ShantanuT01/DACTYL-Pretraining huggingface dataset:
We revisit the following chemotaxis system modeling tumor invasion \begin{equation*} \begin{cases} u_t=\Delta u-\nabla \cdot(u\nabla v),& x\in\Omega, t>0,\\ v_t=\Delta v+wz,& x\in\Omega, t>0,\\ w_t=-wz,& x\in\Omega, t>0,\\ z_t=\Delta z-z+u, & x\in\Omega, t>0,\\ \end{cases} \end{equation*} in a smooth bounded domain $\Omega \subset \mathbb{R}^n(n\geq 1)$ with homogeneous Neumann boundary and initial conditions. This model was recently proposed by Fujie et al. \cite{FIY14} as a model for tumor invasion with the role of extracellular matrix incorporated, and was analyzed by Fujie et al. \cite{FIWY16}, showing the uniform boundedness and convergence for $n\leq 3$. In this work, we first show that the $L^\infty$-boundedness of the system can be reduced to the boundedness of $\|u(\cdot,t)\|_{L^{\frac{n}{4}+\epsilon}(\Omega)}$ for some $\epsilon>0$ alone, and then, for $n\geq 4$, if the initial data $\|u_0\|_{L^{\frac{n}{4}}}$, $\|z_0\|_{L^\frac{n}{2}}$ and $\|\nabla v_0 \|_{L^n}$ are sufficiently small, we are able to establish the $L^\infty$-boundedness of the system. Furthermore, we show that boundedness implies exponential convergence with explicit convergence rate, which resolves the open problem left in \cite{FIWY16}.
Minimal algebraic surfaces of general type $X$ such that $K^2_X=2\chi(\mathcal{O}_X)-6$ or $K^2_X=2\chi(\mathcal{O}_X)-5$ are called Horikawa surfaces. In this note we study $\mathbb{Z}^2_2$-actions on Horikawa surfaces. The main result is that all the connected components of Gieseker's moduli space of canonical models of surfaces of general type with invariants satisfying these relations contain surfaces with $\mathbb{Z}^2_2$-actions.
We update our previous work on the description of twisted configurations for complex massless scalar field on the Kerr black holes as the sections of complex line bundles over the Kerr black hole topology. From physical point of view the appearance of twisted configurations is linked with the natural presence of Dirac monopoles that arise as connections in the above line bundles. We consider their description in the gauge inequivalent to the one studied previously and discuss a row of new features appearing in this gauge.
Galaxies in clusters undergo several phenomena such as ram pressure stripping and tidal interactions, that can trigger or quench their star formation and, in some cases, lead to galaxies acquiring unusual shapes and long tails. We searched for jellyfish galaxy candidates in a sample of 40 clusters from the DAFT/FADA and CLASH surveys covering the redshift range 0.2<z<0.9. In MACS J0717.5+3745 (MACS0717), our large spatial coverage and abundant sampling of spectroscopic redshifts allowed us to pursue a detailed analysis of jellyfish galaxy candidates in this cluster and its extended filament. We looked at the Hubble Space Telescope images of all the cluster galaxies (based on redshifts), and classified them as a function of their likeliness to be jellyfish galaxies, and give catalogues of jellyfish candidates with positions, redshifts, magnitudes, and projected distance to the respective cluster centre. We found 81 jellyfish candidates in the extended region around MACS0717, and 97 in 22 other clusters. Jellyfish galaxy candidates in MACS0717 tend to avoid the densest regions of the cluster, while this does not appear to be the case in the other clusters. For 79 galaxies in MACS0717 and 31 in other clusters, we computed the best stellar population fits with LePhare through the GAZPAR interface. We find that jellyfish candidates tend to be star forming objects, with blue colours, young ages, high star formation rates and specific star formation rates. In a SFR versus stellar mass diagram, jellyfish galaxy candidates appear to have somewhat larger SFRs than non-jellyfish star forming galaxies Based on several arguments, the jellyfish candidates identified in MACS0717 seem to have fallen rather recently into the cluster. A very rough estimate of the proportions of jellyfish galaxies in the studied clusters is about 10%.
This report summarizes the proceedings of the 2014 Mainz Institute for Theoretical Physics (MITP) scientific program on "High precision fundamental constants at the TeV scale". The two outstanding parameters in the Standard Model dealt with during the MITP scientific program are the strong coupling constant $\alpha_s$ and the top-quark mass $m_t$. Lacking knowledge on the value of those fundamental constants is often the limiting factor in the accuracy of theoretical predictions. The current status on $\alpha_s$ and $m_t$ has been reviewed and directions for future research have been identified.
The fermionic Shastry-Sutherland model has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Weyl fermion. Berry phases defined by the one-dimensional momentum as a parameter are quantized into 0 or pi due to the inversion symmetry combined with the time reversal, or existence of the glide plane, which also protects the massless Dirac cones with continuous parameters. This is the symmetry protected Z2 quantization. We have further demonstrated the Z2 Berry phases generically determine the existence of edge states in various phases and with different types of the boundaries as the bulk-edge correspondence of the massless Dirac fermion systems.
We investigate a dissipative, deterministic ratchet model in the overdamped regime driven by a {\it rectangular force}. Extensive numerical calculations are presented in a diagram depicting the drift velocity as a function of a wide range of the driving parameter values. We also present some theoretical considerations which explain some features of the mentioned diagram. In particular, we proof the existence of regions in the driving parameter space with bounded particle motion possessing zero current. Moreover, we present an explicit analytical expression for the drift velocity in the adiabatic limit.
We show that negative $(\nabla \Phi)^2$, where $\Phi$ is the dilaton, leads to a rapid creation of folded strings. Consequently it appears that the interior of the $SL(2,\mathbb{R})_k/U(1)$ black hole is not empty, but is filled with folded strings.
A study of parameter sensitivity of nuclear energy density functionals, initiated in the first part of this work \cite{NV.16}, is extended by the inclusion of data on ground-state properties of finite nuclei in the application of the manifold boundary approximation method (MBAM). Density functionals used in self-consistent mean-field calculations, and nuclear structure models based on them, are generally "sloppy" and exhibit an exponential range of sensitivity to parameter variations. Concepts of information geometry are used to identify the presence of effective functionals of lower dimension in parameter space associated with parameter combinations that can be tightly constrained by data. The MBAM is used in an iterative procedure that systematically reduces the complexity and the dimension of parameter space of a sloppy functional, with properties of nuclear matter and data on finite nuclei determining not only the values of model parameters, but also the optimal functional form of the density dependence.
A key challenge in video enhancement and action recognition is to fuse useful information from neighboring frames. Recent works suggest establishing accurate correspondences between neighboring frames before fusing temporal information. However, the generated results heavily depend on the quality of correspondence estimation. In this paper, we propose a more robust solution: \emph{sampling and fusing multi-level features} across neighborhood frames to generate the results. Based on this idea, we introduce a new module to improve the capability of 3D convolution, namely, learnable sampling 3D convolution (\emph{LS3D-Conv}). We add learnable 2D offsets to 3D convolution which aims to sample locations on spatial feature maps across frames. The offsets can be learned for specific tasks. The \emph{LS3D-Conv} can flexibly replace 3D convolution layers in existing 3D networks and get new architectures, which learns the sampling at multiple feature levels. The experiments on video interpolation, video super-resolution, video denoising, and action recognition demonstrate the effectiveness of our approach.
In recent years, the Lyman-$\alpha$ absorption observed in the spectra of high-redshift quasars has been used as a tracer of large-scale structure by means of the three-dimensional Lyman-$\alpha$ forest auto-correlation function at redshift $z\simeq 2.3$, but the need to fit the quasar continuum in every absorption spectrum introduces a broadband distortion that is difficult to correct and causes a systematic error for measuring any broadband properties. We describe a $k$-space model for this broadband distortion based on a multiplicative correction to the power spectrum of the transmitted flux fraction that suppresses power on scales corresponding to the typical length of a Lyman-$\alpha$ forest spectrum. Implementing the distortion model in fits for the baryon acoustic oscillation (BAO) peak position in the Lyman-$\alpha$ forest auto-correlation, we find that the fitting method recovers the input values of the linear bias parameter $b_{F}$ and the redshift-space distortion parameter $\beta_{F}$ for mock data sets with a systematic error of less than 0.5\%. Applied to the auto-correlation measured for BOSS Data Release 11, our method improves on the previous treatment of broadband distortions in BAO fitting by providing a better fit to the data using fewer parameters and reducing the statistical errors on $\beta_{F}$ and the combination $b_{F}(1+\beta_{F})$ by more than a factor of seven. The measured values at redshift $z=2.3$ are $\beta_{F}=1.39^{+0.11\ +0.24\ +0.38}_{-0.10\ -0.19\ -0.28}$ and $b_{F}(1+\beta_{F})=-0.374^{+0.007\ +0.013\ +0.020}_{-0.007\ -0.014\ -0.022}$ (1$\sigma$, 2$\sigma$ and 3$\sigma$ statistical errors). Our fitting software and the input files needed to reproduce our main results are publicly available.
Let $a, b$ be distinct, non-constant polynomials in ${\mathbb F}_2 [z]$. Let $\xi_{a, b}$ be the power series in ${\mathbb F}_2((z^{-1}))$ whose sequence of partial quotients is the Thue-Morse sequence over $\{a, b\}$. We establish that $\xi_{a,b}$ is algebraic of degree $4$.
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $\mathbf{R}^d$ relates to the wet part of that measure. This extends classical results for the uniform distribution from a convex set [B\'ar\'any and Larman 1988]. The lower bound of B\'ar\'any and Larman continues to hold in the general setting, but the upper bound must be relaxed by a factor of $\log n$. We show by an example that this is tight.
In this paper, we have considered the interplay between phase transitions and configuration mixing of intruder excitations in the 118-128Te isotopes. A transitional interacting boson model Hamiltonian in both IBM-1 and IBM-2 versions which are based on affine Lie Algebra are employed to describe the evolution from spherical to deformed gamma unstable shapes along the chain of Te isotopes. The excitation energies, B(E0) and B(E2) transition rates are rather well reproduced in comparison with experimental counterparts when the weight of SO(6) limit is increased in Hamiltonian. Also our results show obvious relations between the configuration mixing ratio and quadrupole, hexadecapole and hexacontatetrapole deformation values in this isotopic chain.
We study four-dimensional black hole configurations which result from wrapping M5-branes on a Calabi-Yau manifold, as well as U-dual realizations. Our aim is to understand the microscopic degrees of freedom responsible for the existence of bound states of multiple branes. The details depend on the chosen U-frame; in some cases, they are massless string junctions. We also identify a perturbative description in which these states correspond to twisted strings of intersecting D3-branes at an orbifold singularity. In each case, these are the preponderant states of the spacetime infrared conformal field theory and account for the entropy of the blackhole.
We aim to understand the role of Coulomb interactions as well as of different equations of state on the disappearance of transverse flow for various asymmetric reactions leading to same total mass. For the present study, the total mass of the system is kept constant (ATOT = 152) and asymmetry of the reaction is varied between 0.2 and 0.7. We find that the contribution of mean-field at low incident energies is more for nearly symmetric systems, while the trend is opposite at higher incident energies. The Coulomb interactions as well as different equations of state are found to affect the balance energy significantly for larger asymmetric reactions.
Charged-pion decay offers many opportunities to study Lorentz violation. Using an effective field theory approach, we study Lorentz violation in the lepton, W-boson, and quark sectors and derive the differential pion-decay rate, including muon polarization. Using coordinate redefinitions we are able to relate the first-generation quark sector, in which no bounds were previously reported, to the lepton and W-boson sector. This facilitates a tractable calculation, enabling us to place bounds on the level of $10^{-4}$ on first-generation quark parameters. Our expression for the pion-decay rate can be used to constrain Lorentz violation in future experiments.
In this paper, we present a universal control technique, the non-holonomic control, which allows us to impose any arbitrarily prescribed unitary evolution to any quantum system through the alternate application of two well-chosen perturbations.
Par-Lup3-4 is a very low-mass star (spectral type M5) in the Lupus III star-forming region. The object is underluminous by ~4 mag when compared to objects of similar mass in the same association. To better understand the origin of its underluminosity, we have analyzed high angular resolution near-IR imaging data and mid-IR spectroscopy. We have also compared the SED of the target (from the optical to the sub-millimeter regime) to a grid of radiative transfer models of circumstellar disks. The diffraction-limited infrared observations do not show obvious extended emission, allowing us to put an upper limit to the disk outer radius of ~20AU. The lack of extended emission, together with the non detection of a strong 9.8 microns silicate in absorption indicates that Par-Lup3-4 is probably in a Class II (rather than Class I) evolutionary stage. The SED of Par-Lup3-4 resembles that of objects with edge-on disks seen in scattered light, that is, a double peaked-SED and a dip at ~10 microns. We can fit the whole SED with a single disk model with an inclination of 81+/-6 degrees which provides a natural explanation for the under-luminosity of the target. Our analysis allows to put constraints on the disk inner radius, Rin < 0.05 AU, which is very close to the dust sublimation radius, and the maximum size of the dust grains, a_max > 10 microns, which indicates that dust processing has already taken place in Par-Lup3-4.
This text is a slightly expanded version of a survey article on certain aspects of low dimensional dynamics and number theory written after a kind invitation by the editors of the Notices of the American Mathematical Society.
The primary objective of this paper is the study of different instances of the elliptic Stark conjectures of Darmon, Lauder and Rotger, in a situation where the elliptic curve attached to the modular form $f$ has split multiplicative reduction at $p$ and the arithmetic phenomena are specially rich. For that purpose, we resort to the principle of improved $p$-adic $L$-functions and study their $\mathcal L$-invariants. We further interpret these results in terms of derived cohomology classes coming from the setting of diagonal cycles, showing that the same $\mathcal L$-invariant which arises in the theory of $p$-adic $L$-functions also governs the arithmetic of Euler systems. Thus, we can reduce, in the split multiplicative situation, the conjecture of Darmon, Lauder and Rotger to a more familiar statement about higher order derivatives of a triple product $p$-adic $L$-function at a point lying inside the region of classical interpolation, in the realm of the more well-known exceptional zero conjectures.
INTEGRAL has two sensitive gamma-ray instruments that have detected 46 gamma-ray bursts (GRBs) up to July 2007. We present the spectral, spatial, and temporal properties of the bursts in the INTEGRAL GRB catalogue using data from the imager, IBIS, and spectrometer, SPI. Spectral properties of the GRBs are determined using power-law, Band model and quasithermal model fits to the prompt emission. Spectral lags, i.e. the time delay in the arrival of low-energy gamma-rays with respect to high-energy gamma-rays, are measured for 31 of the GRBs. The photon index distribution of power-law fits to the prompt emission spectra is consistent with that obtained by Swift. The peak flux distribution shows that INTEGRAL detects proportionally more weak GRBs than Swift because of its higher sensitivity in a smaller field of view. The all-sky rate of GRBs above ~0.15 ph cm^-2 s^-1 is ~1400 yr^-1 in the fully coded field of view of IBIS. Two groups are identified in the spectral lag distribution, one with short lags <0.75 s (between 25-50 keV and 50-300 keV) and one with long lags >0.75 s. Most of the long-lag GRBs are inferred to have low redshifts because of their long spectral lags, their tendency to have low peak energies and their faint optical and X-ray afterglows. They are mainly observed in the direction of the supergalactic plane with a quadrupole moment of Q=-0.225+/-0.090 and hence reflect the local large-scale structure of the Universe. The rate of long-lag GRBs with inferred low luminosity is ~25% of Type Ib/c supernovae. Some of these bursts could be produced by the collapse of a massive star without a supernova or by a different progenitor, such as the merger of two white dwarfs or a white dwarf with a neutron star or black hole, possibly in the cluster environment without a host galaxy.
The disk galaxy UGC8802 has high neutral gas content and a flat profile of star formation rate compared to other disk galaxies with similar stellar mass. It also shows a steep metallicity gradient. We construct a chemical evolution model to explore its growth history by assuming its disk grows gradually from continuous gas infall, which is shaped by a free parameter -- the infall-peak time. By adopting the recently observed molecular surface density related star formation law, we show that a late infall-peak time can naturally explain the observed high neutral gas content, while an inside-out disk formation scenario can fairly reproduce the steep oxygen abundance gradient. Our results show that most of the observed features of UGC8802 can be well reproduced by simply `turning the knob' on gas inflow with one single parameter, which implies that the observed properties of gas-rich galaxies could also be modelled in a similar way.
The reflection coefficient of bulk spin waves from multilayer ferromagnetic structure with periodically modulated parameters of exchange interaction, uniaxial and rhombic magnetic anisotropy and saturation magnetization is calculated with a non-ideal coupling between layers. The strong dependence of spin-wave reflection coefficient on frequency, magnetic field and parameter of interfacial coupling is revealed. It allows changing the reflection intensity from 0 to 1 by changing either only external magnetic field value or frequency. The proposed model of boundary conditions gives the opportunity to take into account the quality of interfaces when studying the reflection processes of spin waves in multilayer structures.
This paper is devoted to the study of degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type. By means of blow-up analysis techniques, we prove an a-priori estimate in a weighted space of continuous functions. From this compactness result, the existence of a solution to our problem is proved by exploiting the homotopy invariance of the Leray-Schauder degree.
In this note we complete the study made in a previous paper on a Kirchhoff type equation with a Berestycki-Lions nonlinearity. We also correct Theorem 0.6 inside.
Fast radio bursts (FRBs) are an emerging class of bright, highly dispersed radio pulses. Recent work by Thornton et al. (2013) has revealed a population of FRBs in the High Time Resolution Universe (HTRU) survey at high Galactic latitudes. A variety of progenitors have been proposed including cataclysmic events at cosmological distances, Galactic flare stars, and terrestrial radio frequency interference. Here we report on a search for FRBs at intermediate Galactic latitudes ($-15^{\circ}$ $< b <$ 15$^{\circ}$) in data taken as part of the HTRU survey. No FRBs were discovered in this region. Several effects such as dispersion, scattering, sky temperature and scintillation decrease the sensitivity by more than 3$\sigma$ in $\sim$20\% of survey pointings. Including all of these effects, we exclude the hypothesis that FRBs are uniformly distributed on the sky with 99\% confidence. This low probability implies that additional factors -- not accounted for by standard Galactic models -- must be included to ease the discrepancy between the detection rates at high and low Galactic latitudes. A revised rate estimate or another strong and heretofore unknown selection effect in Galactic latitude would provide closer agreement between the surveys' detection rates. The dearth of detections at low Galactic latitude disfavors a Galactic origin for these bursts.
In this paper, the high-precision light curves of $Kepler$ target KIC 5950759 are analyzed. The Fourier analysis of the long cadence light curve reveals 3 independent frequencies. Two of them are main pulsation modes: F0 = 14.221373(21) $\rm{d^{-1}}$ and F1 = 18.337249(44) $\rm{d^{-1}}$. The third independent frequency $f_m$ = 0.3193 d$^{-1}$ is found in long cadence data with a signal-to-noise ratio of 6.2. A weak modulation of $f_m$ to F0 and F1 modes (triplet structures centred on F0 and F1) are detected both in long and short cadence data. This is the first detection of the modulation effect in a double-mode HADS star. The most possible cause of the modulation effect in the light curves is amplitude modulation with the star's rotation frequency of 0.3193 d$^{-1}$. The preliminary analysis suggests that KIC 5950759 is in the bottom of the HADS instability strip and likely situated in the main sequence. Spectroscopic observations are necessary to verify the true nature of the modulation terms.
We present Herschel/HIFI observations of 30 transitions of water isotopologues toward the high-mass star forming region NGC 6334 I. The line profiles of H_2^{16}O, H_2^{17}O, H_2^{18}O, and HDO show a complex pattern of emission and absorption components associated with the embedded hot cores, a lower-density envelope, two outflow components, and several foreground clouds, some associated with the NGC 6334 complex, others seen in projection against the strong continuum background of the source. Our analysis reveals an H2O ortho/para ratio of 3 +/- 0.5 in the foreground clouds, as well as the outflow. The water abundance varies from ~10^{-8} in the foreground clouds and the outer envelope to ~10^{-6} in the hot core. The hot core abundance is two orders of magnitude below the chemical model predictions for dense, warm gas, but within the range of values found in other Herschel/HIFI studies of hot cores and hot corinos. This may be related to the relatively low gas and dust temperature (~100 K), or time dependent effects, resulting in a significant fraction of water molecules still locked up in dust grain mantles. The HDO/H_2O ratio in NGC 6334 I, ~2 10^{-4}, is also relatively low, but within the range found in other high-mass star forming regions.