cssi/SciSciGPT-SciSciNet huggingface dataset:
Pattern-avoiding polytopes

Abstract Two well-known polytopes whose vertices are indexed by permutations in the symmetric group S n are the permutohedron P n and the Birkhoff polytope B n . We consider polytopes P n ( Π ) and B n ( Π ) , whose vertices correspond to the permutations in S n avoiding a set of patterns Π . For various choices of Π , we explore the Ehrhart polynomials and h ∗ -vectors of these polytopes as well as other aspects of their combinatorial structure. For P n ( Π ) , we consider all subsets Π ⊆ S 3 and are able to provide results in most cases. To illustrate, P n ( 123 , 132 ) is a Pitman–Stanley polytope, the number of interior lattice points in P n ( 132 , 312 ) is a derangement number, and the normalized volume of P n ( 123 , 231 , 312 ) is the number of trees on n vertices. The polytopes B n ( Π ) seem much more difficult to analyze, so we focus on four particular choices of Π . First we show that the B n ( 231 , 321 ) is exactly the Chan–Robbins–Yuen polytope. Next we prove that for any Π containing { 123 , 312 } we have h ∗ ( B n ( Π ) ) = 1 . Finally, we study B n ( 132 , 312 ) and B ˜ n ( 123 ) , where the tilde indicates that we choose vertices corresponding to alternating permutations avoiding the pattern 123. In both cases we use order complexes of posets and techniques from toric algebra to construct regular, unimodular triangulations of the polytopes. The posets involved turn out to be isomorphic to the lattices of Young diagrams contained in a certain shape, and this permits us to give an exact expression for the normalized volumes of the corresponding polytopes via the hook formula. Finally, Stanley’s theory of ( P , ω ) -partitions allows us to show that their h ∗ -vectors are symmetric and unimodal. Various questions and conjectures are presented throughout.
Sequential Inverse Approximation of a Regularized Sample Covariance Matrix

One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is well known that covariance matrix estimation is problematic when the number of observations is relatively small compared to the number of variables. A common way to tackle this problem is through the use of a shrinkage estimator that offers a compromise between the sample covariance matrix and a well-conditioned matrix, with the aim of minimizing the mean-squared error. We derived sequential update rules to approximate the inverse shrinkage estimator of the covariance matrix. The approach paves the way for improved large-scale machine learning methods that involve sequential updates.
Intracycle angular velocity control of cross-flow turbines

Cross-flow turbines, also known as vertical-axis turbines, are attractive for power generation from wind and water currents. Some cross-flow turbine designs optimize unsteady fluid forces and maximize power output by controlling blade kinematics within one rotation. One established method is to dynamically pitch the blades. Here we introduce a mechanically simpler alternative: optimize the turbine rotation rate as a function of angular blade position. We demonstrate experimentally that this approach results in a 59% increase in power output over standard control methods. Analysis of fluid forcing and blade kinematics suggest that power increase is achieved through modification of the local flow conditions and alignment of fluid force and rotation rate extrema. The result is a low-speed, structurally robust turbine that achieves high efficiency and could enable a new generation of environmentally benign turbines for renewable power generation. Unlike ubiquitous axial-flow turbines, cross-flow turbines have rotation axes perpendicular to the flow they sit in. This study presents a control scheme that optimizes blade angular velocity as a function of blade position with no extra degrees of freedom, yielding a 59% increase in power output.
Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes

A new weak Galerkin (WG) finite element method is introduced and analyzed in this article for the biharmonic equation in its primary form. This method is highly robust and flexible in the element construction by using discontinuous piecewise polynomials on general finite element partitions consisting of polygons or polyhedra of arbitrary shape. The resulting WG finite element formulation is symmetric, positive definite, and parameter-free. Optimal order error estimates in a discrete H2 norm is established for the corresponding WG finite element solutions. Error estimates in the usual L2 norm are also derived, yielding a suboptimal order of convergence for the lowest order element and an optimal order of convergence for all high order of elements. Numerical results are presented to confirm the theory of convergence under suitable regularity assumptions. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1003–1029, 2014
Shrink or Substitute: Handling Process Failures in HPC Systems Using In-Situ Recovery

Efficient utilization of today's high-performance computing (HPC) systems with complex software and hardware components requires that the HPC applications are designed to tolerate process failures at runtime. With low mean-time-to-failure (MTTF) of current and future HPC systems, long running simulations on these systems requires capabilities for gracefully handling process failures by the applications themselves. In this paper, we explore the use of fault tolerance extensions to Message Passing Interface (MPI) called user-level failure mitigation (ULFM) for handling process failures without the need to discard the progress made by the application. We explore two alternative recovery strategies, which use ULFM along with application-driven in-memory checkpointing. In the first case, the application is recovered with only the surviving processes, and in the second case, spares are used to replace the failed processes, such that the original configuration of the application is restored. Our experimental results demonstrate that graceful degradation is a viable alternative for recovery in environments where spares may not be available.
Model Selection for Topic Models via Spectral Decomposition

Topic models have achieved signicant successes in analyzing large-scale text corpus. In practical applications, we are always confronted with the challenge of model selection, i.e., how to appropriately set the number of topics. Following the recent advances in topic models via tensor decomposition, we make a rst attempt to provide theoretical analysis on model selection in latent Dirichlet allocation. With mild conditions, we derive the upper bound and lower bound on the number of topics given a text collection of nite size. Experimental results demonstrate that our bounds are correct and tight. Furthermore, using Gaussian mixture model as an example, we show that our methodology can be easily generalized to model selection analysis in other latent models.
Multi-invariant measures and subsets on nilmanifolds

Given a Zr-action α on a nilmanifold X by automorphisms and an ergodic α-invariant probability measure μ, we show that μ is the uniform measure on X unless, modulo finite index modification, one of the following obstructions occurs for an algebraic factor action We also deduce a rigidity property for invariant closed subsets.
Solitary water waves with discontinuous vorticity

Abstract We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing waves of this form that exhibit a discontinuous distribution of vorticity. More precisely, this means that the velocity limits both upstream and downstream to a laminar flow that is merely Lipschitz continuous. We prove that, for any choice of background velocity with this regularity, there exists a global curve of solutions bifurcating from a critical laminar flow and including waves arbitrarily close to having stagnation points. Each of these waves has an axis of even symmetry, and the height of their streamlines above the bed decreases monotonically as one moves to the right of the crest.
Two-point functions and their applications in geometry

The maximum principle is one of the most important tools in the analysis of geometric partial differential equations. Traditionally, the maximum principle is applied to a scalar function defined on a manifold, but in recent years more sophisticated versions have emerged. One particularly interesting direction involves applying the maximum principle to functions that depend on a pair of points. This technique is particularly effective in the study of problems involving embedded surfaces. In this survey, we first describe some foundational results on curve shortening flow and mean curvature flow. We then describe Huisken's work on the curve shortening flow where the method of two-point functions was introduced. Finally, we discuss several recent applications of that technique. These include sharp estimates for mean curvature flow, as well as the proof of Lawson's 1970 conjecture concerning minimal tori in S^3.
OPEN PROJECTIONS IN OPERATOR ALGEBRAS II: COMPACT PROJECTIONS

We generalize some aspects of the theory of compact projections relative to a C � -algebra, to the setting of more general algebras. Our main re- sult is that compact projections are the decreasing limits of 'peak projections', and in the separable case compact projections are just the peak projections. We also establish new forms of the noncommutative Urysohn lemma relative to an operator algebra, and we show that a projection is compact iff the asso- ciated face in the state space of the algebra is weak* closed.
Accelerated Gradient Temporal Difference Learning.

The family of temporal difference (TD) methods span a spectrum from computationally frugal linear methods like TD({\lambda}) to data efficient least squares methods. Least square methods make the best use of available data directly computing the TD solution and thus do not require tuning a typically highly sensitive learning rate parameter, but require quadratic computation and storage. Recent algorithmic developments have yielded several sub-quadratic methods that use an approximation to the least squares TD solution, but incur bias. In this paper, we propose a new family of accelerated gradient TD (ATD) methods that (1) provide similar data efficiency benefits to least-squares methods, at a fraction of the computation and storage (2) significantly reduce parameter sensitivity compared to linear TD methods, and (3) are asymptotically unbiased. We illustrate these claims with a proof of convergence in expectation and experiments on several benchmark domains and a large-scale industrial energy allocation domain.
Click Carving: Segmenting Objects in Video with Point Clicks

We present a novel form of interactive video object segmentation where a few clicks by the user helps the system produce a full spatio-temporal segmentation of the object of interest. Whereas conventional interactive pipelines take the user's initialization as a starting point, we show the value in the system taking the lead even in initialization. In particular, for a given video frame, the system precomputes a ranked list of thousands of possible segmentation hypotheses (also referred to as object region proposals) using image and motion cues. Then, the user looks at the top ranked proposals, and clicks on the object boundary to carve away erroneous ones. This process iterates (typically 2-3 times), and each time the system revises the top ranked proposal set, until the user is satisfied with a resulting segmentation mask. Finally, the mask is propagated across the video to produce a spatio-temporal object tube. On three challenging datasets, we provide extensive comparisons with both existing work and simpler alternative methods. In all, the proposed Click Carving approach strikes an excellent balance of accuracy and human effort. It outperforms all similarly fast methods, and is competitive or better than those requiring 2 to 12 times the effort.
Search-to-Decision Reductions for Lattice Problems with Approximation Factors (Slightly) Greater Than One

We show the first dimension-preserving search-to-decision reductions for approximate SVP and CVP. In particular, for any gamma <= 1 + O(log n/n), we obtain an efficient dimension-preserving reduction from gamma^{O(n/log n)}-SVP to gamma-GapSVP and an efficient dimension-preserving reduction from gamma^{O(n)}-CVP to gamma-GapCVP. These results generalize the known equivalences of the search and decision versions of these problems in the exact case when gamma = 1. For SVP, we actually obtain something slightly stronger than a search-to-decision reduction - we reduce gamma^{O(n/log n)}-SVP to gamma-unique SVP, a potentially easier problem than gamma-GapSVP.
Stable separation and super-resolution of mixture models ☆

Abstract We consider simultaneously identifying the membership and locations of point sources that are convolved with different band-limited point spread functions, from the observation of their superpositions. This problem arises in three-dimensional super-resolution single-molecule imaging, neural spike sorting, multi-user channel identification, among other applications. We propose a novel algorithm, based on convex programming, and establish its near-optimal performance guarantee for exact recovery in the noise-free setting by exploiting the spectral sparsity of the point source models as well as the incoherence between point spread functions. Furthermore, robustness of the recovery algorithm in the presence of bounded noise is also established. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.
Nonparametric Bandits with Covariates

We consider a bandit problem which involves sequential sampling from two populations (arms). Each arm produces a noisy reward realization which depends on an observable random covariate. The goal is to maximize cumulative expected reward. We derive general lower bounds on the performance of any admissible policy, and develop an algorithm whose performance achieves the order of said lower bound up to logarithmic terms. This is done by decomposing the global problem into suitably “localized” bandit problems. Proofs blend ideas from nonparametric statistics and traditional methods used in the bandit literature.
Learning Correspondence From the Cycle-Consistency of Time

We introduce a self-supervised method for learning visual correspondence from unlabeled video. The main idea is to use cycle-consistency in time as free supervisory signal for learning visual representations from scratch. At training time, our model learns a feature map representation to be useful for performing cycle-consistent tracking. At test time, we use the acquired representation to find nearest neighbors across space and time. We demonstrate the generalizability of the representation -- without finetuning -- across a range of visual correspondence tasks, including video object segmentation, keypoint tracking, and optical flow. Our approach outperforms previous self-supervised methods and performs competitively with strongly supervised methods.
A Framework for Vehicle Routing Approximation Schemes in Trees

We develop a general framework for designing polynomial-time approximation schemes (PTASs) for various vehicle routing problems in trees. In these problems, the goal is to optimally route a fleet of vehicles, originating at a depot, to serve a set of clients, subject to various constraints. For example, in Minimum Makespan Vehicle Routing, the number of vehicles is fixed, and the objective is to minimize the longest distance traveled by a single vehicle. Our main insight is that we can often greatly restrict the set of potential solutions without adding too much to the optimal solution cost. This simplification relies on partitioning the tree into clusters such that there exists a near-optimal solution in which every vehicle that visits a given cluster takes on one of a few forms. In particular, only a small number of vehicles serve clients in any given cluster. By using these coarser building blocks, a dynamic programming algorithm can find a near-optimal solution in polynomial time. We show that the framework is flexible enough to give PTASs for many problems, including Minimum Makespan Vehicle Routing, Distance-Constrained Vehicle Routing, Capacitated Vehicle Routing, and School Bus Routing, and can be extended to the multiple depot setting.
Computational prediction of lattice thermal conductivity: A comparison of molecular dynamics and Boltzmann transport approaches

The predictive modeling of lattice thermal conductivity is of fundamental importance for the understanding and design of materials for a wide range of applications. Two major approaches, namely molecular dynamics (MD) simulations and calculations solving approximately the Boltzmann transport equation (BTE), have been developed to compute the lattice thermal conductivity. We present a detailed direct comparison of these two approaches, using as prototypical cases MgO and PbTe. The comparison, carried out using empirical potentials, takes into account the effects of fourth order phonon scattering, temperature-dependent phonon frequencies (phonon renormalization), and investigates the effects of quantum vs classical statistics. We clarify that equipartition, as opposed to Maxwell-Boltzmann, govern the statistics of phonons in MD simulations. We find that lattice thermal conductivity values from MD and BTE show an apparent, satisfactory agreement; however such an agreement is the result of error cancellations. We also show that the primary effect of statistics on thermal conductivity is via the scattering rate dependence on phonon populations.
Fooling polytopes

We give a pseudorandom generator that fools m-facet polytopes over {0,1}n with seed length polylog(m) · log(n). The previous best seed length had superlinear dependence on m. An immediate consequence is a deterministic quasipolynomial time algorithm for approximating the number of solutions to any {0,1}-integer program.
Knot types of generalized Kirchhoff rods

Kirchhoff energy is a classical functional on the space of arclength-parameterized framed curves whose critical points approximate configurations of springy elastic rods. We introduce a generalized...
Integrating Concept Maps into a Medical Student Oncology Curriculum

Expanding frontiers of knowledge have prompted medical schools to reconsider how best to promote learning in the face of information overload. Concept mapping (CM) promotes knowledge retention and integration. Students have perceived CM positively in prior studies, but the feasibility and utility of integrating CM into a medical student oncology curriculum as a learning and assessment tool have not been described. At the University of California, San Francisco, 152 medical students in a second-year hematology/oncology course produced concept maps about a single cancer type over 4 weeks. We collected student evaluations about CM. Two of three graders independently scored each map using a standard rubric. We compared CM scores with USMLE Step 1 scores and clerkship grades using regression. All students produced a concept map. Student perception was mixed, and students provided feedback to improve CM utility as a learning tool. Grading was feasible, and inter-rater reliability was high. CM scores did not predict USMLE Step 1 scores or clerkship grades. CM was feasible as a learning tool, and we present strategies based on student feedback and literature review to improve utility. CM was feasible and reliable as an assessment tool; additional validity evidence may improve utility. Future studies should explore whether CM integrated into medical student oncology curricula early, serially, and collaboratively, with iterative practice and feedback, may predict meaningful learning and performance outcomes.
Area Compressibility Moduli of the Monolayer Leaflets of Asymmetric Bilayers from Simulations

Abstract Extraction from simulations of the area compressibility moduli of the monolayers in a bilayer is considered theoretically. A statistical mechanical derivation shows that the bilayer modulus is the sum of the two monolayer moduli, as is often supposed but contrary to a recent study. Seemingly plausible assumptions regarding fluctuations are tested rigorously. Prospects for future research are discussed.
Dynamic contagion in a banking system with births and defaults

We consider a dynamic model of interconnected banks. New banks can emerge, and existing banks can default, creating a birth-and-death setup. Microscopically, banks evolve as independent geometric Brownian motions. Systemic effects are captured through default contagion: as one bank defaults, reserves of other banks are reduced by a random proportion. After examining the long-term stability of this system, we investigate mean-field limits as the number of banks tends to infinity. Our main results concern the measure-valued scaling limit which is governed by a McKean–Vlasov jump-diffusion. The default impact creates a mean-field drift, while the births and defaults introduce jump terms tied to the current distribution of the process. Individual dynamics in the limit is described by the propagation of chaos phenomenon. In certain cases, we explicitly characterize the limiting average reserves.
Phase Transitions and Cyclic Phenomena in Bandits with Switching Constraints

We consider the classical stochastic multi-armed bandit problem with a constraint on the total cost incurred by switching between actions. Under the unit switching cost structure, where the constraint limits the total number of switches, we prove matching upper and lower bounds on regret and provide near-optimal algorithms for this problem. Surprisingly, we discover phase transitions and cyclic phenomena of the optimal regret. That is, we show that associated with the multi-armed bandit problem, there are equal-length phases defined by the number of arms and switching costs, where the regret upper and lower bounds in each phase remain the same and drop significantly between phases. The results enable us to fully characterize the trade-off between regret and incurred switching cost in the stochastic multi-armed bandit problem, contributing new insights to this fundamental problem. Under the general switching cost structure, our analysis reveals a surprising connection between the bandit problem and the shortest Hamiltonian path problem.
Auxin-sensitive Aux/IAA proteins mediate drought tolerance in Arabidopsis by regulating glucosinolate levels

A detailed understanding of abiotic stress tolerance in plants is essential to provide food security in the face of increasingly harsh climatic conditions. Glucosinolates (GLSs) are secondary metabolites found in the Brassicaceae that protect plants from herbivory and pathogen attack. Here we report that in Arabidopsis, aliphatic GLS levels are regulated by the auxin-sensitive Aux/IAA repressors IAA5, IAA6, and IAA19. These proteins act in a transcriptional cascade that maintains expression of GLS levels when plants are exposed to drought conditions. Loss of IAA5/6/19 results in reduced GLS levels and decreased drought tolerance. Further, we show that this phenotype is associated with a defect in stomatal regulation. Application of GLS to the iaa5,6,19 mutants restores stomatal regulation and normal drought tolerance. GLS action is dependent on the receptor kinase GHR1, suggesting that GLS may signal via reactive oxygen species. These results provide a novel connection between auxin signaling, GLS levels and drought response.
On Witten’s Extremal Partition Functions

In his famous 2007 paper on three-dimensional quantum gravity, Witten defined candidates for the partition functions \( \mathit Z_k(q) = \sum_{n=-k}^{\infty} \omega_k(n)q^n \) of potential extremal conformal field theories (CFTs) with central charges of the form c = 24k. Although such CFTs remain elusive, he proved that these modular functions are well defined. In this note, we point out several explicit representations of these functions. These involve the partition function p(n), Faber polynomials, traces of singular moduli, and Rademacher sums. Furthermore, for each prime p ≤ 11, the p series Zk(q), where k e {1, . . . , p−1}∪{p+1}, possess a Ramanujan congruence. More precisely, for every non-zero integer n we have that .
Small area prediction of quantiles for zero-inflated data and an informative sample design

The Conservation Effects Assessment Project (CEAP) is a survey intended to quantify soil and nutrient loss on cropland. Estimates of the quantiles of CEAP response variables are published. Previous...
Bacterial Swarming Reduces Proteus mirabilis and Vibrio parahaemolyticus Cell Stiffness and Increases β-Lactam Susceptibility.

ABSTRACT Swarmer cells of the Gram-negative uropathogenic bacteria Proteus mirabilis and Vibrio parahaemolyticus become long (>10 to 100 μm) and multinucleate during their growth and motility on polymer surfaces. We demonstrated that the increasing cell length is accompanied by a large increase in flexibility. Using a microfluidic assay to measure single-cell mechanics, we identified large differences in the swarmer cell stiffness (bending rigidity) of P. mirabilis (5.5 × 10−22 N m2) and V. parahaemolyticus (1.0 × 10−22 N m2) compared to vegetative cells (1.4 × 10−20 N m2 and 2.2 × 10−22 N m2, respectively). The reduction in bending rigidity (∼2-fold to ∼26-fold) was accompanied by a decrease in the average polysaccharide strand length of the peptidoglycan layer of the cell wall from 28 to 30 disaccharides to 19 to 22 disaccharides. Atomic force microscopy revealed a reduction in P. mirabilis peptidoglycan thickness from 1.5 nm (vegetative cells) to 1.0 nm (swarmer cells), and electron cryotomography indicated changes in swarmer cell wall morphology. P. mirabilis and V. parahaemolyticus swarmer cells became increasingly sensitive to osmotic pressure and susceptible to cell wall-modifying antibiotics (compared to vegetative cells)—they were ∼30% more likely to die after 3 h of treatment with MICs of the β-lactams cephalexin and penicillin G. The adaptive cost of “swarming” was offset by the increase in cell susceptibility to physical and chemical changes in their environment, thereby suggesting the development of new chemotherapies for bacteria that leverage swarming for the colonization of hosts and for survival. IMPORTANCEProteus mirabilis and Vibrio parahaemolyticus are bacteria that infect humans. To adapt to environmental changes, these bacteria alter their cell morphology and move collectively to access new sources of nutrients in a process referred to as “swarming.” We found that changes in the composition and thickness of the peptidoglycan layer of the cell wall make swarmer cells of P. mirabilis and V. parahaemolyticus more flexible (i.e., reduce cell stiffness) and that they become more sensitive to osmotic pressure and cell wall-targeting antibiotics (e.g., β-lactams). These results highlight the importance of assessing the extracellular environment in determining antibiotic doses and the use of β-lactam antibiotics for treating infections caused by swarmer cells of P. mirabilis and V. parahaemolyticus.
On Kernel Method–Based Connectionist Models and Supervised Deep Learning without Backpropagation

We propose a novel family of connectionist models based on kernel machines and consider the problem of learning layer by layer a compositional hypothesis class (i.e., a feedforward, multilayer arch...
IntegraTag: A Framework for High-Fidelity Web Client Measurement.

Collecting information from web clients without explicit input from users is important in a variety of contexts including content customization, experience personalization, accounting and online advertising. A standard approach for gathering web client telemetry is through deployment of Javascript instrumentation that is placed either directly on web pages or through third-party "tags" that are referenced in web pages. In this paper we present a design study of web client measurement methods. The objective of our work is to enhance understanding of best practices in web client measurement toward the goal of developing future tags that are reliable, robust and efficient. We begin by conducting a detailed examination of Javascript instrumentation collected from five well known third party services. Our analysis shows that these code-bases have diverse capabilities and return a broad range of client characteristics. Next, we describe a web client measurement framework and an implementation that we call IntegraTag, which enables us to examine details of performance, accuracy and reliability through live deployments. We use IntegraTag to conduct case studies of tag behavior on a single website which resulted in over 500K page-loads, and on a publisher network which resulted in over 150M page-loads. We establish a lower-bound on the tag's reporting fidelity using a Bernoulli trial. We report on the wide range of client characteristics returned by IntegraTag, as well as its performance and robustness.
Reverse Markov- and Bernstein-type inequalities for incomplete polynomials

Let ${\mathcal P}_k$ denote the set of all algebraic polynomials of degree at most $k$ with real coefficients. Let ${\mathcal P}_{n,k}$ be the set of all algebraic polynomials of degree at most $n+k$ having exactly $n+1$ zeros at $0$. Let $$\|f\|_A := \sup_{x \in A}{|f(x)|}$$ for real-valued functions $f$ defined on a set $A \subset {\Bbb R}$. Let $$V_a^b(f) := \int_a^b{|f^{\prime}(x)| \, dx}$$ denote the total variation of a continuously differentiable function $f$ on an interval $[a,b]$. We prove that there are absolute constants $c_1 > 0$ and $c_2 > 0$ such that $$c_1 \frac nk\leq \min_{P \in {\mathcal P}_{n,k}}{\frac{\|P^{\prime}\|_{[0,1]}}{V_0^1(P)}} \leq \min_{P \in {\mathcal P}_{n,k}}{\frac{\|P^{\prime}\|_{[0,1]}}{|P(1)|}} \leq c_2 \left( \frac nk + 1 \right)$$ for all integers $n \geq 1$ and $k \geq 1$. We also prove that there are absolute constants $c_1 > 0$ and $c_2 > 0$ such that $$c_1 \left(\frac nk\right)^{1/2} \leq \min_{P \in {\mathcal P}_{n,k}}{\frac{\|P^{\prime}(x)\sqrt{1-x^2}\|_{[0,1]}}{V_0^1(P)}} \leq \min_{P \in {\mathcal P}_{n,k}}{\frac{\|P^{\prime}(x)\sqrt{1-x^2}\|_{[0,1]}}{|P(1)|}} \leq c_2 \left(\frac nk + 1\right)^{1/2}$$ for all integers $n \geq 1$ and $k \geq 1$.
Regulation of terminal hypertrophic chondrocyte differentiation in Prmt5 mutant mice modeling infantile idiopathic scoliosis

Idiopathic scoliosis (IS) is the most common type of musculoskeletal defect affecting children worldwide, and is classified by age of onset, location and degree of spine curvature. Although rare, IS with onset during infancy is the more severe and rapidly progressive form of the disease, associated with increased mortality due to significant respiratory compromise. The pathophysiology of IS, in particular for infantile IS, remains elusive. Here, we demonstrate the role of PRMT5 in the infantile IS phenotype in mouse. Conditional genetic ablation of PRMT5 in osteochondral progenitors results in impaired terminal hypertrophic chondrocyte differentiation and asymmetric defects of endochondral bone formation in the perinatal spine. Analysis of these several markers of endochondral ossification revealed increased type X collagen (COLX) and Ihh expression, coupled with a dramatic reduction in Mmp13 and RUNX2 expression, in the vertebral growth plate and in regions of the intervertebral disc in the Prmt5 conditional mutant mice. We also demonstrate that PRMT5 has a continuous role in the intervertebral disc and vertebral growth plate in adult mice. Altogether, our results establish PRMT5 as a critical promoter of terminal hypertrophic chondrocyte differentiation and endochondral bone formation during spine development and homeostasis.This article has an associated First Person interview with the first author of the paper.
Consistency Regularization for Generative Adversarial Networks

Generative Adversarial Networks are plagued by training instability, despite considerable research effort. Progress has been made on this topic, but many of the proposed interventions are complicated, computationally expensive, or both. In this work, we propose a simple and effective training stabilizer based on the notion of Consistency Regularization - a popular technique in the Semi-Supervised Learning literature. In particular, we augment data passing into the GAN discriminator and penalize the sensitivity of the ultimate layer of the discriminator to these augmentations. This regularization reduces memorization of the training data and demonstrably increases the robustness of the discriminator to input perturbations. We conduct a series of ablation studies to demonstrate that the consistency regularization is compatible with various GAN architectures and loss functions. Moreover, the proposed simple regularization can consistently improve these different GANs variants significantly. Finally, we show that applying consistency regularization to GANs improves state-of-the-art FID scores from 14.73 to 11.67 on the CIFAR-10 dataset.
A comment on 4d and 5d BPS states

We discuss a phenomenon in supersymmetric field theory and string theory whereby compactifying one of the dimensions of spacetime on an arbitrarily large circle can cause BPS states to become unstable. We exemplify this by considering 5d $$ \mathcal{N} $$ = 1 theories on a circle and their embeddings into M-theory via geometric engineering. This implicates a subtle relationship between the BPS states of M-theory on a Calabi-Yau threefold, X , and those of type IIA on X with an arbitrary value of the coupling constant. Intuition for this phenomenon is provided by considering F-theory on a complex K3 surface in a limit where it degenerates to a real K3 surface.
Spin current from sub-terahertz-generated antiferromagnetic magnons

Spin dynamics in antiferromagnets has much shorter timescales than in ferromagnets, offering attractive properties for potential applications in ultrafast devices1–3. However, spin-current generation via antiferromagnetic resonance and simultaneous electrical detection by the inverse spin Hall effect in heavy metals have not yet been explicitly demonstrated4–6. Here we report sub-terahertz spin pumping in heterostructures of a uniaxial antiferromagnetic Cr2O3 crystal and a heavy metal (Pt or Ta in its β phase). At 0.240 terahertz, the antiferromagnetic resonance in Cr2O3 occurs at about 2.7 tesla, which excites only right-handed magnons. In the spin-canting state, another resonance occurs at 10.5 tesla from the precession of induced magnetic moments. Both resonances generate pure spin currents in the heterostructures, which are detected by the heavy metal as peaks or dips in the open-circuit voltage. The pure-spin-current nature of the electrically detected signals is unambiguously confirmed by the reversal of the voltage polarity observed under two conditions: when switching the detector metal from Pt to Ta, reversing the sign of the spin Hall angle7–9, and when flipping the magnetic-field direction, reversing the magnon chirality4,5. The temperature dependence of the electrical signals at both resonances suggests that the spin current contains both coherent and incoherent magnon contributions, which is further confirmed by measurements of the spin Seebeck effect and is well described by a phenomenological theory. These findings reveal the unique characteristics of magnon excitations in antiferromagnets and their distinctive roles in spin–charge conversion in the high-frequency regime. Pure spin currents are simultaneously generated and detected electrically through sub-terahertz magnons in the antiferromagnetic insulator Cr2O3, demonstrating the potential of magnon excitations in antiferromagnets for high-frequency spintronic devices.
Doping of the Semiconducting Polymer Poly(3-hexylthiophene) (P3HT) in Organic Photoelectrochemical Cells

We demonstrate the dependence of photoelectrochemical properties of the organic semiconductor film poly(3-hexylthiophene) (P3HT) on the dopant species. We use cyclic voltammetry to characterize ele...
Quantitative Methods to Investigate the 4D Dynamics of Heterochromatic Repair Sites in Drosophila Cells

Heterochromatin is mostly composed of long stretches of repeated DNA sequences prone to ectopic recombination during double-strand break (DSB) repair. In Drosophila, "safe" homologous recombination (HR) repair of heterochromatic DSBs relies on a striking relocalization of repair sites to the nuclear periphery. Central to understanding heterochromatin repair is the ability to investigate the 4D dynamics (movement in space and time) of repair sites. A specific challenge of these studies is preventing phototoxicity and photobleaching effects while imaging the sample over long periods of time, and with sufficient time points and Z-stacks to track repair foci over time. Here we describe an optimized approach for high-resolution live imaging of heterochromatic DSBs in Drosophila cells, with a specific emphasis on the fluorescent markers and imaging setup used to capture the motion of repair foci over long-time periods. We detail approaches that minimize photobleaching and phototoxicity with a DeltaVision widefield deconvolution microscope, and image processing techniques for signal recovery postimaging using SoftWorX and Imaris software. We present a method to derive mean square displacement curves revealing some of the biophysical properties of the motion. Finally, we describe a method in R to identify tracts of directed motions (DMs) in mixed trajectories. These approaches enable a deeper understanding of the mechanisms of heterochromatin dynamics and genome stability in the three-dimensional context of the nucleus and have broad applicability in the field of nuclear dynamics.
Logarithmic Potentials and Quasiconformal Flows on the Heisenberg Group

Abstract Let H be the sub-Riemannian Heisenberg group. That H supports a rich family of quasiconformal mappings was demonstrated by Koranyi and Reimann using the so-called flow method. Here we supply further evidence of the flexible nature of this family, constructing quasiconformal mappings with extreme behavior on small sets. More precisely, we establish criteria to determine when a given logarithmic potential Λ on H is such that there exists a quasiconformal mapping of H with Jacobian comparable to e 2 Λ (so that the Jacobian is zero or infinity at the same points as e 2 Λ ). When Λ is continuous and meets the criteria, we show the canonical (sub-Riemannian) metric g 0 and the weighted metric g = e Λ g 0 generate bi-Lipschitz equivalent distance functions. These results rest on an extension to the theory of quasiconformal flows on H and constructions that adapt the iterative method of Bonk, Heinonen, and Saksman.
Portfolio optimization with expectile and omega functions

This paper proves equivalences of portfolio optimization problems with negative expectile and omega ratio. We derive subgradients for the negative expectile as a function of the portfolio from a known dual representation of expectile and general theory about subgradients of risk measures. We also give an elementary derivation of the gradient of negative expectile under some assumptions and provide an example where negative expectile is demonstrably not differentiable. We conducted a case study and solved portfolio optimization problems with negative expectile objective and constraint (code and data are posted on the web).
Functional Connectivity Evoked by Orofacial Tactile Perception of Velocity.

The cortical representations of orofacial pneumotactile stimulation involve complex neuronal networks, which are still unknown. This study aims to identify the characteristics of functional connectivity (FC) evoked by three different saltatory velocities over the perioral and buccal surface of the lower face using functional magnetic resonance imaging in twenty neurotypical adults. Our results showed a velocity of 25 cm/s evoked stronger connection strength between the right dorsolateral prefrontal cortex and the right thalamus than a velocity of 5 cm/s. The decreased FC between the right secondary somatosensory cortex and right posterior parietal cortex for 5-cm/s velocity versus all three velocities delivered simultaneously (“All ON”) and the increased FC between the right thalamus and bilateral secondary somatosensory cortex for 65 cm/ s vs “All ON” indicated that the right secondary somatosensory cortex might play a role in the orofacial tactile perception of velocity. Our results have also shown different patterns of FC for each seed (bilateral primary and secondary somatosensory cortex) at various velocity contrasts (5 vs 25 cm/s, 5 vs 65 cm/s, and 25 vs 65 cm/s),. The similarities and differences of FC among three velocities shed light on the neuronal networks encoding the orofacial tactile perception of velocity.
A hotspot atop: rivers of the Guyana Highlands hold high diversity of endemic pencil catfish (Teleostei: Ostariophysi: Siluriformes)

ABSTRACT Aim The Pakaraima Mountains are an ancient mountain range along the borders of Guyana, Brazil, and Venezuela. The high plateau is drained by multiple river systems in all directions. Although hypotheses have been presented for the biogeographic relationships of lowland rivers, the interconnectivity of rivers on the top of the plateau is unknown. With multiple complex rivers in a small, upland area we predicted a high level of endemism for stream fishes and complex biogeographic relationships. We explore this with the incredibly diverse pencil catfish genus Trichomycterus. Only two species are known from the region. In this study, we 1) confirm the discovery of multiple endemic Trichomycterus species in the region, 2) determine the phylogenetic placement of our samples to posit biogeographical scenarios, and 3) provide clarification for the identification of T. guianensis based on morphology. Location Pakaraima Mountains, a part of the Guiana Shield in Guyana, South America Taxon Pencil catfish genus Trichomycterus Methods Using collections from recent expeditions to the Pakaraima Mountains of Guyana, we amplified three mitochondrial (16S, COI, and cytb) and two nuclear markers (myh6 and RAG2). We constructed individual gene trees as well as a concatenated tree to determine the placement of these taxa within the Trichomycterus of the Trans-andean/Amazonian clade. Results Our results identify six unique lineages in the highlands of Guyana. Only two species, Trichomycterus guianensis and T. conradi, were previously known to science. Main Conclusions The Pakaraima Mountains of South America are a region of high endemism, as demonstrated here in Trichomycterus catfishes. We find two species occupying multiple basins, suggesting that Pakaraima streams either maintain or had some degree of recent connectivity. We identify six endemic lineages of Trichomycterus from the highlands of the Pakaraima Mountains. The upper portions of the study rivers have been connected either through surface flow or by stream capture. Both processes have occurred on multiple time scales and are independent of the patterns seen in the lowlands.
Catalan intervals and uniquely sorted permutations

Abstract For each positive integer k, we consider five well-studied posets defined on the set of Dyck paths of semilength k. We prove that uniquely sorted permutations avoiding various patterns are equinumerous with intervals in these posets. While most of our proofs are bijective, some use generating trees and generating functions. We end with several conjectures.
embarcadero: Species distribution modelling with Bayesian additive regression trees in r

Abstract Classification and regression tree methods, like random forests (RF) or boosted regression trees (BRT), are one of the most popular methods of mapping species distributions. Bayesian additive regression trees (BARTs) are a relatively new alternative to other popular regression tree approaches. Whereas BRT iteratively fits an ensemble of trees each explaining smaller fractions of the total variance, BART starts by fitting a sum-of-trees model and then uses Bayesian backfitting with an MCMC algorithm to create a posterior draw. So far, BARTs have yet to be applied to species distribution modeling. embarcadero is an R package of convenience tools for researchers interested in species distribution modeling with BARTs. It includes functionality for spatial prediction, an automated variable selection and importance procedure, and other functionality for rapid implementation and data visualization. To show how embarcadero can be used by ecologists, we re-map the distribution of Crimean-Congo haemorrhagic fever and a likely vector, Hyalomma truncatum, in Africa.
Order-Fairness for Byzantine Consensus

Decades of research in both cryptography and distributed systems has extensively studied the problem of state machine replication, also known as Byzantine consensus. A consensus protocol must satisfy two properties: consistency and liveness. These properties ensure that honest participating nodes agree on the same log and dictate when fresh transactions get added. They fail, however, to ensure against adversarial manipulation of the actual ordering of transactions in the log. Indeed, in leader-based protocols (almost all protocols used today), malicious leaders can directly choose the final transaction ordering.
New Practical Advances in Polynomial Root Clustering

We report an ongoing work on clustering algorithms for complex roots of a univariate polynomial p of degree d with real or complex coefficients. As in their previous best subdivision algorithms our root-finders are robust even for multiple roots of a polynomial given by a black box for the approximation of its coefficients, and their complexity decreases at least proportionally to the number of roots in a region of interest (ROI) on the complex plane, such as a disc or a square, but we greatly strengthen the main ingredient of the previous algorithms. We build the foundation for a new counting test that essentially amounts to the evaluation of a polynomial p and its derivative \(p'\), which is a major benefit, e.g., for sparse polynomials p. Moreover with evaluation at about \(\log (d)\) points (versus the previous record of order d) we output correct number of roots in a disc whose contour has no roots of p nearby. Our second and less significant contribution concerns subdivision algorithms for polynomials with real coefficients. Our tests demonstrate the power of the proposed algorithms.
Religion and Politics in the International System Today

Introduction: the view from Silicon Valley -- Religion and politics in the new global paradigm -- A new paradigm for world politics? -- A political perspective on religion and politics -- A religious perspective on religion and politics -- The religions of the book, meditative experience, and public life -- Religion in contemporary world politics -- The west : Christianity, secularization, and immigration -- East Asia : modernization and ideology -- South and central Asia : the legacies of Gandhi and Khomeini and the bomb -- The Middle East and North Africa : Jewish and Islamic politics -- Latin America : indigenous religions, Christianity, and globalization -- Religion and politics for the next millennium -- Appendix I: Thirty years of Nobel Peace prize winners, 1975-2004 -- Appendix II: Paradigm chart and category questions.