, we prove the existence of symmetric group actions on the
KhovanovRozansky invariants of cabled tangles and we introduce spectral
sequences that aid in computing the homologies of generalized Hopf links.
Finally, we conjecture a characterization of the horizontal traces of Rouquier
complexes of Coxeter braids in other types.
https://escholarship.org/uc/item/74n254xw
Tue, 17 Mar 2020 00:00:00 +0000

Links of plane curve singularities are Lspace links
https://escholarship.org/uc/item/7297z06r
© 2016, Mathematical Sciences Publishers. All rights reserved. We prove that a sufficiently large surgery on any algebraic link is an Lspace. For torus links we give a complete classification of integer surgery torus links we give a complete classification of integer surgery coefficients providing Lspaces.
https://escholarship.org/uc/item/7297z06r
Tue, 17 Mar 2020 00:00:00 +0000

Refined knot invariants and Hilbert schemes
https://escholarship.org/uc/item/6c02656f
© 2015 Elsevier Masson SAS. We consider the construction of refined ChernSimons torus knot invariants by M. Aganagic and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's conjecture on the stabilization of superpolynomials, and then use the results of O. Schiffmann and E. Vasserot to relate knot invariants to the Hilbert scheme of points on C2. Then we use the methods of the second author to compute these invariants explicitly in the uncolored case. We also propose a conjecture relating these constructions to the rational Cherednik algebra, as in the work of the first author, A. Oblomkov, J. Rasmussen and V. Shende. Among the combinatorial consequences of this work is a statement of the mn shuffle conjecture.
https://escholarship.org/uc/item/6c02656f
Tue, 17 Mar 2020 00:00:00 +0000

The equivariant Euler characteristic of moduli spaces of curves
https://escholarship.org/uc/item/6997k34s
We derive a formula for the S nequivariant Euler characteristic of the moduli space Mg,n of genus g curves with n marked points. © 2013 Elsevier Inc.
https://escholarship.org/uc/item/6997k34s
Tue, 17 Mar 2020 00:00:00 +0000

Generalized $q,t$Catalan numbers
https://escholarship.org/uc/item/68k9s8q9
Recent work of the first author, Negut and Rasmussen, and of Oblomkov and
Rozansky in the context of KhovanovRozansky knot homology produces a family
of polynomials in $q$ and $t$ labeled by integer sequences. These polynomials
can be expressed as equivariant Euler characteristics of certain line bundles
on flag Hilbert schemes. The $q,t$Catalan numbers and their rational analogues
are special cases of this construction. In this paper, we give a purely
combinatorial treatment of these polynomials and show that in many cases they
have nonnegative integer coefficients.
For sequences of length at most 4, we prove that these coefficients enumerate
subdiagrams in a certain fixed Young diagram and give an explicit symmetric
chain decomposition of the set of such diagrams. This strengthens results of
Lee, Li and Loehr for $(4,n)$ rational $q,t$Catalan numbers.
https://escholarship.org/uc/item/68k9s8q9
Tue, 17 Mar 2020 00:00:00 +0000

Affine permutations and rational slope parking functions
https://escholarship.org/uc/item/5v06r2j1
© 2016 American Mathematical Society. We introduce a new approach to the enumeration of rational slope parking functions with respect to the area and a generalized dinv statistics, and relate the combinatorics of parking functions to that of affine permutations. We relate our construction to two previously known combinatorial constructions: Haglund’s bijection ζ exchanging the pairs of statistics (area, dinv) and (bounce, area) on Dyck paths, and the PakStanley labeling of the regions of kShi hyperplane arrangements by kparking functions. Essentially, our approach can be viewed as a generalization and a unification of these two constructions. We also relate our combinatorial constructions to representation theory. We derive new formulas for the Poincaré polynomials of certain affine Springer fibers and describe a connection to the theory of finitedimensional representations of DAHA and nonsymmetric Macdonald polynomials.
https://escholarship.org/uc/item/5v06r2j1
Tue, 17 Mar 2020 00:00:00 +0000

Cable links and lspace surgeries
https://escholarship.org/uc/item/5pp1c0vd
© European Mathematical Society. An Lspace link is a link in S3 on which all sufficiently large integral surgeries are Lspaces. We prove that for m; n relatively prime, the rcomponent cable link Krm;rn is an Lspace link if and only if K is an Lspace knot and n/m ≥2g.K/  1. We also compute HFL– and HFL of an Lspace cable link in terms of its Alexander polynomial. As an application, we confirm a conjecture of Licata [7] regarding the structure of HFL for.n; n/ torus links.
https://escholarship.org/uc/item/5pp1c0vd
Tue, 17 Mar 2020 00:00:00 +0000

Representations of rational Cherednik algebras with minimal support and torus knots
https://escholarship.org/uc/item/5ns4m9t5
© 2015 Elsevier Inc. In this paper we obtain several results about representations of rational Cherednik algebras, and discuss their applications. Our first result is the CohenMacaulayness property (as modules over the polynomial ring) of Cherednik algebra modules with minimal support. Our second result is an explicit formula for the character of an irreducible minimal support module in type An1 for c=mn, and an expression of its quasispherical part (i.e., the isotypic part of "hooks") in terms of the HOMFLY polynomial of a torus knot colored by a Young diagram. We use this formula and the work of Calaque, Enriquez and Etingof to give explicit formulas for the characters of the irreducible equivariant Dmodules on the nilpotent cone for SLm. Our third result is the construction of the KoszulBGG complex for the rational Cherednik algebra, which generalizes the construction of the KoszulBGG resolution from [3] and [21], and the calculation of its homology in type A. We also...
https://escholarship.org/uc/item/5ns4m9t5
Tue, 17 Mar 2020 00:00:00 +0000

On stable Sl3homology of torus knots
https://escholarship.org/uc/item/4v83d64t
© 2015 Taylor and Francis Group, LLC. The stable KhovanovRozansky homology of torus knots has been conjecturally described as the Koszul homology of an explicit irregular sequence of polynomials. We verify this conjecture using newly available computational data forhomology. Special attention is paid to torsion. In addition, explicit conjectural formulas are given for thehomology of (3, m)torus knots for all N and m, which are motivated by higher categorified JonesWenzl projectors. Structurally similar formulas are proven for HeegardFloer homology.
https://escholarship.org/uc/item/4v83d64t
Tue, 17 Mar 2020 00:00:00 +0000

Lattice and Heegaard Floer Homologies of Algebraic Links
https://escholarship.org/uc/item/4nj4h40h
© 2015 The Author(s). We compute the Heegaard Floer link homology of algebraic links in terms of the multivariate Hilbert function of the corresponding plane curve singularities. The main result of the paper identifies four homologies: (a) the Heegaard Floer link homology of the local embedded link, (b) the lattice homology associated with the Hilbert function, (c) the homologies of the projectivized complements of local hyperplane arrangements cut out from the local algebra, and (d) a generalized version of the OrlikSolomon algebra of these local arrangements. In particular, the PoincarCrossed D sign polynomials of all these homology groups are the same, and we also show that they agree with the coefficients of the motivic PoincarCrossed D sign series of the singularity.
https://escholarship.org/uc/item/4nj4h40h
Tue, 17 Mar 2020 00:00:00 +0000

Rational parking functions and LLT polynomials
https://escholarship.org/uc/item/4nf4p8zq
© 2016 Elsevier Inc. We prove that the combinatorial side of the "Rational Shuffle Conjecture" provides a Schurpositive symmetric polynomial. Furthermore, we prove that the contribution of a given rational Dyck path can be computed as a certain skew LLT polynomial, thus generalizing the result of Haglund, Haiman, Loehr, Remmel and Ulyanov. The corresponding skew diagram is described explicitly in terms of a certain (m, n)core.
https://escholarship.org/uc/item/4nf4p8zq
Tue, 17 Mar 2020 00:00:00 +0000

Derived traces of Soergel categories
https://escholarship.org/uc/item/4638g7zb
We study two kinds of categorical traces of (monoidal) dg categories, with
particular interest in categories of Soergel bimodules. First, we explicitly
compute the usual Hochschild homology, or derived vertical trace, of the
category of Soergel bimodules in arbitrary types. Secondly, we introduce the
notion of derived horizontal trace of a monoidal dg category and compute the
derived horizontal trace of Soergel bimodules in type A. As an application we
obtain a derived annular KhovanovRozansky link invariant with an action of
full twist insertion, and thus a categorification of the HOMFLYPT skein module
of the solid torus.
https://escholarship.org/uc/item/4638g7zb
Tue, 17 Mar 2020 00:00:00 +0000

Infinitesimal change of stable basis
https://escholarship.org/uc/item/4084s83b
© 2017, Springer International Publishing. The purpose of this note is to study the Maulik–Okounkov Ktheoretic stable basis for the Hilbert scheme of points on the plane, which depends on a “slope” m∈ R. When m=ab is rational, we study the change of stable matrix from slope m ε to m+ ε for small ε> 0 , and conjecture that it is related to the Leclerc–Thibon conjugation in the qFock space for Uqgl^ b. This is part of a wide framework of connections involving derived categories of quantized Hilbert schemes, modules for rational Cherednik algebras and Hecke algebras at roots of unity.
https://escholarship.org/uc/item/4084s83b
Tue, 17 Mar 2020 00:00:00 +0000

On the set of Lspace surgeries for links
https://escholarship.org/uc/item/3t43x4mj
© 2018 Elsevier Inc. We study the qualitative structure of the set LS of integral Lspace surgery slopes for links with two components. It is known that the set of Lspace surgery slopes for a nontrivial Lspace knot is always a positive halfline. However, already for twocomponent torus links the set LS has a very complicated structure, e.g. in some cases it can be unbounded from below. In order to probe the geometry of this set, we ask if it is bounded from below for more general Lspace links with two components. For algebraic twocomponent links we provide three complete characterizations for the boundedness from below: one in terms of the Alexander polynomial, one in terms of the embedded resolution graph, and one in terms of the socalled hfunction introduced by the authors in [9]. It turns out that LS is bounded from below for most algebraic links. If it is unbounded from below, it must contain a negative halfline parallel to one of the axes. We also give a sufficient...
https://escholarship.org/uc/item/3t43x4mj
Tue, 17 Mar 2020 00:00:00 +0000

Rational Dyck paths in the non relatively prime case
https://escholarship.org/uc/item/3f29k218
© 2017, Australian National University. All rights reserved. We study the relationship between rational slope Dyck paths and invariant sub sets of ℤ, extending the work of the first two authors in the relatively prime case. We also find a bijection between (dn,dm)Dyck paths and dtuples of (n,m)Dyck paths endowed with certain gluing data. These are the first steps towards understanding the relationship between rational slope Catalan combinatorics and the geometry of affine Springer fibers and knot invariants in the non relatively prime case.
https://escholarship.org/uc/item/3f29k218
Tue, 17 Mar 2020 00:00:00 +0000

Recursions for rational q,tCatalan numbers
https://escholarship.org/uc/item/1st349kg
© 2020 Elsevier Inc. We give a simple recursion labeled by binary sequences which computes rational q,tCatalan power series, both in relatively prime and non relatively prime cases. It is inspired by, but not identical to recursions due to B. Elias, M. Hogancamp, and A. Mellit, obtained in their study of link homology. We also compare our recursion with the HogancampMellit's recursion and verify a connection between the KhovanovRozansky homology of N,Mtorus links and the rational q,tCatalan power series for general positive N,M.
https://escholarship.org/uc/item/1st349kg
Tue, 17 Mar 2020 00:00:00 +0000

Flag Hilbert schemes, colored projectors and KhovanovRozansky homology
https://escholarship.org/uc/item/1f61q9zd
We construct a categorification of the maximal commutative subalgebra of the
type $A$ Hecke algebra. Specifically, we propose a monoidal functor from the
(symmetric) monoidal category of coherent sheaves on the flag Hilbert scheme to
the (nonsymmetric) monoidal category of Soergel bimodules. The adjoint of this
functor allows one to match the Hochschild homology of any braid with the Euler
characteristic of a sheaf on the flag Hilbert scheme. The categorified
JonesWenzl projectors studied by Abel, Elias and Hogancamp are idempotents in
the category of Soergel bimodules, and they correspond to the renormalized
Koszul complexes of the torus fixed points on the flag Hilbert scheme. As a
consequence, we conjecture that the endomorphism algebras of the categorified
projectors correspond to the dg algebras of functions on affine charts of the
flag Hilbert schemes. We define a family of differentials $d_{N}$ on these dg
algebras and conjecture that their homology matches that of the
$\mathfrak{gl}_N$...
https://escholarship.org/uc/item/1f61q9zd
Tue, 17 Mar 2020 00:00:00 +0000

Quadruplygraded colored homology of knots
https://escholarship.org/uc/item/0zh8n5mh
© Instytut Matematyczny PAN, 2018 We conjecture the existence of four independent gradings in colored HOMFLYPT homology, and make qualitative predictions of various interesting structures and symmetries in the colored homology of arbitrary knots. We propose an explicit conjectural description for the rectangular colored homology of torus knots, and identify the new gradings in this context. While some of these structures have a natural interpretation in the physical realization of knot homologies based on counting supersymmetric configurations (BPS states, instantons, and vortices), others are completely new. They suggest new geometric and physical realizations of colored HOMFLYPT homology as the Hochschild homology of the category of branes in a LandauGinzburg Bmodel or, equivalently, in the mirror Amodel. Supergroups and supermanifolds are surprisingly ubiquitous in all aspects of this work.
https://escholarship.org/uc/item/0zh8n5mh
Tue, 17 Mar 2020 00:00:00 +0000

Competitive effects between stationary chemical reaction centres: a theory based on offcenter monopoles.
https://escholarship.org/uc/item/6vc529st
The subject of this paper is competitive effects between multiple reaction sinks. A theory based on offcenter monopoles is developed for the steadystate diffusion equation and for the convectiondiffusion equation with a constant flow field. The dipolar approximation for the diffusion equation with two equal reaction centres is compared with the exact solution. The former turns out to be remarkably accurate, even for two touching spheres. Numerical evidence is presented to show that the same holds for larger clusters (with more than two spheres). The theory is extended to the convectiondiffusion equation with a constant flow field. As one increases the convective velocity, the competitive effects between the reactive centres gradually become less significant. This is demonstrated for a number of cluster configurations. At high flow velocities, the current methodology breaks down. Fixing this problem will be the subject of future research. The current method is useful as an...
https://escholarship.org/uc/item/6vc529st
Wed, 5 Feb 2020 00:00:00 +0000

Layer Formation in Semiconvection
https://escholarship.org/uc/item/6368f5jn
Layer formation in a thermally destabilized fluid with stable density
gradient has been observed in laboratory experiments and has been proposed as a
mechanism for mixing molecular weight in late stages of stellar evolution in
regions which are unstable to semiconvection. It is not yet known whether such
layers can exist in a very low viscosity fluid: this work undertakes to address
that question. Layering is simulated numerically both at high Prandtl number
(relevant to the laboratory) in order to describe the onset of layering
intability, and the astrophysically important case of low Prandtl number. It is
argued that the critical stability parameter for interfaces between layers, the
Richardson number, increases with decreasing Prandtl number. Throughout the
simulations the fluid has a tendency to form large scale flows in the first
convecting layer, but only at low Prandtl number do such structures have
dramatic consequences for layering. These flows are shown to drive large
interfacial...
https://escholarship.org/uc/item/6368f5jn
Wed, 5 Feb 2020 00:00:00 +0000

A reconstructed total precipitation framework
https://escholarship.org/uc/item/5rd1q3df
© 2019, The Author(s). Climate change is expected to alter the statistical properties of precipitation. There are two related but consequentially distinct theories for changes to precipitation that have received some consensus: (1) the timeandspace integrated global total precipitation should increase with longwave cooling as the surface warms, (2) the most intense precipitation rates should increase at a faster rate related to the increase in vapor saturation. Herein, these two expectations are combined with an analytic integration of three conceptually independent properties of the tropical hydrological cycle, the intensity, probability, and frequency of precipitation. The total precipitation in both a cloudresolving model and tropical Global Precipitation Measurement mission data is decomposed and reconstructed with the analytic integral. By applying (1) and (2) to the precipitation characteristics from the model and observations to form a warming proxy model, it is suggested...
https://escholarship.org/uc/item/5rd1q3df
Wed, 5 Feb 2020 00:00:00 +0000

A Note on ComplexHyperbolic Kleinian Groups
https://escholarship.org/uc/item/0wf791r7
© 2020, Institute for Mathematical Sciences (IMS), Stony Brook University, NY. Let Γ be a discrete group of isometries acting on the complex hyperbolic nspace HCn. In this note, we prove that if Γ is convexcocompact, torsionfree, and the critical exponent δ(Γ) is strictly lesser than 2, then the complex manifold HCn/Γ is Stein. We also discuss several related conjectures.
https://escholarship.org/uc/item/0wf791r7
Tue, 21 Jan 2020 00:00:00 +0000

Lectures on complex hyperbolic Kleinian groups
https://escholarship.org/uc/item/8030m3x1
These are lectures on discrete groups of isometries of complex hyperbolic
spaces, aimed to discuss interactions between the function theory on complex
hyperbolic manifolds and the theory of discrete groups.
https://escholarship.org/uc/item/8030m3x1
Sat, 14 Dec 2019 00:00:00 +0000

The hilbert scheme of a plane curve singularity and the HOMFLY homology of its link
https://escholarship.org/uc/item/31f9w49x
© 2018, Mathematical Sciences Publishers. All rights reserved. We conjecture an expression for the dimensions of the KhovanovRozansky HOMFLY homology groups of the link of a plane curve singularity in terms of the weight polynomials of Hilbert schemes of points schemetheoretically supported on the singularity. The conjecture specializes to our previous conjecture (2012) relating the HOMFLY polynomial to the Euler numbers of the same spaces upon setting t=1. By generalizing results of Piontkowski on the structure of compactified Jacobians to the case of Hilbert schemes of points, we give an explicit prediction of the HOMFLY homology of a (k,n) torus knot as a certain sum over diagrams. The Hilbert scheme series corresponding to the summand of the HOMFLY homology with minimal “a” grading can be recovered from the perverse filtration on the cohomology of the compactified Jacobian. In the case of (k,n) torus knots, this space furnishes the unique finitedimensional simple representation...
https://escholarship.org/uc/item/31f9w49x
Tue, 12 Nov 2019 00:00:00 +0000

Interplay between DNA sequence and negative superhelicity drives Rloop structures.
https://escholarship.org/uc/item/0vz4t8b4
Rloops are abundant threestranded nucleicacid structures that form in cis during transcription. Experimental evidence suggests that Rloop formation is affected by DNA sequence and topology. However, the exact manner by which these factors interact to determine Rloop susceptibility is unclear. To investigate this, we developed a statistical mechanical equilibrium model of Rloop formation in superhelical DNA. In this model, the energy involved in forming an Rloop includes four termsjunctional and basepairing energies and energies associated with superhelicity and with the torsional winding of the displaced DNA single strand around the RNA:DNA hybrid. This model shows that the significant energy barrier imposed by the formation of junctions can be overcome in two ways. First, basepairing energy can favor RNA:DNA over DNA:DNA duplexes in favorable sequences. Second, Rloops, by absorbing negative superhelicity, partially or fully relax the rest of the DNA domain, thereby...
https://escholarship.org/uc/item/0vz4t8b4
Tue, 15 Oct 2019 00:00:00 +0000

Hausdorff dimension of nonconical limit sets
https://escholarship.org/uc/item/8ff3f26t
© 2020 American Mathematical Society Geometrically infinite Kleinian groups have nonconical limit sets with the cardinality of the continuum. In this paper, we construct a geometrically infinite Fuchsian group such that the Hausdorff dimension of the nonconical limit set equals zero. For finitely generated, geometrically infinite Kleinian groups, we prove that the Hausdorff dimension of the nonconical limit set is positive.
https://escholarship.org/uc/item/8ff3f26t
Wed, 2 Oct 2019 00:00:00 +0000

Polymer stress growth in viscoelastic fluids in oscillating extensional flows with applications to microorganism locomotion
https://escholarship.org/uc/item/7r57q2kp
© 2019 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...
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

Sullivan's structural stability of expanding 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. We
generalize the theorem by weakening these axioms substantially, while adding
more details to Sullivan's original proof. We then present a number of examples
satisfying Sullivan's axioms, such as Anosov subgroups of Lie groups as well as
hyperbolic and nonhyperbolic groups acting on metric spaces.
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
© 2018, Mathematical Sciences Publishers. All rights reserved. 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
© 2017 IOP Publishing Ltd. 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...
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
© 2018 Society for Industrial and Applied Mathematics. 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
© 2019 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...
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
© 2016, Springer International Publishing. 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
© 2018 American Institute of Physics Inc. All rights reserved. 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

Surgery on links of linking number zero and the heegaard floer Dinvariant
https://escholarship.org/uc/item/7961x6km
© European Mathematical Society. We study Heegaard Floer homology and various related invariants (such as the hfunction) for twocomponent Lspace links with linking number zero. For such links, we explicitly describe the relationship between the hfunction, the Sato–Levine invariant and the Casson invariant. We give a formula for the Heegaard Floer dinvariants of integral surgeries on twocomponent Lspace links of linking number zero in terms of the hfunction, generalizing a formula of Ni and Wu. As a consequence, for such links with unknotted components, we characterize Lspace surgery slopes in terms of the v+invariants of the knots obtained from blowing down the components. We give a proof of a skein inequality for the dinvariants of C1 surgeries along linking number zero links that differ by a crossing change. We also describe bounds on the smooth fourgenus of links in terms of the hfunction, expanding on previous work of the second author, and use these bounds to...
https://escholarship.org/uc/item/7961x6km
Tue, 6 Nov 2018 00:00:00 +0000

Helly numbers of algebraic subsets of R<sup>d</sup> and an extension of doignon's theorem
https://escholarship.org/uc/item/78d6r5wb
© 2017 by Walter de Gruyter Berlin/Boston 2017. We study Sconvex sets, which are the geometric objects obtained as the intersection of the usual convex sets in Rd with a proper subset S ? Rd, and contribute new results about their SHelly numbers. We extend prior work for S = Rd, Zd, and Zdk × Rk, and give some sharp bounds for several new cases: lowdimensional situations, sets that have some algebraic structure, in particular when S is an arbitrary subgroup of Rd or when S is the difference between a lattice and some of its sublattices. By abstracting the ingredients of Lovász method we obtain colorful versions of many monochromatic HellyType results, including several colorful versions of our own results.
https://escholarship.org/uc/item/78d6r5wb
Tue, 23 Oct 2018 00:00:00 +0000

Orientation dependent elastic stress concentration at tips of slender objects translating in viscoelastic fluids
https://escholarship.org/uc/item/84t3t1w3
© 2019 American Physical Society. Elastic stress concentration at the tips of long slender objects moving in viscoelastic fluids has been observed in numerical simulations, but despite the prevalence of flagellated motion in complex fluids in many biological functions, the physics of stress accumulation near the tips has not been analyzed. Here, we theoretically investigate elastic stress development at the tips of slender objects by computing the leadingorder viscoelastic correction to the equilibrium viscous flow around long cylinders, using the weakcoupling limit. In this limit, nonlinearities in the fluid are retained, allowing us to study the biologically relevant parameter regime of high Weissenberg number. We calculate a stretch rate from the viscous flow around cylinders to predict when large elastic stress develops at the tips, find thresholds for large stress development depending on orientation, and calculate greater stress accumulation near the tips of cylinders...
https://escholarship.org/uc/item/84t3t1w3
Wed, 10 Oct 2018 00:00:00 +0000

Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation
https://escholarship.org/uc/item/2rc9c3fs
© 2018 We present an efficient and reliable algorithm for solving a class of nonlinear eigenvalue problems arising from the modeling of particle accelerator cavities. The eigenvalue nonlinearity in these problems results from the use of waveguides to couple external power sources or to allow certain excited electromagnetic modes to exit the cavity. We use a rational approximation to reduce the nonlinear eigenvalue problem first to a rational eigenvalue problem. We then apply a special linearization procedure to turn the rational eigenvalue problem into a larger linear eigenvalue problem with the same eigenvalues, which can be solved by existing iterative methods. By using a compact scheme to represent both the linearized operator and the eigenvectors to be computed, we obtain a numerical method that only involves solving linear systems of equations of the same dimension as the original nonlinear eigenvalue problem. We refer to this method as a compact rational Krylov (CORK) method....
https://escholarship.org/uc/item/2rc9c3fs
Tue, 25 Sep 2018 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
© 2018 Australian Mathematical SocietyÂ. 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...
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
© 2018, SpringerVerlag GmbH Germany, part of Springer Nature. 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
© 2015 IEEE. 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...
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
© 2018 IEEE. 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

Effect of overturning circulation on long equatorial waves: A lowfrequency cutoff
https://escholarship.org/uc/item/9tf5n22k
© 2018 American Meteorological Society. Zonally long tropicalwaves in the presence of a largescalemeridional and vertical overturning circulation are studied in an idealized model based on the intraseasonal multiscalemoist dynamics (IMMD) theory. Themodel consists of a systemof shallowwater equations describing barotropic and first baroclinic vertical modes coupled to one another by the zonally symmetric, timeindependent background circulation. To isolate the effects of the meridional circulation alone, an idealized background flow is chosen to mimic the meridional and vertical components of the flow of theHadley cell; the background flowmeridionally converges and rises at the equator. The resulting linear eigenvalue problem is a generalization of the longwavescaled version of Matsuno's equatorial wave problem with the addition of meridional and vertical advection. The results demonstrate that the meridional circulation couples equatorially trapped baroclinic Rossby waves...
https://escholarship.org/uc/item/9tf5n22k
Tue, 5 Jun 2018 00:00:00 +0000

Novel genetic loci associated with hippocampal volume.
https://escholarship.org/uc/item/4w18x7tz
The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genomewide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg=0.155). Our findings suggest novel biological pathways through which...
https://escholarship.org/uc/item/4w18x7tz
Fri, 25 May 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