ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that for a smooth hypersurface $X\subset \bbP^n$ of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties $Y\subset X$ which are not an intersection $X\cap{S}$ for a codimension two subvariety $S\subset\bbP^n$. We also show there exist $Y\subset X$ as above for which the normal bundle sequence for the inclusion $Y\subset X\subset\bbP^n$ does not split.
The dark energy problem has led to speculation that not only may LCDM be wrong, but that the FLRW models themselves may not even provide the correct family of background models. We discuss how direct measurements of H(z) can be used to formulate tests of the standard paradigm in cosmology. On their own, such measurements can be used to test for deviations from flat LCDM. When combined with supernovae distances, Hubble rate measurements provide a test of the Copernican principle and the homogeneity assumption of the standard model, which is independent of dark energy or metric based theory of gravity. A modification of this test also provides a model independent observable for flatness which decorrelates curvature determination from dark energy. We investigate these tests using Hubble rate measurements from age data, as well as from a Hubble rate inferred from recent measurements of the baryon acoustic oscillations. While the current data is too weak to say anything significant, these tests are exciting prospects for the future.
The detection of the first gravitational wave events by the Advanced LIGO Scientific Collaboration has opened a new possibility for the study of fundamental physics of gravitational interaction.   This work conducts an analysis of possible polarization states of gravitational waves (GW) radiated by the most promising types of sources to be detected by the modern interferometric antennas: coalescing compact binaries and collapsing supernovae. Several theoretical approaches to the current as well as future gravitational wave signals interpretation are discussed together with a strategy for a search for corresponding transients by means of multimessenger astronomy.   One of the aims of this thesis is to develop a new method for GW source localization depending on a polarization state of an incoming GW in the case of a detection by two interferometric antennas. Additionally, there is elaborated a further method focused on a possibility to recognise different polarization states of a GW detected by means of a network with three and more antennas in operation. The both proposed methods have been applied to the LIGO events GW150914, GW151226 and LVT151012, together with the matching of the results with the currently known electromagnetic follow-ups to these GW events.   The conclusion of this research is that there are opportunities for verifying different predictions of the scalar-tensor theories of gravitation by means of the analysis of the polarization states of the detected gravitational waves.   All in all, this work provides a new test of the theoretical assumptions about the nature of gravity as well as about the processes in relativistic compact objects of various types.
Interbank deposits (loans and credits) are quite common in banking system all over the world. Such interbank co-operation is profitable for banks but it can also lead to collective financial failures. In this paper we introduce a new model of directed percolation as a simple representation for contagion process and mass bankruptcies in banking systems. Directed connections that are randomly distributed between junctions of bank lattice simulate flows of money in our model. Critical values of a mean density of interbank connections as well as static and dynamic scaling laws for the statistic of avalange bankruptcies are found. Results of computer simulations for the universal profile of bankruptcies spreading are in a qualitative agreement with the third wave of bank suspensions during The Great Depression in the USA.
Let $f$ be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric power lifting $\mathrm{Sym}^n f$ for every $n \geq 1$. We establish the same result for a more general class of cuspidal Hecke eigenforms, including all those associated to semistable elliptic curves over $\mathbb{Q}$.
By using silicon oxide based aerogels we show numerically that the Casimir force can be reduced several orders of magnitude, making its effect negligible in nanodevices. This decrease in the Casimir force is also present even when the aerogels are deposited on metallic substrates. To calculate the Casimir force we model the dielectric function of silicon oxide aerogels using an effective medium dielectric function such as the Clausius-Mossotti approximation. The results show that both the porosity of the aerogel and its thickness can be use as control parameters to reduce the magnitude of the Casimir force.
We calculate the light scattering spectrum of the anisotropic diffusion of impurities (dye) in a compressible nematic solvent. We use a fluctuating hydrodynamic description when the system is in fully thermodynamic equilibrium and in a non-equilibrium steady state ($NESS$) induced by a dye-concentration gradient. We find that the equilibrium spectrum is symmetric (Lorentzian) with respect to the frequency shifts, but anisotropic through its explicit dependence on the ratio of the parallel and normal diffusion coefficients of the dye. The values of these coefficients were taken from experimental measurements of diffusion of methylred and nitrozo di-methyl aniline in a $MBBA$ solvent. We find that the compressibility of the solvent increases the maximum and the width at half height of the Rayleigh peak, with respect to the incompressible case \cite{suspension1}. This increase varies between 12% and 25%, respectively, when the impurities concentrations is the range of 1% - 5%. The $NESS$ induces a coupling between the concentration fluctuations of the dye and the hydrodynamic fluctuations of the solvent. In this case the compressibility effects may increase the maximum and the width of the central peak up to $% 25%$, for values of the concentration gradient four orders of magnitude smaller than those considered in the incompressible case. For the nonequilibrium Brillouin part of the spectrum we find that the intensities of the sound propagation modes are unequal and one of the peaks shrinks in the same amount as the other increases. This asymmetry increases linearly with the magnitude of the solute concentration gradient. The maximum difference between the nonequilibrium and equilibrium contributions to the Brillouin spectrum for various values of the external gradient is also estimated.
Tracking the star formation rate to high redshifts requires knowledge of the contribution from both optically visible and obscured sources. The dusty, optically-obscured galaxies can be located by X-ray and infrared surveys. To establish criteria for selecting such sources based only on X-ray and infrared surveys, we determine the ratio of infrared to X-ray brightness that would be observed by SIRTF and Chandra for objects with the same spectral shapes as nearby starbursts if seen at high redshift. The parameter IR/X is defined as IR/X = (flux density observed in SIRTF MIPS 24 $\mu$m filter in mJy)/(total flux observed within 0.5-2.0 keV in units of 10^-16 ergs\s\cm^2). Based on observations of NGC 4038/39 (``The Antennae''), NGC 3690+IC 694 (Arp 299 or Mkn 171), M 82, and Arp 220, nine starburst regions are compared using mid-infrared spectra taken by the Infrared Space Observatory (ISO) and X-ray spectra obtained with Chandra . The IR/X are determined as they would appear for 1<z<3. The mean IR/X over this redshift range is 1.3 and is not a significant function of redshift or luminosity, indicating that SIRTF surveys reaching 0.4 mJy at 24 $\mu$m should detect the same starbursts as deep CXO surveys detect at a flux of 0.3x10^-16 ergs/s/cm^2. The lower bound of IR/X for starbursts is about 0.2, suggesting that objects with IR/X smaller than this have an AGN X-ray component in addition to the starburst. Values of IR/X for the obscured AGN within NGC 1068, the Circinus galaxy, and NGC 6240 are also determined for comparison although interpretation is complicated by the circumnuclear starbursts in these galaxies. Any sources found in surveys having IR/X>4 would not match any of the objects considered.
We prove that every smooth projective variety with maximal Albanese dimension has a good minimal model. We also treat Ueno's problem on subvarieties of Abelian varieties.
Many layered metals such as quasi-two-dimensional organic molecular crystals show properties consistent with a Fermi liquid description at low temperatures. The effective masses extracted from the temperature dependence of the magnetic oscillations observed in these materials are in the range, m^*_c/m_e \sim 1-7, suggesting that these systems are strongly correlated. However, the ratio m^*_c/m_e contains both the renormalization due to the electron-electron interaction and the periodic potential of the lattice. We show that for any quasi-two-dimensional band structure, the cyclotron mass is proportional to the density of states at the Fermi energy. Due to Luttinger's theorem, this result is also valid in the presence of interactions. We then evaluate m_c for several model band structures for the \beta, \kappa, and \theta families of (BEDT-TTF)_2X, where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene) and X is an anion. We find that for \kappa-(BEDT-TTF)_2X, the cyclotron mass of the \beta-orbit, m^{*\beta}_c, is close to 2 m^{*\alpha}_c, where m^{*\alpha}_c is the effective mass of the \alpha- orbit. This result is fairly insensitive to the band structure details. For a wide range of materials we compare values of the cyclotron mass deduced from band structure calculations to values deduced from measurements of magnetic oscillations and the specific heat coefficient.
Similar to the three-qubit Greenberger-Horne-Zeilinger (GHZ) symmetry we explore the four-qubit GHZ symmetry group and its subgroup called restricted GHZ symmetry group. While the set of symmetric states under the whole group transformation is represented by three real parameters, the set of symmetric states under the subgroup transformation is represented by two real parameters. After comparing the symmetric states for whole and subgroup, the entanglement is examined for the latter set. It is shown that the set has only two SLOCC classes, $L_{abc_2}$ and $G_{abcd}$. Extension to the multi-qubit system is briefly discussed.
In this work we show how to define the action of a scalar field in a such a way that Robin boundary condition is implemented dynamically, i.e., as a consequence of the stationary action principle. We discuss the quantization of that system via functional integration. Using this formalism, we derive an expression for the Casimir energy of a massless scalar field under Robin boundary conditions on a pair of parallel plates, characterized by constants $c_1$ and $c_2$. Some special cases are discussed; in particular, we show that for some values of $c_1$ and $c_2$ the Casimir energy as a function of the distance between the plates presents a minimum. We also discuss the renormalization at one-loop order of the two-point Green function in the $\lambda\phi^4$ theory submitted to Robin boundary condition on a plate.
We investigate the electronic structure of high-quality single-crystal LaNiO$_3$ (LNO) thin films using in situ photoemission spectroscopy (PES). The in situ high-resolution soft x-ray PES measurements on epitaxial thin films reveal the intrinsic electronic structure of LNO. We find a new sharp feature in the PES spectra crossing the Fermi level, which is derived from the correlated Ni 3$d$ $e_g$ electrons. This feature shows significant enhancement of spectral weight with decreasing temperature. From a detailed analysis of resistivity data, the enhancement of spectral weight is attributed to increasing electron correlations due to antiferromagnetic fluctuations.
Early X-ray observations suggested that the intracluster medium cools and condenses at the centers of clusters, leading to a cooling flow of plasma in the cluster core. The increased incidence of emission-line nebulosity, excess blue light, AGN activity, and molecular gas in the cores of clusters with short central cooling times seemed to support this idea. However, high-resolution spectroscopic observations from XMM-Newton and Chandra have conclusively ruled out simple, steady cooling flow models. We review the history of this subject, the current status of X-ray observations, and some recent models that have been proposed to explain why the core gas does not simply cool and condense.
We carried out an unbiased survey for massive dense cores in the giant molecular cloud associated with eta Carinae with the NANTEN telescope in 12CO, 13CO, and C18O 1-0 emission lines. We identified 15 C18O cores. Two of the 15 cores are associated with IRAS point sources whose luminosities are larger than 10^4 Lo, which indicates that massive star formation is occuring within these cores. Five cores including the two with IRAS sources are associated with MSX point sources. We detected H13CO+ (1-0) emission toward 4 C18O cores, one of which is associated with neither IRAS nor MSX point sources. This core shows the presence of a bipolar molecular outflow in 12CO (2-1), which indicates that star formation is also occuring in the core. In total, six C18O cores out of 15 are experienced star formation, and at least 2 of 15 are massive-star forming cores in the eta Car GMC. We found that massive star formation occurs preferentially in cores with larger column density, mass, number density, and smaller ratio of virial mass to LTE mass Mvir/M. We also found that the cores in the eta Car GMC are characterized by large line width and Mvir/M on average compared to the cores in other GMCs. We investigated the origin of a large amount of turbulence in the eta Car GMC. We propose the possibility that the large turbulence was pre-existing when the GMC was formed, and is now dissipating. Mechanisms such as multiple supernova explosions in the Carina flare supershell may have contributed to form a GMC with a large amount of turbulence.
We present a theoretical framework to describe the effects of decoherence on matter waves in Talbot-Lau interferometry. Using a Wigner description of the stationary beam the loss of interference contrast can be calculated in closed form. The formulation includes both the decohering coupling to the environment and the coherent interaction with the grating walls. It facilitates the quantitative distinction of genuine quantum interference from the expectations of classical mechanics. We provide realistic microscopic descriptions of the experimentally relevant interactions in terms of the bulk properties of the particles and show that the treatment is equivalent to solving the corresponding master equation in paraxial approximation.
Recent studies have shown that the cross-correlation coefficient between galaxies and dark matter is very close to unity on scales outside a few virial radii of galaxy halos, independent of the details of how galaxies populate dark matter halos. This finding makes it possible to determine the dark matter clustering from measurements of galaxy-galaxy weak lensing and galaxy clustering. We present new cosmological parameter constraints based on large-scale measurements of spectroscopic galaxy samples from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). We generalise the approach of Baldauf et al. (2010) to remove small scale information (below 2 and 4 Mpc/h for lensing and clustering measurements, respectively), where the cross-correlation coefficient differs from unity. We derive constraints for three galaxy samples covering 7131 sq. deg., containing 69150, 62150, and 35088 galaxies with mean redshifts of 0.11, 0.28, and 0.40. We clearly detect scale-dependent galaxy bias for the more luminous galaxy samples, at a level consistent with theoretical expectations. When we vary both \sigma_8 and \Omega_m (and marginalise over non-linear galaxy bias) in a flat LCDM model, the best-constrained quantity is \sigma_8 (\Omega_m/0.25)^{0.57}=0.80 +/- 0.05 (1-sigma, stat. + sys.), where statistical and systematic errors have comparable contributions, and we fixed n_s=0.96 and h=0.7. These strong constraints on the matter clustering suggest that this method is competitive with cosmic shear in current data, while having very complementary and in some ways less serious systematics. We therefore expect that this method will play a prominent role in future weak lensing surveys. When we combine these data with WMAP7 CMB data, constraints on \sigma_8, \Omega_m, H_0, w_{de} and \sum m_{\nu} become 30--80 per cent tighter than with CMB data alone, since our data break several parameter degeneracies.
In this paper, we report the multiwavelength observations of the partial filament eruption associated with a C1.2 class flare in NOAA active region 11236 on 13 June 2011. The event occurred at the eastern limb in the field of view (FOV) of Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) spacecraft and was close to the disk center in the FOV of Extreme-UltraViolet Imager (EUVI) on board the behind Solar Terrestrial Relations Observatory (STEREO) spacecraft. During eruption, the filament splits into two parts: the major part and runaway part. The major part flows along closed loops and experiences bifurcation at the loop top. Some of the materials move forward and reach the remote footpoint, while others return back to the original footpoint. The runaway part flows along open field lines, which is evidenced by a flare-related type III radio burst. The runaway part also undergoes bifurcation. The upper branch of escapes the corona and evolves into a jet-like narrow coronal mass ejection (CME) at a speed of 324 km s-1, while the lower branch falls back to the solar surface. A schematic cartoon is proposed to explain the event and provides a new mechanism of partial filament eruptions
In this paper, we study the problem of making brighter images from dark images found in the wild. The images are dark because they are taken in dim environments. They suffer from color shifts caused by quantization and from sensor noise. We don't know the true camera reponse function for such images and they are not RAW. We use a supervised learning method, relying on a straightforward simulation of an imaging pipeline to generate usable dataset for training and testing. On a number of standard datasets, our approach outperforms the state of the art quantitatively. Qualitative comparisons suggest strong improvements in reconstruction accuracy.
We introduce and develop the theory of Newton nondegenerate local Weil divisors $(X,0)$ in toric affine varieties. We characterize in terms of the toric combinatorics of the Newton diagram different properties of such singular germs: normality, Gorenstein property, or being an Cartier divisor in the ambient space. We discuss certain properties of their (canonical) resolution $\tilde{X}\to X $ and the corresponding canonical divisor. We provide combinatorial formulae for the delta--invariant $\delta(X,0)$ and for the cohomology groups $H^i(\tilde X,\mathcal{O}_{\tilde X})$ for $i>0$. In the case $\dim(X,0)=2$, we provide the (canonical) resolution graph from the Newton diagram and we also prove that if such a Weil divisor is normal and Gorenstein, and the link is a rational homology sphere, then the geometric genus is given by the minimal path cohomology, a topological invariant of the link.
In any physical theory that admits true indeterminism, the thermodynamic arrow of time can arise regardless of the system's initial conditions. Hence on such theories time's arrow emerges out of the basic physical interactions. The example of the GRW theory is studied in detail.
We investigate exclusive leptoproduction of $\rho^0$ meson. These reactions were analyzed within the factorizing handbag approach. In our model good agreement of observables for light meson production with experimental data in a wide energy range was found.   Using the model results we calculate the ratio of different helicity amplitudes for a transversely polarized proton target to the leading twist longitudinal amplitude. Our results are close to the amplitude ratios measured by HERMES.
We report the analysis result of UV/X-ray emission from AR~Scorpii, which is an intermediate polar (IP) composed of a magnetic white dwarf and a M-type star, with the XMM-Newton data. The X-ray/UV emission clearly shows a large variation over the orbit, and their intensity maximum (or minimum) is located at the superior conjunction (or inferior conjunction) of the M-type star orbit. The hardness ratio of the X-ray emission shows a small variation over the orbital phase, and shows no indication of the absorption by an accretion column. These properties are naturally explained by the emission from the M-type star surface rather than from the accretion column on the WD's star similar to the usual IPs. Beside, the observed X-ray emission also modulates with WD's spin with a pulse fraction of $\sim 14\%$. The peak position is aligned in the optical/UV/X-ray band. This supports the hypothesis that the electrons in AR~Scorpii are accelerated to a relativistic speed, and emit non-thermal photons via the synchrotron radiation. In the X-ray bands, the evidence of the power-law spectrum is found in the pulsed component, although the observed emission is dominated by the optically thin thermal plasma emissions with several different temperatures. It is considered that the magnetic dissipation/reconnection process on the M-type star surface heats up the plasma to a temperature of several keV, and also accelerates the electrons to the relativistic speed. The relativistic electrons are trapped in the WD's closed magnetic field lines by the magnetic mirror effect. In this model, the observed pulsed component is explained by the emissions from the first magnetic mirror point.
The variational cluster approximation is used to study the frustrated Hubbard model at half filling defined on the two-dimensional square lattice with anisotropic next-nearest-neighbor hopping parameters. We calculate the ground-state phase diagrams of the model in a wide parameter space for a variety of lattice geometries, including square, crossed-square, and triangular lattices. We examine the Mott metal-insulator transition and show that, in the Mott insulating phase, magnetic phases with N\'eel, collinear, and spiral orders appear in relevant parameter regions, and in an intermediate region between these phases, a nonmagnetic insulating phase caused by the quantum fluctuations in the geometrically frustrated spin degrees of freedom emerges.
We derive a fundamental solution $\mathscr{E}$ to a space-fractional diffusion problem on the half-line. The equation involves the Caputo derivative. We establish properties of $\mathscr{E}$ as well as formulas for solutions to the Dirichlet and Neumann problems in terms of convolution of $\mathscr{E}$ with data. We also study integrability of derivative of solutions given in this way. We present conditions sufficient for uniqueness. Finally, we show the infinite speed of signal propagation.