ShantanuT01/DACTYL-Pretraining huggingface dataset:
For $\gamma>0$, we are interested in blow up solutions $u\in C^+(B)$ of the fractional problem in the unit ball $B$ \begin{equation}\label{2nov} \left\{\begin{array} {rcll} \Delta^{\frac{\alpha}{2}} u &=& u^\gamma&\ \text{in }B\\ u &=& 0&\ \text{in }B^c.\end{array}\right. \end{equation} We distinguish particularly two orders of singularity at the boundary: solutions exploding at the same rate than $\delta^{1-\frac{\alpha}{2}}$ ($\delta$ denotes the Euclidean distance) and those higher singular than $\delta^{1-\frac{\alpha}{2}}.$ As a consequence, it will be shown that the classical Keller-Osserman condition can not be readopted in the fractional setting.
In 1988 S. Mori, D. Morrison, and I. Morrison gave a computer-based conjectural classification of four-dimensional cyclic quotient singularities of prime index. It was partially proven in 1990 by G. Sankaran. In 1991 Jim Lawrence basically proved this and much more, been unaware of algebro-geometric meaning of what he did. In this short note I just bring this all together to prove that all n-dimensional toric singularities with log-discrepancy greater than (or equal to) $\epsilon$ form finitely many "series".
We have observed the B I 2497 A line to derive the boron abundances of two very metal-poor stars selected to help in tracing the origin and evolution of this element in the early Galaxy: BD +23 3130 and HD 84937. The observations were conducted using the Goddard High Resolution Spectrograph on board the Hubble Space Telescope. A very detailed abundance analysis via spectral synthesis has been carried out for these two stars, as well as for two other metal-poor objects with published spectra, using both Kurucz and OSMARCS model photospheres, and taking into account consistently the NLTE effects on the line formation. We have also re-assessed all published boron abundances of old disk and halo unevolved stars. Our analysis shows that the combination of high effective temperature (Teff > 6000 K, for which boron is mainly ionized) and low metallicity ([Fe/H]<-1) makes it difficult to obtain accurate estimates of boron abundances from the B I 2497 A line. This is the case of HD 84937 and three other published objects (including two stars with [Fe/H] ~ -3), for which only upper limits can be established. BD +23 3130, with [Fe/H] ~ -2.9 and logN(B)_NLTE=0.05+/-0.30, appears then as the most metal-poor star for which a firm measurement of the boron abundance presently exists. The evolution of the boron abundance with metallicity that emerges from the seven remaining stars with Teff < 6000 K and [Fe/H]<-1, for which beryllium abundances were derived using the same stellar parameters, shows a linear increase with a slope ~ 1. Furthermore, the B/Be ratio found is constant at a value ~ 20 for stars in the range -3<[Fe/H]<-1. These results point to spallation reactions of ambient protons and alpha particles with energetic particles enriched in CNO as the origin of boron and beryllium in halo stars.
Context. Searching for high-redshift galaxies is a field of intense activity in modern observational cosmology that will continue to grow with future ground-based and sky observatories. Over the last few years, a lot has been learned about the high-z Universe. Aims. Despite extensive Ly-alpha Blobs (LAB) surveys from low to high redshifts, giant LABs over 100 kpc have been found mostly at z~2-4. This redshift range is coincident with the transition epoch of galactic gas-circulation processes from inflows to outflows at z~2.5-3. This suggests that the formation of giant LABs may be related to a combination of gas inflows and outflows. Their extreme youth makes them interesting objects in the study of galaxy formation as they provide insight into some of the youngest known highly star forming galaxies, with only modest time investments using ground-based telescopes. Methods. Systematic narrow-band Ly-alpha nebula surveys are ongoing, but they are limited in their covered redshift range and their comoving volume. This poses a significant problem when searching for such rare sources. To address this problem, we developed a systematic searching tool, ATACAMA (A Tool for seArChing for lArge LyMan Alpha nebulae) designed to find large Ly-alpha nebulae at any redshift within deep multi-wavelength broad-band imaging. Results. We identified a Ly-alpha nebula candidate at zphot~3.3 covering an isophotal area of 29.4sq.arcsec. Its morphology shows a bright core and a faint core which coincides with the morphology of previously known Ly-alpha blobs. A first estimation of the Ly-alpha equivalent width and line flux agree with the values from the study led by several groups.
We report on microscopic study of the ferromagnetism enhancement in the Ru doped ferromagnetic superconductor (FM SC) UCoGe. For that purpose, two single crystals with composition UCo0.97Ru0.03Ge and UCo0.88Ru0.12Ge were prepared. Both single crystals were investigated by polarized neutron diffraction (PND) at low temperatures in magnetic fields and the latter one also by the soft X-ray magnetic circular dichroism (XMCD) method. UCo0.96Ru0.03Ge and UCo0.88Ru0.12Ge have been found ordering ferromagnetically below the Curie temperature TC = 6 K and 8.5 K, respectively, which are considerable higher than TC = 3 K of UCoGe. The increase of TC is accompanied by enhancement of the spontaneous moment to ms = 0.11 mB/f.u. and ms = 0.21 mB/f.u., respectively. The analysis of the PND results assigns the ferromagnetism enhancement mainly to the growth of the orbital part of uranium 5 f moment. In contrast to the published results of PND study of the parent UCoGe, we have found parallel orientation of the U and Co moments in both doped compounds. Evolution of magnetic characteristics with Ru concentration is discussed within a scenario considering the varying 5 f-ligand hybridization as the key mechanism.
Recent observations have shown that the majority of the Andromeda galaxy's satellites are aligned in a thin plane. On the theoretical side it has been proposed that galaxies acquire their gas via cold streams. In addition, numerical simulations show that the same streams also deliver gas clumps which could potentially develop into satellite galaxies. Assuming that cold streams are a major source of satellite systems around galaxies we calculate the probabilities in two different models to find a certain fraction of satellites within a thin plane around the central galaxy of the host halo with and without having the same sense of rotation. Using simple geometrical considerations and adopting a random orientation of the streams we demonstrate that the vast thin disk of satellites detected around Andromeda can naturally be explained within this framework. In fact, without any satellite scattering, two streams would lead to too many satellites in the thin plane, compared with the observations. Three streams reproduce the observations very well. Natural implications from our model are that all massive galaxies should have a thin plane of satellites and that the satellites should naturally distribute themselves not only into a single plane but into several inclined ones. We estimate the effect of additional satellites accreted from random directions and find it to be of minor relevance for a mild inflow of satellites from random directions.
We investigate magnetic instabilities in charge-neutral twisted bilayer graphene close to so-called "magic angles" using a combination of real-space Hartree-Fock and dynamical mean-field theories. In view of the large size of the unit cell close to magic angles, we examine a previously proposed rescaling that permits to mimic the same underlying flat minibands at larger twist angles. We find that localized magnetic states emerge for values of the Coulomb interaction $U$ that are significantly smaller than what would be required to render an isolated layer antiferromagnetic. However, this effect is overestimated in the rescaled system, hinting at a complex interplay of flatness of the minibands close to the Fermi level and the spatial extent of the corresponding localized states. Our findings shed new light on perspectives for experimental realization of magnetic states in charge-neutral twisted bilayer graphene.
We study multi-charged rotating string states on Type IIB regular backgrounds dual to confining SU(N) gauge theories with (softly broken) {\cal N}=1 supersymmetry, in the infra red regime. After exhibiting the classical energy/charge relations for the folded and circular two-charge strings, we compute in the latter case the one loop sigma-model quantum correction. The classical relation has an expansion in positive powers of the analogous of the BMN effective coupling, while the quantum corrections are non perturbative in nature and are not subleading in the limit of infinite charge. We comment about the dual field theory multi-charged hadrons and the implications of our computation for the AdS/{\cal N}=4 duality.
We revisit the predictions for the expected Cosmic Microwave Background bispectrum signal from the primary-lensing-Rees-Sciama correlation; we point out that it can be a significant contaminant to the bispectrum signal from primordial non-Gaussianity of the local type. This non-Gaussianity, usually parameterized by the non-Gaussian parameter f_NL, arises, for example, in multi-field inflation. In particular both signals are frequency independent, and are maximized for nearly squeezed configurations. While their detailed scale-dependence and harmonic imprints are different for generic bispectrum shapes, we show that, if not included in the modeling, the primary-lensing-Rees-Sciama contribution yields an effective f_{NL} of 10 when using a bispectrum estimator optimized for local non-Gaussianity. Considering that expected 1-sigma errors on f_{NL} are < 10 from forthcoming experiments, we conclude that the contribution from this signal must be included in future constraints on f_{NL} from the Cosmic Microwave Background bispectrum.
Transport phenomena on a quantum scale appear in a variety of systems, ranging from photosynthetic complexes to engineered quantum devices. It has been predicted that the efficiency of quantum transport can be enhanced through dynamic interaction between the system and a noisy environment. We report the first experimental demonstration of such environment-assisted quantum transport, using an engineered network of laser-written waveguides, with relative energies and inter-waveguide couplings tailored to yield the desired Hamiltonian. Controllable decoherence is simulated via broadening the bandwidth of the input illumination, yielding a significant increase in transport efficiency relative to the narrowband case. We show integrated optics to be suitable for simulating specific target Hamiltonians as well as open quantum systems with controllable loss and decoherence.
BL Lacertae (BL Lac) is categorized as TeV blazar and considered as a possible source of astrophysical neutrinos. In 2020, the brightest X-ray flare ever detected from it. A detailed study can answer many puzzling questions related to multiband emissions and fast-flux variability often seen in this kind of source. We have performed the temporal and spectral analysis of the brightest flare. The variability is characterized by the fractional variability amplitude and the variability time. We found that the source has crossed all its previous limits of flux and reached the maximum ever seen from it in optical and X-rays. It is highly variable in X-rays with fractional variability above 100$\%$ (1.8397$\pm$0.0181) and the fastest variability time of 11.28 hours within a day. The broadband light curves correlation with X-ray suggest a time lag of one day. A broadband SED modeling is pursued to understand the possible physical mechanisms responsible for broadband emission. Modeling requires two emission regions located at two different sites to explain the low and high flux states. A significant spectral change is observed in the optical-UV and X-ray spectrum during the high state, which eventually leads to shifts in the location of the synchrotron peak towards higher energy, suggesting an emergence of a new HBL component.
We present a face detection algorithm based on Deformable Part Models and deep pyramidal features. The proposed method called DP2MFD is able to detect faces of various sizes and poses in unconstrained conditions. It reduces the gap in training and testing of DPM on deep features by adding a normalization layer to the deep convolutional neural network (CNN). Extensive experiments on four publicly available unconstrained face detection datasets show that our method is able to capture the meaningful structure of faces and performs significantly better than many competitive face detection algorithms.
Computational acceleration of performance-metric-based materials discovery via high-throughput screening and machine learning methods is becoming widespread. Nevertheless, development and optimization of the opto-electronic properties that depend on dilute concentrations of point defects in new materials have not significantly benefited from these advances. Here, we present an informatics and simulation suite to computationally accelerate these processes. This will enable faster and more fundamental materials research, and reduce the cost and time associated with the materials development cycle. Analogous to the new avenues enabled by current first-principles-based property databases, this type of framework will open entire new research frontiers as it proliferates.
We investigated the Dirac-cone state and its modulation when an ultrathin film of topological insulator Bi2Se3 was epitaxially grown on a van-der-Waals ferromagnet Cr2Si2Te6 (CST) by angle-resolved photoemission spectroscopy. We observed a gapless Dirac-cone surface state in 6 quintuple-layer (QL) Bi2Se3 on CST, whereas the Dirac cone exhibits a gap of 0.37 eV in 2QL counterpart. Intriguingly, this gap is much larger than those for Bi2Se3 films on Si(111). We also revealed no discernible change in the gap magnitude across the ferromagnetic transition of CST, suggesting the very small characteristic length and energy scale of the magnetic proximity effect. The present results suggest a crucial role of interfacial coupling for modulating Dirac electrons in topological-insulator hybrids.
A convenient method has been developed to thin electron beam fabricated Silicon nanopillars under controlled surface manipulation by transforming the surface of the pillars to an oxide shell layer followed by the growth of sacrificial ammonium silicon fluoride coating. The results show the formation of an oxide shell and a Silicon core without significantly changing the original length and shape of the pillars. The oxide shell layer thickness can be controlled from few nanometers up to few hundred nanometers. While down sizing in diameter, smooth Si pillar surfaces of less than 10 nm roughness within 2 {\mu}m were produced after exposure to vapors of HF and HNO3 mixture as evidenced by transmission electron microscopy (TEM) analysis. The attempt to expose for long durations leads to the growth of a thick oxide whose strain effect on pillars can be assessed by coupled LO-TO vibrational modes of Si-O bonds. Photoluminescence (PL) on the pillar structures which have been down sized exhibit visible and infrared emissions, which are attributable to microscopic pillars and to the confinement of excited carriers in Si core, respectively. The formation of a smooth core-shell structures while reducing the diameter of the Si pillars has a potential in fabricating nanoscale electronic devices and functional components.
We study the extended Hubbard model away from half-filling on a two-dimensional square lattice using cluster dynamical mean field theory on clusters of size $8$. We show that the model exhibits metallic, compressible charge ordered, and insulating charge ordered phases. We determine the location of the charge ordering phase transition line at finite temperature and the properties of the phases as a function of doping, temperature, local interaction, and nearest neighbor interaction. An analysis of the energetics of the charge order transition shows that the charge ordering transition mainly results in a rearrangement of local and non-local potential energy. We show the doping evolution of the spectral function from the isotropic metal via a charge ordered metal to a charge ordered insulator with a big gap, and study finite size effects of the approximation.
Numerous surveys are underway or planned that aim to exploit the Lyman-alpha emission line as a probe of the distant universe. We investigate the reliability of such high-z Lya studies and the validity of the conclusions that are based upon them. We examine whether reliable Lya fluxes (F_Lya) and equivalent widths (W_Lya) can be estimated from narrowband imaging surveys and whether any observational biases may be present. We have developed software to simulate the observed line and continuum properties of synthetic LAEs in the distant universe by adopting various typical observational techniques. This was used to investigate how detected F_Lya and W_Lya vary with properties of the host or IGM: internal dust reddening; intervening Lya absorption systems; the presence of underlying stellar populations. None of the techniques studied are greatly susceptible to underlying stellar populations or the contribution of nebular gas. We find that techniques that use one off-line filter on the red side of Lya result in highly inaccurate measurements of W_Lya. Adopting two off-line filters to estimate continuum at Lya is an improvement but is still unreliable when dust extinction is considered. Techniques that employ single narrow- and broad-band filters with the same central wavelength are not susceptible to internal dust, but IGM Lya absorption can cause W_Lya to be overestimated by factors of up to 2: at z=6, the median W_Lya is overestimated by ~25%. The most robust approach is a SED fitting technique that fits E(B-V) and burst-age from synthetic models - broadband observations are needed that sample the UV continuum slope, 2175AA dust feature, and the 4000AA discontinuity. We also notice a redshift-dependent incompleteness that results from DLA systems close to the target LAEs, amounting to ~10% at z=6.
We demonstrate magnetic field sensing using an ensemble of nitrogen-vacancy centers by recording the variation in the pump-light absorption due to the spin-polarization dependence of the total ground state population. Using a 532 nm pump laser, we measure the absorption of native nitrogen-vacancy centers in a chemical vapor deposited diamond placed in a resonant optical cavity. For a laser pump power of 0.4 W and a cavity finesse of 45, we obtain a noise floor of $\sim$ 100 nT/$\sqrt{\textrm{Hz}}$ spanning a bandwidth up to 125 Hz. We project a photon shot-noise-limited sensitivity of $\sim$ 1 pT/$\sqrt{\textrm{Hz}}$ by optimizing the nitrogen-vacancy concentration and the detection method.
We provide the first example of a sign pattern $S$ for which there exist orthogonal matrices $Q_1$ and $Q_2$ with sign pattern $S$ such that $\det Q_1=1$ and $\det Q_2=-1$. The existence of such matrices is raised by C. Waters in {"Sign Pattern Matrices That Allow Orthogonality"}, Linear Algebra and Its Applications, 235:1-13 (1996).
Properties of intervals in the lattice of antichains of subsets of a universe of finite size are investigated. New objects and quantities in this lattice are defined. Expressions and numerical values are deduced for the number of connected antichains and the number of fully distinguishing antichains. The latter establish a connection with Stirling numbers of the second kind. Decomposition properties of intervals in the lattice of antichains are proven. A new operator allowing partitioning the full lattice in intervals derived from lower dimensional sub-lattices is introduced. Special posets underlying an interval of antichains are defined. The poset allows the derivation of a powerful formula for the size of an interval. This formula allows computing intervals in the six dimensional space. Combinatorial coefficients allowing another decomposition of the full lattice are defined. In some specific cases, related to connected components in graphs, these coefficients can be efficiently computed. This formula allows computing the size of the lattice of order 8 efficiently. This size is the number of Dedekind of order 8, the largest one known so far.
We prove that if $X$ is a complex projective K3 surface and $g>0$, then there exist infinitely many families of curves of geometric genus $g$ on $X$ with maximal, i.e., $g$-dimensional, variation in moduli. In particular every K3 surface contains a curve of geometric genus 1 which moves in a non-isotrivial family. This implies a conjecture of Huybrechts on constant cycle curves and gives an algebro-geometric proof of a theorem of Kobayashi that a K3 surface has no global symmetric differential forms.
In this paper, we study the asymptotic behavior of the normalized cadlag functions generated by the discrete Fourier transforms of a stationary centered square-integrable process, started at a point.   We prove that the quenched invariance principle holds for averaged frequencies under no assumption other than ergodicity, and that this result holds also for almost every fixed frequency under a certain generalization of the Hannan condition and a certain rotated form of the Maxwell and Woodroofe condition which, under a condition of weak dependence that we specify, is guaranteed for a.e. frequency. If the process is in particular weakly mixing, our results describe the asymptotic distributions of the normalized discrete Fourier transforms at every frequency other than $0$ and $\pi$ under the generalized Hannan condition.   We prove also that under a certain regularity hypothesis the conditional centering is irrelevant for averaged frequencies, and that the same holds for a given fixed frequency under the rotated Maxwell and Woodroofe condition but not necessarily under the generalized Hannan condition. In particular, this implies that the hypothesis of regularity is not sufficient for functional convergence without random centering at a.e. fixed frequency.   The proofs are based on martingale approximations and combine results from Ergodic theory of recent and classical origin with approximation results by contemporary authors and with some facts from Harmonic Analysis and Functional Analysis.
We present a novel approach of identifying the Milky Way (MW) and Andromeda (M31) progenitors that could be visible as LAEs at z~6: we couple a snapshot from the Constrained Local UniversE Simulations (CLUES) project, that successfully reproduces the MW and M31 galaxies situated in their correct environment, to a Lyman Alpha Emitter (LAE) model. Exploring intergalactic medium (IGM) ionization states ranging from an almost neutral to a fully ionized one, we find that including (excluding) the effects of clustered sources the first local group progenitor appears as a LAE for a neutral hydrogen fraction of 0.4 (0.1). This number increases to 5 progenitors each of the MW and M31 being visible as LAEs for a completely ionized IGM; the contribution from clustered sources is crucial in making many of the progenitors visible in the Lyman Alpha, for all the ionization states considered. We also put constrains on the physical properties of such progenitors. Finally, we find that the number density of these LAEs are higher than that of general field LAEs (observed in cosmological volumes) by about two (one) orders of magnitude for a neutral hydrogen fraction of 10^-5 (0.4). Detections of such high LAE number densities at z ~ 6 would be a clear signature of an over-dense region that could evolve and resemble the local group volume at z=0.