AbstractWe establish an explicit isomorphism between the associated graded of the filtered chiral operad and the classical operad, which is important for computing the cohomology of vertex algebras.

AbstractIn this paper we study the long-time behavior of solutions to the Dirac equation $$\begin{equation*} \big ( -i\gamma^\mu \partial_\mu + m \big) \psi= \left(V \ast ( \overline \psi \psi)\right) \psi \ \ \textrm{in } \ {\mathbb{R}}^{1+2},\end{equation*}$$where $V$ is the Yukawa potential in ${\mathbb{R}}^{2}$. It is proved that if $m>0$ and the initial data is small in $H^s({\mathbb{R}}^2)$ for

AbstractWe give an expression for the Garsia entropy of Bernoulli convolutions in terms of products of matrices. This gives an explicit rate of convergence of the Garsia entropy and shows that one can calculate the Hausdorff dimension of the Bernoulli convolution $\nu _{\beta }$ to arbitrary given accuracy whenever $\beta $ is algebraic. In particular, if the Garsia entropy $H(\beta )$ is not equal

AbstractLet $(M,g)$ be a three-dimensional Riemannian manifold. The goal of the paper is to show that if $P_{0}\in M$ is a nondegenerate critical point of the scalar curvature, then a neighborhood of $P_{0}$ is foliated by area-constrained Willmore spheres. Such a foliation is unique among foliations by area-constrained Willmore spheres having Willmore energy less than $32\pi $; moreover, it is regular

AbstractThis is the 3rd paper in a series [6, 9] analyzing the asymptotic distribution of the phase shifts in the semiclassical limit. We analyze the distribution of phase shifts, or equivalently, eigenvalues of the scattering matrix $S_h$, at some fixed energy $E$, for semiclassical Schrödinger operators on $\mathbb{R}^d$ that are perturbations of the free Hamiltonian $h^2 \Delta $ on $L^2(\mathbb{R}^d)$

AbstractWe introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The 1st type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain by applying a family of functors to a single module. For the 2nd type we follow a completely different

AbstractWe study non-Gaussian log-correlated multiplicative chaos, where the random field is defined as a sum of independent fields that satisfy suitable moment and regularity conditions. The convergence, existence of moments, and analyticity with respect to the inverse temperature are proven for the resulting chaos in the full subcritical range. These results are generalizations of the corresponding

AbstractWe show that for solutions of Kapustin–Witten equation with Nahm pole boundary condition on $S^{3}\times \mathbb{R}^{+}$, there exists a universal constant bound on its Yang–Mills energy $\|F_{A}\|_{L^{2}}$.

AbstractWe prove that a nef line bundle ${\mathcal{L}}$ with $c_1({\mathcal{L}})^2 \ne 0$ on a Calabi–Yau threefold $X$ with Picard number $2$ and with $c_3(X) \ne 0$ is semiample, that is, some multiple of $\mathcal L$ is generated by global sections.

AbstractLet $\textrm{coh}\ \mathbb{X}$ be the category of coherent sheaves over a weighted projective line $\mathbb{X}$ and let $D^b(\textrm{coh}\ \mathbb{X})$ be its bounded derived category. The present paper focuses on the study of the right and left mutation functors arising in $D^b(\textrm{coh}\ \mathbb{X})$ attached to certain line bundles. As applications, we first show that these mutation functors

AbstractFor $e \in S^{2}$, the unit sphere in $\mathbb{R}^3$, let $\pi _{e}$ be the orthogonal projection to $e^{\perp } \subset \mathbb{R}^{3}$, and let $W \subset \mathbb{R}^{3}$ be any $2$-plane, which is not a subspace. We prove that if $K \subset \mathbb{R}^{3}$ is a Borel set with $\dim _{\textrm{H}} K \leq \tfrac{3}{2}$, then $\dim _{\textrm{H}} \pi _{e}(K) = \dim _{\textrm{H}} K$ for $\mathcal{H}^{1}$

AbstractThe K-homology ring of the affine Grassmannian of $SL_{n}(\mathbb{C})$ was studied by Lam, Schilling, and Shimozono. It is realized as a certain concrete Hopf subring of the ring of symmetric functions. On the other hand, for the quantum K-theory of the flag variety $F\,\! l_{n}$, Kirillov and Maeno provided a conjectural presentation based on the results obtained by Givental and Lee. We construct

Given a sequence of independent standard Gaussian variables (Zn), the classical Pisier algebra P is the class of all continuous functions f on the unit circle T such that for each t ∈ 𝕋, the random Fourier series \( {\sum}_{n\in \mathrm{\mathbb{Z}}}{Z}_n\hat{f}(n)\times \exp \left(2\pi \mathrm{i} nt\right) \) converges in L2 and the corresponding sums constitute a Gaussian process that admits a continuous

Real-time scheduling strategies for safety-critical systems are primarily focused on ensuring correctness, both functional and temporal. In order to provide the desired predictability in such systems, it is often advisable that all timing requirements be guaranteed offline, before putting the system into operation. Formal approaches allow for all necessary and sufficiency conditions corresponding to

This paper considers a joint order acceptance and scheduling problem under a general scenario. A manufacturer receives multiple orders with a given revenue, processing time, release date, due date, deadline, and earliness and tardiness penalties. The manufacturer can be seen as a single-machine system. Due to limited capacity, the manufacturer cannot process every order and needs to determine the optimal

We study the total weighted tardiness problem with rejection on a single machine. We present new recursive algorithms and approximation results for the agreeably weighted case and a variety of related problems with and without deadlines.

This article gives results on fixed complete lattice L-fuzzy pre-proximities, L-fuzzy grills and L-fuzzy filters. Moreover, we investigate the relations among the L-fuzzy pre-proximities , L-fuzzy grills and L-fuzzy filters. We show that there is a Galois correspondence between the category of separated L-fuzzy grill spaces and that of separated L-fuzzy pre-proximity spaces. We introduced the local

Abstract:The explicit upper Bellman function is found for the natural dyadic maximal operator acting from into . As a consequence, it is shown that the norm of the natural operator equals for all , and so does the norm of the classical dyadic maximal operator. The main result is a partial consequence of a theorem for the so-called -trees, which generalize dyadic lattices. The Bellman function in this

Abstract:The classical Grauert and Ramspott theorems constitute the foundation of the Oka principle on Stein spaces. In this paper, similar results are established on the maximal ideal space of the Banach algebra  of bounded holomorphic functions on the open unit disk . The results are illustrated by some examples and applications to the theory of operator-valued functions.

Abstract:The fixed point spectra of Morava -theory under the action of finite subgroups of the Morava stabilizer group , and their -local Spanier-Whitehead duals can be used to approximate the -local sphere in certain cases. For any finite subgroup of at we prove that the -local Spanier-Whitehead dual of the spectrum is . These results are analogous to the known results at height 2 and . The main computational

Abstract:The concept of the th variation of a continuous function along a refining sequence of partitions is the key to a pathwise Itô integration theory with integrator . Here, we analyze the th variation of a class of fractal functions, containing both the Takagi-van der Waerden and Weierstraß functions. We use a probabilistic argument to show that these functions have linear th variation for a parameter

In this paper, we investigate the limits of Riemann solutions to the Euler equations of compressible fluid flow with a source term as the adiabatic exponent tends to one. The source term can represent friction or gravity or both in Engineering. For instance, a concrete physical model is a model of gas dynamics in a gravitational field with entropy assumed to be a constant. The body force source term

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A3427-A3446, January 2020. Standard backward error analyses for numerical linear algebra algorithms provide worst-case bounds that can significantly overestimate the backward error. Our recent probabilistic error analysis, which assumes rounding errors to be independent random variables [SIAM J. Sci. Comput., 41 (2019), pp. A2815--A2835]

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A3397-A3426, January 2020. Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for Newton solution of deterministic inverse problems, as well as Markov chain Monte Carlo sampling of posteriors in the Bayesian setting

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A3367-A3396, January 2020. This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the use of conforming mixed finite element spaces, we then expand these results

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A3340-A3366, January 2020. We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport distance over graph edges. We show that our distance can be computed using a single

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A3313-A3339, January 2020. We study for the first time Schwarz domain decomposition methods for the solution of the Navier equations modeling the propagation of elastic waves. These equations in the time-harmonic regime are difficult to solve by iterative methods, even more so than the Helmholtz equation. We first prove that the classical

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A3285-A3312, January 2020. In this paper, we propose a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wave equations. The PhaseDNN makes use of the fact that common deep neural networks (DNNs) often achieve convergence in the low frequency

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A3250-A3284, January 2020. This paper proposes a new computational method for solving the structured least squares problem that arises in the process of identification of coherent structures in dynamic processes, such as, e.g., fluid flows. It is deployed in combination with dynamic mode decomposition (DMD), which provides a nonorthogonal

The presence of slow–fast Hopf (or singular Hopf) points in slow–fast systems in the plane is often deduced from the shape of a vector field brought into normal form. It can however be quite cumbersome to put a system in normal form. In De Maesschalck et al. (Canards from birth to transition, 2020), Wechselberger (Geometric singular perturbation theory beyond the standard form, Springer, New York,

In this paper, we approximate a nonautonomous neural network with infinite delay and a Heaviside signal function by neural networks with sigmoidal signal functions. We show that the solutions of the sigmoidal models converge to those of the Heaviside inclusion as the sigmoidal parameter vanishes. In addition, we prove the existence of pullback attractors in both cases, and the convergence of the attractors

We prove the existence of almost-periodic solutions for quasi-linear perturbations of the Airy equation. This is the first result about the existence of this type of solutions for a quasi-linear PDE. The solutions turn out to be analytic in time and space. To prove our result we use a Craig–Wayne approach combined with a KAM reducibility scheme and pseudo-differential calculus on \(\mathbb {T}^\infty

The current work is the third of a series of three papers devoted to the study of asymptotic dynamics in the following parabolic–elliptic chemotaxis system with space and time dependent logistic source, $$\begin{aligned} {\left\{ \begin{array}{ll} \partial _tu=\Delta u -\chi \nabla \cdot (u\nabla v)+u(a(x,t)-b(x,t)u),&{}\quad x\in {\mathbb R}^N,\\ 0=\Delta v-\lambda v+\mu u ,&{}\quad x\in {\mathbb

Consider the Kirchhoff equation $$\begin{aligned} \partial _{tt} u - \Delta u \Big ( 1 + \int _{\mathbb {T}^d} |\nabla u|^2 \Big ) = 0 \end{aligned}$$ on the d-dimensional torus \(\mathbb {T}^d\). In a previous paper we proved that, after a first step of quasilinear normal form, the resonant cubic terms show an integrable behavior, namely they give no contribution to the energy estimates. This leads

We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing. We provide an exact count in the case when the quiver is of finite type or is of affine type and the framing is the coordinate vector at the extending vertex. The latter case precisely covers Etingof’s conjecture on the number

Let G be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on G. We prove that if G is nonamenable and \(p > p_c(G)\) then there exists a positive constant \(c_p\) such that $$\begin{aligned} \mathbf {P}_p(n \le |K| < \infty ) \le e^{-c_p n} \end{aligned}$$ for every \(n\ge 1\), where K is the cluster of the origin. We deduce the following two corollaries: 1. Every

Somatic mutations are major genetic contributors to cancers and many other age-related diseases. Many disease-causing somatic mutations can initiate clonal growth prior to the appearance of any disease symptoms, yet experimental models that can be used to examine clonal abnormalities are limited. We describe a mosaic analysis system with Cre or Tomato (MASCOT) for tracking mutant cells and demonstrate

Understanding the mechanisms of nanoparticle interaction with cell membranes is essential for designing materials for applications such as bioimaging and drug delivery, as well as for assessing engineered nanomaterial safety. Much attention has focused on nanoparticles that bind strongly to biological membranes or induce membrane damage, leading to adverse impacts on cells. More subtle effects on membrane

Over the past decade, theranostic imaging has emerged as a powerful clinical tool in oncology for identifying patients likely to respond to targeted therapies and for monitoring the response of patients to treatment. Herein, we report a theranostic approach to pretargeted radioimmunotherapy (PRIT) based on a pair of radioisotopes of copper: positron-emitting copper-64 (64Cu, t1/2 = 12.7 h) and beta

Toxicity from the external presence or internal production of compounds can reduce the growth and viability of microbial cell factories and compromise productivity. Aromatic compounds are generally toxic for microorganisms, which makes their production in microbial hosts challenging. Here we use adaptive laboratory evolution to generate Saccharomyces cerevisiae mutants tolerant to two aromatic acids

Coherent perception relies on integrating multiple dimensions of a sensory modality, for example, color and shape in vision. We reveal how different acoustic dimensions, specifically echo intensity and sonar aperture (or width), are important for correct perception by echolocating bats. We flew bats down a corridor blocked by objects with different intensity–aperture combinations. To our surprise,

Social hierarchies are ubiquitous in social species and profoundly influence physiology and behavior. Androgens like testosterone have been strongly linked to social status, yet the molecular mechanisms regulating social status are not known. The African cichlid fish Astatotilapia burtoni is a powerful model species for elucidating the role of androgens in social status given their rich social hierarchy

Interpretation of the colossal number of genetic variants identified from sequencing applications is one of the major bottlenecks in clinical genetics, with the inference of the effect of amino acid-substituting missense variations on protein structure and function being especially challenging. Here we characterize the three-dimensional (3D) amino acid positions affected in pathogenic and population

Moral behavior requires learning how our actions help or harm others. Theoretical accounts of learning propose a key division between “model-free” algorithms that cache outcome values in actions and “model-based” algorithms that map actions to outcomes. Here, we tested the engagement of these mechanisms and their neural basis as participants learned to avoid painful electric shocks for themselves and

An imbalance in cellular homeostasis occurring as a result of protein misfolding and aggregation contributes to the pathogeneses of neurodegenerative diseases, including amyotrophic lateral sclerosis (ALS). Here, we report the identification of a ubiquitin-specific protease, USP7, as a regulatory switch in a protein quality-control system that defends against proteotoxicity. A genome-wide screen in

Lipid homeostasis in animal cells is maintained by sterol regulatory element-binding proteins (SREBPs), membrane-bound transcription factors whose proteolytic activation requires the cholesterol-sensing membrane protein Scap. In endoplasmic reticulum (ER) membranes, the carboxyl-terminal domain (CTD) of SREBPs binds to the CTD of Scap. When cholesterol levels are low, Scap escorts SREBPs from the ER

Photosynthetic O2 evolution is catalyzed by the Mn4CaO5 cluster of the water oxidation complex of the photosystem II (PSII) complex. The photooxidative self-assembly of the Mn4CaO5 cluster, termed photoactivation, utilizes the same highly oxidizing species that drive the water oxidation in order to drive the incorporation of Mn2+ into the high-valence Mn4CaO5 cluster. This multistep process proceeds

Cyanobacteriochromes (CBCRs) are photoswitchable linear tetrapyrrole (bilin)-based light sensors in the phytochrome superfamily with a broad spectral range from the near UV through the far red (330 to 760 nm). The recent discovery of far-red absorbing CBCRs (frCBCRs) has garnered considerable interest from the optogenetic and imaging communities because of the deep penetrance of far-red light into

The circadian clock is based on a transcriptional feedback loop with an essential time delay before feedback inhibition. Previous work has shown that PERIOD (PER) proteins generate circadian time cues through rhythmic nuclear accumulation of the inhibitor complex and subsequent interaction with the activator complex in the feedback loop. Although this temporal manifestation of the feedback inhibition

Magnetically actuated miniature soft robots are capable of programmable deformations for multimodal locomotion and manipulation functions, potentially enabling direct access to currently unreachable or difficult-to-access regions inside the human body for minimally invasive medical operations. However, magnetic miniature soft robots are so far mostly based on elastomers, where their limited deformability

Conventional models of genome evolution are centered around the principle that mutations form independently of each other and build up slowly over time. We characterized the occurrence of bursts of genome-wide loss-of-heterozygosity (LOH) in Saccharomyces cerevisiae, providing support for an additional nonindependent and faster mode of mutation accumulation. We initially characterized a yeast clone

Genomic alterations including single-base mutations, deletions and duplications, translocations, mitotic recombination events, and chromosome aneuploidy generate genetic diversity. We examined the rates of all of these genetic changes in a diploid strain of Saccharomyces cerevisiae by whole-genome sequencing of many independent isolates (n = 93) subcloned about 100 times in unstressed growth conditions

Soluble guanylate cyclase (sGC) catalyzes the conversion of guanosine triphosphate into cyclic guanosine-3′,5′-monophosphate, a key second messenger in cell signaling and tissue homeostasis. It was recently demonstrated that sGC stimulation is associated with a marked antiinflammatory effect in the liver of mice with experimental nonalcoholic steatohepatitis (NASH). Here, we investigated the mechanisms

Circadian rhythms are generated by interlocked transcription–translation feedback loops that establish cell-autonomous biological timing of ∼24 h. Mutations in core clock genes that alter their stability or affinity for one another lead to changes in circadian period. The human CRY1Δ11 mutant lengthens circadian period to cause delayed sleep phase disorder (DSPD), characterized by a very late onset

Social inequality in mathematical skill is apparent at kindergarten entry and persists during elementary school. To level the playing field, we trained teachers to assess children’s numerical and spatial skills every 10 wk. Each assessment provided teachers with information about a child’s growth trajectory on each skill, information designed to help them evaluate their students' progress, reflect

Escherichia coli ClpXP is one of the most thoroughly studied AAA+ proteases, but relatively little is known about the reactions that allow it to bind and then engage specific protein substrates before the adenosine triphosphate (ATP)-fueled mechanical unfolding and translocation steps that lead to processive degradation. Here, we employ a fluorescence-quenching assay to study the binding of ssrA-tagged

Plague continued to afflict Europe for more than five centuries after the Black Death. Yet, by the 17th century, the dynamics of plague had changed, leading to its slow decline in Western Europe over the subsequent 200 y, a period for which only one genome was previously available. Using a multidisciplinary approach, combining genomic and historical data, we assembled Y. pestis genomes from nine individuals

Marine protected areas (MPAs) are conservation tools that are increasingly implemented, with growing national commitments for MPA expansion. Perhaps the greatest challenge to expanded use of MPAs is the perceived trade-off between protection and food production. Since MPAs can benefit both conservation and fisheries in areas experiencing overfishing and since overfishing is common in many coastal nations

Better understanding myelination of peripheral nerves would benefit patients affected by peripheral neuropathies, including Charcot–Marie–Tooth disease. Little is known about the role the Golgi compartment plays in Schwann cell (SC) functions. Here, we studied the role of Golgi in myelination of peripheral nerves in mice through SC-specific genetic inactivation of phosphatidylinositol 4-kinase beta

The global distribution of primary production and consumption by humans (fisheries) is well-documented, but we have no map linking the central ecological process of consumption within food webs to temperature and other ecological drivers. Using standardized assays that span 105° of latitude on four continents, we show that rates of bait consumption by generalist predators in shallow marine ecosystems