The pro-étale fundamental group of a scheme, introduced by Bhatt and Scholze, generalizes the usual étale fundamental group |$\pi _1^{\acute{\mathrm{e}}{\mathrm{t}}}$| defined in SGA1 and leads to an interesting class of “geometric coverings” of schemes, generalizing finite étale covers. We prove exactness of the general homotopy sequence for the pro-étale fundamental group, i.e., that for a geometric

We prove local |$C^{0,\alpha }$|- and |$C^{1,\alpha }$|-regularity for the local solution to an obstacle problem with nonstandard growth. These results cover as special cases standard, variable exponent, double phase, and Orlicz growth.

In this paper, we extend some recent results of Guedj et al. [V. Guedj, C. H. Lu and A. Zeriahi, Plurisubharmonic envelopes and supersolutions. J. Differ. Geom. 113(2) (2019) 273–313] about psh envelopes of bounded functions on bounded domains in ℂn. We also present a result on the regularity of psh envelopes.

We study existence and uniqueness of solutions of (E1) −Δu+μ|x|2u+g(u)=ν in Ω, u=λ on ∂Ω, where Ω⊂ℝ+N is a bounded smooth domain such that 0∈∂Ω, μ≥−N24 is a constant, g a continuous nondecreasing function satisfying some integral growth condition and ν and λ two Radon measures, respectively, in Ω and on ∂Ω. We show that the situation differs considerably according the measure is concentrated at 0 or

In the present paper we prove that every local and 2-local derivation of the complex finite dimensional simple Filippov algebra is a derivation. As a corollary we have the description of all local and 2-local derivations of complex finite dimensional semisimple Filippov algebras. All local derivations of the ternary Malcev algebra \(M_8\) are described. It is the first example of a finite-dimensional

A generalized modular relation of the form \(F(z, w, \alpha )=F(z, iw,\beta )\), where \(\alpha \beta =1\) and \(i=\sqrt{-1}\), is obtained in the course of evaluating an integral involving the Riemann \(\Xi \)-function. This modular relation involves a surprising new generalization of the Hurwitz zeta function \(\zeta (s, a)\), which we denote by \(\zeta _w(s, a)\). We show that \(\zeta _w(s, a)\)

We describe the second order obstruction to deformation for nearly G 2 structures on compact manifolds. Building on work of Alexandrov and Semmelmann, this allows proving rigidity under deformation for the proper nearly G 2 structure on the Aloff–Wallach space N ( 1 , 1 ) .

In noncommutative algebraic geometry an Artin–Schelter regular (AS-regular) algebra is one of the main interests, and every three-dimensional quadratic AS-regular algebra is a geometric algebra, introduced by Mori, whose point scheme is either $\mathbb {P}^{2}$ or a cubic curve in $\mathbb {P}^{2}$ by Artin et al. [‘Some algebras associated to automorphisms of elliptic curves’, in: The Grothendieck

In this paper we obtain some improved $L^p$-Hardy and $L^p$-Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.

We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

We compute the deficiency spaces of operators of the form $H_A{\hat {\otimes }} I + I{\hat {\otimes }} H_B$, for symmetric $H_A$ and self-adjoint $H_B$. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math

In this paper, we describe the structure of maximal non-trivial uniform t-intersecting families with large size for finite sets. In the special case when t=1, our result gives rise to Kostochka and Mubayi’s result in 2017.

SIAM Journal on Scientific Computing, Volume 43, Issue 3, Page A2295-A2319, January 2021. In this paper, we address the numerical solution of the optimal transport problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient descent dynamics. Among different time stepping procedures for the discretization

SIAM Journal on Scientific Computing, Volume 43, Issue 3, Page A2268-A2294, January 2021. We introduce a control variate Monte Carlo method to estimate $E[f(X)]$ based on a polynomial chaos expansion for $f(X)$. We analyze the mean square error of the control variate estimator when the coefficients of the polynomial chaos approximation are obtained from Monte Carlo simulation. For a fixed computational

Mixed-level designs have a wide application in the fields of medicine, science, and agriculture, being very useful for experiments where there are both, quantitative, and qualitative factors. Traditional construction methods often make use of complex programing specialized software and powerful computer equipment. This article is focused on a subgroup of these designs in which none of the factor levels

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the

A typical growth of cells inside tissue is normally known as a nodular entity. Lung nodule segmentation from computed tomography (CT) images becomes crucial for early lung cancer diagnosis. An issue that pertains to the segmentation of lung nodules is homogenous modular variants. The resemblance among nodules as well as among neighboring regions is very challenging to deal with. Here, we propose an

The linear associator is a classic associative memory model. However, due to its low performance, it is pertinent to note that very few linear associator applications have been published. The reason for this is that this model requires the vectors representing the patterns to be orthonormal, which is a big restriction. Some researchers have tried to create orthogonal projections to the vectors to feed

In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity

To the best knowledge of the authors, in former studies in the field of measuring volume fraction of gas, oil, and water components in a three-phase flow using gamma radiation technique, the existence of a scale layer has not been considered. The formed scale layer usually has a higher density in comparison to the fluid flow inside the oil pipeline, which can lead to high photon attenuation and, consequently

The manufacturing industry has a great impact on the economic growth of countries. It is, therefore, crucial to master the skills of the production system by mathematical tools that enable the evaluation of the production systems’ performance measures. Four mathematical approaches toward the modeling of steady-state behavior of serial Bernoulli production lines were considered in this study, namely

A binary diagnostic test is a medical test that is applied to an individual in order to determine the presence or the absence of a certain disease and whose result can be positive or negative. A positive result indicates the presence of the disease, and a negative result indicates the absence. Positive and negative predictive values represent the accuracy of a binary diagnostic test when it is applied

The purpose of this paper is to analyze solutions of a non-local nonlinear partial integro-differential equation (PIDE) in multidimensional spaces. Such class of PIDE often arises in financial modeling. We employ the theory of abstract semilinear parabolic equations in order to prove existence and uniqueness of solutions in the scale of Bessel potential spaces. We consider a wide class of Lévy measures

General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with discrete time. GFDynamics implies research and obtaining results concerning the general

This work presents a study of a finite-time horizon stochastic control problem with restrictions on both the reward and the cost functions. To this end, it uses standard dynamic programming techniques, and an extension of the classic Lagrange multipliers approach. The coefficients considered here are supposed to be unbounded, and the obtained strategies are of non-stationary closed-loop type. The driving

This article shows that the recently proposed latent D-scoring model of Dimitrov is statistically equivalent to the two-parameter logistic item response model. An analytical derivation and a numerical illustration are employed for demonstrating this finding. Hence, estimation techniques for the two-parameter logistic model can be used for estimating the latent D-scoring model. In an empirical example

In this analysis, we consider the effects of non-quiescent initial conditions driven by pre-impact air–water interactions on the classical Wagner model of impact theory. We consider the problem of a rigid, solid impactor moving vertically towards a liquid pool. Prior to impact, viscous forces in the air act to deform the liquid free surface, inducing a flow in the pool. These interactions are then

Sean Morrison has spent his career studying the mechanisms that regulate stem cell function and the ways in which these mechanisms influence cancer development. He has discovered several important regulators of stem cell self-renewal, as well as factors that influence the self-replication of cancer cells. In addition, Morrison has identified the location and cellular composition of the microenvironment

Antibody–drug conjugates (ADCs) have emerged as valuable targeted anticancer therapeutics with at least 11 approved therapies and over 80 advancing through clinical trials. Enediyne DNA-damaging payloads represented by the flagship of this family of antitumor agents, N-acetyl calicheamicin γ1I, have a proven success track record. However, they pose a significant synthetic challenge in the development

Birth defects of the external genitalia are among the most common in the world. Proper formation of the external genitalia requires a highly orchestrated process that involves special cell populations and sexually dimorphic hormone signaling. It is clear what the end result of the sexually dimorphic development is (a penis in the male versus clitoris in the female); however, the cell populations involved

In rice, a small increase in nighttime temperature reduces grain yield and quality. How warm nighttime temperatures (WNT) produce these detrimental effects is not well understood, especially in field conditions where the typical day-to-night temperature fluctuation exceeds the mild increase in nighttime temperature. We observed genome-wide disruption of gene expression timing during the reproductive

Aberrant inflammation, such as that associated with inflammatory bowel disease (IBD), is fueled by the inordinate activity of RelA/NF-κB factors. As such, the canonical NF-κB module mediates controlled nuclear activation of RelA dimers from the latent cytoplasmic complexes. What provokes pathological RelA activity in the colitogenic gut remains unclear. The noncanonical NF-κB pathway typically promotes

A chromosome 1q21.3 region that is frequently amplified in diverse cancer types encodes phosphatidylinositol (PI)-4 kinase IIIβ (PI4KIIIβ), a key regulator of secretory vesicle biogenesis and trafficking. Chromosome 1q21.3–amplified lung adenocarcinoma (1q-LUAD) cells rely on PI4KIIIβ for Golgi-resident PI-4-phosphate (PI4P) synthesis, prosurvival effector protein secretion, and cell viability. Here

The interaction between spontaneous and externally evoked neuronal activity is fundamental for a functional brain. Increasing evidence suggests that bursts of high-power oscillations in the 15- to 30-Hz beta-band represent activation of internally generated events and mask perception of external cues. Yet demonstration of the effect of beta-power modulation on perception in real time is missing, and

When exposed to high light, plants produce reactive oxygen species (ROS). In Arabidopsis thaliana, local stress such as excess heat or light initiates a systemic ROS wave in phloem and xylem cells dependent on NADPH oxidase/respiratory burst oxidase homolog (RBOH) proteins. In the case of excess light, although the initial local accumulation of ROS preferentially takes place in bundle-sheath strands

Unicellular eukaryotic predators play a crucial role in the functioning of the ocean ecosystem by recycling nutrients and energy that are channeled to upper trophic levels. Traditionally, these evolutionarily diverse organisms have been combined into a single functional group (heterotrophic flagellates), overlooking their organismal differences. Here, we investigated four evolutionarily related species

Artificial lighting, day-length changes, shift work, and transmeridian travel all lead to sleep–wake disturbances. The nychthemeral sleep–wake cycle (SWc) is known to be controlled by output from the central circadian clock in the suprachiasmatic nuclei (SCN), which is entrained to the light–dark cycle. Additionally, via intrinsically photosensitive retinal ganglion cells containing the photopigment

Genetic variation segregates as linked sets of variants or haplotypes. Haplotypes and linkage are central to genetics and underpin virtually all genetic and selection analysis. Yet, genomic data often omit haplotype information due to constraints in sequencing technologies. Here, we present “haplotagging,” a simple, low-cost linked-read sequencing technique that allows sequencing of hundreds of individuals

The most represented components of clathrin-coated vesicles (CCVs) are clathrin triskelia and the adaptors clathrin assembly lymphoid myeloid leukemia protein (CALM) and the heterotetrameric complex AP2. Investigation of the dynamics of AP180-amino-terminal-homology (ANTH) recruitment during CCV formation has been hampered by CALM toxicity upon overexpression. We used knock-in gene editing to express

Shift current is a direct current generated from nonlinear light–matter interaction in a noncentrosymmetric crystal and is considered a promising candidate for next-generation photovoltaic devices. The mechanism for shift currents in real materials is, however, still not well understood, especially if electron–hole interactions are included. Here, we employ a first-principles interacting Green’s-function

MICROBIOLOGY Correction for “Visualizing active viral infection reveals diverse cell fates in synchronized algal bloom demise,” by Flora Vincent, Uri Sheyn, Ziv Porat, Daniella Schatz, and Assaf Vardi, …

BIOCHEMISTRY Correction to Supporting Information for “Two-step release of kinase autoinhibition in discoidin …

Given the role of myeloid cells in T cell activation and in the antitumor response, targeting checkpoint molecules expressed on this population represents a promising strategy to augment antitumor immunity. However, myeloid checkpoints that can be effectively used as immunotherapy targets are still lacking. Here, we demonstrate the therapeutic potential of targeting the myeloid receptors Siglec-7 and

Van Peer (1) contests the conclusions of our article on Neanderthal disappearance in Northwest Europe (2), but we think his argument may reflect a misunderstanding of the stratigraphy at Spy Cave and/or incomplete reading of our article. We provide here a response to his arguments.

Devièse et al. argue that Neanderthals disappeared from Northwest Europe between 44,200 and 40,600 cal B.P. (1). The stratigraphy at Spy, however, qualifies this conclusion as premature. Except for Spy 572a, the dates are on skeletal parts found on the slope in front of the cave long after the fossil discoveries of 1885 and 1886, most probably in waste of earlier excavations. Some, however, can be

Anti-Müllerian hormone (AMH), or Müllerian-inhibiting substance, is a protein hormone that promotes Müllerian duct regression during male fetal sexual differentiation and regulation of folliculogenesis in women. AMH is a member of the transforming growth factor beta (TGF-β) family, which has evolved to signal through its own dedicated type II receptor, AMH receptor type II (AMHR2). Structures of other

Wnt signals bind to Frizzled receptors to trigger canonical and noncanonical signaling responses that control cell fates during animal development and tissue homeostasis. All Wnt signals are relayed by the hub protein Dishevelled. During canonical (β-catenin–dependent) signaling, Dishevelled assembles signalosomes via dynamic head-to-tail polymerization of its Dishevelled and Axin (DIX) domain, which

Although leaded gasoline was banned at the end of the last century, lead (Pb) remains significantly enriched in airborne particles in large cities. The remobilization of historical Pb deposited in soils from atmospheric removal has been suggested as an important source providing evidence for the hypothetical long-term persistency of lead, and possibly other pollutants, in the urban environment. Here

Complement is an important effector mechanism for antibody-mediated clearance of infections and tumor cells. Upon binding to target cells, the antibody’s constant (Fc) domain recruits complement component C1 to initiate a proteolytic cascade that generates lytic pores and stimulates phagocytosis. The C1 complex (C1qr2s2) consists of the large recognition protein C1q and a heterotetramer of proteases

Many latitudinal insect migrants including agricultural pests, disease vectors, and beneficial species show huge fluctuations in the year-to-year abundance of spring immigrants reaching temperate zones. It is widely believed that this variation is driven by climatic conditions in the winter-breeding regions, but evidence is lacking. We identified the environmental drivers of the annual population dynamics

The large fluctuations in traffic during the COVID-19 pandemic provide an unparalleled opportunity to assess vehicle emission control efficacy. Here we develop a random-forest regression model, based on the large volume of real-time observational data during COVID-19, to predict surface-level NO2, O3, and fine particle concentration in the Los Angeles megacity. Our model exhibits high fidelity in reproducing

Curvature invariants are the most natural invariants, with a wide application in science and engineering. A known condition for a Riemannian manifold to admit a minimal immersion in any Euclidean space is \(Ric\le 0\). In order to find other obstructions, one needs to introduce new types of Riemannian invariants, different in nature from classical ones (Chen in pseudo-riemannian geometry, \(\delta

Female mosquitoes transmit numerous devastating human diseases because they require vertebrate blood meal for egg development. MicroRNAs (miRNAs) play critical roles across multiple reproductive processes in female Aedes aegypti mosquitoes. However, how miRNAs are controlled to coordinate their activity with the demands of mosquito reproduction remains largely unknown. We report that the ecdysone receptor

We consider an analogue of the well-known Casson knot invariant for knotoids. We start with a direct analogue of the classical construction which gives two different integer-valued knotoid invariants and then focus on its homology extension. The value of the extension is a formal sum of subgroups of the first homology group \(H_1(\varSigma )\) where \(\varSigma \) is an oriented surface with (maybe)

Value is a foundational concept in reinforcement learning and economic choice theory. In these frameworks, individuals choose by assigning values to objects and learn by updating values with experience. These theories have been instrumental for revealing influences of probability, risk, and delay on choices. However, they do not explain how values are shaped by intrinsic properties of the choice objects

Foraminiferal wall microstructures, consistent with the molecular-based high-rank classification, are critical to understanding foraminiferal evolution and advanced taxonomic relationships. Although test structures are well documented for recent, Cenozoic, and some Mesozoic foraminifera, the diagnostic characteristics of Paleozoic taxa are largely unexplored. The majority of calcareous Paleozoic foraminifera

Most stars in the Universe are red dwarfs. They outnumber stars like our Sun by a factor of 5 and outlive them by another factor of 20 (population-weighted mean). When combined with recent observations uncovering an abundance of temperate, rocky planets around these diminutive stars, we are faced with an apparent logical contradiction—Why do we not see a red dwarf in our sky? To address this “red sky

TET/JBP (ten-eleven translocation/base J binding protein) enzymes are iron(II)- and 2-oxo-glutarate–dependent dioxygenases that are found in all kingdoms of life and oxidize 5-methylpyrimidines on the polynucleotide level. Despite their prevalence, few examples have been biochemically characterized. Among those studied are the metazoan TET enzymes that oxidize 5-methylcytosine in DNA to hydroxy, formyl

Are women more likely to quit politics after losing their first race than men? Women’s first-time candidacies skyrocketed in the wake of the 2016 presidential election. Yet we have little sense of the long-term impact of this surge in women candidates on women’s representation writ large: Inexperienced candidates are more likely to lose, and women might be especially discouraged by a loss. This might

We prove that for a generic element in a nonhyperelliptic component of an abelian stratum H g ( μ ) in genus g , the underlying curve has maximal gonality. We extend this result to the case of quadratic strata when the partition μ has positive entries. As a consequence we deduce that all nonhyperelliptic components of H 9 ( μ ) are uniruled when μ is a positive partition of 16 and all nonhyperelliptic