cssi/SciSciGPT-SciSciNet huggingface dataset:
DNA-binding studies of Cu(T4), a bulky cationic porphyrin

Abstract The potential for therapeutic applications has provided much of the impetus for investigating the DNA-binding interactions of cationic metalloporphyrins, but there are also signs of intriguing base and sequence dependences. More recent work has established that the stem regions of DNA hairpins are extremely useful as model duplexes. Mainly the focus has been on 16-mers with generic sequence 5′-GANNAC-NNNN-GTNNTC-3′, where the letters A, C, G, and T denote adenine, cytosine, guanine, and thymine nucleotides, respectively. N is the symbol for a variable nucleotide in the string; and the inner dashes enclose the loop sequence: TTTT, GTTA or GAAA. Because of its spectroscopic properties, the porphyrin of interest has been Cu(T4), the Cu(II) derivative of H 2 T4 (H 2 T4, meso -tetrakis (4-( N -methylpyridiniumyl))porphyrin). Spectral data have revealed that the hairpins retain their stem structures in the adducts with Cu(T4) and have provided important new insights into the interactions that occur. One is that the local rigidity of the DNA is the most important factor that shapes the binding. A run of DNA that includes at least 50% G C base pairs can support intercalative binding with or without contiguous G C base pairs in the sequence. As demonstrated by inosine-for-guanine base replacement experiments, the real pre-requisite for intercalative binding is a robust hydrogen bonding framework that overcomes the steric strain generated within the minor groove by pyridyl substituents pressing against the sugar–phosphate backbones. Cu(T4) binds externally to DNA that is richer in the more flexible A T base pairs. The intercalated form of Cu(T4) is unique in exhibiting an appreciable photoluminescence signal, and the intensity appears to increase with the rigidity of the overall DNA structure. Changes in the stability of the loop structure can perturb external binding interactions as indicated by the shape of the porphyrin's induced circular dichroism (CD) signal. However, the stem composition determines whether intercalation or external binding occurs, though these two adducts may actually be the limiting structures of a continuum of binding motifs. One technique rarely suffices to characterize an adduct but the combination of absorbance, emission and CD spectroscopies is very powerful.
Propellane as a conformational device for the stabilization of the β-lactone of salinosporamide A

The synthesis of a propellane derivative of salinosporamide A having increased stability under physiological-like conditions is reported. The synthesis took advantage of a substrate-controlled stereoselective Ugi 4-center 3-component reaction to construct the required syn-bicyclic pyroglutamic acid framework.
Synthesis and Reactivity of 4-(2-Chloro-5-nitrophenyl)-1,2,3-thiadiazole. A Novel One-pot Synthesis of N-Substituted Indole-2-thiols†

4-(2-Chloro-5-nitrophenyl)-1,2,3-thiadiazole undergoes ring opening to produce a thioketene intermediate that reacts with an O- or N-nucleophile, forming an ester or an amide of the aryl-substituted thioacetic acid. Intermolecular cyclization of the thioacetic acid derivative via nucleophilic substitution of halogen in the aromatic ring gives an N-substituted indole-2-thiol (in case of an N-nucleophile) or a 2-alkoxy-substituted benzo[b]thiophene (in case of an O-nucleophile). The reaction is also applicable to the synthesis of heterocyclic analogues of N-substituted indole-2-thiols: 1-butyl-1,3-dihydropyrrolo[2,3-b]pyridine-2-thione was synthesized as an example. In the presence of potassium thioacetate (an S-nucleophile) 4-nitro-2-(1,2,3-thiadiazol-4-yl)benzenethiol is formed more quickly than thiadiazole ring opening occurs, making the heterocyclic ring tolerant toward the base.
Enantio- and diastereoselective synthesis of β-substituted-δ-aminoboronic esters from nitriles

Abstract The first stereocontrolled synthesis of the title δ-aminoboronic esters—proceeding from commercially available nitriles—via a reduction, Brown’s ‘allyl’ boration reaction, a Boc-protection, a hydroboration, an oxidative elimination of α-pinene, and an esterification reaction, has been reported in excellent enantio- and diastereoselectivities.
A New Fluorous Methoxymethyl (FMOM) Protecting Group for Alcohols

A new fluorous analogue of the popular MOM (methoxymethyl) protecting group can be introduced by reactions of alcohols with 1H,1H,2H,2H,3H,3H-perfluoroundecyloxymethyl chloride (C8F17(CH2)3OCH2Cl) and the resulting fluorous methoxymethyl (FMOM) adducts can be deprotected under Bronsted or Lewis acidic conditions. The results suggest that the FMOM protecting group will find use in a number of fluorous synthesis settings.
Nonpolar residues in the presumptive pore-lining helix of mechanosensitive channel MSL10 influence channel behavior and establish a nonconducting function

Mechanosensitive (MS) ion channels provide a universal mechanism for sensing and responding to increased membrane tension. MscS-like (MSL) 10 is a relatively well-studied MS ion channel from Arabidopsis thaliana that is implicated in cell death signaling. The relationship between the amino acid sequence of MSL10 and its conductance, gating tension, and opening and closing kinetics remains unstudied. Here, we identify several nonpolar residues in the presumptive pore-lining transmembrane helix of MSL10 (TM6) that contribute to these basic channel properties. F553 and I554 are essential for wild type channel conductance and the stability of the open state. G556, a glycine residue located at a predicted kink in TM6, is essential for channel conductance. The increased tension sensitivity of MSL10 compared to close homolog MSL8 may be attributed to F563, but other channel characteristics appear to be dictated by more global differences in structure. Finally, MSL10 F553V and MSL10 G556V provided the necessary tools to establish that MSL10's ability to trigger cell death is independent of its ion channel function.
In Vitro Induction and In Vivo Engraftment of Lung Bud Tip Progenitor Cells Derived from Human Pluripotent Stem Cells

The current study aimed to understand the developmental mechanisms regulating bud tip progenitor cells in the human fetal lung, which are present during branching morphogenesis, and to use this information to induce a bud tip progenitor-like population from human pluripotent stem cells (hPSCs) in vitro. We identified cues that maintained isolated human fetal lung epithelial bud tip progenitor cells in vitro and induced three-dimensional hPSC-derived organoids with bud tip-like domains. Bud tip-like domains could be isolated, expanded, and maintained as a nearly homogeneous population. Molecular and cellular comparisons revealed that hPSC-derived bud tip-like cells are highly similar to native lung bud tip progenitors. hPSC-derived epithelial bud tip-like structures survived in vitro for over 16 weeks, could be easily frozen and thawed, maintained multilineage potential, and successfully engrafted into the airways of immunocompromised mouse lungs, where they persisted for up to 6 weeks and gave rise to several lung epithelial lineages.
GRep: Gene Set Representation via Gaussian Embedding

Molecular interaction networks are our basis for understanding functional interdependencies among genes. Network embedding approaches analyze these complicated networks by representing genes as low-dimensional vectors based on the network topology. These low-dimensional vectors have recently become the building blocks for a larger number of systems biology applications. Despite the success of embedding genes in this way, it remains unclear how to effectively represent gene sets, such as protein complexes and signaling pathways. The direct adaptation of existing gene embedding approaches to gene sets cannot model the diverse functions of genes in a set. Here, we propose GRep, a novel gene set embedding approach, which represents each gene set as a multivariate Gaussian distribution rather than a single point in the low-dimensional space. The diversity of genes in a set, or the uncertainty of their contribution to a particular function, is modeled by the covariance matrix of the multivariate Gaussian distribution. By doing so, GRep produces a highly informative and compact gene set representation. Using our representation, we analyze two major pharmacogenomics studies and observe substantial improvement in drug target identification from expression-derived gene sets. Overall, the GRep framework provides a novel representation of gene sets that can be used as input features to off-the-shelf machine learning classifiers for gene set analysis.
Structural Insights into Hearing Loss Genetics from Polarizable Protein Repacking.

Abstract Hearing loss is associated with ∼8100 mutations in 152 genes, and within the coding regions of these genes are over 60,000 missense variants. The majority of these variants are classified as “variants of uncertain significance” to reflect our inability to ascribe a phenotypic effect to the observed amino acid change. A promising source of pathogenicity information is biophysical simulation, although input protein structures often contain defects because of limitations in experimental data and/or only distant homology to a template. Here, we combine the polarizable atomic multipole optimized energetics for biomolecular applications force field, many-body optimization theory, and graphical processing unit acceleration to repack all deafness-associated proteins and thereby improve average structure MolProbity score from 2.2 to 1.0. We then used these optimized wild-type models to create over 60,000 structures for missense variants in the Deafness Variation Database, which are being incorporated into the Deafness Variation Database to inform deafness pathogenicity prediction. Finally, this work demonstrates that advanced polarizable atomic multipole force fields are efficient enough to repack the entire human proteome.
Deep Convolutional and Recurrent Neural Networks for Cell Motility Discrimination and Prediction

Cells in culture display diverse motility behaviors that may reflect differences in cell state and function, providing motivation to discriminate between different motility behaviors. Current methods to do so rely upon manual feature engineering. However, the types of features necessary to distinguish between motility behaviors can vary greatly depending on the biological context, and it is not always clear which features may be most predictive in each setting for distinguishing particular cell types or disease states. Convolutional neural networks (CNNs) are machine learning models allowing for relevant features to be learned directly from spatial data. Similarly, recurrent neural networks (RNNs) are a class of models capable of learning long term temporal dependencies. Given that cell motility is inherently spacio-temporal data, we present an approach utilizing both convolutional and long- short-term memory (LSTM) recurrent neural network units to analyze cell motility data. These RNN models provide accurate classification of simulated motility and experimentally measured motility from multiple cell types, comparable to results achieved with hand-engineered features. The variety of cell motility differences we can detect suggests that the algorithm is generally applicable to additional cell types not analyzed here. RNN autoencoders based on the same architecture are capable of learning motility features in an unsupervised manner and capturing variation between myogenic cells in the latent space. Adapting these RNN models to motility prediction, RNNs are capable of predicting muscle stem cell motility from past tracking data with performance superior to standard motion prediction models. This advance in cell motility prediction may be of practical utility in cell tracking applications.
Syntax-aware Neural Semantic Role Labeling with Supertags

We introduce a new syntax-aware model for dependency-based semantic role labeling that outperforms syntax-agnostic models for English and Spanish. We use a BiLSTM to tag the text with supertags extracted from dependency parses, and we feed these supertags, along with words and parts of speech, into a deep highway BiLSTM for semantic role labeling. Our model combines the strengths of earlier models that performed SRL on the basis of a full dependency parse with more recent models that use no syntactic information at all. Our local and non-ensemble model achieves state-of-the-art performance on the CoNLL 09 English and Spanish datasets. SRL models benefit from syntactic information, and we show that supertagging is a simple, powerful, and robust way to incorporate syntax into a neural SRL system.
Infinite server queueing networks with deadline based routing

Motivated by timeouts in Internet services, we consider networks of infinite server queues in which routing decisions are based on deadlines. Specifically, at each node in the network, the total service time equals the minimum of several independent service times (e.g. the minimum of the amount of time required to complete a transaction and a deadline). Furthermore, routing decisions depend on which of the independent service times achieves the minimum (e.g. exceeding a deadline will require the customer to be routed so they can re-attempt the transaction). Because current routing decisions are dependent on past service times, much of the existing theory on product-form queueing networks does not apply. In spite of this, we are able to show that such networks have product-form equilibrium distributions. We verify our analytic characterization with a simulation of a simple network. We also discuss extensions of this work to more general settings.
Equilibrium States for Expanding Thurston Maps

In this paper, we use the thermodynamical formalism to show that there exists a unique equilibrium state $${\mu_\phi}$$ for each expanding Thurston map $${f : S^2\rightarrow S^2}$$ together with a real-valued Holder continuous potential $${\phi}$$ . Here the sphere S2 is equipped with a natural metric induced by f, called a visual metric. We also prove that identical equilibrium states correspond to potentials that are co-homologous up to a constant, and that the measure-preserving transformation f of the probability space $${(S^2,\mu_\phi)}$$ is exact, and in particular, mixing and ergodic. Moreover, we establish versions of equidistribution of preimages under iterates of f, and a version of equidistribution of a random backward orbit, with respect to the equilibrium state. As a consequence, we recover various results in the literature for a postcritically-finite rational map with no periodic critical points on the Riemann sphere equipped with the chordal metric.
Rational points on certain families of symmetric equations

We generalize the work of Dem'janenko and Silverman for the Fermat quartics, effectively determining the rational points on the curves x2m + axm + aym + y2m = b whenever the ranks of some companion hyperelliptic Jacobians are at most one. As an application, we explicitly describe Xd(ℚ) for certain d ≥ 3, where Xd : Td(x) + Td(y) = 1 and Td is the monic Chebychev polynomial of degree d. Moreover, we show how this later problem relates to orbit intersection problems in dynamics. Finally, we construct a new family of genus 3 curves which break the Hasse principle, assuming the parity conjecture, by specifying our results to quadratic twists of x4 - 4x2 - 4y2 + y4 = -6.
Evolutionary Multi-objective Optimization of Real-Time Strategy Micro

We investigate an evolutionary multi-objective approach to generating micro for real-time strategy games. Good micro helps a player win skirmishes and is one of the keys to developing better real-time strategy game play. In prior work, the same multi-objective approach of maximizing damage done while minimizing damage received was used to evolve micro for a group of ranged units versus a group of melee units. We extend this work to consider groups composed from two types of units. Specifically, this paper uses evolutionary multi-objective optimization to generate micro for one group composed from both ranged and melee units versus another group of ranged and melee units. Our micro behavior representation uses influence maps to represent enemy spatial information and potential fields generated from distance, health, and weapons cool down to guide unit movement. Experimental results indicate that our multi-objective approach leads to a Pareto front of diverse high-quality micro encapsulating multiple possible tactics. This range of micro provided by the Pareto front enables a human or AI player to trade-off among short term tactics that better suit the player’s longer term strategy - for example, choosing to minimize friendly unit damage at the cost of only lightly damaging the enemy versus maximizing damage to the enemy units at the cost of increased damage to friendly units. We believe that our results indicate the usefulness of potential fields as a representation, and of evolutionary multi-objective optimization as an approach, for generating micro.
A PI degree theorem for quantum deformations

Abstract We prove that if a filtered quantization A of a finitely generated commutative domain over a field k is a PI algebra, then A is commutative if char ( k ) = 0 , and its PI degree is a power of p if char ( k ) = p .
Non-linear ground state representations and sharp Hardy inequalities

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.
Online Optimization as a Feedback Controller: Stability and Tracking

This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the algorithm is based on continuous-time primal-dual dynamics, properly modified to incorporate feedback from the LTI dynamical system, applied to a proximal augmented Lagrangian function. The resultant closed-loop algorithm tracks the solution of the time-varying optimization problem without requiring knowledge of (time varying) disturbances in the dynamical system. The analysis leverages integral quadratic constraints to provide linear matrix inequality (LMI) conditions that guarantee global exponential stability and bounded tracking error. Analytical results show that under a sufficient time-scale separation between the dynamics of the LTI dynamical system and the algorithm, the LMI conditions can be always satisfied. This paper further proposes a modified algorithm that can track an approximate solution trajectory of the constrained optimization problem under less restrictive assumptions. As an illustrative example, the proposed algorithms are showcased for power transmission systems, to compress the time scales between secondary and tertiary control, and allow to simultaneously power rebalancing and tracking of the DC optimal power flow points.
Repulsive behavior in an exceptional family

The existence of a Landau-Siegel zero leads to the Deuring-Heilbronn phenomenon, here appearing in the 1-level density in a family of quadratic twists of a fixed genus character L-function. We obtain explicit lower order terms describing the vertical distribution of the zeros, and realize the influence of the Landau-Siegel zero as a resonance phenomenon.
Pseudo-wigner matrices from dual BCH codes

We consider the problem of generating symmetric pseudo-random sign (±1) matrices based on the similarity of their spectra to Wigner's semicircular law. We introduce r-independent pseudo-Wigner ensembles and prove closeness of their spectra to the semicircular density in Kolmogorov distance. We give an explicit construction of a family of N × N pseudo-Wigner ensembles using dual BCH codes and show that the Kolmogorov complexity of the obtained matrices is of the order of log (N) bits for a fixed Kolmogorov distance precision. Finally, we provide numerical simulations verifying our theoretical results.
Nearest neighbor Markov dynamics on Macdonald processes

Abstract Macdonald processes are certain probability measures on two-dimensional arrays of interlacing particles introduced by Borodin and Corwin in [7] . They are defined in terms of nonnegative specializations of the Macdonald symmetric functions and depend on two parameters q , t ∈ [ 0 ; 1 ) . Our main result is a classification of continuous time, nearest neighbor Markov dynamics on the space of interlacing arrays that act nicely on Macdonald processes. The classification unites known examples of such dynamics and also yields many new ones. When t = 0 , one dynamics leads to a new integrable interacting particle system on the one-dimensional lattice, which is a q-deformation of the PushTASEP (= long-range TASEP). When q = t , the Macdonald processes become the Schur processes of Okounkov and Reshetikhin [41] . In this degeneration, we discover new Robinson–Schensted-type correspondences between words and pairs of Young tableaux that govern some of our dynamics.
Bayesian representation learning with oracle constraints

Abstract: Representation learning systems typically rely on massive amounts of labeled data in order to be trained to high accuracy. Recently, high-dimensional parametric models like neural networks have succeeded in building rich representations using either compressive, reconstructive or supervised criteria. However, the semantic structure inherent in observations is oftentimes lost in the process. Human perception excels at understanding semantics but cannot always be expressed in terms of labels. Thus, \emph{oracles} or \emph{human-in-the-loop systems}, for example crowdsourcing, are often employed to generate similarity constraints using an implicit similarity function encoded in human perception. In this work we propose to combine \emph{generative unsupervised feature learning} with a \emph{probabilistic treatment of oracle information like triplets} in order to transfer implicit privileged oracle knowledge into explicit nonlinear Bayesian latent factor models of the observations. We use a fast variational algorithm to learn the joint model and demonstrate applicability to a well-known image dataset. We show how implicit triplet information can provide rich information to learn representations that outperform previous metric learning approaches as well as generative models without this side-information in a variety of predictive tasks. In addition, we illustrate that the proposed approach compartmentalizes the latent spaces semantically which allows interpretation of the latent variables.
Resolving dark matter subhalos with future sub-GeV gamma-ray telescopes

Abstract Annihilating dark matter particles in nearby subhalos could generate potentially observable fluxes of gamma rays, unaccompanied by emission at other wavelengths. Furthermore, this gamma-ray emission is expected to be spatially extended, providing us with a powerful way to discriminate dark matter subhalos from other astrophysical gamma-ray sources. Fermi has detected two dark matter subhalo candidates which exhibit a statistically significant degree of spatial extension (3FGL J2212.5+0703 and 3FGL J1924.8-1034). It has been argued that the most likely non-dark matter interpretation of these observations is that they are each in fact multiple nearby point sources, too close to one another on the sky to be individually resolved. In this study, we consider the ability of next generation gamma-ray telescopes to spatially resolve the gamma-ray emission from subhalo candidates, focusing on the proposed e-ASTROGAM mission. We find that such an instrument could significantly clarify the nature of Fermi’s dark matter subhalo candidates, and provide an unprecedented level of sensitivity to the presence of annihilating dark matter in nearby subhalos.
Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds

We prove the existence of Kolmogorov-Petrovsky-Piskunov (KPP) type traveling fronts in space-time periodic and mean zero incompressible advection, and establish a variational (minimization) formula for the minimal speeds. We approach the existence by considering limit of a sequence of front solutions to a regularized traveling front equation where the nonlinearity is combustion type with ignition cut-off. The limiting front equation is degenerate parabolic and does not permit strong solutions, however, the necessary compactness follows from monotonicity of fronts and degenerate regularity. We apply a dynamic argument to justify that the constructed KPP traveling fronts propagate at minimal speeds, and derive the speed variational formula. The dynamic method avoids the degeneracy in traveling front equations, and utilizes the parabolic maximum principle of the governing reaction-diffusion-advection equation. The dynamic method does not rely on existence of traveling fronts.
Coxeter group actions on 4F3(1) hypergeometric series

In this paper we investigate a certain linear combination $K(\vec{x})=K(a;b,c,d;e,f,g)$ of two Saalschutzian hypergeometric series of type 4 F 3(1). We first show that $K(\vec{x})$ is invariant under the action of a certain matrix group G K , isomorphic to the symmetric group S 6, acting on the affine hyperplane V={(a,b,c,d,e,f,g)∈ℂ7:e+f+g−a−b−c−d=1}. We further develop an algebra of three-term relations for K(a;b,c,d;e,f,g). We show that, for any three elements μ 1,μ 2,μ 3 of a certain matrix group M K , isomorphic to the Coxeter group W(D 6) (of order 23040) and containing the above group G K , there is a relation among $K(\mu_{1}\vec{x})$ , $K(\mu_{2}\vec{x})$ , and $K(\mu_{3}\vec{x})$ , provided that no two of the μ j ’s are in the same right coset of G K in M K . The coefficients in these three-term relations are seen to be rational combinations of gamma and sine functions in a,b,c,d,e,f,g. The set of $\bigl({|M_{K}|/|G_{K}|\atop3}\bigr)=\bigl({32\atop3}\bigr)=4960$ resulting three-term relations may further be partitioned into five subsets, according to the Hamming type of the triple (μ 1,μ 2,μ 3) in question. Each three-term relation of a given Hamming type may be transformed into any other of the same type by a change of variable. An explicit example of each of the five types of three-term relations is provided. It is seen that the number of monomials constituting the coefficient of a given K function, in a given three-term relation, increases geometrically with the Hamming distance between the other two K functions in that relation. Two-term and three-term relations for a certain different linear combination of Saalschutzian 4 F 3(1) series have been studied elsewhere, by Whipple, Raynal, and others. Coxeter group theory allows us to highlight the structural differences between those situations and the present one, and generally provides for enhanced insight into the phenomenon of relations among hypergeometric series. Further, previously established relations among terminating, Saalschutzian 4 F 3(1) series, and among not necessarily Saalschutzian 3 F 2(1) series, are seen to arise in straightforward ways as limits of the relations developed in this paper.
For high-precision bosonic Josephson junctions, many-body effects matter

Typical treatments of superconducting or superfluid Josephson junctions rely on mean-field or two-mode models; we explore many-body dynamics of an isolated, ultracold, Bose-gas long Josephson junction using time-evolving block decimation simulations. We demonstrate that with increasing repulsive interaction strength, localized dynamics emerge that influence macroscopic condensate behavior and can lead to formation of solitons that directly oppose the symmetry of the junction. Initial state population and phase yield insight into dynamic tunneling regimes of a quasi one-dimensional double well potential, from Josephson oscillations to macroscopic self-trapping. Population imbalance simulations reveal substantial deviation of many-body dynamics from mean-field Gross-Pitaevskii predictions, particularly as the barrier height and interaction strength increase. In addition, the sudden approximation supports localized particle-hole formation after a diabatic quench, and correlation measures unveil a new dynamic regime: the Fock flashlight.
Polynomial factorization over finite fields by computing Euler–Poincaré characteristics of Drinfeld modules

Abstract We propose and rigorously analyze two randomized algorithms to factor univariate polynomials over finite fields using rank 2 Drinfeld modules. The first algorithm estimates the degree of an irreducible factor of a polynomial from Euler–Poincare characteristics of random Drinfeld modules. Knowledge of a factor degree allows one to rapidly extract all factors of that degree. As a consequence, the problem of factoring polynomials over finite fields in time nearly linear in the degree is reduced to finding Euler–Poincare characteristics of random Drinfeld modules with high probability. The second algorithm is a random Drinfeld module analogue of Berlekamp's algorithm. During the course of its analysis, we prove a new bound on degree distributions in factorization patterns of polynomials over finite fields in certain short intervals.
Bruhat graphs and pattern avoidance

We characterize permutations whose Bruhat graphs can be drawn in the plane and those whose Bruhat graphs can be drawn in the torus. In particular, we show these properties are characterized by avoiding finitely many permutations.
Quasi-splines and their moduli

Abstract We study what we call quasi-spline sheaves over locally Noetherian schemes. This is done with the intention of considering splines from the point of view of moduli theory. In other words, we study the way in which certain objects that arise in the theory of splines can be made to depend on parameters. In addition to quasi-spline sheaves, we treat ideal difference-conditions, and individual quasi-splines. Under certain hypotheses each of these types of objects admits a fine moduli scheme. The moduli of quasi-spline sheaves are proper, and there is a natural compactification of the moduli of ideal difference-conditions. We include some speculation on the uses of these moduli in the theory of splines and topology, and an appendix with a treatment of the Billera–Rose homogenization in scheme theoretic language.
A Supermodular Optimization Framework for Leader Selection Under Link Noise in Linear Multi-Agent Systems

In many applications of multi-agent systems (MAS), a set of leader agents acts as control inputs to the remaining follower agents. In this paper, we introduce an analytical approach to selecting leader agents in order to minimize the total mean-square error of the follower agent states from their desired value in steady-state in the presence of noisy communication links. We show that, for a set of link weights based on the second-order noise statistics, the problem of choosing leaders in order to minimize this error can be solved using supermodular optimization techniques, leading to efficient algorithms that are within a provable bound of the optimum. We formulate two leader selection problems within our framework, namely the problem of choosing a fixed number of leaders to minimize the error, as well as the problem of choosing the minimum number of leaders to achieve a tolerated level of error. We study both leader selection criteria for different scenarios, including MAS with static topologies, topologies experiencing random link or node failures, switching topologies, and topologies that vary arbitrarily in time due to node mobility. In addition to providing provable bounds for all of these cases, simulation results demonstrate that our approach outperforms other leader selection methods, such as node degree-based and random selection methods, and provides comparable performance to current state of the art algorithms.
Towards a Better Approximation for Sparsest Cut

We give a new (1 + e)-approximation for SPARSEST CUT problem on graphs where small sets expand significantly more than the sparsest cut (expansion of sets of size n/r exceeds that of the sparsest cut by a factor √log n log r, for some small r; this condition holds for many natural graph families). We give two different algorithms. One involves Guruswami-Sinop rounding on the level-r Lasserre relaxation. The other is combinatorial and involves a new notion called Small Set Expander Flows (inspired by the expander flows of [1]) which we show exists in the input graph. Both algorithms run in time 2O(r)poly(n). We also show similar approximation algorithms in graphs with genus g with an analogous local expansion condition. This is the first algorithm we know of that achieves (1 + e)-approximation on such general family of graphs.
Detangling People: Individuating Multiple Close People and Their Body Parts via Region Assembly

Todays person detection methods work best when people are in common upright poses and appear reasonably well spaced out in the image. However, in many real images, thats not what people do. People often appear quite close to each other, e.g., with limbs linked or heads touching, and their poses are often not pedestrian-like. We propose an approach to detangle people in multi-person images. We formulate the task as a region assembly problem. Starting from a large set of overlapping regions from body part semantic segmentation and generic object proposals, our optimization approach reassembles those pieces together into multiple person instances. Since optimal region assembly is a challenging combinatorial problem, we present a Lagrangian relaxation method to accelerate the lower bound estimation, thereby enabling a fast branch and bound solution for the global optimum. As output, our method produces a pixel-level map indicating both 1) the body part labels (arm, leg, torso, and head), and 2) which parts belong to which individual person. Our results on challenging datasets show our method is robust to clutter, occlusion, and complex poses. It outperforms a variety of competing methods, including existing detector CRF methods and region CNN approaches. In addition, we demonstrate its impact on a proxemics recognition task, which demands a precise representation of whose body part is where in crowded images.
Homology over trivial extensions of commutative DG algebras

AbstractConditions on the Koszul complex of a noetherian local ring R guarantee that ToriR(M,N) is nonzero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.
Commensurability Classes of Fake Quadrics

A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the commensurability class of their fundamental group. To accomplish this task, we develop a number of new techniques that explicitly bound the arithmetic invariants of a fake quadric and more generally of an arithmetic manifold of bounded volume arising from a form of $${{\,\mathrm{SL}\,}}_2$$ over a number field.
Shirtless and Dangerous: Quantifying Linguistic Signals of Gender Bias in an Online Fiction Writing Community.

Imagine a princess asleep in a castle, waiting for her prince to slay the dragon and rescue her. Tales like the famous Sleeping Beauty clearly divide up gender roles. But what about more modern stories, borne of a generation increasingly aware of social constructs like sexism and racism? Do these stories tend to reinforce gender stereotypes, or counter them? In this paper, we present a technique that combines natural language processing with a crowdsourced lexicon of stereotypes to capture gender biases in fiction. We apply this technique across 1.8 billion words of fiction from the Wattpad online writing community, investigating gender representation in stories, how male and female characters behave and are described, and how authors' use of gender stereotypes is associated with the community's ratings. We find that male over-representation and traditional gender stereotypes (e.g., dominant men and submissive women) are common throughout nearly every genre in our corpus. However, only some of these stereotypes, like sexual or violent men, are associated with highly rated stories. Finally, despite women often being the target of negative stereotypes, female authors are equally likely to write such stereotypes as men.
DID: Distributed Incremental Block Coordinate Descent for Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) has attracted much attention in the last decade as a dimension reduction method in many applications. Due to the explosion in the size of data, naturally the samples are collected and stored distributively in local computational nodes. Thus, there is a growing need to develop algorithms in a distributed memory architecture. We propose a novel distributed algorithm, called distributed incremental block coordinate descent (DID), to solve the problem. By adapting the block coordinate descent framework, closed-form update rules are obtained in DID. Moreover, DID performs updates incrementally based on the most recently updated residual matrix. As a result, only one communication step per iteration is required. The correctness, efficiency, and scalability of the proposed algorithm are verified in a series of numerical experiments.
The Core Consistency of a Compressed Tensor

Tensor decomposition on big data has attracted significant attention recently. Among the most popular methods is a class of algorithms that leverages compression in order to reduce the size of the tensor and potentially parallelize computations. A fundamental requirement for such methods to work properly is that the low-rank tensor structure is retained upon compression. In lieu of efficient and realistic means of computing and studying the effects of compression on the low rank of a tensor, we study the effects of compression on the core consistency; a widely used heuristic that has been used as a proxy for estimating that low rank. We provide theoretical analysis, where we identify sufficient conditions for the compression such that the core consistency is preserved, and we conduct extensive experiments that validate our analysis. Further, we explore popular compression schemes and how they affect the core consistency.
Crosscap numbers and the Jones polynomial

Abstract We give sharp two-sided linear bounds of the crosscap number (non-orientable genus) of alternating links in terms of their Jones polynomial. Our estimates are often exact and we use them to calculate the crosscap numbers for several infinite families of alternating links and for several alternating knots with up to twelve crossings. We also discuss generalizations of our results for classes of non-alternating links.
Deterministic non-autoregressive neural sequence modeling by iterative refinement

We propose a conditional non-autoregressive neural sequence model based on iterative refinement. The proposed model is designed based on the principles of latent variable models and denoising autoencoders, and is generally applicable to any sequence generation task. We extensively evaluate the proposed model on machine translation (En-De and En-Ro) and image caption generation, and observe that it significantly speeds up decoding while maintaining the generation quality comparable to the autoregressive counterpart.
2-plectic geometry, Courant algebroids, and categorified prequantization

A 2-plectic manifold is a manifold equipped with a closed nondegenerate 3-form, just as a symplectic manifold is equipped with a closed nondegenerate 2-form. In 2-plectic geometry one finds the higher analogues of many structures familiar from symplectic geometry. For example, any 2-plectic manifold has a Lie 2-algebra consisting of smooth functions and Hamiltonian 1-forms. This is equipped with a Poisson-like bracket which only satisfies the Jacobi identity up to “coherent chain homotopy”. Over any 2-plectic manifold is a vector bundle equipped with extra structure called an exact Courant algebroid. This Courant algebroid is the 2-plectic analogue of a transitive Lie algebroid over a symplectic manifold. Its space of global sections also forms a Lie 2-algebra. We show that this Lie 2-algebra contains an important sub-Lie 2-algebra which is isomorphic to the Lie 2-algebra of Hamiltonian 1-forms. Furthermore, we prove that it is quasi-isomorphic to a central extension of the (trivial) Lie 2-algebra of Hamiltonian vector fields, and therefore is the higher analogue of the well-known Kostant–Souriau central extension in symplectic geometry. We interpret all of these results within the context of a categorified prequantization procedure for 2-plectic manifolds. In doing so, we describe how $U(1)$-gerbes, equipped with a connection and curving, and Courant algebroids are the 2-plectic analogues of principal $U(1)$ bundles equipped with a connection and their associated Atiyah Lie algebroids.
The atomic hypothesis

A review is presented of the origin and development of the atomic hypothesis from antiquity till about the first millennium of the common era.
The Jacquet-Langlands correspondence, Eisenstein congruences, and integral L-values in weight 2

We use the Jacquet-Langlands correspondence to generalize well-known congruence results of Mazur on Fourier coefficients and L-values of elliptic modular forms for prime level in weight 2 both to nonsquare level and to Hilbert modular forms.
Cohen-Lenstra heuristics and local conditions

We prove function field theorems supporting the Cohen–Lenstra heuristics for real quadratic fields, and natural strengthenings of these analogs from the affine class group to the Picard group of the associated curve. Our function field theorems also support a conjecture of Bhargava on how local conditions on the quadratic field do not affect the distribution of class groups. Our results lead us to make further conjectures refining the Cohen–Lenstra heuristics, including on the distribution of certain elements in class groups. We prove instances of these conjectures in the number field case. Our function field theorems use a homological stability result of Ellenberg, Venkatesh, and Westerland.
A quorum sensing inspired algorithm for dynamic clustering

Quorum sensing is a decentralized biological process, through which a community of cells with no global awareness coordinate their functional behaviors based only on cell-medium interactions and local decisions. This paper draws inspiration from quorum sensing and colony competition to derive a new algorithm for data clustering. The algorithm treats each data as a single cell, and uses knowledge of local connectivity to cluster cells into multiple colonies simultaneously. It simulates auto-inducers secretion in quorum sensing to tune the influence radius for each cell. At the same time, sparsely distributed core cells spread their influences to form colonies, and interactions between colonies eventually determine each cell's identity. The algorithm has the flexibility to analyze both static and time-varying data, and its stability and convergence properties are established. The algorithm is tested on several applications, including both synthetic and real benchmarks datasets, alleles clustering, dynamic systems grouping and model identification. Although the algorithm is originally motivated by curiosity about biology-inspired computation, the results suggests that in parallel implementation it performs as well as state-of-the art methods on static data, while showing promising performance on time-varying data such as e.g. clustering robotic swarms.
Capture of planets into mean-motion resonances and the origins of extrasolar orbital architectures

The early stages of dynamical evolution of planetary systems are often shaped by dissipative processes that drive orbital migration. In multi-planet systems, convergent amassing of orbits inevitably leads to encounters with rational period ratios, which may result in establishment of mean-motion resonances. The success or failure of resonant capture yields exceedingly different subsequent evolutions, and thus plays a central role in determining the ensuing orbital architecture of planetary systems. In this work, we employ an integrable Hamiltonian formalism for first order planetary resonances that allows both secondary bodies to have finite masses and eccentricities, and construct a comprehensive theory for resonant capture. Particularly, we derive conditions under which orbital evolution lies within the adiabatic regime, and provide a generalized criterion for guaranteed resonant locking as well as a procedure for calculating capture probabilities when capture is not certain. Subsequently, we utilize the developed analytical model to examine the evolution of Jupiter and Saturn within the protosolar nebula, and investigate the origins of the dominantly non-resonant orbital distribution of sub-Jovian extrasolar planets. Our calculations show that the commonly observed extrasolar orbital structure can be understood if planet pairs encounter mean-motion commensurabilities on slightly eccentric (e ~ 0.02) orbits. Accordingly, we speculate that resonant capture among low-mass planets is typically rendered unsuccessful due to subtle axial asymmetries inherent to the global structure of protoplanetary discs.
Resolution depth of positive braids

The depth of a link measures the minimum height of a resolving tree for the link whose leaves are all unlinks. We show that the depth of the closure of a strictly positive braid word is the length of the word minus the number of distinct letters.
Tridiagonal Substitution Hamiltonians

We consider a family of discrete Jacobi operators on the one-dimensional integer lattice with Laplacian and potential terms modulated by a primitive invertible two-letter substitution. We investigate the spectrum and the spectral type, the fractal structure and fractal dimensions of the spectrum, exact dimensionality of the integrated density of states, and the gap structure. We present a review of previous results, some applications, and open problems. Our investigation is based largely on the dynamics of trace maps. This work is an extension of similar results on Schrodinger operators, although some of the results that we obtain differ qualitatively and quantitatively from those for the Schrodinger operators. The nontrivialities of this extension lie in the dynamics of the associated trace map as one attempts to extend the trace map formalism from the Schrodinger cocycle to the Jacobi one. In fact, the Jacobi operators considered here are, in a sense, a test item, as many other models can be attacked via the same techniques, and we present an extensive discussion on this.
Gromov-Wasserstein Learning for Graph Matching and Node Embedding.

A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and find their correspondence, according to the learned optimal transport. The node embeddings associated with the two graphs are learned under the guidance of the optimal transport, the distance of which not only reflects the topological structure of each graph but also yields the correspondence across the graphs. These two learning steps are mutually-beneficial, and are unified here by minimizing the Gromov-Wasserstein discrepancy with structural regularizers. This framework leads to an optimization problem that is solved by a proximal point method. We apply the proposed method to matching problems in real-world networks, and demonstrate its superior performance compared to alternative approaches.