ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present an analytical description of the probability distribution function (PDF) of the smoothed three-dimensional matter density field for modified gravity and dark energy. Our approach, based on the principles of Large Deviations Theory, is applicable to general extensions of the standard $\Lambda$CDM cosmology. We show that late-time changes to the law of gravity and background expansion can be included through Einstein-de Sitter spherical collapse dynamics combined with linear theory calculations and a calibration measurement of the non-linear variance of the smoothed density field from a simple numerical simulation. In a comparison to $N$-body simulations for $f(R)$, DGP and evolving dark energy theories, we find percent level accuracy around the peak of the distribution for predictions in the mildly non-linear regime. A Fisher forecast of an idealised experiment with a Euclid-like survey volume demonstrates the power of combining measurements of the 3D matter PDF with the 3D matter power spectrum. This combination is shown to halve the uncertainty on parameters for an evolving dark energy model, relative to a power spectrum analysis on its own. The PDF is also found to substantially increase the detection significance for small departures from General Relativity, with improvements of up to six times compared to the power spectrum alone. This analysis is therefore very promising for future studies including non-Gaussian statistics, as it has the potential to alleviate the reliance of these analyses on expensive high resolution simulations and emulators.
Carbon is likely the most fascinating element of the periodic table because of the diversity of its allotropes stemming from its variable (sp, sp2, and sp3) bonding motifs. Exploration of new forms of carbon has been an eternal theme of contemporary scientific research. Here we report on novel amorphous carbon phases containing high fraction of sp3 bonded atoms recovered after compressing fullerene C60 to previously unexplored high pressure and temperature. The synthesized carbons are the hardest and strongest amorphous materials known to date, capable of scratching diamond crystal and approaching its strength which is evidenced by complimentary mechanical tests. Photoluminescence and absorption spectra of the materials demonstrate they are semiconductors with tunable bandgaps in the range of 1.5-2.2 eV, comparable to that of amorphous silicon. A remarkable combination of the outstanding mechanical and electronic properties makes this class of amorphous carbons an excellent candidate for photovoltaic applications demanding ultrahigh strength and wear resistance.
Iwaniec and Sarnak showed that at the minimum 25% of L-values associated to holomorphic newforms of fixed even integral weight and level $N \rightarrow \infty$ do not vanish at the critical point when N is square-free and $\phi(N)\sim N$. In this paper we extend the given result to the case of prime power level $N=p^{\nu}$, $\nu\geq 2$.
Blur detection is the separation of blurred and clear regions of an image, which is an important and challenging task in computer vision. In this work, we regard blur detection as an image segmentation problem. Inspired by the success of the U-net architecture for image segmentation, we design a Multi-Scale Dilated convolutional neural network based on U-net, which we call MSDU-net. The MSDU-net uses a group of multi-scale feature extractors with dilated convolutions to extract texture information at different scales. The U-shape architecture of the MSDU-net fuses the different-scale texture features and generates a semantic feature which allows us to achieve better results on the blur detection task. We show that using the MSDU-net we are able to outperform other state of the art blur detection methods on two publicly available benchmarks.
We study the agglomerative percolation (AP) models on the Bethe lattice and the triangular cactus to establish the exact mean-field theory for AP. Using the self-consistent simulation method, based on the exact self-consistent equation, we directly measure the order parameter $P_{\infty}$ and average cluster size $S$. From the measured $P_{\infty}$ and $S$ we obtain the critical exponents $\beta_k$ and $\gamma_k$ for $k=2$ and 3. Here $\beta_k$ and $\gamma_k$ are the critical exponents for $P_\infty$ and $S$ when the growth of clusters spontaneously breaks the $Z_k$ symmetry of the $k$-partite graph (Lau, Paczuski, and Grassberger, 2012). The obtained values are $\beta_2=1.79(3)$, $\gamma_2=0.88(1)$, $\beta_3=1.35(5)$, and $\gamma_3=0.94(2)$. By comparing these values of exponents with those for ordinary percolation ($\beta_{\infty}=1$ and $\gamma_{\infty}=1$) we also find the inequalities between the exponents, as $\beta_\infty<\beta_3<\beta_2$ and $\gamma_\infty>\gamma_3>\gamma_2$. These results quantitatively verify the conjecture that the AP model belongs to a new universality class if $Z_k$ symmetry is broken spontaneously, and the new universality class depends on $k$ [Lau et al., Phys. Rev. E 86, 011118 (2012)].
Recently Sahoo and Sen obtained a series of remarkable results concerning sub-leading soft photon and graviton theorems in four dimensions. Even though the S- matrix is infrared divergent, they have shown that the sub-leading soft theorems are well defined and exact statements in QED and perturbative Quantum Gravity. However unlike the well studied Cachazo-Strominger soft theorems in tree-level amplitudes, the new sub-leading soft expansion is at the order ln {\omega} (where {\omega} is the soft frequency) and the corresponding soft factors structurally show completely different properties then their tree-level counterparts. Whence it is natural to ask if these theorems are associated to asymptotic symmetries of the S-matrix. We consider this question in the context of sub-leading soft photon theorem in scalar QED and show that there are indeed an infinity of conservation laws whose Ward identities are equivalent to the loop-corrected soft photon theorem. This shows that in the case of four dimensional QED, the leading and sub-leading soft photon theorems are equivalent to Ward identities of (asymptotic) charges.
We consider microwave spectroscopy of Josephon junctions composed of hybridized Majorana states in topological 1-D superconductors. We point out how spectroscopic features of the junction appear in the current phase relation under microwave irradiation. Moreover, we discuss a way to directly probe the nonequilibrium state associated with the 4{\pi} periodic Josephson effect. In particular, we show how the microwave driving can be used to switch from a 4{\pi} to a 2{\pi} Shapiro step in the current voltage relation.
We consider the random walk Metropolis algorithm on $\mathbb{R}^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one-dimensional law. In the limit $n\to\infty$, it is well known (see [Ann. Appl. Probab. 7 (1997) 110-120]) that, when the variance of the proposal scales inversely proportional to the dimension $n$ whereas time is accelerated by the factor $n$, a diffusive limit is obtained for each component of the Markov chain if this chain starts at equilibrium. This paper extends this result when the initial distribution is not the target probability measure. Remarking that the interaction between the components of the chain due to the common acceptance/rejection of the proposed moves is of mean-field type, we obtain a propagation of chaos result under the same scaling as in the stationary case. This proves that, in terms of the dimension $n$, the same scaling holds for the transient phase of the Metropolis-Hastings algorithm as near stationarity. The diffusive and mean-field limit of each component is a diffusion process nonlinear in the sense of McKean. This opens the route to new investigations of the optimal choice for the variance of the proposal distribution in order to accelerate convergence to equilibrium (see [Optimal scaling for the transient phase of Metropolis-Hastings algorithms: The longtime behavior Bernoulli (2014) To appear]).
We study a class of oscillating bounce solutions to the Euclidean field equations for gravity coupled to a scalar field theory with two, possibly degenerate, vacua. In these solutions the scalar field crosses the top of the potential barrier $k>1$ times. Using analytic and numerical methods, we examine how the maximum allowed value of $k$ depends on the parameters of the theory. For a wide class of potentials $k_{\rm max}$ is determined by the value of the second derivative of the scalar field potential at the top of the barrier. However, in other cases, such as potentials with relatively flat barriers, the determining parameter appears instead to be the value of this second derivative averaged over the width of the barrier. As a byproduct, we gain additional insight into the conditions under which a Coleman-De Luccia bounce exists. We discuss the physical interpretation of these solutions and their implications for vacuum tunneling transitions in de Sitter spacetime.
Using a theory of large amplitude collective motion, the adiabatic self-consistent collective coordinate method, we derive reaction path for the fusion process at sub-barrier energies. The collective Hamiltonian to describe the fusion process is constructed, based on the obtained reaction path and canonical variables. We study the reaction of N=Z stable nuclei, alpha+16O, 16O+16O, and alpha+12C. The results suggest that, after two nuclei touch, the reaction path is significantly deviated from the simple relative motion, which may affect the deep sub-barrier fusion cross section.
A full three-dimensional angular momentum projection on top of a triaxial relativistic mean-Geld calculation is implemented for the first time. The underlying Lagrangian is a point coupling model and pairing correlations are taken into account by a monopole force. This method is applied for the low-lying excited states in 24Mg. Good agreement with the experimental data is found for the ground state properties. A minimum in the potential energy surface for the 2+ state, with beta = 0.55, gamma = 10 deg, is used as the basis to investigate the rotational energy spectrum as well as the corresponding B(E2) transition probabilities as compared to the available data.
We prove the local in time existence of the classical solutions to the system of equations of isothermal viscoelasticity with clamped boundary conditions. We deal with a general form of viscous stress tensor $\mathcal{Z}(F,\dot F)$, assuming a Korn-type condition on its derivative $D_{\dot F}\mathcal{Z}(F, \dot F)$. This condition is compatible with the balance of angular momentum, frame invariance and the Claussius-Duhem inequality. We give examples of linear and nonlinear (in $\dot F$) tensors $\mathcal{Z}$ satisfying these required conditions.
We report on the crystallographic structure of the layered compound Pb3Mn7O15. Previous analysis based on laboratory X-ray data at room temperature gave contradictory results in terms of the description of the unit cell. Motivated by recent magnetic bulk measurements of this system, we re-investigated the chemical structure with high-resolution synchrotron powder diffraction at temperatures between 15 K and 295 K. Our results show that the crystal structure of stoichiometric Pb3Mn7O15 has a pronounced 2-dimensional character and can be described in the orthorhombic space group Pnma.
We present GazeDirector, a new approach for eye gaze redirection that uses model-fitting. Our method first tracks the eyes by fitting a multi-part eye region model to video frames using analysis-by-synthesis, thereby recovering eye region shape, texture, pose, and gaze simultaneously. It then redirects gaze by 1) warping the eyelids from the original image using a model-derived flow field, and 2) rendering and compositing synthesized 3D eyeballs onto the output image in a photorealistic manner. GazeDirector allows us to change where people are looking without person-specific training data, and with full articulation, i.e. we can precisely specify new gaze directions in 3D. Quantitatively, we evaluate both model-fitting and gaze synthesis, with experiments for gaze estimation and redirection on the Columbia gaze dataset. Qualitatively, we compare GazeDirector against recent work on gaze redirection, showing better results especially for large redirection angles. Finally, we demonstrate gaze redirection on YouTube videos by introducing new 3D gaze targets and by manipulating visual behavior.
The exclusive reaction $pp \to pp (K^{*0} \bar{K}^{*0} \to K^{+}\pi^{-}K^{-}\pi^{+})$ for the LHC experiments is discussed. The amplitudes for the reaction are formulated within the tensor-pomeron approach. We consider two diffractive mechanisms: the $f_{2}(1950)$ $s$-channel exchange mechanism and the $K^{*0}$-exchange mechanism. First mechanism is a candidate for central diffractive production of tensor glueball and the second one is an irreducible continuum. Comparison with data from WA102 experiment are made and predictions for LHC experiments are given. We find that including the continuum contribution alone one can describe the WA102 data reasonably well. A similar behaviour of the continuum and resonance contributions makes an identification of a broad tensor-glueball state in this reaction rather difficult.
We investigate the existence of linear magnetism in the metal organic framework materials MOF-74-Fe, MOF-74-Co, and MOF-74-Ni, using first-principles density functional theory. MOF-74 displays regular quasi-linear chains of open-shell transition metal atoms, which are well separated. Our results show that within these chains-for all three materials-ferromagnetic coupling of significant strength occurs. In addition, the coupling in-between chains is at least one order of magnitude smaller, making these materials almost perfect 1D magnets at low temperature. The inter-chain coupling is found to be anti-ferromagnetic, in agreement with experiments. While some quasi-1D materials exist that exhibit linear magnetism-mostly complex oxides, polymers, and a few other rare material-they are typically very difficult to synthesize. The significance of our finding is that MOF-74 is very easy to synthesize and it is likely the simplest realization of the 1D Ising model in nature. MOF-74 could thus be used in future experiments to study 1D magnetism at low temperature.
We study the simplest superstring bit model at finite N using the characters of the SU(N) group. We obtain exact, analytic expressions for small N partition functions and Gaussian approximations for them in the high temperature limit for all N. We use numerical evidence to identify two temperature regimes where the partition function has different limiting behaviors. The temperature at which this transition takes place is identified as the Hagedorn temperature.
The paper is concerned with the existence of positive weak solutions for a new class of $\left( p,q\right) $-Laplacian elliptic systems in a bounded domain by means of the method of sub-super solutions. Particularly, we do not need any sign conditions for $\gamma \left( 0\right), g\left( 0\right), f\left( 0\right) $ and $h\left(0\right) $. Moreover, a multiplicity result is obtained when $\gamma \left(0\right)=g\left( 0\right)=f\left( 0\right)=h\left( 0\right)=0.$ Finally, we give some examples to verify our main results.
We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. Motivated by recent applications in the field of micro- and nanofluidics, we consider the model in such generality that electrokinetic flows are included. This prohibits employing the assumption of electroneutrality of the total solution, which is a common approach in the mathematical literature in order to determine the electrical potential. Therefore we complement the system of mass and momentum balances with a Poisson equation for the electrostatic potential, with the charge density stemming from the concentrations of the ionic species. For the resulting Navier-Stokes-Nernst-Planck-Poisson system we prove the existence of unique local strong solutions in bounded domains in $\R^n$ for any $n\geq2$ as well as the existence of unique global strong solutions and exponential convergence to uniquely determined steady states in two dimensions.
In this paper we study the molecular gas content of a representative sample of 67 of the most massive early-type galaxies in the local universe, drawn uniformly from the MASSIVE survey. We present new IRAM-30m telescope observations of 30 of these galaxies, allowing us to probe the molecular gas content of the entire sample to a fixed molecular-to-stellar mass fraction of 0.1%. The total detection rate in this representative sample is 25$^{+5.9}_{-4.4}$%, and by combining the MASSIVE and ATLAS$^{\rm 3D}$ molecular gas surveys we find a joint detection rate of 22.4$^{+2.4}_{-2.1}$%. This detection rate seems to be independent of galaxy mass, size, position on the fundamental plane, and local environment. We show here for the first time that true slow rotators can host molecular gas reservoirs, but the rate at which they do so is significantly lower than for fast-rotators. Objects with a higher velocity dispersion at fixed mass (a higher kinematic bulge fraction) are less likely to have detectable molecular gas, and where gas does exist, have lower molecular gas fractions. In addition, satellite galaxies in dense environments have $\approx$0.6 dex lower molecular gas-to-stellar mass ratios than isolated objects. In order to interpret these results we created a toy model, which we use to constrain the origin of the gas in these systems. We are able to derive an independent estimate of the gas-rich merger rate in the low-redshift universe. These gas rich mergers appear to dominate the supply of gas to ETGs, but stellar mass loss, hot halo cooling and transformation of spiral galaxies also play a secondary role.
For N=1,2,..., let S_N be a simple random sample of size n=n_N from a population A_N of size N, where 0<=n<=N. Then with f_N=n/N, the sampling fraction, and 1_A the inclusion indicator that A is in S_N, for any H a subset of A_N of size k>= 0, the high order correlations Corr(k) = E (\prod_{A \in H} (1_A-f_N)) depend only on k, and if the sampling fraction f_N -> f as N -> infinity, then N^{k/2}Corr(k) -> [f(f-1)]^{k/2}EZ^k, k even and N^{(k+1)/2}Corr(k) -> [f(f-1)]^{(k-1)/2}(2f-1)(1/3)(k-1)EZ^{k+1}, k odd where Z is a standard normal random variable. This proves a conjecture given in [2].
It has been proposed recently to observe the change in cosmological redshift of distant galaxies or quasars with the next generation of large telescope and ultra-stable spectrographs (the so-called Sandage-Loeb test). Here we investigate the possibility of observing the change in peculiar velocity in nearby clusters and galaxies. This ``peculiar acceleration'' could help reconstructing the gravitational potential without assuming virialization. We show that the expected effect is of the same order of magnitude of the cosmological velocity shift. Finally, we discuss how to convert the theoretical predictions into quantities directly related to observations.
In this note we discuss the wave functional approach to the spectrum of pure Yang-Mills theory in 2+1 and 3+1 dimensions by highlighting the issues of dynamical mass generation and the role played by the kinetic term. We extrapolate our recent analysis of 2+1 Yang-Mills theory to 3+1 dimensions, and under certain heuristic assumptions use a simple quasi-Gaussian vacuum wavefunctional for 3+1 Yang-Mills theory for a preliminary study of the spectrum of glueballs which nicely fits the available lattice simulations.
Specific heat data for the quasi one dimensional quantum magnet Copper Benzoate (Cu(C_6D_5COO)_2 \cdot 3D_2O) is analyzed in the framework of an effective low-energy description in terms of a Sine-Gordon theory.
We study, using Monte Carlo simulations, the steady state properties of a system of particles interacting via hard core exclusion and moving in a discrete flashing disordered ratchet potential. Quenched disorder is introduced by breaking the periodicity of the ratchet potential through changing shape of the potential across randomly chosen but fixed periods. We show that the effects of quenched disorder can be broadly classified as strong or weak with qualitatively different behaviour of the steady state particle flux as a function of overall particle density. We further show that most of the effects including a density driven nonequilibrium phase transition observed can be understood by constructing an effective asymmetric simple exclusion process (ASEP) with quenched disorder in the hop rates.
This paper is devoted to $\phi$-entropies applied to Fokker-Planck and kinetic Fokker-Planck equations in the whole space, with confinement. The so-called $\phi$-entropies are Lyapunov functionals which typically interpolate between Gibbs entropies and L2 estimates. We review some of their properties in the case of diffusion equations of Fokker-Planck type, give new and simplified proofs, and then adapt these methods to a kinetic Fokker-Planck equation acting on a phase space with positions and velocities. At kinetic level, since the diffusion only acts on the velocity variable, the transport operator plays an essential role in the relaxation process. Here we adopt the H1 point of view and establish a sharp decay rate. Rather than giving general but quantitatively vague estimates, our goal here is to consider simple cases, benchmark available methods and obtain sharp estimates on a key example. Some $\phi$-entropies give rise to improved entropy -- entropy production inequalities and, as a consequence, to faster decay rates for entropy estimates of solutions to non-degenerate diffusion equations. Our main result is to prove that faster entropy decay also holds at kinetic level and that optimal decay rates are achieved only in asymptotic regimes.
We prove that for any proper metric space $X$ and a function $\psi:(0,\infty)\to(0,\infty)$ from a suitable class of approximation functions, the Hausdorff dimensions of the set $W_\psi(Q)$ of all points $\psi$-well-approximable by a well-distributed subset $Q\subset X$, and the set $E_\psi(Q)$ of points that are exactly $\psi$-approximable by $Q$, coincide. This answers in a general setting, a question of Beresnevich-Dickinson-Velani in the case of approximation of reals by rationals, and answered by Bugeaud in that case using the continued-fraction expansion of reals. Our main result applies in particular to approximation by orbits of fixed points of a wide class of discrete groups of isometries acting on the boundary of hyperbolic metric spaces.
The orthodox quantum mechanics has been commonly regarded as being supported decisively by the polarization EPR experiments, in which Bell's inequalities have been violated. The given conclusion has been based, however, on several mistakes that have not been yet commonly known and sufficiently analyzed. The whole problem will be newly discussed and a corresponding solution will be proposed.
In the context of percolation in a regular tree, we study the size of the largest cluster and the length of the longest run starting within the first d generations. As d tends to infinity, we prove almost sure and weak convergence results.