ShantanuT01/DACTYL-Pretraining huggingface dataset:
Giant oxygen isotope effects observed in colossal magnetoresistance manganites are investigated by employing the combined model of the double exchange and interacting lattice polaron mechanism. We have shown that the isotope effects on $ T_C$ in the metallic phase and $ T_{CO}$ in the charge ordered phase of manganites can be explained well in terms of the double exchange and polaron narrowing factors with reasonable physical parameters.
We derive an explicit form of the dilaton potential in improved holographic QCD (IHQCD) from the QCD lattice data of the chiral condensate as a function of the quark mass. This establishes a data-driven holographic modeling of QCD -- machine learning holographic QCD. The modeling consists of two steps for solving inverse problems. The first inverse problem is to find the emergent bulk geometry consistent with the lattice QCD simulation data at the boundary. We solve this problem with the refinement of neural ordinary differential equation, a machine learning technique. The second inverse problem is to derive a bulk gravity action with a dilaton potential such that its solution is the emergent bulk geometry. We solve this problem at non-zero temperature, and derive the explicit form of the dilaton potential. The dilaton potential determines the bulk action, the Einstein-dilaton system, thus we derive holographically the bulk system from the QCD chiral condensate data. The usefulness of the model is shown in the example of the prediction of the string breaking distance, whose value is found to be consistent with another lattice QCD data.
Non locality appearing in QFT during the free evolution of localized field states and in the Feynman propagator function is analyzed. It is shown to be connected to the initial non local properties present at the level of quantum states and then it does not imply a violation of Einstein's causality. Then it is investigated a simple QFT system with interaction, consisting of a classical source coupled linearly to a quantum scalar field, that is exactly solved. The expression for the time evolution of the state describing the system is given. The expectation value of any arbitrary ``good'' local observable, expressed as a function of the field operator and its space and time derivatives, is obtained explicitly at all order in the field-matter coupling constant. These expectation values have a source dependent part that is shown to be always causally retarded, while the non local contributions are source independent and related to the non local properties of zero point vacuum fluctuations.
We investigate the product of $n$ complex non-Hermitian, independent random matrices, each of size $N\times N$ in the class of elliptic matrices, with independent identically distributed entries. The joint probability distribution of the complex eigenvalues of the product matrix is found to be given by a determinantal point process.
We report an experimental demonstration of optimal measurements of small displacement and tilt of a Gaussian beam - two conjugate variables - involving a homodyne detection with a TEM10 local oscillator. We verify that the standard split detection is only 64% efficient. We also show a displacement measurement beyond the quantum noise limit, using a squeezed vacuum TEM10 mode within the input beam.
We propose an alternative axiomatic description for non-commutative field theories (NCFT) based on some ideas by Soloviev to nonlocal quantum fields. The local commutativity axiom is replaced by the weaker condition that the fields commute at sufficiently large spatial separations, called asymptotic commutativity, formulated in terms of the theory of analytic functionals. The question of a possible violation of the CPT and Spin-Statistics theorems caused by nonlocality of the commutation relations $[\hat{x}_\mu,\hat{x}_\nu]=i\theta_{\mu\nu}$ is investigated. In spite of this inherent nonlocality, we show that the modification aforementioned is sufficient to ensure the validity of these theorems for NCFT. We restrict ourselves to the simplest model of a scalar field in the case of only space-space non-commutativity.
Single image deraining is important for many high-level computer vision tasks since the rain streaks can severely degrade the visibility of images, thereby affecting the recognition and analysis of the image. Recently, many CNN-based methods have been proposed for rain removal. Although these methods can remove part of the rain streaks, it is difficult for them to adapt to real-world scenarios and restore high-quality rain-free images with clear and accurate structures. To solve this problem, we propose a Structure-Preserving Deraining Network (SPDNet) with RCP guidance. SPDNet directly generates high-quality rain-free images with clear and accurate structures under the guidance of RCP but does not rely on any rain-generating assumptions. Specifically, we found that the RCP of images contains more accurate structural information than rainy images. Therefore, we introduced it to our deraining network to protect structure information of the rain-free image. Meanwhile, a Wavelet-based Multi-Level Module (WMLM) is proposed as the backbone for learning the background information of rainy images and an Interactive Fusion Module (IFM) is designed to make full use of RCP information. In addition, an iterative guidance strategy is proposed to gradually improve the accuracy of RCP, refining the result in a progressive path. Extensive experimental results on both synthetic and real-world datasets demonstrate that the proposed model achieves new state-of-the-art results. Code: https://github.com/Joyies/SPDNet
Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with reversible reactions. Starting from the exact Langevin equations describing these models, we derive expressions for two-time correlation and autoresponse functions and obtain a simple aging behavior for these quantities. The autoresponse function is thereby found to depend on the specific nature of the chosen perturbation of the system.
In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of "good" automorphisms --- a key component of quantum hash funciton. We prove some restrictions on Hilbert space dimension and group used in quantum hash function
In this paper, we extend the correspondence between Bayes' estimation and optimal interpolation in a Reproducing Kernel Hilbert Space (RKHS) to the case of linear inequality constraints such as boundedness, monotonicity or convexity. In the unconstrained interpolation case, the mean of the posterior distribution of a Gaussian Process (GP) given data interpolation is known to be the optimal interpolation function minimizing the norm in the RKHS associated to the GP. In the constrained case, we prove that the Maximum A Posteriori (MAP) or Mode of the posterior distribution is the optimal constrained interpolation function in the RKHS. So, the general correspondence is achieved with the MAP estimator and not the mean of the posterior distribution. A numerical example is given to illustrate this last result.
We extend the results of Ref. [arXiv:0705.4294] to noncommutative gauge theories at finite temperature. In particular, by making use of the background field method, we analyze renormalization issues and the high-temperature asymptotics of the one-loop Euclidean free energy of the noncommutative U(1) gauge model within imaginary time formalism. As a by-product, the heat trace of the non-minimal photon kinetic operator on noncommutative $S^1 \times R^3$ manifold taken in an arbitrary background gauge is investigated. All possible types of noncommutativity on $S^1 \times R^3$ are considered. It is demonstrated that the non-planar sector of the model does not contribute to the free energy of the system at high temperature. The obtained results are discussed.
We show how Boundary Conformal Field Theory deformation techniques allow for a complete characterisation of the coupling between the discrete geometry inherited uniformizing a random Regge triangulations and open string theory.
Analyzing a sample of 84 early-type galaxies with directly-measured super-massive black hole masses---nearly doubling the sample size of such galaxies with multi-component decompositions---a symmetric linear regression on the reduced (merger-free) sample of 76 galaxies reveals $M_{BH}\propto M_{*,sph}^{1.27\pm 0.07}$ with a total scatter of $\Delta_{rms}=$ 0.52 dex in the $\log(M_{BH})$ direction. However, and importantly, we discover that the ES/S0-type galaxies with disks are offset from the E-type galaxies by more than a factor of ten in their $M_{BH}/M_{*,sph}$ ratio, with ramifications for formation theories, simulations, and some virial factor measurements used to convert AGN virial masses into $M_{BH}$. Separately, each population follows a steeper relation with slopes of $1.86\pm0.20$ and $1.90\pm0.20$, respectively. The offset mass ratio is mainly due to the exclusion of the disk mass, with the two populations offset by only a factor of two in their $M_{BH}/M_{*,gal}$ ratio in the $M_{BH}$-$M_{*,gal}$ diagram where $M_{BH}\propto M_{*,gal}^{1.8\pm 0.2}$ and $\Delta_{rms}=0.6\pm 0.1$ dex depending on the sample. For $M_{BH} \gtrsim 10^7 M_{\odot}$, we detect no significant bend nor offset in either the $M_{BH}$-$M_{*,sph}$ or $M_{BH}$-$M_{*,gal}$ relations due to barred versus non-barred, or core-S\'ersic versus S\'ersic, early-type galaxies. For reference, the ensemble of late-type galaxies (which invariably are S\'ersic galaxies) follow $M_{BH}$-$M_{*,sph}$ and $M_{BH}$-$M_{*,gal}$ relations with slopes equal to $2.16\pm 0.32$ and $3.05\pm 0.70$, respectively. Finally, we provide some useful conversion coefficients, $\upsilon$, accounting for the different stellar mass-to-light ratios used in the literature, and we report the discovery of a local, compact massive spheroid in NGC 5252.
The state equation of the charged AdS black hole is reviewed in the $T-r$ plane. Thinking of the phase transition, the $T-S$, $P-V$, $P-\nu$ graphs are plotted and then the equal area law is used in the three cases to get the phase transition point (P,T). The analytical phase transition point relations for P-T of charged AdS black hole has been obtained successfully. By comparing the three results, we find that the equal area law possibly cannot be used directly for $P-\nu$ plane. According to the $T-S$, $P-V$ results, we plot the $P-T-Q$ graph and find that for a highly charged black hole a very low temperature condition is required for the phase transition.
We present new narrow-band Ha, [N II], and [O III] high-resolution images of the quadrupolar planetary nebula (PN) NGC 6309 that show in great detail its bipolar lobes and reveal new morphological features. New high- and low-dispersion long-slit spectra have been obtained to help in the investigation of the new nebular components. The images and spectra unveil two diffuse blobs, one of them located at 55 arcsec from the central star along the NE direction (PA= +71) and the other at 78 arcsec in the SW direction (PA= -151). Therefore, these structures do not share the symmetry axes of the inner bipolar outflows. Their radial velocities relative to the system are quite low: +3 and -4 km/s, respectively. Spectroscopic data confirm a high [O III] to Ha ratio, indicating that the blobs are being excited by the UV flux from the central star. Our images convincingly show a spherical halo 60 arcsec in diameter encircling the quadrupolar nebula. The expansion velocity of this shell is low, 66 km/s. The software SHAPE has been used to construct a morpho-kinematic model for the ring and the bipolar flows that implies an age of 4,000 yrs, the expansion of the halo sets a lower limit for its age 46,000 yrs, and the very low expansion of the blobs suggests they are part of a large structure corresponding to a mass ejection that took place 150,000 yrs ago. In NGC 6309 we have direct evidence of a change in the geometry of mass-loss, from spherical in the halo to axially-symmetric in the two pairs of bipolar lobes.
We consider an $n$-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schr\"odiner equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension $n$ and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary $\beta>0$ loss. This is in contrast to \cite{ChWu-lsm}, where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension.
In this study we extend the results of Kurtz (1970,1971) to show the weak convergence of epidemic processes that include explicit time dependence, specifically where the transmission parameter,$\beta(t)$, carries a time dependency. We first show that when population size goes to infinity, the time inhomogeneous process converges weakly to the solution of the mean-field ODE. Our second result is that, under proper scaling, the central limit type fluctuations converge to a diffusion process.
Non-abelian horizontal symmetry has been considered to solve potentially SUSY flavor problem, but simple models are suffering from various problems. In this talk, we point out that (anomalous) U(1)_A gauge symmetry solves all the problems in a natural way, especially, in the E_6 grand unified theories. Combining the GUT scenario with anomalous U(1)_A gauge symmetry, in which doublet-triplet splitting and natural gauge coupling unification are realized, and realistic quark and lepton mass matrices are obtained including bi-large neutrino mixings, complete E_6* SU(3)_H (or E_6*SU(2)_H) GUTs can be obtained, in which all the three generation quarks and leptons are unified into a single multiplet (27,3) (or two multiplets (27,2+1)). This talk is based on Ref.[1].
Suppose X and Y are two independent irreducible Markov chains on n states. We consider the intersection time, which is the first time their trajectories intersect. We show for reversible and lazy chains that the total variation mixing time is always upper bounded by the expected intersection time taken over the worst starting states. For random walks on trees we show the two quantities are equivalent. We obtain an expression for the expected intersection time in terms of the eigenvalues for reversible and transitive chains. For such chains we also show that it is up to constants the geometric mean of n and E[I], where I is the number of intersections up to the uniform mixing time. Finally for random walks on regular graphs we obtain sharp inequalities that relate the expected intersection time to maximum hitting time and mixing time.
A new approach, "$\mathfrak{B}\text{-Function}$ Method", to the analysis of the reconstruction methods, phase space, and exact solutions of the alternative theories of gravity is suggested. The $\mathfrak{B}\text{-function}$ method which is constructed by suggesting eight new model-independent physical theorems, extracts the physically admissible ranges of the evolution of the parameters (i.e. the variables and constant parameters of action and those which emerged by differential equations as the constants of integration) and helps one for quick data analysis. The most significant feature and beauty of the $\mathfrak{B}\text{-function}$ method are that all conditions leading to physically admissible domains, can be expressed only by one new function, $\mathfrak{B}\text{-Function}$, which is the Lie derivative of $\ln(\mathcal{F}(x))$ along a vector field, $\mathbf{X}=x+c$, on a singleton $Q=\{x\}$.
In this work, we tackle the problem of real-world fluid animation from a still image. The key of our system is a surface-based layered representation deriving from video decomposition, where the scene is decoupled into a surface fluid layer and an impervious background layer with corresponding transparencies to characterize the composition of the two layers. The animated video can be produced by warping only the surface fluid layer according to the estimation of fluid motions and recombining it with the background. In addition, we introduce surface-only fluid simulation, a $2.5D$ fluid calculation version, as a replacement for motion estimation. Specifically, we leverage the triangular mesh based on a monocular depth estimator to represent the fluid surface layer and simulate the motion in the physics-based framework with the inspiration of the classic theory of the hybrid Lagrangian-Eulerian method, along with a learnable network so as to adapt to complex real-world image textures. We demonstrate the effectiveness of the proposed system through comparison with existing methods in both standard objective metrics and subjective ranking scores. Extensive experiments not only indicate our method's competitive performance for common fluid scenes but also better robustness and reasonability under complex transparent fluid scenarios. Moreover, as the proposed surface-based layer representation and surface-only fluid simulation naturally disentangle the scene, interactive editing such as adding objects to the river and texture replacing could be easily achieved with realistic results.
We study the rough asymptotic behaviour of a general economic risk model in a discrete setting. Both financial and insurance risks are taken into account. Loss during the first $n$ years is modelled as a random variable $B_1+A_1B_2+\ldots+A_1\ldots A_{n-1}B_n$, where $A_i$ corresponds to the financial risk of the year $i$ and $B_i$ represents the insurance risk respectively. Risks of the same year $i$ are not assumed to be independent.   The main result shows that ruin probabilities exhibit power law decay under general assumptions. Our objective is to give a complete characterisation of the relevant quantities that describe the speed at which the ruin probability vanishes as the amount of initial capital grows. These quantities can be expressed as maximal moments, called moment indices, of suitable random variables. In addition to the study of ultimate ruin, the case of finite time interval ruin is considered. Both of these investigations make extensive use of the new properties of moment indices developed during the first half of the paper.
The Barcelona-Catania-Paris-Madrid (BCPM) functional recently proposed to describe nuclear structure properties of finite nuclei is generalized as to include a realistic effective mass. The resulting functional is as good as the previous one in describing binding energies, radii, deformation properties, etc and, in addition, the description of Giant Quadrupole Resonance energies is greatly improved.
The quantum Zeno effect describes the inhibition of quantum evolution by frequent measurements. Here, we propose a scheme for entangling two given photons based on this effect. We consider a linear-optics set-up with an absorber medium whose two-photon absorption rate $\xi_{2\gamma}$ exceeds the one-photon loss rate $\xi_{1\gamma}$. In order to reach an error probability $P_{\rm error}$, we need $\xi_{1\gamma}/\xi_{2\gamma}<2P_{\rm error}^2/\pi^2$, which is a factor of 64 better than previous approaches (e.g., by Franson et al). Since typical media have $\xi_{2\gamma}<\xi_{1\gamma}$, we discuss three mechanisms for enhancing two-photon absorption as compared to one-photon loss. The first mechanism again employs the quantum Zeno effect via self-interference effects when sending two photons repeatedly through the same absorber. The second mechanism is based on coherent excitations of many atoms and exploits the fact that $\xi_{2\gamma}$ scales with the number of excitations but $\xi_{1\gamma}$ does not. The third mechanism envisages three-level systems where the middle level is meta-stable ($\Lambda$-system). In this case, $\xi_{1\gamma}$ is more strongly reduced than $\xi_{2\gamma}$ and thus it should be possible to achieve $\xi_{2\gamma}/\xi_{1\gamma}\gg1$. In conclusion, although our scheme poses challenges regarding the density of active atoms/molecules in the absorber medium, their coupling constants and the detuning, etc., we find that a two-photon gate with an error probability $P_{\rm error}$ below 25% might be feasible using present-day technology.
The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical results for the influences of interaction and disorder on the compressibility as a function of the particle density and the strength of the magnetic field are presented. Localization-delocalization transitions associated with highly compressible region in the energy spectrum are found at half-integer filling factors. Coulomb blockade effects are found near integer fillings in the regions of low compressibility. Results are compared with recent experiments.
Dirac, Schwinger and Zwanziger theories of electric and magnetic charges are obtained via duality transformation. Analogous construction for three Euclidean dimensions, with magnetic charges interacting with electric currents, is also done. The role of Dirac strings as dislocations in the configurations of gauge potential is emphasized.
The Wegner-Houghton formulation of the exact renormalization group evolution equation is used in order to study the chiral symmetry breaking of the linear sigma model coupled to an isospin doublet of quarks. A numerical investigation for a particular truncation of the equation which includes the scalar field renormalization function is presented.
We present the results of a series of observations of the near- and mid-infrared polarisation properties of the Seyfert 2 galaxy NGC1068. Our data agree well with previously published results in showing the need for a separate polarisation mechanism in the near infrared apart from scattering. We find that the predictions of a simple model in which this component arises through absorptive dichroism due to aligned grains within the extended warm (~400K) dust fits the data reasonably if the obscured background source is itself due to dust emission (at temperature >1000K). By considering the change of polarisation with wavelength we show that the extinction to this hot dust region is in the range AV=20-40. Consideration of the observed data then leads us to the conclusion that if viewed face-on, NGC1068 would have a strong near-infrared excess similar to Seyfert 1 galaxies. Comparison with other independent measures of the extinction to the active nucleus itself lead us to the conclusion that the hot dust must provide screening equivalent to at least AV=40, and possibly much higher. We speculate that this component alone may be the `classical' torus discussed in terms of the unified model, and the more extensive mid-infrared emission may arise from circumnuclear molecular cloud material, and dust in the ionisation cones.