Recent ucdavismath_oapdeposits items

Quantification of flagellar gait changes with combined shape mode analysis and swimming simulations

Wed, 29 Jul 2026 00:00:00 +0000

Many different microswimmers propel themselves using flagella that beat periodically. The shape of the flagellar beat and swimming speed have been observed to change with fluid rheology. We quantify changes in the flagellar waveforms of Chlamydomonas reinhardtii in response to changes in fluid viscosity using (i) shape mode analysis and (ii) a full swimmer simulation to analyse how shape changes affect the swimming speed and to explore the dimensionality of the shape space. By decomposing the gait into the time-independent mean shape and the time-varying stroke, we find that the flagellar mean shape substantially changes in response to viscosity, while the changes in the time-varying stroke are more subtle. Using the swimmer simulation, we quantify how the swimming speed is affected by the dimensionality of the flagellar shape reconstruction, and we show that the observed change in swimming speed with viscosity is explained by the variations in mean flagellar shape and...

Optimizing metachronal paddling with reinforcement learning at low Reynolds number

Wed, 29 Jul 2026 00:00:00 +0000

Metachronal paddling is a swimming strategy in which an organism oscillates sets of adjacent limbs with a constant phase lag, propagating a metachronal wave through its limbs and propelling it forward. This limb coordination strategy is utilized by swimmers across a wide range of Reynolds numbers, which suggests that this metachronal rhythm was selected for its optimality of swimming performance. In this study, we apply reinforcement learning to a swimmer at zero Reynolds number and investigate whether the learning algorithm selects this metachronal rhythm, or if other coordination patterns emerge. We design the swimmer agent with an elongated body and pairs of straight, inflexible paddles placed along the body for various fixed paddle spacings. Based on paddle spacing, the swimmer agent learns qualitatively different coordination patterns. At tight spacings, a back-to-front metachronal wave-like stroke emerges which resembles the commonly observed biological rhythm, but at wide...

Pumping and steady streaming driven by two-frequency oscillations of a cylinder

Wed, 29 Jul 2026 00:00:00 +0000

The classical problem of steady streaming induced by an oscillating object has been studied extensively, but prior work has focused almost exclusively on single-frequency oscillations, which result in symmetric, quadrupole-like flows. Here we demonstrate that dual-frequency oscillations induce asymmetric steady streaming with a non-zero net flux in a direction determined by the polarity of the oscillation-the oscillator serves as a pump. We use numerical simulations and asymptotic analysis at small amplitude to examine two-dimensional steady streaming around a cylinder, first focusing on frequency ratio 2. The computational experiments show asymmetrical streaming and pumping, i.e. net flux downstream. It is well known from asymptotic analysis that steady streaming is second order in amplitude, and we show that pumping occurs at third order. We then extend the analysis to general frequency ratios, where we give necessary conditions for pumping, and predict the order in amplitude...

Flag Gromov-Witten invariants via crystals

Wed, 15 Jul 2026 00:00:00 +0000

We apply ideas from crystal theory to affine Schubert calculus and flag Gromov-Witten invariants. By defining operators on certain decompositions of elements in the type-A affine Weyl group, we produce a crystal reflecting the internal structure of Specht modules associated to permutation diagrams. We show how this crystal framework can be applied to study the product of a Schur function with a k-Schur function. Consequently, we prove that a subclass of 3-point Gromov-Witten invariants of complete flag varieties for Cⁿ enumerate the highest weight elements under these operators.

Affine charge and the k-bounded Pieri rule

Wed, 15 Jul 2026 00:00:00 +0000

We provide a new description of the Pieri rule of the homology of the affine Grassmannian and an affine analogue of the charge statistics in terms of bounded partitions. This makes it possible to extend the formulation of the Kostka–Foulkes polynomials in terms of solvable lattice models by Nakayashiki and Yamada to the affine setting.

The mystery of plethysm coefficients

Wed, 15 Jul 2026 00:00:00 +0000

Composing two representations of the general linear groups gives rise to Littlewood’s (outer) plethysm. On the level of characters, this poses the question of finding the Schur expansion of the plethysm of two Schur functions. A combinatorial interpretation for the Schur expansion coefficients of the plethysm of two Schur functions is, in general, still an open problem. We identify a proof technique of combinatorial representation theory, which we call the “ -perp trick”, and point out several examples in the literature where this idea is used. We use the -perp trick to give algorithms for computing monomial and Schur expansions of symmetric functions. In several special cases, these algorithms are more efficient than those currently implemented in SageMath .

Combinatorial Characterization of Queer Supercrystals (Survey)

Wed, 15 Jul 2026 00:00:00 +0000

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 simply-laced 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 crystal. 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.

Dimension of Splines on Graphs in the Case of Degree Two and Smoothness One in Two Variables

Wed, 15 Jul 2026 00:00:00 +0000

Dimension of Splines on Graphs in the Case of Degree Two and Smoothness One in Two Variables

A minimaj-preserving crystal structure on ordered multiset partitions

Wed, 15 Jul 2026 00:00:00 +0000

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 yields a bijective proof of the equidistributivity of the minimaj statistic with the major index statistic on ordered multiset partitions.

Queer supercrystals in SageMath

Wed, 15 Jul 2026 00:00:00 +0000

We describe the implementation of queer supercrystals. Our code is documented with test suites and has been integrated into SageMath. Through computer explorations using this implementation, we provide a counterexample to Assaf's and Oguz' conjecture that their local queer axioms uniquely characterize the queer supercrystal.

Structural classification of locally stationary time series based on second-order characteristics

Fri, 10 Jul 2026 00:00:00 +0000

Abstract Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing between two classes of locally stationary time series based on their time-domain, second-order characteristics. Our approach builds on the autoregressive approximation for locally stationary time series, imposes no requirement on the training sample size, and is shown to achieve zero misclassification error rate asymptotically when the underlying time series differ only mildly in their second-order characteristics. The new method is demonstrated to outperform a variety of state-of-the-art solutions, including wavelet-based, tree-based, convolution-based methods, as well as modern deep learning methods, through intensive numerical simulations and a real electroencephalography data analysis for epilepsy classification.

Multiscale Hodge scattering networks for data analysis

Thu, 26 Mar 2026 00:00:00 +0000

We propose new scattering networks for signals measured on simplicial complexes, which we call Multiscale Hodge Scattering Networks (MHSNs). Our construction builds on multiscale basis dictionaries on simplicial complexes—namely, the κ-GHWT and κ-HGLET—which we recently developed for simplices of dimension κ ∈ N in a given simplicial complex by generalizing the node-based Generalized Haar–Walsh Transform (GHWT) and Hierarchical Graph Laplacian Eigen Transform (HGLET). Both the κ-GHWT and the κ-HGLET form redundant sets (i.e., dictionaries) of multiscale basis vectors and the corresponding expansion coefficients of a given signal. Our MHSNs adopt a layered structure analogous to a convolutional neural network (CNN), cascading the moments of the modulus of the dictionary coefficients. The resulting features are invariant to reordering of the simplices (i.e., node permutation of the underlying graphs). Importantly, the use of multiscale basis dictionaries in our MHSNs admits a natural...

Explainable and Class-Revealing Signal Feature Extraction via Scattering Transform and Constrained Zeroth-Order Optimization

Thu, 26 Mar 2026 00:00:00 +0000

We propose a new method to extract discriminant and explainable features from a particular machine learning model, i.e., a combination of the scattering transform and the multiclass logistic regression. Although this model is well-known for its ability to learn various signal classes with high classification rate, it remains elusive to understand why it can generate such successful classification, mainly due to the nonlinearity of the scattering transform. In order to uncover the meaning of the scattering transform coefficients selected by the multiclass logistic regression (with the Lasso penalty), we adopt zeroth-order optimization algorithms to search an input pattern that maximizes the class probability of a class of interest given the learned model. In order to do so, it turns out that imposing sparsity and smoothness of input patterns is important. We demonstrate the effectiveness of our proposed method using a couple of synthetic time-series classification problems.

Explainable and Class-Revealing Signal Feature Extraction via Scattering Transform and Constrained Zeroth-Order Optimization

Thu, 26 Mar 2026 00:00:00 +0000

Plabic tangles and cluster promotion maps

Wed, 11 Mar 2026 00:00:00 +0000

Inspired by the BCFW recurrence for tilings of the amplituhedron, we introduce the general framework of plabic tangles that utilizes plabic graphs to define rational maps between products of Grassmannians called promotions. The central conjecture of the paper is that promotion maps are quasi-cluster homomorphisms, which we prove for several classes of promotions. In order to define promotion maps, we utilize m-vector-relation configurations (m-VRCs) on plabic graphs. We relate m-VRCs to the degree (a.k.a ‘intersection number’) of the amplituhedron map on positroid varieties and characterize all plabic trees with intersection number one and their VRCs. Finally, we show that promotion maps admit an operad structure and, supported by the class of 4-mass box promotions, we point at new positivity properties for non-rational maps beyond cluster algebras. Promotion maps have important connections to the geometry and cluster structure of the amplituhedron and singularities of scattering...

Hook-Valued Tableau Uncrowding and Tableau Switching

Wed, 11 Mar 2026 00:00:00 +0000

Hook-Valued Tableau Uncrowding and Tableau Switching

Braid variety cluster structures, II: general type

Wed, 11 Mar 2026 00:00:00 +0000

We show that braid varieties for any complex simple algebraic group G$$G$$ are cluster varieties. This includes open Richardson varieties inside the flag variety G/B$$G/B$$.

The symplectic isotopy problem for rational cuspidal curves

Wed, 25 Feb 2026 00:00:00 +0000

We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex projective plane. We prove that every such curve is isotopic to a complex curve in degrees up to five, and for curves with one singularity whose link is a torus knot. Classification results of symplectic isotopy classes rely on pseudo-holomorphic curves together with a symplectic version of birational geometry of log pairs and techniques from four-dimensional topology.

Rational cuspidal curves and symplectic fillings

Wed, 25 Feb 2026 00:00:00 +0000

Rational cuspidal curves and symplectic fillings

Equivariant Perturbation in Gomory and Johnson’s Infinite Group Problem. VII. Inverse Semigroup Theory, Closures, Decomposition of Perturbations

Sat, 14 Feb 2026 00:00:00 +0000

In this self-contained paper, we present a theory of the piecewise linear minimal valid functions for the 1-row Gomory–Johnson infinite group problem. The non-extreme minimal valid functions are those that admit effective perturbations. We give a precise description of the space of these perturbations as a direct sum of certain finite- and infinite-dimensional subspaces. The infinite-dimensional subspaces have partial symmetries; to describe them, we develop a theory of inverse semigroups of partial bijections, interacting with the functional equations satisfied by the perturbations. Our paper provides the foundation for grid-free algorithms for the Gomory–Johnson model, in particular for testing extremality of piecewise linear functions whose breakpoints are rational numbers with huge denominators.

Dual-feasible functions for integer programming and combinatorial optimization: Algorithms, characterizations, and approximations

Sat, 14 Feb 2026 00:00:00 +0000

Within the framework of the superadditive duality theory of integer programming, we study two types of dual-feasible functions of a single real variable (Alves et al., 2016). We introduce software that automates testing piecewise linear functions for maximality and extremality, enabling a computer-based search. We build a connection to cut-generating functions in the Gomory–Johnson and related models, complete the characterization of maximal functions, and prove analogues of the Gomory–Johnson 2-slope theorem and the Basu–Hildebrand–Molinaro approximation theorem.

Integer points in arbitrary convex cones: the case of the PSD and SOC cones

Wed, 11 Feb 2026 00:00:00 +0000

We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral cones can sometimes have a notion of finite generating set with the help of a group action. We show this is true for the cone of positive semidefinite matrices (PSD) and the second-order cone (SOC). Both cones have a finite generating set of integer points, similar in spirit to Hilbert bases, under the action of a finitely generated group. We also extend notions of total dual integrality, Gomory-Chvátal closure, and Carathéodory rank to integer points in arbitrary cones.

On contact 3‐manifolds that admit a nonfree toric action

Wed, 28 Jan 2026 00:00:00 +0000

Abstract We classify all contact structures on 3‐manifolds that admit a nonfree toric action, up to contactomorphism, and present them through explicit topological descriptions. Our classification is based on Lerman's classification of toric contact 3‐manifolds up to equivariant contactomorphism [Lerman, J. Symplectic Geom. 1 (2003), 785–828]. We also prove that every contact 3‐manifold with a nonfree toric action arises as the concave boundary of a toric linear plumbing over spheres inspired by Marinković et al. As a corollary of both results, we classify which contact 3‐manifolds arise as the concave boundary of a linear plumbing of spheres.

An extended Vinogradov’s mean value theorem

Sun, 7 Dec 2025 00:00:00 +0000

In this paper, we provide novel mean value estimates for exponential sums related to the extended main conjecture of Vinogradov’s mean value theorem, by developing the Hardy-Littlewood circle method together with a refined shifting variables argument.

Let be a natural number and . Define the exponential sum For , consider mean values of the exponential sums where we wrote . By making use of the aforementioned tools, we obtain the sharp upper bound for , for and . Furthermore, for , we obtain analogous results depending on a small cap decoupling inequality for the moment curves in .

The contact cut graph and a Weinstein L$\mathcal {L}$‐invariant

Mon, 1 Dec 2025 00:00:00 +0000

Abstract We define and study the contact cut graph which is an analogue of Hatcher and Thurston's cut graph for contact geometry, inspired by contact Heegaard splittings (Giroux, Proceedings of the International Congress of Mathematicians , Beijing, 2002; Torisu, Internat. Math. Res. Notices (2000), 441–454). We show how oriented paths in the contact cut graph correspond to Lefschetz fibrations and multisection with divides diagrams. We also give a correspondence for achiral Lefschetz fibrations. We use these correspondences to define a new invariant of Weinstein domains, the Weinstein ‐invariant , that is a symplectic analogue of the Kirby–Thompson's ‐invariant of smooth 4‐manifolds. We discuss the relation of Lefschetz stabilization with the Weinstein ‐invariant. We present topological and geometric constraints of Weinstein domains with . We also give two families of examples of multisections with divides that have arbitrarily large ‐invariant.

Morse actions of discrete groups on symmetric spaces: local-to-global principle

Wed, 24 Sep 2025 00:00:00 +0000

Our main result is a local-to-global principle for Morse quasigeodesics, maps and actions. As an application of our techniques we show algorithmic recognizability of Morse actions and construct Morse “Schottky subgroups” of higher-rank semisimple Lie groups via arguments not based on Tits pingpong. Our argument is purely geometric and proceeds by constructing equivariant Morse quasiisometric embeddings of trees into higher-rank symmetric spaces.

The Combinatorial Theory Flip

Wed, 27 Aug 2025 00:00:00 +0000

The Combinatorial Theory Flip

Interview with Anne Schilling

Wed, 27 Aug 2025 00:00:00 +0000

Interview with Anne Schilling

Complexity of Finite Semigroups: History and Decidability

Wed, 13 Aug 2025 00:00:00 +0000

Margolis, Rhodes and Schilling recently submitted two papers that proved that the complexity of a finite semigroup is computable. The purpose of this paper is to survey the basic results of Krohn–Rhodes complexity of finite semigroups and to outline the proof of its computability.

Weinstein Handlebodies for Complements of Smoothed Toric Divisors

Thu, 17 Jul 2025 00:00:00 +0000

We study the interactions between toric manifolds and Weinstein handlebodies. We define a partially-centeredness condition on a Delzant polytope, which we prove ensures that the complement of a corresponding partial smoothing of the total toric divisor supports an explicit Weinstein structure. Many examples which fail this condition also fail to have Weinstein (or even exact) complement to the partially smoothed divisor. We investigate the combinatorial possibilities of Delzant polytopes that realize such Weinstein domain complements. We also develop an algorithm to construct a Weinstein handlebody diagram in Gompf standard form for the complement of such a partially smoothed total toric divisor. The algorithm we develop more generally outputs a Weinstein handlebody diagram for any Weinstein 4-manifold constructed by attaching 2-handles to the disk cotangent bundle of any surface , where the 2-handles are attached along the co-oriented conormal lifts of curves on ...

Optimization tools for computing colorings of [ 1 , … , n ] with few monochromatic solutions on 3-variable linear equations

Sun, 25 May 2025 00:00:00 +0000

A famous result in arithmetic Ramsey theory says that for many linear homogeneous equations E there is a threshold value Rk(E) (the Rado number of E) such that for any k-coloring of the integers in the interval [1,n], with n≥Rk(E), there exists at least one monochromatic solution. But one can further ask, how many monochromatic solutions is the minimum possible in terms of n? Several authors have estimated this function before, here we offer new tools from integer and semidefinite optimization that help find either optimal or near optimal 2-colorings minimizing the number of monochromatic solutions of several families of 3-variable non-regular homogeneous linear equations. In the last part of the paper we further extend to three and more colors for the Schur equation, improving earlier work.

Lipschitz decompositions of domains with bilaterally flat boundaries

Mon, 28 Apr 2025 00:00:00 +0000

Abstract: We study classes of domains in with sufficiently flat boundaries that admit a decomposition or covering of bounded overlap by Lipschitz graph domains with controlled total surface area. This study is motivated by the following result proved by Peter Jones as a piece of his proof of the Analyst's Traveling Salesman Theorem in the complex plane: Any simply connected domain with finite boundary length can be decomposed into Lipschitz graph domains with total boundary length at most for some independent of . In this paper, we prove an analogous Lipschitz decomposition result in higher dimensions for domains with Reifenberg flat boundaries satisfying a uniform beta‐squared sum bound. We use similar techniques to show that domains with general Reifenberg flat or uniformly rectifiable boundaries admit similar Lipschitz decompositions while allowing the constituent domains to have bounded overlaps rather than be disjoint.

The geometry of colors in van Gogh’s Sunflowers

Thu, 10 Apr 2025 00:00:00 +0000

“Paintings fade like flowers”: van Gogh’s prediction on the impact of age on paintings came true for most of his paintings. We have studied the consequences of this aging on the Sunflowers in a vase with a yellow background series, namely its original, F454, currently in London, and two replicates, F457, in Tokyo, and F458, in Amsterdam, which van Gogh painted using the original as a model. The background and flower renditions in those paintings have faded and turned brown, making them less vibrant that van Gogh had most likely intended. We have attempted to restore van Gogh’s intent using a computational approach based on data science. After identifications of regions of interest (ROI) within the three paintings F454, F457, and F458 that capture the flowers, stems of the flowers, and background, respectively, we studied the geometry of the color space (in RGB representation) occupied by those ROIs. By comparing those color spaces with those occupied by similar ROIs in photographs...

Continued fractions and lines across the Stern–Brocot diagram

Wed, 9 Apr 2025 00:00:00 +0000

Continued fractions and lines across the Stern–Brocot diagram

Farey recursive functions

Wed, 9 Apr 2025 00:00:00 +0000

Farey recursive functions

The lattice of submonoids of the uniform block permutations containing the symmetric group

Wed, 26 Mar 2025 00:00:00 +0000

We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive under union and intersection by relating the submonoids containing the symmetric group to downsets in a new partial order on integer partitions. Furthermore, we show that the sizes of the J$$\mathscr {J}$$-classes of the uniform block permutation monoid are sums of squares of dimensions of irreducible modules of the monoid algebra.

The immersion poset on partitions

Wed, 12 Mar 2025 00:00:00 +0000

Abstract: We introduce the immersion poset $$({\mathcal {P}}(n), \leqslant _I)$$ ( P ( n ) , ⩽ I ) on partitions, defined by $$\lambda \leqslant _I \mu $$ λ ⩽ I μ if and only if $$s_\mu (x_1, \ldots , x_N) - s_\lambda (x_1, \ldots , x_N)$$ ...

Corrigendum: A Demazure crystal construction for Schubert polynomials

Wed, 26 Feb 2025 00:00:00 +0000

We give a corrigendum to our paper [4] entitled “A Demazure crystal construction for Schubert polynomials”.

The strong Haken theorem via sphere complexes

Wed, 29 Jan 2025 00:00:00 +0000

The strong Haken theorem via sphere complexes

Tree polynomials identify a link between co-transcriptional R-loops and nascent RNA folding

Mon, 20 Jan 2025 00:00:00 +0000

R-loops are a class of non-canonical nucleic acid structures that typically form during transcription when the nascent RNA hybridizes the DNA template strand, leaving the non-template DNA strand unpaired. These structures are abundant in nature and play important physiological and pathological roles. Recent research shows that DNA sequence and topology affect R-loops, yet it remains unclear how these and other factors contribute to R-loop formation. In this work, we investigate the link between nascent RNA folding and the formation of R-loops. We introduce tree-polynomials, a new class of representations of RNA secondary structures. A tree-polynomial representation consists of a rooted tree associated with an RNA secondary structure together with a polynomial that is uniquely identified with the rooted tree. Tree-polynomials enable accurate, interpretable and efficient data analysis of RNA secondary structures without pseudoknots. We develop a computational pipeline for investigating...

THE BEST WAYS TO SLICE A POLYTOPE

Fri, 17 Jan 2025 00:00:00 +0000

We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of possible combinatorial types of sections and craft algorithms that compute optimal sections of the polytope according to various combinatorial and metric criteria, including sections that maximize the number of k-dimensional faces, maximize the volume, and maximize the integral of a polynomial. Our optimization algorithms run in polynomial time in fixed dimension, but the same problems show computational complexity hardness otherwise. Our tools can be extended to intersection with halfspaces and projections onto hyperplanes. Finally, we present several experiments illustrating our theorems and algorithms on famous polytopes.

Weighted Ehrhart theory: Extending Stanley's nonnegativity theorem

Fri, 17 Jan 2025 00:00:00 +0000

We generalize R. P. Stanley's celebrated theorem that the h⁎-polynomial of the Ehrhart series of a rational polytope has nonnegative coefficients and is monotone under containment of polytopes. We show that these results continue to hold for weighted Ehrhart series where lattice points are counted with polynomial weights, as long as the weights are homogeneous polynomials decomposable as sums of products of linear forms that are nonnegative on the polytope. We also show nonnegativity of the h⁎-polynomial as a real-valued function for a larger family of weights. We explore the case when the weight function is the square of a single (arbitrary) linear form. We show stronger results for two-dimensional convex lattice polygons and give concrete examples showing tightness of the hypotheses. As an application, we construct a counterexample to a conjecture by Berg, Jochemko, and Silverstein on Ehrhart tensor polynomials.

The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg

Fri, 17 Jan 2025 00:00:00 +0000

We discuss five fundamental results of discrete mathematics: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg from combinatorial geometry. We explore their connections and emphasize their broad impact in application areas such as data science, game theory, graph theory, mathematical optimization, computational geometry, etc.

Klein–Maskit combination theorem for Anosov subgroups: Amalgams

Wed, 20 Nov 2024 00:00:00 +0000

Abstract: The classical Klein–Maskit combination theorems provide sufficient conditions to construct new Kleinian groups using old ones. There are two distinct but closely related combination theorems: the first deals with amalgamated free products, whereas the second deals with HNN extensions. This article gives analogs of both combination theorems for Anosov subgroups.

From Quasi-Symmetric to Schur Expansions with Applications to Symmetric Chain Decompositions and Plethysm

Wed, 20 Nov 2024 00:00:00 +0000

It is an important problem in algebraic combinatorics to deduce the Schur function expansion of a symmetric function whose expansion in terms of the fundamental quasisymmetric function is known. For example, formulas are known for the fundamental expansion of a Macdonald symmetric function and for the plethysm of two Schur functions, while the Schur expansions of these expressions are still elusive. Based on work of Egge, Loehr and Warrington, Garsia and Remmel provided a method to obtain the Schur expansion from the fundamental expansion by replacing each quasisymmetric function by a Schur function (not necessarily indexed by a partition) and using straightening rules to obtain the Schur expansion. Here we provide a new method that only involves the coefficients of the quasisymmetric functions indexed by partitions and the quasi-Kostka matrix. As an application, we identify the lexicographically largest term in the Schur expansion of the plethysm of two Schur functions. We provide...

Fair Data Representation for Machine Learning at the Pareto Frontier.

Wed, 13 Nov 2024 00:00:00 +0000

As machine learning powered decision-making becomes increasingly important in our daily lives, it is imperative to strive for fairness in the underlying data processing. We propose a pre-processing algorithm for fair data representation via which -objective supervised learning results in estimations of the Pareto frontier between prediction error and statistical disparity. Particularly, the present work applies the optimal affine transport to approach the post-processing Wasserstein barycenter characterization of the optimal fair -objective supervised learning via a pre-processing data deformation. Furthermore, we show that the Wasserstein geodesics from learning outcome marginals to their barycenter characterizes the Pareto frontier between -loss and total Wasserstein distance among the marginals. Numerical simulations underscore the advantages: (1) the pre-processing step is compositive with arbitrary conditional expectation estimation supervised learning methods and unseen...

Complete characterizations of hyperbolic Coxeter groups with Sierpiński curve boundary and with Menger curve boundary

Wed, 23 Oct 2024 00:00:00 +0000

Complete characterizations of hyperbolic Coxeter groups with Sierpiński curve boundary and with Menger curve boundary

A multiscale predictive digital twin for neurocardiac modulation

Mon, 16 Sep 2024 00:00:00 +0000

Cardiac function is tightly regulated by the autonomic nervous system (ANS). Activation of the sympathetic nervous system increases cardiac output by increasing heart rate and stroke volume, while parasympathetic nerve stimulation instantly slows heart rate. Importantly, imbalance in autonomic control of the heart has been implicated in the development of arrhythmias and heart failure. Understanding of the mechanisms and effects of autonomic stimulation is a major challenge because synapses in different regions of the heart result in multiple changes to heart function. For example, nerve synapses on the sinoatrial node (SAN) impact pacemaking, while synapses on contractile cells alter contraction and arrhythmia vulnerability. Here, we present a multiscale neurocardiac modelling and simulator tool that predicts the effect of efferent stimulation of the sympathetic and parasympathetic branches of the ANS on the cardiac SAN and ventricular myocardium. The model includes a layered...

Effect of fluid elasticity on the emergence of oscillations in an active elastic filament

Tue, 25 Jun 2024 00:00:00 +0000

Many microorganisms propel themselves through complex media by deforming their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, the passive elastic response from deformations of the flagellum and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there are limited data on how systematic changes in elasticity alter the beat. This work analyses a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip of a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. Compared to a Newtonian fluid, it takes more force to induce the instability in viscoelastic fluids, and the frequency of the oscillation is higher. The linear analysis predicts that the frequency increases with the fluid relaxation...

Reproducibility of 3D chromatin configuration reconstructions

Mon, 17 Jun 2024 00:00:00 +0000

It is widely recognized that the three-dimensional (3D) architecture of eukaryotic chromatin plays an important role in processes such as gene regulation and cancer-driving 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 high-throughput molecular techniques have changed this situation. Notably, the development of a suite of chromatin conformation capture (CCC) assays has enabled elicitation of contacts-spatially close chromosomal loci-which 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 statistically-the purpose of this paper. We use a constrained...

The ENIGMA Consortium: large-scale collaborative analyses of neuroimaging and genetic data

Sun, 16 Jun 2024 00:00:00 +0000

The Enhancing NeuroImaging Genetics through Meta-Analysis (ENIGMA) Consortium is a collaborative network of researchers working together on a range of large-scale studies that integrate data from 70 institutions worldwide. Organized into Working Groups that tackle questions in neuroscience, genetics, and medicine, ENIGMA studies have analyzed neuroimaging data from over 12,826 subjects. In addition, data from 12,171 individuals were provided by the CHARGE consortium for replication of findings, in a total of 24,997 subjects. By meta-analyzing results from many sites, ENIGMA has detected factors that affect the brain that no individual site could detect on its own, and that require larger numbers of subjects than any individual neuroimaging study has currently collected. ENIGMA’s first project was a genome-wide association study identifying common variants in the genome associated with hippocampal volume or intracranial volume. Continuing work is exploring genetic associations...

Private measures, random walks, and synthetic data

Wed, 12 Jun 2024 00:00:00 +0000

Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex—but very common—machine learning tasks such as clustering or classification. In this paper we overcome some of these limitations. Working with metric privacy, a powerful generalization of differential privacy, we develop a polynomial-time algorithm that creates a private measure from a data set. This private measure allows us to efficiently construct private synthetic data that are accurate for a wide range of statistical analysis tools. Moreover, we prove an asymptotically sharp min-max result for private measures and synthetic data in general compact...

Early career Latinas in STEM: Challenges and solutions

Thu, 9 May 2024 00:00:00 +0000

Mexican, Puerto Rican, and Central American Ancestry (MPRCA) individuals represent 82% of US Latinos. An intergenerational group of MPRCA women and allies met to discuss persistent underrepresentation of MPRCA women in STEM, identifying multi-level challenges and solutions. Implementation of these solutions is important and will benefit MPRCA women and the entire academic community.

Multiscale transforms for signals on simplicial complexes

Wed, 8 May 2024 00:00:00 +0000

Our previous multiscale graph basis dictionaries/graph signal transforms—Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen Transform (HGLET); Natural Graph Wavelet Packets (NGWPs); and their relatives—were developed for analyzing data recorded on vertices of a given graph. In this article, we propose their generalization for analyzing data recorded on edges, faces (i.e., triangles), or more generally κ$$\kappa $$-dimensional simplices of a simplicial complex (e.g., a triangle mesh of a manifold). The key idea is to use the Hodge Laplacians and their variants for hierarchical partitioning of a set of κ$$\kappa $$-dimensional simplices in a given simplicial complex, and then build localized basis functions on these partitioned subsets. We demonstrate their usefulness for data representation on both illustrative synthetic examples and real-world simplicial complexes generated from a co-authorship/citation dataset and an ocean current/flow dataset.

Modeling time-varying phytoplankton subsidy reveals at-risk species in a Chilean intertidal ecosystem

Mon, 1 Apr 2024 00:00:00 +0000

The allometric trophic network (ATN) framework for modeling population dynamics has provided numerous insights into ecosystem functioning in recent years. Herein we extend ATN modeling of the intertidal ecosystem off central Chile to include empirical data on pelagic chlorophyll-a concentration. This intertidal community requires subsidy of primary productivity to support its rich ecosystem. Previous work models this subsidy using a constant rate of phytoplankton input to the system. However, data shows pelagic subsidies exhibit highly variable, pulse-like behavior. The primary contribution of our work is incorporating this variable input into ATN modeling to simulate how this ecosystem may respond to pulses of pelagic phytoplankton. Our model results show that: (1) closely related sea snails respond differently to phytoplankton variability, which is explained by the underlying network structure of the food web; (2) increasing the rate of pelagic-intertidal mixing increases fluctuations...

A computational model predicts sex-specific responses to calcium channel blockers in mammalian mesenteric vascular smooth muscle

Tue, 26 Mar 2024 00:00:00 +0000

The function of the smooth muscle cells lining the walls of mammalian systemic arteries and arterioles is to regulate the diameter of the vessels to control blood flow and blood pressure. Here, we describe an in silico model, which we call the 'Hernandez-Hernandez model', of electrical and Ca²⁺ signaling in arterial myocytes based on new experimental data indicating sex-specific differences in male and female arterial myocytes from murine resistance arteries. The model suggests the fundamental ionic mechanisms underlying membrane potential and intracellular Ca²⁺ signaling during the development of myogenic tone in arterial blood vessels. Although experimental data suggest that K_V1.5 channel currents have similar amplitudes, kinetics, and voltage dependencies in male and female myocytes, simulations suggest that the K_V1.5 current is the dominant current regulating membrane potential in male myocytes. In female cells, which have larger...

PrestoCell: A persistence-based clustering approach for rapid and robust segmentation of cellular morphology in three-dimensional data

Tue, 12 Mar 2024 00:00:00 +0000

Light microscopy methods have continued to advance allowing for unprecedented analysis of various cell types in tissues including the brain. Although the functional state of some cell types such as microglia can be determined by morphometric analysis, techniques to perform robust, quick, and accurate measurements have not kept pace with the amount of imaging data that can now be generated. Most of these image segmentation tools are further burdened by an inability to assess structures in three-dimensions. Despite the rise of machine learning techniques, the nature of some biological structures prevents the training of several current day implementations. Here we present PrestoCell, a novel use of persistence-based clustering to segment cells in light microscopy images, as a customized Python-based tool that leverages the free multidimensional image viewer Napari. In evaluating and comparing PrestoCell to several existing tools, including 3DMorph, Omipose, and Imaris, we demonstrate...

Transitions between Distinct Compaction Regimes in Complexes of Multivalent Cationic Lipids and DNA

Mon, 4 Mar 2024 00:00:00 +0000

Cationic lipids (CLs) have found widespread use as nonviral gene carriers (vectors), including applications in clinical trials of gene therapy. However, their observed transfection efficiencies (TEs) are inferior to those of viral vectors, providing a strong incentive for a detailed understanding of CL-DNA complex behavior. In recent systematic studies employing monovalent as well as newly synthesized multivalent lipids (MVLs), the membrane cationic charge density has been identified as a key parameter governing the TE of lamellar CL-DNA complexes. In this work, we use x-ray scattering and molecular simulations to investigate the structural properties of complexes containing MVLs. At low mole fraction of neutral lipids (NLs), Phi(NL), the complexes show dramatic DNA compaction, down to essentially close-packed DNA arrays with a DNA interaxial spacing d(DNA) = 25 A. A gradual increase in Phi(NL) does not lead to a continuous increase in d(DNA) as observed for DNA complexes of monovalent...

Tracking Mechanical Stress and Cell Migration with Inexpensive Polymer Thin‐Film Sensors

Wed, 24 Jan 2024 00:00:00 +0000

Polydiacetylene (PDA) Langmuir films are well known for their blue to red chromatic transitions in response to a variety of stimuli, including UV light, heat, bio-molecule bindings and mechanical stress. In this work, we detail the ability to tune PDA Langmuir films to exhibit discrete chromatic transitions in response to applied mechanical stress. Normal and shear-induced transitions were quantified using the Surface Forces Apparatus and established to be binary and tunable as a function of film formation conditions. Both monomer alkyl tail length and metal cations were used to manipulate the chromatic transition force threshold to enable discrete force sensing from ~50 to ~500 nN μm^-2 for normal loading and ~2 to ~40 nN μm^-2 for shear-induced transitions, which are appropriate for biological cells. The utility of PDA thin-film sensors was demonstrated with the slime mold Physarum polycephalum. The fluorescence readout of the films enabled: the area...

On Viazovska’s modular form inequalities

Wed, 15 Nov 2023 00:00:00 +0000

Viazovska proved that the [Formula: see text] lattice sphere packing is the densest sphere packing in [Formula: see text] dimensions. Her proof relies on two inequalities between functions defined in terms of modular and quasimodular forms. We give a direct proof of these inequalities that does not rely on computer calculations.

Common population codes produce extremely nonlinear neural manifolds

Wed, 4 Oct 2023 00:00:00 +0000

Populations of neurons represent sensory, motor, and cognitive variables via patterns of activity distributed across the population. The size of the population used to encode a variable is typically much greater than the dimension of the variable itself, and thus, the corresponding neural population activity occupies lower-dimensional subsets of the full set of possible activity states. Given population activity data with such lower-dimensional structure, a fundamental question asks how close the low-dimensional data lie to a linear subspace. The linearity or nonlinearity of the low-dimensional structure reflects important computational features of the encoding, such as robustness and generalizability. Moreover, identifying such linear structure underlies common data analysis methods such as Principal Component Analysis (PCA). Here, we show that for data drawn from many common population codes the resulting point clouds and manifolds are exceedingly nonlinear, with the dimension...

Using machine learning to detect coronaviruses potentially infectious to humans

Tue, 18 Jul 2023 00:00:00 +0000

Establishing the host range for novel viruses remains a challenge. Here, we address the challenge of identifying non-human animal coronaviruses that may infect humans by creating an artificial neural network model that learns from spike protein sequences of alpha and beta coronaviruses and their binding annotation to their host receptor. The proposed method produces a human-Binding Potential (h-BiP) score that distinguishes, with high accuracy, the binding potential among coronaviruses. Three viruses, previously unknown to bind human receptors, were identified: Bat coronavirus BtCoV/133/2005 and Pipistrellus abramus bat coronavirus HKU5-related (both MERS related viruses), and Rhinolophus affinis coronavirus isolate LYRa3 (a SARS related virus). We further analyze the binding properties of BtCoV/133/2005 and LYRa3 using molecular dynamics. To test whether this model can be used for surveillance of novel coronaviruses, we re-trained the model on a set that excludes SARS-CoV-2 and...

A Note on Cumulant Technique in Random Matrix Theory

Tue, 18 Jul 2023 00:00:00 +0000

We discuss the cumulant approach to spectral properties of large random matrices. In particular, we study in detail the joint cumulants of high traces of large unitary random matrices and prove Gaussian fluctuation for pair-counting statistics with non-smooth test functions.

SPARCoC: A New Framework for Molecular Pattern Discovery and Cancer Gene Identification

Thu, 13 Jul 2023 00:00:00 +0000

It is challenging to cluster cancer patients of a certain histopathological type into molecular subtypes of clinical importance and identify gene signatures directly relevant to the subtypes. Current clustering approaches have inherent limitations, which prevent them from gauging the subtle heterogeneity of the molecular subtypes. In this paper we present a new framework: SPARCoC (Sparse-CoClust), which is based on a novel Common-background and Sparse-foreground Decomposition (CSD) model and the Maximum Block Improvement (MBI) co-clustering technique. SPARCoC has clear advantages compared with widely-used alternative approaches: hierarchical clustering (Hclust) and nonnegative matrix factorization (NMF). We apply SPARCoC to the study of lung adenocarcinoma (ADCA), an extremely heterogeneous histological type, and a significant challenge for molecular subtyping. For testing and verification, we use high quality gene expression profiling data of lung ADCA patients, and identify...

SparRec: An effective matrix completion framework of missing data imputation for GWAS

Thu, 13 Jul 2023 00:00:00 +0000

Genome-wide association studies present computational challenges for missing data imputation, while the advances of genotype technologies are generating datasets of large sample sizes with sample sets genotyped on multiple SNP chips. We present a new framework SparRec (Sparse Recovery) for imputation, with the following properties: (1) The optimization models of SparRec, based on low-rank and low number of co-clusters of matrices, are different from current statistics methods. While our low-rank matrix completion (LRMC) model is similar to Mendel-Impute, our matrix co-clustering factorization (MCCF) model is completely new. (2) SparRec, as other matrix completion methods, is flexible to be applied to missing data imputation for large meta-analysis with different cohorts genotyped on different sets of SNPs, even when there is no reference panel. This kind of meta-analysis is very challenging for current statistics based methods. (3) SparRec has consistent performance and achieves...

Scratch-AID, a deep learning-based system for automatic detection of mouse scratching behavior with high accuracy

Sat, 8 Jul 2023 00:00:00 +0000

Mice are the most commonly used model animals for itch research and for development of anti-itch drugs. Most laboratories manually quantify mouse scratching behavior to assess itch intensity. This process is labor-intensive and limits large-scale genetic or drug screenings. In this study, we developed a new system, Scratch-AID (Automatic Itch Detection), which could automatically identify and quantify mouse scratching behavior with high accuracy. Our system included a custom-designed videotaping box to ensure high-quality and replicable mouse behavior recording and a convolutional recurrent neural network trained with frame-labeled mouse scratching behavior videos, induced by nape injection of chloroquine. The best trained network achieved 97.6% recall and 96.9% precision on previously unseen test videos. Remarkably, Scratch-AID could reliably identify scratching behavior in other major mouse itch models, including the acute cheek model, the histaminergic...

TAaCGH Suite for Detecting Cancer—Specific Copy Number Changes Using Topological Signatures

Mon, 3 Jul 2023 00:00:00 +0000

Copy number changes play an important role in the development of cancer and are commonly associated with changes in gene expression. Persistence curves, such as Betti curves, have been used to detect copy number changes; however, it is known these curves are unstable with respect to small perturbations in the data. We address the stability of lifespan and Betti curves by providing bounds on the distance between persistence curves of Vietoris-Rips filtrations built on data and slightly perturbed data in terms of the bottleneck distance. Next, we perform simulations to compare the predictive ability of Betti curves, lifespan curves (conditionally stable) and stable persistent landscapes to detect copy number aberrations. We use these methods to identify significant chromosome regions associated with the four major molecular subtypes of breast cancer: Luminal A, Luminal B, Basal and HER2 positive. Identified segments are then used as predictor variables to build machine learning...

Use of machine-learning algorithms to aid in the early detection of leptospirosis in dogs

Fri, 30 Jun 2023 00:00:00 +0000

Leptospirosis is a life-threatening, zoonotic disease with various clinical presentations, including renal injury, hepatic injury, pancreatitis, and pulmonary hemorrhage. With prompt recognition of the disease and treatment, 90% of infected dogs have a positive outcome. Therefore, rapid, early diagnosis of leptospirosis is crucial. Testing for Leptospira-specific serum antibodies using the microscopic agglutination test (MAT) lacks sensitivity early in the disease process, and diagnosis can take >2 wk because of the need to demonstrate a rise in titer. We applied machine-learning algorithms to clinical variables from the first day of hospitalization to create machine-learning prediction models (MLMs). The models incorporated patient signalment, clinicopathologic data (CBC, serum chemistry profile, and urinalysis = blood work [BW] model), with or without a MAT titer obtained at patient intake (=BW + MAT model). The models were trained with data from 91 dogs with confirmed...

Vaping discussion in the COVID-19 pandemic: An observational study using Twitter data

Tue, 27 Jun 2023 00:00:00 +0000

BACKGROUND: With the spread of COVID-19, significant concerns have been raised about the potential increased risk for electronic cigarette (e-cigarette) users for COVID-19 infection and related syndromes. Social media is an increasingly popular source for health information dissemination and discussion, and can affect health outcomes. OBJECTIVE: This study aims to identify the topics in the public vaping discussion in COVID-19-related Twitter posts in order to get insight into public vaping-related perceptions, attitudes and concerns, and to discern possible misinformation and misconceptions around vaping in the COVID-19 pandemic. METHODS: Using the tweets ID database maintained by Georgia State University's Panacea Lab, we downloaded the tweets related to COVID-19 from March 11, 2020, when the World Health Organization declared COVID-19 a pandemic, to February 12, 2021. We used R to analyze the tweets that contained a list of 79 keywords related to vaping. After removing duplicates...

Ion-dependent DNA configuration in bacteriophage capsids

Fri, 23 Jun 2023 00:00:00 +0000

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than...

Rate-dependent effects of lidocaine on cardiac dynamics: Development and analysis of a low-dimensional drug-channel interaction model

Thu, 22 Jun 2023 00:00:00 +0000

State-dependent sodium channel blockers are often prescribed to treat cardiac arrhythmias, but many sodium channel blockers are known to have pro-arrhythmic side effects. While the anti and proarrhythmic potential of a sodium channel blocker is thought to depend on the characteristics of its rate-dependent block, the mechanisms linking these two attributes are unclear. Furthermore, how specific properties of rate-dependent block arise from the binding kinetics of a particular drug is poorly understood. Here, we examine the rate-dependent effects of the sodium channel blocker lidocaine by constructing and analyzing a novel drug-channel interaction model. First, we identify the predominant mode of lidocaine binding in a 24 variable Markov model for lidocaine-sodium channel interaction by Moreno et al. Specifically, we find that (1) the vast majority of lidocaine bound to sodium channels is in the neutral form, i.e., the binding of charged lidocaine to sodium channels is negligible,...

Dynamics of adrenergic signaling in cardiac myocytes and implications for pharmacological treatment

Mon, 19 Jun 2023 00:00:00 +0000

Dense innervation of the heart by the sympathetic nervous system (SNS) allows cardiac output to respond appropriately to the needs of the body under varying conditions, but occasionally the abrupt onset of SNS activity can trigger cardiac arrhythmias. Sympathetic activity leads to the release of norepinephrine (NE) onto cardiomyocytes, activating β₁-adrenergic receptors (β₁-ARs) and leading to the production of the second messenger cyclic AMP (cAMP). Upon sudden activation of β₁-ARs in experiments, intracellular cAMP can transiently rise to a high concentration before converging to a steady state level. Although changes to cellular cAMP concentration are important in modulating the overall cardiovascular response to sympathetic tone, the underlying mechanisms of the cAMP transients and the parameters that control their magnitude are unclear. We reduce a detailed computational model of the β₁-adrenergic signaling cascade to a system of...

Emerging roles for R-loop structures in the management of topological stress

Wed, 7 Jun 2023 00:00:00 +0000

R-loop structures are a prevalent class of alternative non-B DNA structures that form during transcription upon invasion of the DNA template by the nascent RNA. R-loops form universally in the genomes of organisms ranging from bacteriophages, bacteria, and yeasts to plants and animals, including mammals. A growing body of work has linked these structures to both physiological and pathological processes, in particular to genome instability. The rising interest in R-loops is placing new emphasis on understanding the fundamental physicochemical forces driving their formation and stability. Pioneering work in Escherichia coli revealed that DNA topology, in particular negative DNA superhelicity, plays a key role in driving R-loops. A clear role for DNA sequence was later uncovered. Here, we review and synthesize available evidence on the roles of DNA sequence and DNA topology in controlling R-loop formation and stability. Factoring in recent developments in R-loop modeling and...

Synchronization of Electrically Coupled Resonate-and-Fire Neurons.

Fri, 2 Jun 2023 00:00:00 +0000

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with electrical coupling show a diversity of post-spike subthreshold fluctuations, often linked to subthreshold resonance, which are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with damped subthreshold oscillations and a range of post-spike voltage dynamics. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuous post-spike reset rule. We find that both spikes and subthreshold fluctuations can jointly promote synchronization. The subthreshold...

Computing trisections of 4-manifolds

Tue, 23 May 2023 00:00:00 +0000

We describe an algorithm to compute trisections of orientable four-manifolds using arbitrary triangulations as input. This results in explicit complexity bounds for the trisection genus of a 4-manifold in terms of the number of pentachora (4-simplices) in a triangulation.

Highly accurate model for prediction of lung nodule malignancy with CT scans

Sat, 20 May 2023 00:00:00 +0000

Computed tomography (CT) examinations are commonly used to predict lung nodule malignancy in patients, which are shown to improve noninvasive early diagnosis of lung cancer. It remains challenging for computational approaches to achieve performance comparable to experienced radiologists. Here we present NoduleX, a systematic approach to predict lung nodule malignancy from CT data, based on deep learning convolutional neural networks (CNN). For training and validation, we analyze >1000 lung nodules in images from the LIDC/IDRI cohort. All nodules were identified and classified by four experienced thoracic radiologists who participated in the LIDC project. NoduleX achieves high accuracy for nodule malignancy classification, with an AUC of ~0.99. This is commensurate with the analysis of the dataset by experienced radiologists. Our approach, NoduleX, provides an effective framework for highly accurate nodule malignancy prediction with the model trained on a large patient population....

Flagellar swimming in viscoelastic fluids: role of fluid elastic stress revealed by simulations based on experimental data

Mon, 15 May 2023 00:00:00 +0000

Many important biological functions depend on microorganisms' ability to move in viscoelastic fluids such as mucus and wet soil. The effects of fluid elasticity on motility remain poorly understood, partly because the swimmer strokes depend on the properties of the fluid medium, which obfuscates the mechanisms responsible for observed behavioural changes. In this study, we use experimental data on the gaits of Chlamydomonas reinhardtii swimming in Newtonian and viscoelastic fluids as inputs to numerical simulations that decouple the swimmer gait and fluid type in order to isolate the effect of fluid elasticity on swimming. In viscoelastic fluids, cells employing the Newtonian gait swim faster but generate larger stresses and use more power, and as a result the viscoelastic gait is more efficient. Furthermore, we show that fundamental principles of swimming based on viscous fluid theory miss important flow dynamics: fluid elasticity provides an elastic memory effect that...

Intracellular Pressure Dynamics in Blebbing Cells

Tue, 2 May 2023 00:00:00 +0000

Blebs are pressure-driven protrusions that play an important role in cell migration, particularly in three-dimensional environments. A bleb is initiated when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol toward the area of detachment and local expansion of the cell membrane. Recent experiments involving blebbing cells have led to conflicting hypotheses regarding the timescale of intracellular pressure propagation. The interpretation of one set of experiments supports a poroelastic model of the cytoplasm that leads to slow pressure equilibration when compared to the timescale of bleb expansion. A different study concludes that pressure equilibrates faster than the timescale of bleb expansion. To address this discrepancy, a dynamic computational model of the cell was developed that includes mechanics of and the interactions among the cytoplasm, the actin cortex, the cell membrane, and the cytoskeleton. The model results quantify...

Landmark-free geometric methods in biological shape analysis

Fri, 28 Apr 2023 00:00:00 +0000

In this paper, we propose a new approach for computing a distance between two shapes embedded in three-dimensional space. We take as input a pair of triangulated genus zero surfaces that are topologically equivalent to spheres with no holes or handles, and construct a discrete conformal map f between the surfaces. The conformal map is chosen to minimize a symmetric deformation energy Esd(f) which we introduce. This measures the distance of f from an isometry, i.e. a non-distorting correspondence. We show that the energy of the minimizing map gives a well-behaved metric on the space of genus zero surfaces. In contrast to most methods in this field, our approach does not rely on any assignment of landmarks on the two surfaces. We illustrate applications of our approach to geometric morphometrics using three datasets representing the bones and teeth of primates. Experiments on these datasets show that our approach performs remarkably well both in shape recognition and in identifying...

An immersed boundary method for two-fluid mixtures

Mon, 24 Apr 2023 00:00:00 +0000

We present an Immersed Boundary method for interactions between elastic boundaries and mixtures of two fluids. Each fluid has its own velocity field and volume-fraction. A penalty method is used to enforce the condition that both fluids' velocities agree with that of the elastic boundaries. The method is applied to several problems: Taylor's swimming sheet problem for a mixture of two viscous fluids, peristaltic pumping of a mixture of two viscous fluids, with and without immersed particles, and peristaltic pumping of a mixture of a viscous fluid and a viscoelastic fluid. The swimming sheet and peristalsis problems have received much attention recently in the context of a single viscoelastic fluid. Numerical results demonstrate that the method converges and show its capability to handle a number of flow problems of substantial current interest. They illustrate that for each of these problems, the relative motion between the two fluids changes the observed behaviors profoundly...

Coordination of contractility, adhesion and flow in migrating Physarum amoebae

Mon, 17 Apr 2023 00:00:00 +0000

This work examines the relationship between spatio-temporal coordination of intracellular flow and traction stress and the speed of amoeboid locomotion of microplasmodia of Physarum polycephalum. We simultaneously perform particle image velocimetry and traction stress microscopy to measure the velocity of cytoplasmic flow and the stresses applied to the substrate by migrating Physarum microamoebae. In parallel, we develop a mathematical model of a motile cell which includes forces from the viscous cytosol, a poro-elastic, contractile cytoskeleton and adhesive interactions with the substrate. Our experiments show that flow and traction stress exhibit back-to-front-directed waves with a distinct phase difference. The model demonstrates that the direction and speed of locomotion are determined by this coordination between contraction, flow and adhesion. Using the model, we identify forms of coordination that generate model predictions consistent with experiments. We demonstrate that...

Actin-Myosin Spatial Patterns from a Simplified Isotropic Viscoelastic Model

Sat, 8 Apr 2023 00:00:00 +0000

F-actin networks are involved in cell mechanical processes ranging from motility to endocytosis. The mesoscale architecture of assemblies of individual F-actin polymers that gives rise to micrometer-scale rheological properties is poorly understood, despite numerous in vivo and vitro studies. In vitro networks have been shown to organize into spatial patterns when spatially confined, including dense spherical shells inside spherical emulsion droplets. Here we develop a simplified model of an isotropic, compressible, viscoelastic material continually assembling and disassembling. We demonstrate that spherical shells emerge naturally when the strain relaxation rate (corresponding to internal network reorganization) is slower than the disassembly rate (corresponding to F-actin depolymerization). These patterns are consistent with recent experiments, including a collapse of shells to a central high-density focus of F-actin when either assembly or disassembly is reduced with drugs....

Linear Algebra as an Introduction to Abstract Mathematics

Wed, 15 Feb 2023 00:00:00 +0000

Linear Algebra as an Introduction to Abstract Mathematics

Dissipation-Dependent Thermal Escape from a Potential Well

Sun, 9 Oct 2022 00:00:00 +0000

Langevin simulations are conducted to investigate the Josephson escape statistics over a large set of parameter values for damping and temperature. The results are compared to both Kramers and Büttiker-Harris-Landauer (BHL) models, and good agreement is found with the Kramers model for high to moderate damping, while the BHL model provides further good agreement down to lower damping values. However, for extremely low damping, even the BHL model fails to reproduce the progression of the escape statistics. In order to explain this discrepancy, we develop a new model which shows that the bias sweep effectively cools the system below the thermodynamic value as the potential well broadens due to the increasing bias. A simple expression for the temperature is derived, and the model is validated against direct Langevin simulations for extremely low damping values.

eGHWT: The Extended Generalized Haar–Walsh Transform

Wed, 22 Jun 2022 00:00:00 +0000

Extending computational harmonic analysis tools from the classical setting of regular lattices to the more general setting of graphs and networks is very important, and much research has been done recently. The generalized Haar–Walsh transform (GHWT) developed by Irion and Saito (2014) is a multiscale transform for signals on graphs, which is a generalization of the classical Haar and Walsh–Hadamard transforms. We propose the extended generalized Haar–Walsh transform (eGHWT), which is a generalization of the adapted time–frequency tilings of Thiele and Villemoes (1996). The eGHWT examines not only the efficiency of graph-domain partitions but also that of “sequency-domain” partitions simultaneously. Consequently, the eGHWT and its associated best-basis selection algorithm for graph signals significantly improve the performance of the previous GHWT with the similar computational cost, O(NlogN)$$O(N \log N)$$, where N is the number of nodes of an input graph. While the GHWT best-basis...

An evolving perspective on the dynamic brain: Notes from the Brain Conference on Dynamics of the brain: Temporal aspects of computation

Fri, 20 Aug 2021 00:00:00 +0000

An evolving perspective on the dynamic brain: Notes from the Brain Conference on Dynamics of the brain: Temporal aspects of computation

Robust parallel decision-making in neural circuits with nonlinear inhibition

Fri, 20 Aug 2021 00:00:00 +0000

An elemental computation in the brain is to identify the best in a set of options and report its value. It is required for inference, decision-making, optimization, action selection, consensus, and foraging. Neural computing is considered powerful because of its parallelism; however, it is unclear whether neurons can perform this max-finding operation in a way that improves upon the prohibitively slow optimal serial max-finding computation (which takes [Formula: see text] time for N noisy candidate options) by a factor of N, the benchmark for parallel computation. Biologically plausible architectures for this task are winner-take-all (WTA) networks, where individual neurons inhibit each other so only those with the largest input remain active. We show that conventional WTA networks fail the parallelism benchmark and, worse, in the presence of noise, altogether fail to produce a winner when N is large. We introduce the nWTA network, in which neurons are equipped with a second nonlinearity...

Natural Graph Wavelet Packet Dictionaries

Wed, 12 May 2021 00:00:00 +0000

We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their “dual” domains by incorporating the “natural” distances between graph Laplacian eigenvectors, rather than simply using the eigenvalue ordering. These basis dictionaries can be seen as generalizations of the classical Shannon wavelet packet dictionary to arbitrary graphs, and do not rely on the frequency interpretation of Laplacian eigenvalues. We describe the algorithms (involving either vector rotations or orthogonalizations) to construct these basis dictionaries, use them to efficiently approximate graph signals through the best basis search, and demonstrate the strengths of these basis dictionaries for graph signals measured on sunflower graphs and street networks.

Quantitative Study of the Chiral Organization of the Phage Genome Induced by the Packaging Motor

Tue, 5 Jan 2021 00:00:00 +0000

Molecular motors that translocate DNA are ubiquitous in nature. During morphogenesis of double-stranded DNA bacteriophages, a molecular motor drives the viral genome inside a protein capsid. Several models have been proposed for the three-dimensional 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...

Fine structure of viral dsDNA encapsidation

Tue, 4 Aug 2020 00:00:00 +0000

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 plank-shaped molecular compounds, we develop a first-principles 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...

Identification of Copy Number Aberrations in Breast Cancer Subtypes Using Persistence Topology