cssi/SciSciGPT-SciSciNet huggingface dataset:
Local structures on stratified spaces

Abstract We develop a theory of conically smooth stratified spaces and their smooth moduli, including a notion of classifying maps for tangential structures. We characterize continuous space-valued sheaves on these conically smooth stratified spaces in terms of tangential data, and we similarly characterize 1-excisive invariants of stratified spaces. These results are based on the existence of open handlebody decompositions for conically smooth stratified spaces, an inverse function theorem, a tubular neighborhood theorem, an isotopy extension theorem, and functorial resolutions of singularities to smooth manifolds with corners.
Learning Cognitive Models Using Neural Networks

A cognitive model of human learning provides information about skills a learner must acquire to perform accurately in a task domain. Cognitive models of learning are not only of scientific interest, but are also valuable in adaptive online tutoring systems. A more accurate model yields more effective tutoring through better instructional decisions. Prior methods of automated cognitive model discovery have typically focused on well-structured domains, relied on student performance data or involved substantial human knowledge engineering. In this paper, we propose Cognitive Representation Learner (CogRL), a novel framework to learn accurate cognitive models in ill-structured domains with no data and little to no human knowledge engineering. Our contribution is two-fold: firstly, we show that representations learnt using CogRL can be used for accurate automatic cognitive model discovery without using any student performance data in several ill-structured domains: Rumble Blocks, Chinese Character, and Article Selection. This is especially effective and useful in domains where an accurate human-authored cognitive model is unavailable or authoring a cognitive model is difficult. Secondly, for domains where a cognitive model is available, we show that representations learned through CogRL can be used to get accurate estimates of skill difficulty and learning rate parameters without using any student performance data. These estimates are shown to highly correlate with estimates using student performance data on an Article Selection dataset.
Probabilistic human mobility model in indoor environment

Understanding human mobility is important for the development of intelligent mobile service robots as it can provide prior knowledge and predictions of human distribution for robot-assisted activities. In this paper, we propose a probabilistic method to model human motion behaviors which is determined by both internal and external factors in an indoor environment. While the internal factors are represented by the individual preferences, aims and interests, the external factors are indicated by the stimulation of the environment. We model the randomness of human macro-level movement, e.g., the probability of visiting a specific place and staying time, under the Bayesian framework, considering the influence of both internal and external variables. We use two case studies in a shopping mall and in a college student dorm building to show the effectiveness of our proposed probabilistic human mobility model. Real surveillance camera data are used to validate the proposed model together with survey data in the case study of student dorm.
Cluster fans, stability conditions, and domains of semi-invariants

We show that the cone of finite stability conditions of a quiver Q without oriented cycles has a fan covering given by (the dual of) the cluster fan of Q. Along the way, we give new proofs of Schofield's results (1991) on perpendicular categories. From our results, we recover Igusa-Orr-Todorov-Weyman's theorem on cluster complexes and domains of semi-invariants for Dynkin quivers. For arbitrary quivers, we also give a description of the domains of semi-invariants labeled by real Schur roots in terms of quiver exceptional sets.
IntLIM: integration using linear models of metabolomics and gene expression data.

Integration of transcriptomic and metabolomic data improves functional interpretation of disease-related metabolomic phenotypes, and facilitates discovery of putative metabolite biomarkers and gene targets. For this reason, these data are increasingly collected in large (> 100 participants) cohorts, thereby driving a need for the development of user-friendly and open-source methods/tools for their integration. Of note, clinical/translational studies typically provide snapshot (e.g. one time point) gene and metabolite profiles and, oftentimes, most metabolites measured are not identified. Thus, in these types of studies, pathway/network approaches that take into account the complexity of transcript-metabolite relationships may neither be applicable nor readily uncover novel relationships. With this in mind, we propose a simple linear modeling approach to capture disease-(or other phenotype) specific gene-metabolite associations, with the assumption that co-regulation patterns reflect functionally related genes and metabolites. The proposed linear model, metabolite ~ gene + phenotype + gene:phenotype, specifically evaluates whether gene-metabolite relationships differ by phenotype, by testing whether the relationship in one phenotype is significantly different from the relationship in another phenotype (via a statistical interaction gene:phenotype p-value). Statistical interaction p-values for all possible gene-metabolite pairs are computed and significant pairs are then clustered by the directionality of associations (e.g. strong positive association in one phenotype, strong negative association in another phenotype). We implemented our approach as an R package, IntLIM, which includes a user-friendly R Shiny web interface, thereby making the integrative analyses accessible to non-computational experts. We applied IntLIM to two previously published datasets, collected in the NCI-60 cancer cell lines and in human breast tumor and non-tumor tissue, for which transcriptomic and metabolomic data are available. We demonstrate that IntLIM captures relevant tumor-specific gene-metabolite associations involved in known cancer-related pathways, including glutamine metabolism. Using IntLIM, we also uncover biologically relevant novel relationships that could be further tested experimentally. IntLIM provides a user-friendly, reproducible framework to integrate transcriptomic and metabolomic data and help interpret metabolomic data and uncover novel gene-metabolite relationships. The IntLIM R package is publicly available in GitHub ( https://github.com/mathelab/IntLIM ) and includes a user-friendly web application, vignettes, sample data and data/code to reproduce results.
Efficient Neural Network Robustness Certification with General Activation Functions

Finding minimum distortion of adversarial examples and thus certifying robustness in neural networks classifiers is known to be a challenging problem. Nevertheless, recently it has been shown to be possible to give a non-trivial certified lower bound of minimum distortion, and some recent progress has been made towards this direction by exploiting the piece-wise linear nature of ReLU activations. However, a generic robustness certification for \textit{general} activation functions still remains largely unexplored. To address this issue, in this paper we introduce CROWN, a general framework to certify robustness of neural networks with general activation functions. The novelty in our algorithm consists of bounding a given activation function with linear and quadratic functions, hence allowing it to tackle general activation functions including but not limited to the four popular choices: ReLU, tanh, sigmoid and arctan. In addition, we facilitate the search for a tighter certified lower bound by \textit{adaptively} selecting appropriate surrogates for each neuron activation. Experimental results show that CROWN on ReLU networks can notably improve the certified lower bounds compared to the current state-of-the-art algorithm Fast-Lin, while having comparable computational efficiency. Furthermore, CROWN also demonstrates its effectiveness and flexibility on networks with general activation functions, including tanh, sigmoid and arctan.
A Note on Reductions Between Compressed Sensing Guarantees

In compressed sensing, one wishes to acquire an approximately sparse high-dimensional signal $x\in \mathbb{R}^{n}$ via $m\ll n$ noisy linear measurements, then later approximately recover $x$ given only those measurement outcomes. Various guarantees have been studied in terms of the notion of approximation in recovery, and some isolated folklore results are known stating that some forms of recovery are stronger than others, via black-box reductions. In this note we provide a general theorem concerning the hierarchy of strengths of various recovery guarantees. As a corollary of this theorem, by reducing from well-known results in the compressed sensing literature, we obtain an efficient $\ell_{p}/\ell_{p}$ scheme for any $0 with the fewest number of measurements currently known amongst efficient schemes, improving recent bounds of [1] and with a simpler algorithm and analysis.
Hypergeometric type identities in the $p$-adic setting and modular forms

We prove hypergeometric type identities for a function defined in terms of quotients of the $p$-adic gamma function. We use these identities to prove a supercongruence conjecture of Rodriguez-Villegas between a truncated $_4F_3$ hypergeometric series and the Fourier coefficients of certain weight four modular form.
Blocking avoidance in transportation systems

The blocking problem naturally arises in transportation systems as multiple vehicles with different itineraries share available resources. In this paper, we investigate the impact of the blocking problem to the waiting time at the intersections of transportation systems. We assume that different vehicles, depending on their Internet connection capabilities, may communicate their intentions (e.g., whether they will turn left or right or continue straight) to intersections (specifically to devices attached to traffic lights). We consider that information collected by these devices are transmitted to and processed in a cloud-based traffic control system. Thus, a cloud-based system, based on the intention information, can calculate average waiting times at intersections. We consider this problem as a queuing model, and we characterize average waiting times by taking into account (i) blocking probability, and (ii) vehicles' ability to communicate their intentions. Then, by using average waiting times at intersection, we develop a shortest delay algorithm that calculates the routes with shortest delays between two points in a transportation network. Our simulation results confirm our analysis, and demonstrate that our shortest delay algorithm significantly improves over baselines that are unaware of the blocking problem.
Asymptotics for the partial fractions of the restricted partition generating function I

The generating function for pN(n), the number of partitions of n into at most N parts, may be written as a product of N factors. We find the behavior of coefficients in the partial fraction decomposition of this product as N → ∞ by applying the saddle-point method, where the saddle-point we need is associated to a zero of the analytically continued dilogarithm. Our main result disproves a conjecture of Rademacher.
Linear stability of compressible vortex sheets in two-dimensional elastodynamics

Abstract The linear stability of rectilinear compressible vortex sheets is studied for two-dimensional isentropic elastic flows. This problem has a free boundary and the boundary is characteristic. A necessary and sufficient condition is obtained for the linear stability of the rectilinear vortex sheets. More precisely, it is shown that, besides the stable supersonic zone, the elasticity exerts an additional stable subsonic zone. We also find that there is a class of states in the interior of subsonic zone where the stability of such states is weaker than the stability of other states in the sense that there is an extra loss of tangential derivatives with respect to the source terms. This is a new feature that the Euler flow does not possess. One of the difficulties for the elastic flow is that the non-differentiable points of the eigenvalues may coincide with the roots of the Lopatinskii determinant. As a result, the Kreiss symmetrization cannot be applied directly. Instead, we perform an upper triangularization of the system to separate only the outgoing modes at all points in the frequency space, so that an exact estimate of the outgoing modes can be obtained. Moreover, all the outgoing modes are shown to be zero due to the L 2 -regularity of solutions. The estimates for the incoming modes can be derived directly from the Lopatinskii determinant. This new approach avoids the lengthy computation and estimates for the outgoing modes when Kreiss symmetrization is applied. This method can also be applied to the Euler flow and MHD flow.
Probabilistic model validation for uncertain nonlinear systems

Abstract This paper presents a probabilistic model validation methodology for nonlinear systems in time-domain. The proposed formulation is simple, intuitive, and accounts both deterministic and stochastic nonlinear systems with parametric and nonparametric uncertainties. Instead of hard invalidation methods available in the literature, a relaxed notion of validation in probability is introduced. To guarantee provably correct inference, algorithm for constructing probabilistically robust validation certificate is given along with computational complexities. Several examples are worked out to illustrate its use.
Polarizations on abelian varieties

Every isogeny class over an algebraically closed field contains a principally polarized abelian variety ([ 10 , corollary 1 to theorem 4 in section 23]). Howe ([ 3 ]; see also [ 4 ]) gave examples of isogeny classes of abelian varieties over finite fields with no principal polarizations (but not with the degrees of all the polarizations divisible by a given non-zero integer, as in Theorem 1·1 below). In [ 17 ] we obtained, for all odd primes [lscr ], isogeny classes of abelian varieties in positive characteristic, all of whose polarizations have degree divisible by [lscr ] 2 . We gave results in the more general context of invertible sheaves; see also Theorems 6·1 and 5·2 below. Our results gave the first examples for which all the polarizations of the abelian varieties in an isogeny class have degree divisible by a given prime. Inspired by our results in [ 17 ], Howe [ 5 ] recently obtained, for all odd primes [lscr ], examples of isogeny classes of abelian varieties over fields of arbitrary characteristic different from [lscr ] (including number fields), all of whose polarizations have degree divisible by [lscr ] 2 .
THE GRAM MATRIX OF A TEMPERLEY-LIEB ALGEBRA IS SIMILAR TO THE MATRIX OF CHROMATIC JOINS

We show that the matrix of chromatic joins and the Gram matrix of a Temperley-Lieb algebra are similar.
Towards Learning to Perceive and Reason About Liquids

Recent advances in AI and robotics have claimed many incredible results with deep learning, yet no work to date has applied deep learning to the problem of liquid perception and reasoning. In this paper, we apply fully-convolutional deep neural networks to the tasks of detecting and tracking liquids. We evaluate three models: a single-frame network, multi-frame network, and a LSTM recurrent network. Our results show that the best liquid detection results are achieved when aggregating data over multiple frames and that the LSTM network outperforms the other two in both tasks. This suggests that LSTM-based neural networks have the potential to be a key component for enabling robots to handle liquids using robust, closed-loop controllers.
Spectral clustering with imbalanced data

Spectral clustering is sensitive to how graphs are constructed from data. In particular, if the data has proximal and imbalanced clusters, spectral clustering can lead to poor performance on well-known graphs such as k-NN, ϵ-neighborhood and full-RBF graphs. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on clusters to deal with imbalanced data. Our approach parameterizes a family of graphs by adaptively modulating node degrees on a fixed node set, to yield a set of parameter dependent cuts reflecting varying levels of imbalance. The solution to our problem is then obtained by optimizing over these parameters. We present asymptotic limit cut analysis to justify our approach. Experiments on synthetic and real data sets demonstrate the superiority of our method.
Empirical Distributions of Eigenvalues of Product Ensembles

Assume a finite set of complex random variables form a determinantal point process; we obtain a theorem on the limit of the empirical distribution of these random variables. The result is applied to two types of n-by-n random matrices as n goes to infinity. The first one is the product of m i.i.d. (complex) Ginibre ensembles, and the second one is the product of truncations of m independent Haar unitary matrices with sizes $$n_j\times n_j$$ for $$1\le j \le m$$ . Assuming m depends on n, by using the special structures of the eigenvalues we developed, explicit limits of spectral distributions are obtained regardless of the speed of m compared to n. For the product of m Ginibre ensembles, as m is fixed, the limiting distribution is known by various authors, e.g., Gotze and Tikhomirov (On the asymptotic spectrum of products of independent random matrices, 2010. http://arxiv.org/pdf/1012.2710v3.pdf ), Bordenave (Electron Commun Probab 16:104–113, 2011), O’Rourke and Soshnikov (Electron J Probab 16(81):2219–2245, 2011) and O’Rourke et al. (J Stat Phys 160(1):89–119, 2015). Our results hold for any $$m\ge 1$$ which may depend on n. For the product of truncations of Haar-invariant unitary matrices, we show a rich feature of the limiting distribution as $$n_j/n$$ ’s vary. In addition, some general results on arbitrary rotation-invariant determinantal point processes are also derived. In particular, we obtain an inequality for the fourth moment of linear statistics of complex random variables forming a determinantal point process. This inequality is known for the complex Ginibre ensemble only (Hwang in Random matrices and their applications (Brunswick, Maine, 1984), Contemporary Mathematics, American Mathematics Society, Providence, vol 50, pp 145–152, 1986). Our method is the determinantal point process rather than the contour integral by Hwang.
Early prediction for physical human robot collaboration in the operating room

To enable a natural and fluent human robot collaboration flow, it is critical for a robot to comprehend their human peers’ on-going actions, predict their behaviors in the near future, and plan its actions correspondingly. Specifically, the capability of making early predictions is important, so that the robot can foresee the precise timing of a turn-taking event and start motion planning and execution early enough to smooth the turn-taking transition. Such proactive behavior would reduce human’s waiting time, increase efficiency and enhance naturalness in collaborative task. To that end, this paper presents the design and implementation of an early turn-taking prediction algorithm, catered for physical human robot collaboration scenarios. Specifically, a robotic scrub nurse system which can comprehend surgeon’s multimodal communication cues and perform turn-taking prediction is presented. The developed algorithm was tested on a collected data set of simulated surgical procedures in a surgeon–nurse tandem. The proposed turn-taking prediction algorithm is found to be significantly superior to its algorithmic counterparts, and is more accurate than human baseline when little partial input is given (less than 30% of full action). After observing more information, the algorithm can achieve comparable performances as humans with a F1 score of 0.90.
Sums of dilates

The λ-dilate of a set A is λċA={λa : a∈A}. We give an asymptotically sharp lower bound on the size of sumsets of the form λ1ċA+ċċċ+λkċA for arbitrary integers λ1,. . .,λk and integer sets A. We also establish an upper bound for such sums, which is similar to, but often stronger than Plunnecke's inequality.
Cross-Classification Clustering: An Efficient Multi-Object Tracking Technique for 3-D Instance Segmentation in Connectomics

Pixel-accurate tracking of objects is a key element in many computer vision applications, often solved by iterated individual object tracking or instance segmentation followed by object matching. Here we introduce cross-classification clustering (3C), a technique that simultaneously tracks complex, interrelated objects in an image stack. The key idea in cross-classification is to efficiently turn a clustering problem into a classification problem by running a logarithmic number of independent classifications per image, letting the cross-labeling of these classifications uniquely classify each pixel to the object labels. We apply the 3C mechanism to achieve state-of-the-art accuracy in connectomics -- the nanoscale mapping of neural tissue from electron microscopy volumes. Our reconstruction system increases scalability by an order of magnitude over existing single-object tracking methods (such as flood-filling networks). This scalability is important for the deployment of connectomics pipelines, since currently the best performing techniques require computing infrastructures that are beyond the reach of most laboratories. Our algorithm may offer benefits in other domains that require pixel-accurate tracking of multiple objects, such as segmentation of videos and medical imagery.
On the structure of unique shortest paths in graphs

This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph with arbitrary real edge weights. We say that such a path system is strongly metrizable.An easy fact implicit in the literature is that a strongly metrizable path system must be consistent, meaning that no two of its paths may intersect, split apart, and then intersect again. Our main result characterizes strong metrizability via some new forbidden intersection patterns along these lines. In other words, we describe a family of forbidden patterns beyond consistency, and we prove that a path system is strongly metrizable if and only if it is consistent and it avoids all of the patterns in this family. We offer separate (but closely related) characterizations in this way for the settings of directed, undirected, and directed acyclic graphs.Our characterizations are based on a new connection between shortest paths and topology; in particular, our new forbidden patterns are in natural correspondence with two-colored topological 2-manifolds, which we visualize as polyhedra. We believe that this connection may be of independent interest, and we further show that it implies some additional structural corollaries that seem to suggest new and possibly deep-rooted connections between these areas.
Rigidity of time-flat surfaces in the Minkowski spacetime

A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to constant torsion condition for curves in three dimensional space and has been studied in [2, 4, 5, 12, 13]. In particular, any 2-surface in a static slice of a static spacetime is time-flat. In this article, we address the question in the title and prove several local and global rigidity theorems for such surfaces in the Minkowski spacetime.
On Modules over Infinite Group Rings

Let R be a commutative ring and Γ be an infinite discrete group. The algebraic K-theory of the group ring R[Γ] is an important object of computation in geometric topology and number theory. When the group ring is Noetherian, there is a companion G-theory of R[Γ] which is often easier to compute. However, it is exceptionally rare that the group ring is Noetherian for an infinite group. In this paper, we define a version of G-theory for any finitely generated discrete group. This construction is based on the coarse geometry of the group. It has some expected properties such as independence from the choice of a word metric. We prove that, whenever R is a regular Noetherian ring of finite global homological dimension and Γ has finite asymptotic dimension and a finite model for the classifying space BΓ, the natural Cartan map from the K-theory of R[Γ] to G-theory is an equivalence. On the other hand, our G-theory is indeed better suited for computation as we show in a separate paper. Some results and constructions in this paper might be of independent interest as we learn to construct projective resolutions of finite type for certain modules over group rings.
AN ALTERNATE PROOF OF WISE’S MALNORMAL SPECIAL QUOTIENT THEOREM

We give an alternate proof of Wise’s malnormal special quotient theorem (MSQT), avoiding cubical small cancelation theory. We also show how to deduce Wise’s Quasiconvex Hierarchy Theorem from the MSQT and theorems of Hsu and Wise and Haglund and Wise.
Learning using Local Membership Queries

We introduce a new model of membership query (MQ) learning, where the learning algorithm is restricted to query points that are close to random examples drawn from the underlying distribution. The learning model is intermediate between the PAC model (Valiant, 1984) and the PAC+MQ model (where the queries are allowed to be arbitrary points). Membership query algorithms are not popular among machine learning practitioners. Apart from the obvious diculty of adaptively querying labelers, it has also been observed
Understanding and Mapping Natural Beauty

While natural beauty is often considered a subjective property of images, in this paper, we take an objective approach and provide methods for quantifying and predicting the scenicness of an image. Using a dataset containing hundreds of thousands of outdoor images captured throughout Great Britain with crowdsourced ratings of natural beauty, we propose an approach to predict scenicness which explicitly accounts for the variance of human ratings. We demonstrate that quantitative measures of scenicness can benefit semantic image understanding, content-aware image processing, and a novel application of cross-view mapping, where the sparsity of ground-level images can be addressed by incorporating unlabeled overhead images in the training and prediction steps. For each application, our methods for scenicness prediction result in quantitative and qualitative improvements over baseline approaches.
Discovering patterns in biological sequences by optimal segmentation

Computational methods for discovering patterns of local correlations in sequences are important in computational biology. Here we show how to determine the optimal partitioning of aligned sequences into non-overlapping segments such that positions in the same segment are strongly correlated while positions in different segments are not. Our approach involves discovering the hidden variables of a Bayesian network that interact with observed sequences so as to form a set of independent mixture models. We introduce a dynamic program to efficiently discover the optimal segmentation, or equivalently the optimal set of hidden variables. We evaluate our approach on two computational biology tasks. One task is related to the design of vaccines against polymorphic pathogens and the other task involves analysis of single nucleotide polymorphisms (SNPs) in human DNA. We show how common tasks in these problems naturally correspond to inference procedures in the learned models. Error rates of our learned models for the prediction of missing SNPs are up to 1/3 less than the error rates of a state-of-the-art SNP prediction method. Source code is available at www.uwm.edu/~joebock/segmentation.
Insight into hydrogen production through molecular simulation of an electrode-ionomer electrolyte system

In this work, we examine metal electrode-ionomer electrolyte systems at high voltage (negative surface charge) and at high pH to assess factors that influence hydrogen production efficiency. We simulate the hydrogen evolution electrode interface investigated experimentally in the work of Bates et al. [J. Phys. Chem. C 119, 5467 (2015)] using a combination of first principles calculations and classical molecular dynamics. With this detailed molecular information, we explore the hypotheses posed in the work of Bates et al. In particular, we examine the response of the system to increased bias voltage and oxide coverage in terms of the potential profile, changes in solvation and species concentrations away from the electrode, surface concentrations, and orientation of water at reactive surface sites. We discuss this response in the context of hydrogen production.
Eigenspace arrangements of reflection groups

The lattice of intersections of reflecting hyperplanes of a complex reflection group W may be considered as the poset of 1-eigenspaces of the elements of W . In this paper we replace 1 with an arbitrary eigenvalue and study the topology and homology representation of the resulting poset. After posing the main question of whether this poset is shellable, we show that all its upper intervals are geometric lattices, and then answer the question in the affirmative for the infinite family G(m, p, n) of complex reflection groups, and the first 31 of the 34 exceptional groups, by constructing CL-shellings. In addition, we completely determine when these eigenspaces of W form a K(π, 1) (resp. free) arrangement. For the symmetric group, we also extend the combinatorial model available for its intersection lattice to all other eigenvalues by introducing balanced partition posets, presented as particular upper order ideals of Dowling lattices, study the representation afforded by the top (co)homology group, and give a simple map to the posets of pointed d-divisible partitions. 1. Main question and results Let V denote an n-dimensional C-vector space. A reflection in V is any nonidentity element r in GL(V ) of finite order that fixes some hyperplane Hr, and a finite subgroup W of GL(V ) is called a reflection group if it is generated by reflections. Example. The action of the symmetric group Sn on [n] := {1, 2, . . . , n} gives rise to a faithful action on C via σ(ei) = eσ(i), where e1, e2, . . . , en denote the standard basis vectors. Since the transpositions act as reflections and generate the group, this representation realizes Sn as a reflection group in GL(C). We shall refer to it as the defining representation. For an element g ∈ W and root of unity ζ, let V (g, ζ) denote the ζ-eigenspace of g in V . Define E(W, ζ) to be the W -poset (partially ordered set) of all such ζ-eigenspaces {V (g, ζ)}g∈W ordered by reverse inclusion, with W -action given by h·V (g, ζ) = V (hgh, ζ). The eigenvalue ζ = 1 gives the lattice LW of intersections of reflecting hyperplanes for W ; see [29, Lemma 4.4]. The minimal elements of E(W, ζ) (i.e., the inclusion-maximal ζ-eigenspaces forW ) are the focus of Springer’s theory of regular elements [35], and each has dimension equal to the number a(d) of degrees d1, d2, . . . , dn of W that are divisible by d, the order of ζ; see Proposition 3.7 below. When W is crystallographic, the poset E(W, ζ) itself appears in Broue, Malle, and Michel’s Φ-Sylow theory [8]. 2010 Mathematics Subject Classification. Primary 20F55, 05E10, 05E18, 55P20, 14N20.
A joint graph inference case study: the C. elegans chemical and electrical connectomes

We investigate joint graph inference for the chemical and electrical connectomes of the Caenorhabditis elegans roundworm. The C. elegans connectomes consist of [Formula: see text] non-isolated neurons with known functional attributes, and there are two types of synaptic connectomes, resulting in a pair of graphs. We formulate our joint graph inference from the perspectives of seeded graph matching and joint vertex classification. Our results suggest that connectomic inference should proceed in the joint space of the two connectomes, which has significant neuroscientific implications.
Modular invariance, modular identities and supersingular $j$-invariants

To every $k$-dimensional modular invariant vector space we associate a modular form on $SL(2,\mathbb{Z})$ of weight $2k$. We explore number theoretic properties of this form and find a sufficient condition for its vanishing which yields modular identities (e.g., Ramanujan-Watson's modular identities). Furthermore, we focus on a family of modular invariant spaces coming from suitable two-dimensional spaces via the symmetric power construction. In particular, we consider a two-dimensional space spanned by graded dimensions of certain level one modules for the affine Kac-Moody Lie algebra of type $D_4^{(1)}$. In this case, the reduction modulo prime $p=2k+3 \geq 5$ of the modular form associated to the $k$-th symmetric power classifies supersingular elliptic curves in characteristic $p$. This construction also gives a new interpretation of certain modular forms studied by Kaneko and Zagier.
Exact limits of inference in coalescent models.

Abstract Recovery of population size history from molecular sequence data is an important problem in population genetics. Inference commonly relies on a coalescent model linking the population size history to genealogies. The high computational cost of estimating parameters from these models usually compels researchers to select a subset of the available data or to rely on insufficient summary statistics for statistical inference. We consider the problem of recovering the true population size history from two possible alternatives on the basis of coalescent time data previously considered by Kim et al. (2015). We improve upon previous results by giving exact expressions for the probability of correctly distinguishing between the two hypotheses as a function of the separation between the alternative size histories, the number of individuals, loci, and the sampling times. In more complicated settings we estimate the exact probability of correct recovery by Monte Carlo simulation. Our results give considerably more pessimistic inferential limits than those previously reported. We also extended our analyses to pairwise SMC and SMC’ models of recombination. This work is relevant for optimal design when the inference goal is to test scientific hypotheses about population size trajectories in coalescent models with and without recombination.
Polyhedra, complexes, nets and symmetry.

Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial and algebraic properties. They can be viewed as finite or infinite 3-periodic graphs (nets) equipped with additional structure imposed by the faces, allowed to be skew, zigzag or helical. A polyhedron or complex is regular if its geometric symmetry group is transitive on the flags (incident vertex–edge–face triples). There are 48 regular polyhedra (18 finite polyhedra and 30 infinite apeirohedra), as well as 25 regular polygonal complexes, all infinite, which are not polyhedra. Their edge graphs are nets well known to crystallographers and they are identified explicitly. There are also six infinite families of chiral apeirohedra, which have two orbits on the flags such that adjacent flags lie in different orbits.
Enriched model categories in equivariant contexts

We give a general framework of equivariant model category theory. Our groups G, called Hopf groups, are suitably defined group objects in any well-behaved symmetric monoidal category V. For any V, a discrete group G gives a Hopf group, denoted I[G]. When V is cartesian monoidal, the Hopf groups are just the group objects in V. When V is the category of modules over a commutative ring R, I[G] is the group ring R[G] and the general Hopf groups are the cocommutative Hopf algebras over R. We show how all of the usual constructs of equivariant homotopy theory, both categorical and model theoretic, generalize to Hopf groups for any V. This opens up some quite elementary unexplored mathematical territory, while systematizing more familiar terrain.
Second order accurate distributed eigenvector computation for extremely large matrices

We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that averaging eigenvectors of ra ndomly subsampled matrices efficiently approximates the true eigenvectors of the original matrix under certain conditions on the incoherence of the spectral decomposition. This incoherence assumption is typically milder than those made in matrix completion and allows eigenvectors to be sparse. We discuss applications to spectral methods in dimensionality reduction and information retrieval.
Efficient test-based variable selection for high-dimensional linear models.

Abstract Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression (LARS), among others. These methods typically add variables into the model one by one. For such selection procedures, it is crucial to find a stopping criterion that controls model complexity. One of the most commonly used techniques to this end is cross-validation (CV) which, in spite of its popularity, has two major drawbacks: expensive computational cost and lack of statistical interpretation. To overcome these drawbacks, we introduce a flexible and efficient test-based variable selection approach that can be incorporated into any sequential selection procedure. The test, which is on the overall signal in the remaining inactive variables, is based on the maximal absolute partial correlation between the inactive variables and the response given active variables. We develop the asymptotic null distribution of the proposed test statistic as the dimension tends to infinity uniformly in the sample size. We also show that the test is consistent. With this test, at each step of the selection, a new variable is included if and only if the p -value is below some pre-defined level. Numerical studies show that the proposed method delivers very competitive performance in terms of variable selection accuracy and computational complexity compared to CV.
How Can We Naturally Order and Organize Graph Laplacian Eigenvectors

When attempting to develop wavelet transforms for graphs and networks, some researchers have used graph Laplacian eigenvalues and eigenvectors in place of the frequencies and complex exponentials in the Fourier theory for regular lattices in the Euclidean domains. This viewpoint, however, has a fundamental flaw: on a general graph, the Laplacian eigenvalues cannot be interpreted as the frequencies of the corresponding eigenvectors. In this paper, we discuss this important problem further and propose a new method to organize those eigenvectors by defining and measuring “natural” distances between eigenvectors using the Ramified Optimal Transport Theory followedby embedding them into a low-dimensional Euclidean domain. We demonstrate its effectiveness using a synthetic graph as well as a dendritic tree of a retinal ganglioncell of a mouse.
Reliable Adaptive Cubature Using Digital Sequences

Quasi-Monte Carlo cubature methods often sample the integrand using Sobol’ (or other digital) sequences to obtain higher accuracy than IID sampling. An important question is how to conservatively estimate the error of a digital sequence cubature so that the sampling can be terminated when the desired tolerance is reached. We propose an error bound based on the discrete Walsh coefficients of the integrand and use this error bound to construct an adaptive digital sequence cubature algorithm. The error bound and the corresponding algorithm are guaranteed to work for integrands lying in a cone defined in terms of their true Walsh coefficients. Intuitively, the inequalities defining the cone imply that the ordered Walsh coefficients do not dip down for a long stretch and then jump back up. An upper bound on the cost of our new algorithm is given in terms of the unknown decay rate of the Walsh coefficients.
Single-stride exposure to pulse torque assistance provided by a robotic exoskeleton at the hip and knee joints

Robot assisted gait retraining is an increasingly common method for supporting restoration of walking function after neurological injury. Gait speed, an indicator of walking function, is correlated with propulsive force, a measure modulated by the posture of the trailing limb at push-off. With the ultimate goal of improving efficacy of robot assisted gait retraining, we sought to directly target gait propulsion, by exposing subjects to pulses of joint torque applied at the hip and knee joints to modulate push-off posture. In this work, we utilized a robotic exoskeleton to apply pulses of torque to the hip and knee joints, during individual strides, of 16 healthy control subjects, and quantified the effects of this intervention on hip extension and propulsive impulse during and after application of these pulses. We observed significant effects in the outcome measures primarily at the stride of pulse application and generally no after effects in the following strides. Specifically, when pulses were applied at late stance, we observed a significant increase in propulsive impulse when knee and/or hip flexion pulses were applied and a significant increase in hip extension angle when hip extension torque pulses were applied. When pulses were applied at early stance, we observed a significant increase in propulsive impulse associated with hip extension torque.
MM-MRE: a new technique to quantify individual muscle forces during isometric tasks of the wrist using MR elastography

Non-invasive in-vivo measurement of individual muscle force is limited by the infeasibility of placing force sensing elements in series with the musculo-tendon structures. While different methods based either on shear wave elastography or electromyography have been recently proposed to non-invasively estimate individual muscle forces, they can only be used to quantity forces in a limited set of superficial muscles. As such, they are not suitable to study the neuromuscular control of movements that require coordinated action of multiple muscles. In this work, we present multi-muscle magnetic resonance elastography (MM-MRE), a new technique capable of quantifying force for each muscle in the forearm, thus enabling the study of the neuromuscular control of wrist movements. To quantity individual muscle force, MM-MRE integrates measurements of joint torque provided by an MRI-compatible instrumented handle with muscle-specific measurements of shear wave speed obtained via MRE into a forward dynamic muscle force estimator based on a realistic musculoskeletal model of the forearm. A single-subject pilot experiment demonstrates the possibility of obtaining measurements from individual muscles and establishes that MM-MRE has sufficient sensitivity to detect changes in the muscle specific measurement of shear-wave speed following the application of isometric flexion and extension torques with self-selected intensity.
Changes in Insurance Coverage and Access to Care for Young Adults in 2017.

Abstract Purpose Previous work has demonstrated the Affordable Care Act (ACA) increased young adults' health care access during its first years. However, it is unclear if these trends continued through 2017; recent policies enacted by the Trump administration may have decreased the ACA's effectiveness. Our purpose was to determine changes in young adults' health care access during the transition from Obama to Trump administrations. Methods Data on noninstitutionalized U.S. young adults (18–24 years) was obtained from the Behavioral Risk Factor Surveillance System 2011–2017 (N = 173,848). We used interrupted time series and difference-in-differences analysis to quantify changes in self-reported insurance coverage, access to a primary care physician, and unmet care because of cost from 2013 to 2017. Results Young adults' health care access continued to improve through 2016; for instance, the percentage of respondents experiencing uninsurance declined by 8.7 points from 2013 to 2016 (95% confidence interval [CI] −9.4 to −8.0). However, these trends began to reverse and from 2016 to 2017, the percentage of young adults who experienced uninsurance increased by 1.4 points (95% CI .6–2.1), not having a personal doctor increased by 1.1 points (95% CI .2–2.0), and unmet care because of cost increased by 1.0 points (95% CI .3–1.7). The 2017 declines in access were concentrated in states which did not expand Medicaid and in households earning above 138% of federal poverty level. Conclusions Health care access declined for young adults in 2017, after several years of improvements. These changes correspond with recent policy actions, which may have weakened the ACA's reforms.
Simulating Emergent Properties of Human Driving Behavior Using Multi-Agent Reward Augmented Imitation Learning

Recent developments in multi-agent imitation learning have shown promising results for modeling the behavior of human drivers. However, it is challenging to capture emergent traffic behaviors that are observed in real-world datasets. Such behaviors arise due to the many local interactions between agents that are not commonly accounted for in imitation learning. This paper proposes Reward Augmented Imitation Learning (RAIL), which integrates reward augmentation into the multi-agent imitation learning framework and allows the designer to specify prior knowledge in a principled fashion. We prove that convergence guarantees for the imitation learning process are preserved under the application of reward augmentation. This method is validated in a driving scenario, where an entire traffic scene is controlled by driving policies learned using our proposed algorithm. Further, we demonstrate improved performance in comparison to traditional imitation learning algorithms both in terms of the local actions of a single agent and the behavior of emergent properties in complex, multi-agent settings.
Slow-slip, slow earthquakes, period-two cycles, full and partial ruptures, and deterministic chaos in a single asperity fault

Abstract The assimilation of geological, geophysical, and laboratory data in physics-based models of fault dynamics promises increasingly realistic simulations of the seismic cycle. To assist this effort, I explore the dynamics of a single velocity-weakening asperity to delineate the relationship between a fault physical properties and the style of faulting during the seismic cycle based on a micro-physical model of rate-and-state friction. From a dimensional analysis, four non-dimensional parameters control the characteristics of slip events and the behavior during the interseismic period, including the Dieterich-Ruina-Rice number Ru, which is proportional to the ratio of asperity to critical nucleation size W/h*, and Rb = (b − a)/b, where a and b control the direct and local evolutionary effects, respectively. For sufficiently large Rb, the Ru number controls the spectrum of fault slip, from periodic slow-slip events to aperiodic fast ruptures. In finite faults, but not in semi-infinite faults, the transition between these end-members includes a bifurcation that involves period-two, period-four, period-six cycles, and deterministic chaos with increasing Ru. Macroscopic fault slip is stabilized as Rb vanishes, even as Ru ≫ 1. For finite faults, but not for semi-infinite faults, the transition between slow and fast ruptures for increasing Rb includes another type of bifurcation with period-two and period-four cycles of slow and fast ruptures. For 0