ShantanuT01/DACTYL-Pretraining huggingface dataset:
The lowest stationary quantum state of neutrons in the Earth's gravitational field is identified in the measurement of neutron transmission between a horizontal mirror on the bottom and an absorber on top. Such an assembly is not transparent for neutrons if the absorber height is smaller than the "height" of the lowest quantum state.
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second kind Stirling numbers and generalized Bernoulli polynomials. Moreover, we give the generating function and interpolation function of these modified q-Bernstein polynomials of two variables and also give the derivatives of these polynomials and their generating function.
In this paper, we study normalization methods for neural networks from the perspective of elimination singularity. Elimination singularities correspond to the points on the training trajectory where neurons become consistently deactivated. They cause degenerate manifolds in the loss landscape which will slow down training and harm model performances. We show that channel-based normalizations (e.g. Layer Normalization and Group Normalization) are unable to guarantee a far distance from elimination singularities, in contrast with Batch Normalization which by design avoids models from getting too close to them. To address this issue, we propose BatchChannel Normalization (BCN), which uses batch knowledge to avoid the elimination singularities in the training of channel-normalized models. Unlike Batch Normalization, BCN is able to run in both large-batch and micro-batch training settings. The effectiveness of BCN is verified on many tasks, including image classification, object detection, instance segmentation, and semantic segmentation. The code is here: https://github.com/joe-siyuan-qiao/Batch-Channel-Normalization.
The energy eigenvalues of the anharmonic oscillator characterized by the cubic potential for various eigenstates are determined within the framework of the hypervirial-Pad\'e summation method. For this purpose the E[3,3] and E[3,4] Pad\'e approximants are formed to the energy perturbation series and given the energy eigenvalues up to fourth order in terms of the anharmonicity parameter $\lambda$.
In our hierarchical structure-formation paradigm, the observed morphological evolution of massive galaxies -- from rotationally-supported discs to dispersion-dominated spheroids -- is largely explained via galaxy merging. However, since mergers are likely to destroy discs, and the most massive galaxies have the richest merger histories, it is surprising that any discs exist at all at the highest stellar masses. Recent theoretical work by our group has used a cosmological, hydrodynamical simulation to suggest that extremely massive (M* > 10^11.4 MSun) discs form primarily via minor mergers between spheroids and gas-rich satellites, which create new rotational stellar components and leave discs as remnants. Here, we use UV-optical and HI data of massive galaxies, from the SDSS, GALEX, DECaLS and ALFALFA surveys, to test these theoretical predictions. Observed massive discs account for ~13% of massive galaxies, in good agreement with theory (~11%). ~64% of the observed massive discs exhibit tidal features, which are likely to indicate recent minor mergers, in the deep DECaLS images (compared to ~60% in their simulated counterparts). The incidence of these features is at least four times higher than in low-mass discs, suggesting that, as predicted, minor mergers play a significant (and outsized) role in the formation of these systems. The empirical star-formation rates agree well with theoretical predictions and, for a small galaxy sample with HI detections, the HI masses and fractions are consistent with the range predicted by the simulation. The good agreement between theory and observations indicates that extremely massive discs are indeed remnants of recent minor mergers between spheroids and gas-rich satellites.
A TQFT in terms of general gauge fixing functions is discussed. In a covariant gauge it yields the Donaldson-Witten TQFT. The theory is formulated on a generalized phase space where a simplectic structure is introduced. The Hamiltonian is expressed as the anticommutator of off-shell nilpotent BRST and anti-BRST charges. Following original ideas of Witten a time reversal operation is introduced and an inner product is defined in terms of it. A non-covariant gauge fixing is presented giving rise to a manifestly time reversal invariant Lagrangean and a positive definite Hamiltonian, with the inner product previously introduced. As a consequence, the indefiniteness problem of some of the kinetic terms of the Witten's action is resolved. The construction allows then a consistent interpretation of Floer groups in terms of the cohomology of the BRST charge which is explicitly independent of the background metric.   The relation between the BRST cohomology and the ground states of the Hamiltonian is then completely stablished. The topological theories arising from the covariant, Donaldson-Witten, and non-covariant gauge fixing are shown to be quantum equivalent by using the operatorial approach.
The absolute luminosity of the Fe Kalpha emission line from matter illuminated by X-rays in astrophysical sources is nontrivial to calculate except when the line-emitting medium is optically-thin to absorption and scattering. We characterize the Fe Kalpha line flux using a dimensionless efficiency, defined as the fraction of continuum photons above the Fe K shell absorption edge threshold energy that appear in the line. The optically-thin approximation begins to break down even for column densities as small as 2 x 10^22 cm^-2. We show how to obtain reliable estimates of the Fe Kalpha line efficiency in the case of cold, neutral matter, even for the Compton-thick regime. We find that, regardless of geometry and covering factor, the largest Fe Kalpha line efficiency is attained well before the medium becomes Compton-thick. For cosmic elemental abundances it is difficult to achieve an efficiency higher than a few percent under the most favorable conditions and lines of sight. For a given geometry, Compton-thick lines-of-sight may have Fe Kalpha line efficiencies that are orders of magnitude less than the maximum possible for that geometry. Configurations that allow unobscured views of a Compton-thick reflecting surface are capable of yielding the highest efficiencies. Our results can be used to estimate the predicted flux of the narrow Fe Kalpha line at ~6.4 keV from absorption models in AGN. In particular we show that contrary to a recent claim in the literature, absorption dominated models for the relativistic Fe Kalpha emission line in MCG -6-30-15 do not over-predict the narrow Fe Kalpha line for any column density or covering factor.
The multilayer multiconfiguration time-dependent Hartree method is employed to study vibrationally coupled charge transport in models of single molecule junctions. To increase the efficiency of the simulation method, a representation of the Hamiltonian in terms of the scattering states of the underlying electronic Hamiltonian is used. It is found that with an appropriate choice of the scattering states the artificial electron correlation present in the original representation of the model is greatly reduced. This allows efficient simulation of the steady-state currents in a wide physical parameter space, which is demonstrated by several numerical examples.
A new experimental realization of heat capacity as an entanglement witness (EW) is reported. Entanglement properties of a low dimensional quantum spin system are investigated by heat capacity measurements performed down to very low temperatures (400mK), for various applied magnetic field values. The experimentally extracted results for the value of heat capacity at zero field matches perfectly with the theoretical estimates of entanglement from model Hamiltonians. The studied sample is a spin $\frac{1}{2}$ antiferromagnetic system which shows clear signature of quantum phase transition (QPT) at very low temperatures when the heat capacity is varied as a function of fields at a fixed temperature. The variation of entanglement as a function of field is then explored in the vicinity of the quantum phase transition to capture the sudden loss of entanglement.
We present the largest systematic, HST-based search to date for luminous $z\gtrsim8$ galaxy candidates using $\sim$1267 arcmin$^{2}$ of (pure-)parallel observations from a compilation of 288 random sightlines with ACS and WFC3 observations, derived from the SuperBoRG data set and together representing a factor $\sim1.12\times$ larger than existing space-based data sets. Using NIR color cuts and careful photo-$z$ analyses, we find 31 $z\gtrsim8$ galaxy candidates over 29 unique sightlines, and derive global galaxy properties such as UV magnitudes and continuum slopes, sizes, and rest-frame optical properties (e.g., SFRs, stellar masses, $A_{\rm v}$). Taking advantage of the (pure-)parallel nature of our data set - making it one of the most representative thus far - and derived SFRs, we evaluate the cosmic star formation rate density for the bright end of the UV luminosity function at $z\sim8-10$ and test the validity of luminosity function-derived results using a conversion factor. We find our method yields comparable results to those derived with luminosity functions. Furthermore, we present follow up observations of 5 (Super)BoRG targets with Keck/MOSFIRE, finding no evidence of Ly$\alpha$ in $>3$ hrs of $Y-$band observations in either, consistent with a largely neutral medium at $z\sim8$. Our results offer a definitive HST legacy on the bright end of the luminosity function and provide a valuable benchmark as well as targets for follow up with JWST.
In this work, we propose a zero-shot learning method to effectively model knowledge transfer between classes via jointly learning visually consistent word vectors and label embedding model in an end-to-end manner. The main idea is to project the vector space word vectors of attributes and classes into the visual space such that word representations of semantically related classes become more closer, and use the projected vectors in the proposed embedding model to identify unseen classes. We evaluate the proposed approach on two benchmark datasets and the experimental results show that our method yields significant improvements in recognition accuracy.
We show how to extend the concept of heat capacity to nonequilibrium systems. The main idea is to consider the excess heat released by an already dissipative system when slowly changing the environment temperature. We take the framework of Markov jump processes to embed the specific physics of small driven systems and we demonstrate that heat capacities can be consistently defined in the quasistatic limit. Away from thermal equilibrium, an additional term appears to the usual energy-temperature response at constant volume, explicitly in terms of the excess work. In linear order around an equilibrium dynamics that extra term is an energy-driving response and it is entirely determined from local detailed balance. Examples illustrate how the steady heat capacity can become negative when far from equilibrium.
Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger-Keldysh formalism is used in AdS/CFT instead of conventional Feynman-Witten diagrams technique, permits to calculate values of conformal dimensions in the $O(N)$ symmetric model with conformal or composite Hubbard-Stratonovich field.
Using superspace projection operators we provide a classification of (3/2,2) off-shell supermultiplets which are realized in terms of a real axial vector superfield, with or without compensating superfields. Any linearized supergravity action is shown to be a superposition of those corresponding to (i) old minimal supergravity, (ii) new minimal supergravity and (iii) the novel (3/2,2) off-shell supermultiplet with 12+12 degrees of freedom obtained in hep-th/0201096.
We studied the pressure-induced superconductor CeIrSi$_3$ with the non-centrosymmetric tetragonal structure under high pressure. The electrical resistivity and ac heat capacity were measured in the same run for the same sample. The critical pressure was determined to be $P_{\rm c}$ = 2.25 GPa, where the antiferromagnetic state disappears. The heat capacity $C_{\rm ac}$ shows both antiferromagnetic and superconducting transitions at pressures close to $P_{\rm c}$. On the other hand, the superconducting region is extended to high pressures of up to about 3.5 GPa, with the maximum transition temperature $T_{\rm sc}$ = 1.6 K around $2.5-2.7$ GPa. At 2.58 GPa, a large heat capacity anomaly was observed at $T_{\rm sc}$ = 1.59 K. The jump of the heat capacity in the form of ${\Delta}{C_{\rm ac}}/C_{\rm ac}(T_{\rm sc})$ is 5.7 $\pm$ 0.1. This is the largest observed value among previously reported superconductors, indicating the strong-coupling superconductivity. The electronic specific heat coefficient at $T_{\rm sc}$ is, however, approximately unchanged as a function of pressure, even at $P_{\rm c}$.
The step-wise growth of epitaxial Fe on Cu(001)/Si(001), investigated by in-situ polarized neutron reflectometry is presented. A sputter deposition system was integrated into the neutron reflectometer AMOR at the Swiss neutron spallation source SINQ, which enables the analysis of the microstructure and magnetic moments during all deposition steps of the Fe layer. We report on the progressive evolution of the accessible parameters describing the microstructure and the magnetic properties of the Fe film, which reproduce known features and extend our knowledge on the behavior of ultrathin iron films.
A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of irreducible loop integrals. The method simulates in many interesting features to the momentum cutoff, Pauli-Villars and dimensional regularization. The loop regularization method is also simple and general for the practical calculations to higher loop graphs and can be applied to both underlying and effective quantum field theories including gauge, chiral, supersymmetric and gravitational ones as the new method does not modify either the lagrangian formalism or the space-time dimension of original theory. The appearance of characteristic energy scale $M_c$ and sliding energy scale $\mu_s$ offers a systematic way for studying the renormalization-group evolution of gauge theories in the spirit of Wilson-Kadanoff and for exploring important effects of higher dimensional interaction terms in the infrared regime.
Two-photon absorption (TPA) is of fundamental importance in super-resolution imaging and spectroscopy. Its nonlinear character allows for the prospect of using quantum resources, such as entanglement, to improve measurement precision or to gain new information on, e.g., ultrafast molecular dynamics. Here, we establish the metrological properties of nonclassical squeezed light sources for precision measurements of TPA cross sections. We find that there is no fundamental limit for the precision achievable with squeezed states in the limit of very small cross sections. Considering the most relevant measurement strategies -- namely photon counting and quadrature measurements -- we determine the quantum advantage provided by squeezed states as compared to coherent states. We find that squeezed states outperform the precision achievable by coherent states when performing quadrature measurements, which provide improved scaling of the Fisher information with respect to the mean photon number $\sim n^4$. Due to the interplay of the incoherent nature and the nonlinearity of the TPA process, unusual scaling can also be obtained with coherent states, which feature a $\sim n^3$ scaling in both quadrature and photon-counting measurements.
We introduce an approach for analyzing the variation of features generated by convolutional neural networks (CNNs) with respect to scene factors that occur in natural images. Such factors may include object style, 3D viewpoint, color, and scene lighting configuration. Our approach analyzes CNN feature responses corresponding to different scene factors by controlling for them via rendering using a large database of 3D CAD models. The rendered images are presented to a trained CNN and responses for different layers are studied with respect to the input scene factors. We perform a decomposition of the responses based on knowledge of the input scene factors and analyze the resulting components. In particular, we quantify their relative importance in the CNN responses and visualize them using principal component analysis. We show qualitative and quantitative results of our study on three CNNs trained on large image datasets: AlexNet, Places, and Oxford VGG. We observe important differences across the networks and CNN layers for different scene factors and object categories. Finally, we demonstrate that our analysis based on computer-generated imagery translates to the network representation of natural images.
In this tutorial we introduce the reader to several theoretical methods of determining the exciton wave functions and the corresponding eigenenergies. The methods covered are either analytical, semi-analytical, or numeric. We make explicit all the details associated with the different methods, thus allowing newcomers to do research on their own, without experiencing a steep learning curve. The tutorial starts with a variational method and ends with a simple semi-analytical approach to solve the Bethe-Salpeter equation in two-dimensional (2D) gapped materials. For the first methods addressed in this tutorial, we focus on a single layer of hexagonal Boron Nitride (hBN) and of transition metal dichalcogenide (TMD), as these are exemplary materials in the field of 2D excitons. For explaining the Bethe- Salpeter method we choose the biased bilayer graphene, which presents a tunnable band gap. The system has the right amount of complexity (without being excessive). This allows the presentation of the solution of the Bethe-Salpeter equation in a context that can be easily generalized to more complex systems or to apply it to simpler models.
We propose a function-based temporal pooling method that captures the latent structure of the video sequence data - e.g. how frame-level features evolve over time in a video. We show how the parameters of a function that has been fit to the video data can serve as a robust new video representation. As a specific example, we learn a pooling function via ranking machines. By learning to rank the frame-level features of a video in chronological order, we obtain a new representation that captures the video-wide temporal dynamics of a video, suitable for action recognition. Other than ranking functions, we explore different parametric models that could also explain the temporal changes in videos. The proposed functional pooling methods, and rank pooling in particular, is easy to interpret and implement, fast to compute and effective in recognizing a wide variety of actions. We evaluate our method on various benchmarks for generic action, fine-grained action and gesture recognition. Results show that rank pooling brings an absolute improvement of 7-10 average pooling baseline. At the same time, rank pooling is compatible with and complementary to several appearance and local motion based methods and features, such as improved trajectories and deep learning features.
Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. We show that this is always true in tachyon matter LQC. Different from the classical Friedman-Robertson-Walker (FRW) cosmology, the super inflation can appear in the tachyon matter LQC; furthermore, the inflation can be extended to the region where classical inflation stops. Using numerical method, we give an evolution picture of the tachyon field with an exponential potential in the context of LQC. It indicates that the quantum dynamical solutions have the attractive behavior as the classical solutions do. The whole evolution of the tachyon field is that in the distant past, the tachyon field--being in the contracting cosmology--is accelerates to climb up the potential hill with a negative velocity; then at the boundary the tachyon field is bounced into an expanding universe with positive velocity rolling down to the bottom of the potential. In the slow roll limit, we compare the quantum inflation with the classical case in both an analytic and numerical way.
We considered the most general form of non-static cylindrically symmetric space-times for studying proper curvature symmetry by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature symmetry in each case of the above space-times it is shown that when the above space-times admit proper curvature symmetry, they form an infinite dimensional vector space.
We propose a technique for estimation of the mass m of the young stellar population and the starburst age T in luminous compact galaxies (LCGs). For this purpose we use LCG H{\alpha} emission line luminosities from the Sloan Digital Sky Survey (SDSS) spectra and Galaxy Evolution Explorer (GALEX) FUV and NUV continuum luminosities. The method is intended for quick estimation of m and T in large galaxy samples and does not require spectral energy distribution (SED) fitting. Estimated m and T for the sample of about 550 LCGs are compared with the same values derived from the SED fitting in the wavelength range \lambda\lambda 3800 -- 9200\AA. We obtain the average differences in log m and T of 0.27 and 0.87 Myr, respectively. This technique could be used for selection of galaxies with desired ranges of m and T or for reducing a range of parameter variations in SED fitting.
We consider the $P$- and $Q$-shape parameters in the eigenphase and `bar' phase shift representations for the two Reid potentials and the more recent Moscow potential. The values of these parameters were obtained from integrals of the zero-energy wave function in a similar manner to that for the effective range. Such expressions for the shape parameters yield more reliable numerical values of the shape parameter than those obtained by least-mean-square or polynomial fits. We show that the eigenphase representation is more meaningful than the `bar' phase shift representation and that the variation in the values of $P_\alpha$ in the models may be of significance.
Thermodynamic fluctuation theory originated with Einstein who inverted the relation $S=k_B\ln\Omega$ to express the number of states in terms of entropy: $\Omega= \exp(S/k_B)$. The theory's Gaussian approximation is discussed in most statistical mechanics texts. I review work showing how to go beyond the Gaussian approximation by adding covariance, conservation, and consistency. This generalization leads to a fundamentally new object: the thermodynamic Riemannian curvature scalar $R$, a thermodynamic invariant. I argue that $|R|$ is related to the correlation length and suggest that the sign of $R$ corresponds to whether the interparticle interactions are effectively attractive or repulsive.