ShantanuT01/DACTYL-Pretraining huggingface dataset:
Estimating depth from a single RGB images is a fundamental task in computer vision, which is most directly solved using supervised deep learning. In the field of unsupervised learning of depth from a single RGB image, depth is not given explicitly. Existing work in the field receives either a stereo pair, a monocular video, or multiple views, and, using losses that are based on structure-from-motion, trains a depth estimation network. In this work, we rely, instead of different views, on depth from focus cues. Learning is based on a novel Point Spread Function convolutional layer, which applies location specific kernels that arise from the Circle-Of-Confusion in each image location. We evaluate our method on data derived from five common datasets for depth estimation and lightfield images, and present results that are on par with supervised methods on KITTI and Make3D datasets and outperform unsupervised learning approaches. Since the phenomenon of depth from defocus is not dataset specific, we hypothesize that learning based on it would overfit less to the specific content in each dataset. Our experiments show that this is indeed the case, and an estimator learned on one dataset using our method provides better results on other datasets, than the directly supervised methods.
We study the Josephson current in long ballistic superconductor-monolayer graphene-superconductor junctions. As a first step, we have developed an efficient computational approach to calculate the Josephson current in tight-binding systems. This approach can be particularly useful in the long junction limit, which has hitherto attracted less theoretical interest but has recently become experimentally relevant. We use this computational approach to study the dependence of the critical current on the junction geometry, doping level, and an applied perpendicular magnetic field. In zero magnetic field we find a good qualitative agreement with the recent experiment of Ben Shalom et al. (Reference[12]) for the length dependence of the critical current. For highly doped samples our numerical calculations show a broad agreement with the results of the quasiclassical formalism. In this case the critical current exhibits Fraunhofer-like oscillations as a function of the magnetic field. However, for lower doping levels, where the cyclotron orbit becomes comparable to the characteristic geometrical length scales of the system, deviations from the results of the quasiclassical formalism appear. We argue that due to the exceptional tunability and long mean free path of graphene systems a new regime can be explored where geometrical and dynamical effects are equally important to understand the magnetic field dependence of the critical current.
Consider an independent site percolation model on $\Z^d,\ d\geq 2$, with parameter $p \in (0,1)$, where there are only nearest neighbor bonds and long range bonds of length $k$ parallel to some coordinate axis. We show that the percolation probability is a non-decreasing function of $k$. We also generalize this result for models whose long range bonds have several lengths.
We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results obtained are given.
We employ a helicity-basis kinetic equation approach to investigate the anomalous Hall effect in two-dimensional narrow-band semiconductors considering both Rashba and extrinsic spin-orbit (SO) couplings, as well as a SO coupling directly induced by an external driving electric field. Taking account of long-range electron-impurity scattering up to the second Born approximation, we find that the various components of the anomalous Hall current fit into two classes: (a) side-jump and (b) skew scattering anomalous Hall currents. The side-jump anomalous Hall current involves contributions not only from the extrinsic SO coupling but also from the SO coupling due to the driving electric field. It also contains a component which arises from the Rashba SO coupling and relates to the off-diagonal elements of the helicity-basis distribution function. The skew scattering anomalous Hall effect arises from the anisotropy of the diagonal elements of the distribution function and it is a result of both the Rashba and extrinsic SO interactions. Further, we perform a numerical calculation to study the anomalous Hall effect in a typical InSb/AlInSb quantum well. The dependencies of the side-jump and skew scattering anomalous Hall conductivities on magnetization and on the Rashba SO coupling constant are examined.
The cosmological model of the modified Chaplygin gas interacting with cold dark matter is studied. Our attention is focused on the final state of universe in the model. It turns out that there exists a stable scaling solution, which provides the possibility to alleviate the coincidence problem. In addition, we investigate the effect of the coupling constants $c_{1}$ and $c_{2}$ on the dynamical evolution of this model from the statefinder viewpoint. It is found that the coupling constants play a significant role during the dynamical evolution of the interacting MCG model. Furthermore, we can distinguish this interacting model from other dark energy models in the $s-r$ plane.
We consider infinite or periodic 2D triangular Ising lattices with arbitrary positive or negative nearest-neighbor couplings $K_i(\vec{r})$, where $\vec{r}$ and $i$ indicate the bond position and orientation, respectively. Iterative application of the star-triangle transformation to an initial lattice $\mathcal{T}(0)$ with a set of couplings $\{K_i^{(0)}(\vec{r})\}$ generates a sequence of lattices $\mathcal{T}(n)$, for $n=1,2,\ldots,$ with couplings $\{K_i^{(n)}(\vec{r})\}$. When $\mathcal{T}(0)$ includes sufficiently strongly frustrated plaquettes, complex couplings will appear. We show that, nevertheless, the variables $1/\sinh 2K_i^{(n)}\!(\vec{r})$ remain confined to the union ${\mathbb{R}} \cup \rm{i}{\mathbb{R}}$ of the real and the imaginary axis. The same holds for a lattice with free boundaries, provided we distinguish between "receding" and "advancing" boundaries, the latter having degrees of freedom that must be fixed by an appropriately chosen protocol. This study establishes a framework for future analytic and numerical work on such frustrated Ising lattices.
I present a new formalism of the R-matrix theory where the formal parameters for the resonance energies and widths are identical to the observed values. By allowing the boundary condition parameters to vary from level to level, the freedom required to adjust the formal parameters for the pole positions to the observed values is obtained. The basis of the resulting theory becomes nonorthogonal, and I describe the procedure to construct a consistent R-matrix theory with such a nonorthogonal basis. And by adjusting the normalization of the states that form the basis, the formal parameters for the reduced decay widths also become the same as those observed, leaving no formal parameters that are different from the observed ones. A demonstration of the developed theory to the elastic 12C+p scattering data is presented.
We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a conjecture of Vershik stating that the Poisson-Dirichlet law with parameter theta=1 is the unique invariant distribution for this Markov chain.   Our proof uses a combination of probabilistic, combinatoric, and representation-theoretic arguments.
The Kerr black holes possess a photon region with prograde and retrograde orbits radii, respectively, $M\leq r_p^-\leq 3M$ and $3M\leq r_p^+\leq 4M$, and thereby always cast a closed photon ring or a shadow silhouette for $a\leq M$. For $a>M$, it is a no-horizon spacetime (naked singularity) wherein prograde orbits spiral into the central singularity, and retrograde orbits produce an arc-like shadow with a dark spot at the center. We compare Kerr black holes' photon ring structure with those produced by three rotating regular spacetimes, viz. Bardeen, Hayward, and nonsingular. These are non-Kerr black hole metrics with an additional deviation parameter of $g$ related to the nonlinear electrodynamics charge. It turns out that for a given $ a $, there exists a critical value of $ g $, $g_E$ such that $\Delta=0$ has no zeros for $ g > g_E$, one double zero at $ r = r_E $ for $ g = g_E $, respectively, corresponding to a no-horizon regular spacetime and extremal black hole with degenerate horizon. We demonstrate that, unlike the Kerr naked singularity, no-horizon regular spacetimes can possess closed photon ring when $g_E< g \leq g_c$, e.g., for $a=0.10M$, Bardeen ($g_E=0.763332M<g\leq g_c= 0.816792M$), Hayward ($g_E=1.05297M < g\leq g_c = 1.164846M$) and nonsingular ($g_E=1.2020M < g \leq g_c= 1.222461M$) no-horizon spacetimes have closed photon ring. These results confirm that the mere existence of a closed photon ring does not prove that the compact object is necessarily a black hole. The ring circularity deviation observable $\Delta C$ for the three no-horizon rotating spacetimes satisfy $\Delta C\leq 0.10$ as per the M87* black hole shadow observations. We have also appended the case of Kerr-Newman no-horizon spacetimes (naked singularities) with similar features.
We present a theoretical investigation of the effect of multiple ionisation sources in HII regions on the total elemental abundances derived from the analysis of collisionally excited emission lines. We focus on empirical methods based on direct temperature measurements that are commonly employed in cases when the temperature of the nebular gas can be determined from the ratio of nebular to auroral lines of (e.g.) doubly ionised oxygen. We find that direct temperature methods that employ a two-temperature zone approach (DT2T methods) are very robust against the spatial distribution of sources. Errors smaller than 0.15 dex are estimated for regions where the metallicity is twice solar and errors below 0.05 dex for solar metallicities and below. The biases introduced by the spatial distribution of the ionisation sources are thus much smaller for DT2T methods than for strong line methods, previously investigated by Ercolano, Bastian & Stasinska. Our findings are in agreement with the recent study of HII regions in NGC 300 by Bresolin et al.
We prove an orthogonality relation for the Fourier-Whittaker coefficients of a thin family of $GL(3)$ Maass forms containing all self-dual forms. This is obtained by analysing the Kuznetsov trace formula on $GL(3)$ for a certain family of test functions. The method also yields Weyl's law for the same family of Maass forms.
In this article we provide a novel characterization of the proportionally fair bandwidth allocation of network capacities, in terms of the Fenchel--Legendre transform of the network capacity region. We use this characterization to prove stability (i.e., ergodicity) of network dynamics under proportionally fair sharing, by exhibiting a suitable Lyapunov function. Our stability result extends previously known results to a more general model including Markovian users routing. In particular, it implies that the stability condition previously known under exponential service time distributions remains valid under so-called phase-type service time distributions. We then exhibit a modification of proportional fairness, which coincides with it in some asymptotic sense, is reversible (and thus insensitive), and has explicit stationary distribution. Finally we show that the stationary distributions under modified proportional fairness and balanced fairness, a sharing criterion proposed because of its insensitivity properties, admit the same large deviations characteristics. These results show that proportional fairness is an attractive bandwidth allocation criterion, combining the desirable properties of ease of implementation with performance and insensitivity.
The two-loop electroweak bosonic correction to the muon lifetime and the M_W-M_Z interdependece is computed using analytical methods of asymptotic expansion. Combined with previous calculations this copmletes the full two-loop correction to $\Delta r$ in the Standard Model. The shift to the prediction of W-boson mass due to two-loop bosonic corrections does not exceed 1 MeV for the range of the Higgs mass from 100 to 1000 GeV.
We present a new method to introduce phase-space fluctuations in transport theories, corresponding to a full implementation of the Boltzmann-Langevin equation for fermionic systems. It is based on the procedure originally developed by Bauer et al. for transport codes employing the test particle method. In the new procedure, the Pauli principle is carefully checked, leading to a good reproduction of the correct fluctuations in the ``continuum limit'' ($h \to 0$). Accurate tests are carried out in one and two dimensional idealized systems, and finally results for a full 3D application are shown. We stress the reliability of this method, which can be easily plugged into existing tranport codes using test particles, and its general applicability to systems characterized by instabilities, like for instance multifragmentation processes.
We study the growth of cosmic structure under the assumption that dark matter self-annihilates with an averaged cross section times relative velocity that grows with the scale factor, an increase known as Sommerfeld-enhancement. Such an evolution is expected in models in which a light force carrier in the dark sector enhances the annihilation cross section of dark matter particles, and has been invoked, for instance, to explain anomalies in cosmic ray spectra reported in the past. In order to make our results as general as possible, we assume that dark matter annihilates into a relativistic species that only interacts gravitationally with the standard model. This assumption also allows us to test whether the additional relativistic species mildly favored by cosmic-microwave background data could originate from dark matter annihilation. We do not find evidence for Sommerfeld-enhanced dark matter annihilation and derive the corresponding upper limits on the annihilation cross-section.
We compare the statistical properties of structures normal and transverse to the line of sight which appear in observational data from redshift surveys. We present a statistic which can quantify this effect in a conceptually different way from standard analyses of distortions of the power-spectrum or correlation function. From tests with N-body experiments, we argue that this statistic represents a new, more direct and potentially powerful diagnostic of the cosmological density parameter Omega.
We use the galaxy stellar mass and halo merger tree information from the semi-analytic model galaxy catalogue of Font et al. (2009) to examine the accretion of galaxies into a large sample of groups and clusters, covering a wide range in halo mass (10E12.9 to 10E15.3 Msun/h), and selected from each of four redshift epochs (z=0, 0.5, 1.0 and 1.5). We find that clusters at all examined redshifts have accreted a significant fraction of their final galaxy populations through galaxy groups. A 10E14.5 Msun/h mass cluster at z=0 has, on average, accreted ~ 40% of its galaxies (Mstellar > 10E9 Msun/h) from halos with masses greater than 10E13 Msun/h. Further, the galaxies which are accreted through groups are more massive, on average, than galaxies accreted through smaller halos or from the field population. We find that at a given epoch, the fraction of galaxies accreted from isolated environments is independent of the final cluster or group mass. In contrast, we find that observing a cluster of the same halo mass at each redshift epoch implies different accretion rates of isolated galaxies, from 5-6 % per Gyr at z=0 to 15% per Gyr at z=1.5. We find that combining the existence of a Butcher Oemler effect at z=0.5 and the observations that galaxies within groups display significant environmental effects with galaxy accretion histories justifies striking conclusions. Namely, that the dominant environmental process must begin to occur in halos of 10E12 -- 10E13 Msun/h, and act over timescales of > 2 Gyrs. This argues in favor of a mechanism like "strangulation", in which the hot halo of a galaxy is stripped upon infalling into a more massive halo . This simple model predicts that by z=1.5 galaxy groups and clusters will display little to no environmental effects.
We study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases the number of highly connected hubs. We study a range of complex network architectures produced by the aggregation. Fat-tailed (in particular, scale-free) distributions of connections are obtained both for networks with a finite number of vertices and growing networks. We observe a strong variation of a network structure with growing density of connections and find the phase transition of the condensation of edges. Finally, we demonstrate the importance of structural correlations in these networks.
We study coherent spin transport through helical edge states of topological insulator tunnel-coupled to metallic leads.   We demonstrate that unpolarized incoming electron beam acquires finite polarization after transmission through such a setup provided that edges contain at least one magnetic impurity. The finite polarization appears even in the fully classical regime and is therefore robust to dephasing. There is also a quantum magnetic field-tunable contribution to the polarization, which shows sharp identical Aharonov-Bohm resonances as a function of magnetic flux - with the period $hc/2e$ - and survives at relatively high temperature. We demonstrate that this tunneling interferometer can be described in terms of ensemble of flux-tunable qubits giving equal contributions to conductance and spin polarization. The number of active qubits participating in the charge and spin transport is given by the ratio of the temperature and the level spacing. The interferometer can effectively operate at high temperature and can be used for quantum calculations. In particular, the ensemble of qubits can be described by a single Hadamard operator. The obtained results open wide avenue for applications in the area of quantum computing.
Synchrotron radiation of ultra-relativistic particles accelerated in a pulsar wind nebula may dominate its spectrum up to gamma-ray energies. Because of the short cooling time of the gamma-ray emitting electrons, the gamma-ray emission zone is in the immediate vicinity of the acceleration site. The particle acceleration likely occurs at the termination shock of the relativistic striped wind, where multiple forced magnetic field reconnections provide strong magnetic fluctuations facilitating Fermi acceleration processes. The acceleration mechanisms imply the presence of stochastic magnetic fields in the particle acceleration region, which cause stochastic variability of the synchrotron emission. This variability is particularly strong in the steep gamma-ray tail of the spectrum, where modest fluctuations of the magnetic field lead to strong flares of spectral flux. In particular, stochastic variations of magnetic field, which may lead to quasi-cyclic gamma-ray flares, can be produced by the relativistic cyclotron ion instability at the termination shock. Our model calculations of the spectral and temporal evolution of synchrotron emission in the spectral cut-off regime demonstrate that the intermittent magnetic field concentrations dominate the gamma-ray emission from highest energy electrons and provide fast, strong variability even for a quasi-steady distribution of radiating particles. The simulated light curves and spectra can explain the very strong gamma-ray flares observed in the Crab nebula and the lack of strong variations at other wavelengths. The model predicts high polarization in the flare phase, which can be tested with future polarimetry observations.
Recently, much advance has been made in image captioning, and an encoder-decoder framework has achieved outstanding performance for this task. In this paper, we propose an extension of the encoder-decoder framework by adding a component called guiding network. The guiding network models the attribute properties of input images, and its output is leveraged to compose the input of the decoder at each time step. The guiding network can be plugged into the current encoder-decoder framework and trained in an end-to-end manner. Hence, the guiding vector can be adaptively learned according to the signal from the decoder, making itself to embed information from both image and language. Additionally, discriminative supervision can be employed to further improve the quality of guidance. The advantages of our proposed approach are verified by experiments carried out on the MS COCO dataset.
We present a detailed comparison between ONETEP, our linear-scaling density functional method, and the conventional pseudopotential plane wave approach in order to demonstrate its high accuracy. Further comparison with all-electron calculations shows that only the largest available Gaussian basis sets can match the accuracy of routine ONETEP calculations. Results indicate that our minimisation procedure is not ill-conditioned and that convergence to self-consistency is achieved efficiently. Finally we present calculations with ONETEP, on systems of about 1000 atoms, of electronic, structural and chemical properties of a wide variety of materials such as metallic and semiconducting carbon nanotubes, crystalline silicon and a protein complex.
The cluster of galaxies A2319 was observed in 1999 for 160 ks by the PCA and HEXTE instruments aboard the RXTE satellite. No noticeable variability is seen in the emission measured by either instrument over the 8 week observation. Fitting the RXTE data by a single thermal component we obtain $kT = 8.6 \pm 0.1$ (90% confidence limits), a low iron abundance $Z_{F_e} \sim 0.16 \pm 0.02$, and large positive residuals below 6 keV and between 15 to 30 keV. The quality of the fit is drastically improved if a second component is added. A two-temperature model yields $kT_{1} \simeq 10.1 \pm 0.6$, $kT_{2}\simeq 2.8 \pm 0.6$, and of $Z_{F_e} \sim 0.23 \pm 0.03$. An equally good fit is obtained by a combination of a primary thermal and a secondary nonthermal component, with $kT \simeq 8.9 \pm 0.6$, and power-law index $\alpha \simeq 2.4 \pm 0.3$. We have repeated the analysis by performing joint fits to both these RXTE measurements and archival ASCA data. At most 25% of the RXTE secondary component could be present in the ASCA data. Allowing for this difference, very similar results were obtained, with only somewhat different values for the temperature and power-law index in the latter model. The deduced value of $\alpha$ is consistent with the measured spectrum of extended radio emission. Identifying the power-law emission as Compton scattering of the radio-emitting electrons by the CMB, we obtain $B \sim0.1-0.3$ $\mu G$ for the volume-averaged magnetic field, and $\sim 4 \times 10^{-14}(R/2 Mpc)^{-3}$ erg cm$^{-3}$ for the mean energy density of the emitting electrons in the central region (radius R) of A2319.
In arxiv: 2102.05575 a two-step process $pn \to (pp) \pi^- \to (\Delta N) \pi^- \to (d \pi^+) \pi^-$ was calculated by using experimental total cross sections for the single-pion production processes $pn \to pp \pi^-(I=0)$ and $pp \to d \pi^+$. As a result the authors obtain a resonance-like structure for the total $pn \to d\pi^+\pi^-$ cross section of about the right size and width of the observed $d^*(2380)$ peak at an energy about 40 MeV below the $d^*(2380)$ mass. We object both the results of the sequential process calculation and its presentation as an alternative to the dibaryon interpretation.