ShantanuT01/DACTYL-Pretraining huggingface dataset:
Weak gravitational lensing is a powerful tool for studying both the geometry and the dynamics of the Universe. Its power spectrum contains information on the sources emitting photons and on the large--scale structures that these hotons cross. We calculate the weak lensing cosmic convergence and shear power spectra, in linear theory and Limber's approximation, for two different classes of cosmological models: the standard \LambdaCDM and Unified Dark Matter (UDM) models. The latter models attempt to solve the problems of the dark matter in the dynamics of galaxies and galaxy clusters and of the late-time acceleration of the Universe expansion by introducing a scalar field that mimics both dark matter and dark energy. A crucial feature of the UDM models is the speed of sound c_\infty, that is the value of the sound speed at late times, on which structure formation depends. In this paper, we provide the predictions of the UDM models for the weak lensing signal,with various values of c_\infty. We consider both the Cosmic Microwave Background and background galaxies at different redshifts as sources for the weak lensing power spectra. We find that the power spectra in UDM models are more sensitive to the variations of c_\infty for sources located at low redshifts. Moreover, we find that for c_\infty>10^{-3} (in units of the speed of light), the UDM weak lensing convergence power spectrum C^{\kappa\kappa}(l) for background galaxies is strongly suppressed with respect to the \LambdaCDM spectrum, particularly at small angular scales l\gtrsim100.
Entropy and the second law of thermodynamcs were discovered through study of the behaviour of gases in confined spaces. The related techniques developed in the kinetic theory of gases have failed to resolve the apparent conflict between the time-reversal symmetry of all known laws of nature and the existence of arrows of time that at all times and everywhere in the universe all point in the same direction. I will argue that the failure may due to unconscious application to the universe of the conceptual framework developed for confined systems. If, as seems plausible, the universe is an unconfined system, new concepts are needed.
Recent researches on information bottleneck shed new light on the continuous attempts to open the black box of neural signal encoding. Inspired by the problem of lossy signal compression for wireless communication, this paper presents a Bitwise Information Bottleneck approach for quantizing and encoding neural network activations. Based on the rate-distortion theory, the Bitwise Information Bottleneck attempts to determine the most significant bits in activation representation by assigning and approximating the sparse coefficient associated with each bit. Given the constraint of a limited average code rate, the information bottleneck minimizes the rate-distortion for optimal activation quantization in a flexible layer-by-layer manner. Experiments over ImageNet and other datasets show that, by minimizing the quantization rate-distortion of each layer, the neural network with information bottlenecks achieves the state-of-the-art accuracy with low-precision activation. Meanwhile, by reducing the code rate, the proposed method can improve the memory and computational efficiency by over six times compared with the deep neural network with standard single-precision representation. Codes will be available on GitHub when the paper is accepted \url{https://github.com/BitBottleneck/PublicCode}.
Context. The main feature of the spatial large-scale galaxy distribution is an intricate network of galaxy filaments. Although many attempts have been made to quantify this network, there is no unique and satisfactory recipe for that yet. Aims. The present paper compares the filaments in the real data and in the numerical models, to see if our best models reproduce statistically the filamentary network of galaxies. Methods. We apply an object point process with interactions (the Bisous process) to trace and describe the filamentary network both in the observed samples (the 2dFGRS catalogue) and in the numerical models that have been prepared to mimic the data.We compare the networks. Results. We find that the properties of filaments in numerical models (mock samples) have a large variance. A few mock samples display filaments that resemble the observed filaments, but usually the model filaments are much shorter and do not form an extended network. Conclusions. We conclude that although we can build numerical models that are similar to observations in many respects, they may fail yet to explain the filamentary structure seen in the data. The Bisous-built filaments are a good test for such a structure.
We investigate the momentum distribution function near the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model (the zig-zag Hubbard chain), with the density-matrix renormalization-group technique. We show that for strong interactions the Mott-Hubbard transition occurs between the metallic-phase and an insulating dimerized phase with incommensurate spin excitations, suggesting a decoupling of magnetic and charge excitations not present in weak coupling. We illustrate the signatures for the Mott-Hubbard transition and the commensurate-incommensurate transition in the insulating spin-gapped state in their respective ground-state momentum distribution functions.
We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend the previous result in [6] for unmixed $L_p$-estimates without weights.
We investigate how the consistency relations of large-scale structures are modified when the initial density field is not Gaussian. We consider both scenarios where the primordial density field can be written as a nonlinear functional of a Gaussian field and more general scenarios where the probability distribution of the primordial density field can be expanded around the Gaussian distribution, up to all orders over $\delta_{L0}$. Working at linear order over the non-Gaussianity parameters $f_{\rm NL}^{(n)}$ or $S_n$, we find that the consistency relations for the matter density fields are modified as they include additional contributions that involve all-order mixed linear-nonlinear correlations $\langle \prod \delta_L \prod \delta \rangle$. We derive the conditions needed to recover the simple Gaussian form of the consistency relations. This corresponds to scenarios that become Gaussian in the squeezed limit. Our results also apply to biased tracers, and velocity or momentum cross-correlations.
We examine the anomalous dimension matrix appropriate for the phase space restricted B --> X(u) ell anti-nu and B --> X(s) gamma decay spectra to subleading nonperturbative order. The effects of the time ordered products of the HQET Lagrangian with the leading order shape function operator are calculated, as are the anomalous dimensions of subleading operators. We establish the renormalizability and closure of a subset of the non-local operator basis, a requirement for the establishment of factorization theorems at this order. Operator mixing is found between the operators which occur to subleading order, requiring the subleading operator basis be extended. We comment on the requirement for new shape functions to be introduced to characterize the matrix elements of these new operators, and the phenomenological consequences for extractions of $|V_{ub}|$.
Using the randomized algorithm method developed by Duminil-Copin, Raoufi and Tassion (2019b), we exhibit sharp phase transition for the confetti percolation model. This provides an alternate proof, than that of Ahlberg, Tassion and Texeira (2018), for the critical parameter for percolation in this model to be $1/2$ when the radius of the underlying shapes for the distinct colours arise from the same distribution. In addition, we study the covered area fraction for this model, which is akin to the covered volume fraction in continuum percolation. Modulo a certain `transitivity condition', this study allows us to calculate exact critical parameter for percolation when the underlying shapes for different colours may be of different sizes. Similar results are also obtained for the Poisson Voronoi percolation model when different coloured points have different growth speeds.
We report on neutron diffraction, thermal expansion, magnetostriction, dielectric, and specific heat measurements on polycrystalline FeCr2S4 in external magnetic fields. The ferrimagnetic ordering temperatures $T_{\mathrm{C}}\approx 170$ K and the transition at $T_{\mathrm{OO}}\approx 10$ K, which has been associated with orbital ordering, are only weakly shifted in magnetic fields up to 9 T. The cubic lattice parameter is found to decrease when entering the state below $T_{\mathrm{OO}}$. The magnetic moments of the Cr- and Fe-ions are reduced from the spin-only values throughout the magnetically ordered regime, but approach the spin-only values for fields $>$5.5 T. Thermal expansion in magnetic fields and magnetostriction experiments indicate a contraction of the sample below about 60 K. Below $T_{\mathrm{OO}}$ this contraction is followed by a moderate expansion of the sample for fields larger than $\sim$4.5 T. The transition at $T_{\mathrm{OO}}$ is accompanied by an anomaly in the dielectric constant. The dielectric constant depends on both the strength and orientation of the external magnetic field with respect to the applied electric field for $T<T_{\mathrm{OO}}$. A linear correlation of the magnetic-field-induced change of the dielectric constant and the magnetic-field dependent magnetization is observed. This behaviour is consistent with the existence of a ferroelectric polarization and a multiferroic ground state below 10 K.
A Bose-Einstein condensate in an optical lattice exhibits parametric resonances when the intensity of the lattice is periodically modulated in time. These resonances correspond to an exponential growth of the population of counter-propagating Bogoliubov excitations. A suitable linearization of the Gross-Pitaevskii (GP) equation is used to calculate the stability diagram and the growth rates of the unstable modes. The results agree with the ones extracted from time-dependent GP simulations, supporting our previous claim (M. Kraemer et al., Phys. Rev. A (2005) in press) concerning the key role of parametric resonances in the response observed by Stoeferle et al. (Phys. Rev. Lett. 92, 130403 (2004)) in the superfluid regime. The role of the seed excitations required to trigger the parametric amplification is discussed. The possible amplification of the quantum fluctuations present in the quasiparticle vacuum, beyond GP theory, is also addressed, finding interesting analogies with similar processes in nonlinear quantum optics and with the dynamic Casimir effect. Our results can be used in exploiting parametric instabilities for the purpose of spectroscopy, selective amplification of a particular excitation mode and for establishing a new type of thermometry.
We study the quantum limits of Eisenstein series off the critical line for $\mathrm{PSL}_{2}(\mathcal{O}_{K})\backslash\mathbb{H}^{3}$, where $K$ is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and Risager on $\mathrm{PSL}_{2}(\mathbb{Z})\backslash\mathbb{H}^{2}$. We observe that the measures $\lvert E(p,\sigma_{t}+it)\rvert^{2}d\mu(p)$ become equidistributed only if $\sigma_{t}\rightarrow 1$ as $t\rightarrow\infty$. We use these computations to study measures defined in terms of the scattering states, which are shown to converge to the absolutely continuous measure $E(p,3)d\mu(p)$ under the GRH.
We consider the effects of noncommutativity and the generalized uncertainty principle on the FRW cosmology with a scalar field. We show that, the cosmological constant problem and removability of initial curvature singularity find natural solutions in this scenarios.
A lower bound for the dimension of the $\Q$-vector space spanned by special values of a Dirichlet series with periodic coefficients is given. As a corollary, it is deduced that both special values at even integers and at odd integers contain infinitely many irrational numbers. This result is proved by T.Rivoal if the function considered is the Riemann zeta function, and this paper gives its generalization to more general Dirichlet series.
This paper presents VTN, a transformer-based framework for video recognition. Inspired by recent developments in vision transformers, we ditch the standard approach in video action recognition that relies on 3D ConvNets and introduce a method that classifies actions by attending to the entire video sequence information. Our approach is generic and builds on top of any given 2D spatial network. In terms of wall runtime, it trains $16.1\times$ faster and runs $5.1\times$ faster during inference while maintaining competitive accuracy compared to other state-of-the-art methods. It enables whole video analysis, via a single end-to-end pass, while requiring $1.5\times$ fewer GFLOPs. We report competitive results on Kinetics-400 and present an ablation study of VTN properties and the trade-off between accuracy and inference speed. We hope our approach will serve as a new baseline and start a fresh line of research in the video recognition domain. Code and models are available at: https://github.com/bomri/SlowFast/blob/master/projects/vtn/README.md
We generalize the technique of Lada et al. (1994) to map dust column density through a molecular cloud (NICE) to an optimized multi-band technique (NICER) that can be applied to any multi-band survey of molecular clouds. We present a first application to a ~625 deg^2 subset of the Two Micron All Sky Survey (2MASS) data and show that when compared to NICE, the optimized NICER technique (i) achieves the same extinction peak values, (ii) improves the noise variance of the map by a factor of 2 and (iii) is able to reach 3 \sigma dust extinction measurements as low as A_V = 0.5 magnitudes, better than or equivalent to classical optical star count techniques and below the threshold column density for the formation of CO, the brightest H2 tracer in radio-spectroscopy techniques. The application of the NICER techniques to near-infrared data obtained with a 8 meter-class telescope with a state-of-the-art NIR camera, such as the VLT-ISAAC combination, will be able to achieve dynamic ranges from below 10^21 protons cm^-2 to over 10^23 protons cm^-2 (A_V in the range [0.3, 60]) and spatial resolutions < 10'', making use of a single and straightforward column density tracer, extinction by interstellar dust.
This paper gives applications of the enclosure method introduced by the author to typical inverse obstacle and crack scattering problems in two dimensions. Explicit extraction formulae of the convex hull of unknown polygonal sound-hard obstacles and piecewise linear cracks from the far field pattern of the scattered field at a fixed wave number and at most two incident directions are given. The main new points of this paper are: a combination of the enclosure method and the Herglotz wave function; explicit construction of the density in the Herglotz wave function by using the idea of the Vekua transform. By virtue of the construction, one can avoid any restriction on the wave number in the extraction formulae. An attempt for the case when the far field pattern is given on limited angles is also given.
We give a sufficient condition, in the spirit of Kowalczyk-Martel-Munoz-Van Den Bosch \cite{KMMvdB21AnnPDE}, for the local asymptotic stability of kinks under odd perturbations. In particular, we allow the existence of quite general configuration of internal modes. The extension of our result to moving kinks remains an open problem.
In a recent Letter, Cowsik, Ratnam and Bhattacharjee (1996a) have built a dynamically self-consistent spatial distribution of particles of galactic dark matter. They have come up with the rather unorthodox conclusion that the mean velocity dispersion of dark matter particles ``should be $600 kms$ or larger''. Their letter triggered immediate comments (Evans 1996, Gates et al. 1996). Here we find, as did Cowsik et al. (1996a), that models of the dark matter halo can be made consistent with velocity dispersion much larger than that expected from a simple application of the virial theorem in the solar neighbourhood. But in contrast to their conclusions, we show that using their model, we also obtain solutions with smaller velocity dispersion down to $\sim 270 kms$. These more orthodox dispersions arise because of less constraining boundary conditions for the central density but do not rely on indirect or model dependent measurements of the large scale distance behaviour of the rotation curve.
Twisted two-dimensional structures open new possibilities in band structure engineering. At magic twist angles, flat bands emerge, which give a new drive to the field of strongly correlated physics. In twisted double bilayer graphene dual gating allows changing the Fermi level and hence the electron density and also allows tuning the interlayer potential, giving further control over band gaps. Here, we demonstrate that by applying hydrostatic pressure, an additional control of the band structure becomes possible due to the change of tunnel couplings between the layers. We find that the flat bands and the gaps separating them can be drastically changed by pressures up to 2 GPa, in good agreement with our theoretical simulations. Furthermore, our measurements suggest that in finite magnetic field due to pressure a topologically non-trivial band gap opens at the charge neutrality point at zero displacement field.
We propose a renormalisable model based on $A_4$ family symmetry with an $SU(5)$ grand unified theory (GUT) which leads to the minimal supersymmetric standard model (MSSM) with a two right-handed neutrino seesaw mechanism. Discrete $\mathbb{Z}_9\times \mathbb{Z}_6$ symmetry provides the fermion mass hierarchy in both the quark and lepton sectors, while $\mathbb{Z}_4^R$ symmetry is broken to $\mathbb{Z}_2^R$, identified as usual R-parity. Proton decay is highly suppressed by these symmetries. We discuss both the $A_4$ and $SU(5)$ symmetry breaking sectors, including doublet-triplet splitting, Higgs mixing and the origin of the $\mu$ term. The model provides an excellent fit (better than one sigma) to all quark and lepton (including neutrino) masses and mixing with spontaneous CP violation. With the $A_4$ vacuum alignments, $(0,1,1)$ and $(1,3,1)$, the model predicts the entire PMNS mixing matrix with no free parameters, up to a relative phase, selected to be $2\pi/3$ from a choice of the nine complex roots of unity, providing a direct link between neutrino oscillations and leptogenesis.
We consider a metric which describes Ba$\tilde{\text{n}}$ados geometries and show that the considered metric is a solution of generalized minimal massive gravity (GMMG) model. We consider the Killing vector field which preserves the form of considered metric. Using the off-shell quasi-local approach we obtain the asymptotic conserved charges of given solution. Similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model also, we show that the algebra among the asymptotic conserved charges is isomorphic to two copies of the Virasoro algebra. Eventually, we find relation between the algebra of the near horizon and the asymptotic conserved charges. This relation show that the main part of the horizon fluffs proposal of Refs.\cite{140,14} appear for generic black holes in the class of Ba$\tilde{\text{n}}$ados geometries in the context of GMMG model.
We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band. This assumption is motivated by quantum phase estimation (QPE) and digital adiabatic simulation (DAS). Treating the effective Hamiltonian that generates the Trotterized time evolution using rigorous perturbative methods, we show that the Trotter step size needed to estimate an energy eigenvalue within precision $\epsilon$ using QPE can be improved in scaling from $\epsilon$ to $\epsilon^{1/2}$ for a large class of systems (including any Hamiltonian which can be decomposed as a sum of local terms or commuting layers that each have real-valued matrix elements). For DAS we improve the asymptotic scaling of the Trotter error with the total number of gates $M$ from $\mathcal{O}(M^{-1})$ to $\mathcal{O}(M^{-2})$, and for any fixed circuit depth we calculate an approximately optimal step size that balances the error contributions from Trotterization and the adiabatic approximation. These results partially generalize to diabatic processes, which remain in a narrow energy band separated from the rest of the spectrum by a gap, thereby contributing to the explanation of the observed similarities between the quantum approximate optimization algorithm and diabatic quantum annealing at small system sizes. Our analysis depends on the perturbation of eigenvectors as well as eigenvalues, and on quantifying the error using state fidelity (instead of the matrix norm of the difference of unitaries which is sensitive to an overall global phase).
A method based on sector decomposition is briefly described which is suitable for the calculation of the double real radiation part of e^+e^- to 3 jets at next-to-next-to-leading order in a fully differential way.
We comment on the role of the Cartesian-type Kerr-Schild coordinates in developing a faulty maximal extension of the Kerr-Newman solution in the well-known paper of Carter.
We investigated the effects of gravitational lensing for a system in which a lens is a point mass and a homogeneous disc with a central hole. In such system there is a variety of cases resulting in formation of one, two and three Einstein rings. We found an explicit solution and considered conditions for existence of the second Einstein ring arising on the disc. Numerical modelling of the images was made for various ratios of the central mass to the disc one and for various values of the disc surface density. We also analysed dependence of the magnification factor on a source position for such system. The result of our work can be used in search of astrophysical objects with a toroidal (ring) structure.
Van der Waals heterostructures give access to a wide variety of new phenomena that emerge thanks to the combination of properties brought in by the constituent layered materials. We show here that owing to an enhanced interaction cross section with electrons in a type I van der Waals heterostructure, made of single layer molybdenum disulphide and thin boron nitride films, electrons and holes created in boron nitride can be transferred to the dichalcogenide where they form electron-hole pairs yielding luminescence. This cathodoluminescence can be mapped with a spatial resolution far exceeding what can be achieved in a typical photoluminescence experiment, and is highly valuable to understand the optoelectronic properties at the nanometer scale. We find that in heterostructures prepared following the mainstream dry transfer technique, cathodoluminescence is locally extinguished, and we show that this extinction is associated with the formation of defects, that are detected in Raman spectroscopy and photoluminescence. We establish that to avoid defect formation induced by low-energy electron beams and to ensure efficient transfer of electrons and holes at the interface between the layers, flat and uniform interlayer interfaces are needed, that are free of trapped species, airborne ones or contaminants associated with sample preparation. We show that heterostructure fabrication using a pick-up technique leads to superior, intimate interlayer contacts associated with significantly more homogeneous cathodoluminescence.