ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the cubic-quintic nonlinear Schr\"odinger equation: \[ i\partial_t u = -\Delta u - |u|^2u + |u|^4u. \]   In the first part of the paper, we analyze the one-parameter family of ground-state solitons associated to this equation with particular attention to the shape of the associated mass/energy curve. Additionally, we are able to characterize the kernel of the linearized operator about such solitons and to demonstrate that they occur as optimizers for a one-parameter family of inequalities of Gagliardo--Nirenberg type. Building on this work, in the latter part of the paper we prove that scattering holds for solutions belonging to the region $\mathcal{R}$ of the mass/energy plane where the virial is positive. We show this region is partially bounded by solitons but also by rescalings of solitons (which are not soliton solutions in their own right). The discovery of rescaled solitons in this context is new and highlights an unexpected limitation of any virial-based methodology.
We construct the crystalline comparison isomorphisms for proper smooth formal schemes over an absolutely unramified base. Such isomorphisms hold for \'etale cohomology with nontrivial coefficients, as well as in the relative setting, i.e. for proper smooth morphisms of smooth formal schemes. The proof is formulated in terms of the pro-\'etale topos introduced by Scholze, and uses his primitive comparison theorem for the structure sheaf on the pro-\'etale site. Moreover, we need to prove the Poincar\'e lemma for crystalline period sheaves, for which we adapt the idea of Andreatta and Iovita. Another ingredient for the proof is the geometric acyclicity of crystalline period sheaves, whose computation is due to Andreatta and Brinon.
Let $d\in\mathbb N$, $\alpha\in\mathbb R$, and let $f :\mathbb R^d\setminus \{0\} \rightarrow (0,\infty)$ be locally Lipschitz and positively homogeneous of degree $\alpha$ (e.g. $f$ could be the $\alpha$th power of a norm on $\mathbb R^d$). We study a generalization of the Eden model on $\mathbb Z^d$ wherein the next edge added to the cluster is chosen from the set of all edges incident to the current cluster with probability proportional to the value of $f$ at the midpoint of this edge, rather than uniformly. This model is equivalent to a variant of first passage percolation where the edge passage times are independent exponential random variables with parameters given by the value of $f$ at the midpoint of the edge.   We prove that the $f$-weighted Eden model clusters have an a.s. deterministic limit shape if $\alpha< 1$, which is an explicit functional of $f$ and the limit shape of the standard Eden model, and estimate the rate of convergence to this limit shape. We also prove that if $\alpha>1$, then there is a norm $\nu$ on $\mathbb R^d$ (depending on $\alpha$) such that if we set $f(z) = \nu(z)^{ \alpha}$, then the $f$-weighted Eden model clusters are a.s.\ contained in a Euclidean cone with opening angle $<\pi$ for all time. We further show that there does \emph{not} exist a norm on $\mathbb R^d$ for which this latter statement holds for all $\alpha>1$; and that there is no choice of function $f$ for which the above statement holds with $\alpha=1$.   Our basic approach is to compare the local behavior of the $f$-weighted first passage percolation to that of unweighted first passage percolation with iid exponential edge weights (which is equivalent to the unweighted Eden model).   We include a list of open problems and several computer simulations.
The aim of the paper is to study local Hadamard well-posedness for wave equation with an hyperbolic dynamical boundary condition, internal and/or boundary damping and sources for initial data in the natural energy space. Moreover the regularity of solutions is studied. Finally a dynamical system is generated when sources are at most linear at infinity, or they are dominated by the damping terms.
Crowd counting aims to count the number of instantaneous people in a crowded space, and many promising solutions have been proposed for single image crowd counting. With the ubiquitous video capture devices in public safety field, how to effectively apply the crowd counting technique to video content has become an urgent problem. In this paper, we introduce a novel framework based on temporal aware modeling of the relationship between video frames. The proposed network contains a few dilated residual blocks, and each of them consists of the layers that compute the temporal convolutions of features from the adjacent frames to improve the prediction. To alleviate the expensive computation and satisfy the demand of fast video crowd counting, we also introduce a lightweight network to balance the computational cost with representation ability. We conduct experiments on the crowd counting benchmarks and demonstrate its superiority in terms of effectiveness and efficiency over previous video-based approaches.
This note shows that the prime values of the Ramanujan tau function $\tau(n)=\pm p$ misses every prime $p\leq 8.0\times 10^{25}$.
Recent neural style transfer frameworks have obtained astonishing visual quality and flexibility in Single-style Transfer (SST), but little attention has been paid to Multi-style Transfer (MST) which refers to simultaneously transferring multiple styles to the same image. Compared to SST, MST has the potential to create more diverse and visually pleasing stylization results. In this paper, we propose the first MST framework to automatically incorporate multiple styles into one result based on regional semantics. We first improve the existing SST backbone network by introducing a novel multi-level feature fusion module and a patch attention module to achieve better semantic correspondences and preserve richer style details. For MST, we designed a conceptually simple yet effective region-based style fusion module to insert into the backbone. It assigns corresponding styles to content regions based on semantic matching, and then seamlessly combines multiple styles together. Comprehensive evaluations demonstrate that our framework outperforms existing works of SST and MST.
We explore the effect of relic gravitational waves on the primordial phase change from the quark-gluon plasma into the low density hadron gas that occurred approximately $10^{-5}$s after the beginning. We show that the gravitational wave, through doing work on the fluid, modulates the local volumes, causing a pressure modulation which either suppresses or boosts the bubble cavitation rate. The boosted rate is significant, implying that the phase transition could have occurred earlier than if this interaction is not considered.
The interest of the scientific community for the existence, uniqueness and stability of solutions to PDE's is testified by the numerous works available in the literature. In particular, in some recent publications on the subject an inequality guaranteeing stability is shown to hold provided that the coefficients of the principal part of the differential operator are Log-Lipschitz continuous. Herein this result is improved along two directions. First, we describe how to construct an operator, whose coefficients in the principal part are not Log-Lipschitz continuous, for which the above mentioned inequality does not hold. Second, we show that the stability of the solution is guaranteed, in a suitable functional space, if the coefficients of the principal part are Osgood continuous.
These lectures are intended to provide an introduction to the rich interplay between N-body simulations and stellar-kinematic observations of galaxies. The first section describes the kinematic properties of galaxies that are accessible to observation, and gives a brief introduction to the stellar dynamics that one might wish to infer from such observations. In the next section, the use of N-body simulations in the study of galaxy dynamics is placed in its historical context. The next two sections provide case studies of the stellar-dynamical properties of elliptical and disk galaxies where N-body simulations have been used to explain kinematic data, to test new analysis techniques, and to motivate further observations. The final section contains some speculation as to how the symbiotic relation between observations and N-body simulations may develop in future studies of galaxy dynamics.
We investigate a mechanism for extracting heat from metallic conductors based on the energy-selective transmission of electrons through a spatially asymmetric resonant structure subject to ac driving. This quantum refrigerator can operate at zero net electronic current as it replaces hot by cold electrons through two energetically symmetric inelastic channels. We present numerical results for a specific heterostructure and discuss general trends. We also explore the conditions under which the cooling rate may approach the ultimate limit given by the quantum of cooling power.
A hierarchy of equations was introduced recently to describe the kinetics of homogeneous cooling of the gas of inelastic hard spheres. It is argued that this hierarchy does not describe this system accurately, and a simple test for this is proposed. A stochastic interpretation of the hierarchy is presented.
The Glauber model is extensively applied to heavy ion collision for describing a number of interaction processes over a wide range of energies from near the Coulomb barrier to higher energies. The model gives the nucleus-nucleus interaction in terms of interaction between the constituent nucleons with a given density distribution. The model is a semiclassical model picturing the nuclear collision in the impact parameter representation where the nuclei move along the collision direction in a straight path. In these lectures we derive this model and discuss its applications in variety of problems in nuclear and high energy physics.
We prove that with high probability, d+1 random Bernoulli polynomials in d variables of degree n (n goes to infinity) do not possess a common root.
Single image deraining (SID) is an important and challenging topic in emerging vision applications, and most of emerged deraining methods are supervised relying on the ground truth (i.e., paired images) in recent years. However, in practice it is rather common to have no un-paired images in real deraining task, in such cases how to remove the rain streaks in an unsupervised way will be a very challenging task due to lack of constraints between images and hence suffering from low-quality recovery results. In this paper, we explore the unsupervised SID task using unpaired data and propose a novel net called Attention-guided Deraining by Constrained CycleGAN (or shortly, DerainCycleGAN), which can fully utilize the constrained transfer learning abilitiy and circulatory structure of CycleGAN. Specifically, we design an unsu-pervised attention guided rain streak extractor (U-ARSE) that utilizes a memory to extract the rain streak masks with two constrained cycle-consistency branches jointly by paying attention to both the rainy and rain-free image domains. As a by-product, we also contribute a new paired rain image dataset called Rain200A, which is constructed by our network automatically. Compared with existing synthesis datasets, the rainy streaks in Rain200A contains more obvious and diverse shapes and directions. As a result, existing supervised methods trained on Rain200A can perform much better for processing real rainy images. Extensive experiments on synthesis and real datasets show that our net is superior to existing unsupervised deraining networks, and is also very competitive to other related supervised networks.
The (zeroth-order) energy of a particle in the background of a black hole is given by Carter's integrals. However, exact calculations of a particle's {\it self-energy} (first-order corrections) are still beyond our present reach in many situations. In this paper we use Hawking's area theorem in order to derive bounds on the self-energy of a particle in the vicinity of a black hole. Furthermore, we show that self-energy corrections {\it must} be taken into account in order to guarantee the validity of Penrose cosmic censorship conjecture.
We present relations between cycles with rational coefficients modulo algebraic equivalence on the Jacobian of a curve. These relations depend on the linear systems the curve admits. They are obtained in the tautological ring, the smallest subspace containing (an embedding of) the curve and closed under the basic operations of intersection, Pontryagin product and the pullback and pushdown induced by homotheties.
We discuss a left-right symmetric model with two Higgs bi-doublet and spontaneous P and CP violation. The flavor changing neutral currents is suppressed by assuming approximate global U(1) family symmetry. We calculate the constraints from neural K meson mass difference \Delta m_K and demonstrate that a right-handed gauge boson W_2 contribution in box-diagrams with mass around 600 GeV is allowed due to a negative interference with a light charged Higgs boson around 150 \sim 300 GeV. The W_2 contribution to \epsilon_K is suppressed from appropriate choice of additional CP phases appearing in the right-handed Cabbibo-Kobayashi-Maskawa(CKM) matrix. The model is found fully consistent with B^0 mass difference and the mixing-induced CP asymmetry measurements.
Motivated by Yang-Mills theory in 4n dimensions, and generalizing the notion due to Atiyah, Drinfeld, Hitchin and Manin for n=1, Okonek, Spindler and Trautmann introduced instanton bundles and special instanton bundles as certain algebraic vector bundles of rank 2n on the complex projective space P^{2n+1}. The moduli space of special instanton bundles is shown to be rational.
Per weight graphene is stronger than steel, but because graphene is so thin, it breaks and evidently forms cracks during handling, particularly when supporting polymers are not used for transfer. In this paper, the parameter rupture index is introduced to quantify the density of the cracks and related defects in graphene during processing. The approach takes the advantages of the high contrast achievable in fluorescence quenching microscopy to distinguish between graphene and the background substrate, visible through the cracks in graphene. The rupture index can well compare the effectiveness of different graphene transferring methods in minimizing the formation of the cracks, and quantify the oxidation of metals protected with graphene.
We propose a multi party quantum clock synchronization protocol that makes optimal use of the maximal multipartite entanglement of GHZ-type states. To realize the protocol, different versions of maximally entangled eigenstates of collective energy are generated by local transformations that distinguish between different groupings of the parties. The maximal sensitivity of the entangled states to time differences between the local clocks can then be accessed if all parties share the results of their local time dependent measurements. The efficiency of the protocol is evaluated in terms of the statistical errors in the estimation of time differences and the performance of the protocol is compared to alternative protocols previously proposed.
The density in the core of neutron stars can reach values of about 5 to 10 times nuclear matter saturation density. It is, therefore, a natural assumption that hadrons may have dissolved into quarks under such conditions, forming a hybrid star. This star will have an outer region of hadronic matter and a core of quark matter or even a mixed state of hadrons and quarks. In order to investigate such phases, we discuss different model approaches that can be used in the study of compact stars as well as being applicable to a wider range of temperatures and densities. One major model ingredient, the role of quark interactions in the stability of massive hybrid stars is discussed. In this context, possible conflicts with lattice QCD simulations are investigated.
The peculiar spiral NGC 2782 is the result of a minor merger with a mass ratio ~4:1 occurring ~200 Myr ago. This merger produced a molecular and HI rich, optically bright Eastern tail and an HI-rich, optically faint Western tail. Non-detection of CO in the Western Tail by Braine et al. (2001) suggested that star formation had not yet begun. However, deep UBVR and H-alpha narrowband images show evidence of recent star formation in the Western tail, though it lacks massive star clusters and cluster complexes. Using Herschel PACS spectroscopy, we discover 158 micron [CII] emission at the location of the three most luminous H-alpha sources in the Eastern tail, but not at the location of the even brighter H-alpha source in the Western tail. The Western tail is found to have a normal star formation efficiency (SFE), but the Eastern tail has a low SFE. The lack of CO and [CII] emission suggests the Western tail HII region may have a low carbon abundance and be undergoing its first star formation. The Western tail is more efficient at forming stars, but lacks massive clusters. We propose that the low SFE in the Eastern tail may be due to its formation as a splash region where gas heating is important even though it has sufficient molecular and neutral gas to make massive star clusters. The Western tail, which has lower gas surface density and does not form high mass star clusters, is a tidally formed region where gravitational compression likely enhances star formation.
We study models of the gamma-ray emission of Cyg X-3 observed by Fermi. We calculate the average X-ray spectrum during the gamma-ray active periods. Then, we calculate spectra from Compton scattering of a photon beam into a given direction by isotropic relativistic electrons with a power-law distribution, both based on the Klein-Nishina cross section and in the Thomson limit. Applying the results to scattering of stellar blackbody radiation in the inner jet of Cyg X-3, we find that a low-energy break in the electron distribution at a Lorentz factor of ~ 300--1000 is required by the shape of the observed X-ray/gamma-ray spectrum in order to avoid overproducing the observed X-ray flux. The electrons giving rise to the observed \g-rays are efficiently cooled by Compton scattering, and the power-law index of the acceleration process is ~ 2.5--3. The bulk Lorentz factor of the jet and the kinetic power before the dissipation region depend on the fraction of the dissipation power supplied to the electrons; if it is ~ 1/2, the Lorentz factor is ~ 2.5, and the kinetic power is ~ 10^38 erg/s, which represents a firm lower limit on the jet power, and is comparable to the bolometric luminosity of Cyg X-3. Most of the power supplied to the electrons is radiated. The broad band spectrum constrains the synchrotron and self-Compton emission from the gamma-ray emitting electrons, which requires the magnetic field to be relatively weak, with the magnetic energy density < a few times 10^-3 of that in the electrons. The actual value of the magnetic field strength can be inferred from a future simultaneous measurement of the IR and gamma-ray fluxes.
To any Feynman graph (with 2n edges) we can associate a hypersurface X\subset\PP^{2n-1}. We study the middle cohomology H^{2n-2}(X) of such hypersurfaces. S. Bloch, H. Esnault, and D. Kreimer (Commun. Math. Phys. 267, 2006) have computed this cohomology for the first series of examples, the wheel with spokes graphs WS_n, n\geq 3. Using the same technique, we introduce the generalized zigzag graphs and prove that W_5(H^{2n-2}(X))=\QQ(-2) for all of them (with W_{*} the weight filtration). Next, we study primitively log divergent graphs with small number of edges and the behavior of graph hypersurfaces under the gluing of graphs.
It was shown that if in Quantum Theory a fundamental length exists and a well-known measurement procedure is used, then the density matrix at the Planck scale cannot be defined in the usual way, because in this case density matrix trace is strongly less than one.   Density matrix must be changed by a progenitrix or as we call it throughout this paper, density pro-matrix. This pro-matrix is a deformed density matrix, which at low energy limit turns to usual one.   Below the explicit form of the deformation is described. Implications of obtained results are summarized as well as their application to the interpretation of Information Paradox on the Black Holes.
The new spectropolarimetric observations of HD 22920 with ESPaDOnS at CFHT reveal a strong variability of its spectral line profiles with the phase of stellar rotation. We have obtained Teff = 13640 K, logg=3.72 for this star from the best fit of its nine Balmer line profiles. The respective model of stellar atmosphere was calculated to perform abundance analysis of HD 22920 using the spectra obtained for three different phases of stellar rotation. We have found that silicon and chromium abundances appear to be vertically stratified in the atmosphere of HD 22920. Meanwhile, silicon shows hints for a possible variability of vertical abundance stratification with rotational phase.
Ultra-high cosmic rays (UHECRs) with energies >10^19 eV emitted at cosmological distances will be attenuated by cosmic microwave and infrared background radiation through photohadronic processes. Lower energy extra-galactic cosmic rays (~10^18-10^19 eV) can only travel a linear distance smaller than ~Gpc in a Hubble time due to the diffusion if the extra-galactic magnetic fields are as strong as nano Gauss. These prevent us from directly observing most of the UHECRs in the universe, and thus the observed UHECR intensity reflects only the emissivity in the nearby universe within hundreds of Mpc. However, UHECRs in the distant universe, through interactions with the cosmic background photons, produce UHE electrons and gamma-rays that in turn initiate electromagnetic cascades on cosmic background photons. This secondary cascade radiation forms part of the extragalactic diffuse GeV-TeV gamma-ray radiation and, unlike the original UHECRs, is observable. Motivated by new measurements of extragalactic diffuse gamma-ray background radiation by Fermi/LAT, we obtained upper limits placed on the UHECR emissivity in the distant universe by requiring that the cascade radiation they produce not exceed the observed levels. By comparison with the gamma-ray emissivity of candidate UHECR sources (such as GRBs and AGNs) at high-redshifts, we find that the obtained upper limit for a flat proton spectrum is ~10^1.5 times larger than the gamma-ray emissivity in GRBs and ~10 times smaller than the gamma-ray emissivity in BL Lac objects. In the case of iron nuclei composition, the derived upper limit of the UHECR emissivity is a factor of 3-5 times higher. Robust upper limit on the cosmogenic neutrino flux is further obtained, which is marginally reachable by the Icecube detector and the next-generation detector JEM-EUSO.
We present deep, near-infrared HST/WFC3 grism spectroscopy and imaging for a sample of 14 galaxies at z~2 selected from a mass-complete photometric catalog in the COSMOS field. By combining the grism observations with photometry in 30 bands, we derive accurate constraints on their redshifts, stellar masses, ages, dust extinction and formation redshifts. We show that the slope and scatter of the z~2 mass-size relation of quiescent galaxies is consistent with the local relation, and confirm previous findings that the sizes for a given mass are smaller by a factor of two to three. Finally, we show that the observed evolution of the mass-size relation of quiescent galaxies between z=2 and 0 can be explained by quenching of increasingly larger star-forming galaxies, at a rate dictated by the increase in the number density of quiescent galaxies with decreasing redshift. However, we find that the scatter in the mass-size relation should increase in the quenching-driven scenario in contrast to what is seen in the data. This suggests that merging is not needed to explain the evolution of the median mass-size relation of massive galaxies, but may still be required to tighten its scatter, and explain the size growth of individual z=2 galaxies quiescent galaxies.