ShantanuT01/DACTYL-Pretraining huggingface dataset:
Guided super-resolution is a unifying framework for several computer vision tasks where the inputs are a low-resolution source image of some target quantity (e.g., perspective depth acquired with a time-of-flight camera) and a high-resolution guide image from a different domain (e.g., a grey-scale image from a conventional camera); and the target output is a high-resolution version of the source (in our example, a high-res depth map). The standard way of looking at this problem is to formulate it as a super-resolution task, i.e., the source image is upsampled to the target resolution, while transferring the missing high-frequency details from the guide. Here, we propose to turn that interpretation on its head and instead see it as a pixel-to-pixel mapping of the guide image to the domain of the source image. The pixel-wise mapping is parametrised as a multi-layer perceptron, whose weights are learned by minimising the discrepancies between the source image and the downsampled target image. Importantly, our formulation makes it possible to regularise only the mapping function, while avoiding regularisation of the outputs; thus producing crisp, natural-looking images. The proposed method is unsupervised, using only the specific source and guide images to fit the mapping. We evaluate our method on two different tasks, super-resolution of depth maps and of tree height maps. In both cases, we clearly outperform recent baselines in quantitative comparisons, while delivering visually much sharper outputs.
A generic quartic 3-fold X admits a 7-dimensional family of representations as the Pfaffian of an 8 by 8 skew-symmetric matrix of linear forms. This provides a 7-dimensional moduli space M of rank 2 vector bundles on X. A precise geometric description of a 14-dimensional family of half-canonical curves C of genus 15 in X such that the above vector bundles are obtained by Serre's construction from C is given. It is proved that the Abel-Jacobi map of this family factors through M, and the resulting map from M to the intermediate Jacobian is quasi-finite. In particular, every component of M has non-negative Kodaira dimension. Some other constructions of rank 2 vector bundles with small Chern classes are discussed; it is proved that the smallest possible charge of an instanton on X is 4.
Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$. We show that $|K_X + 6L|$ is base-point free.
We study the inhomogeneous Curie-Weiss model with external field, where the inhomogeneity is introduced by adding a positive weight to every vertex and letting the interaction strength between two vertices be proportional to the product of their weights. In this model, the sum of the spins obeys a central limit theorem outside the critical line. We derive a Berry-Esseen rate of convergence for this limit theorem using Stein's method for exchangeable pairs. For this, we, amongst others, need to generalize this method to a multidimensional setting with unbounded random variables.
We study the dynamics of anisotropic Bianchi type-IX models with matter and cosmological constant. The models can be thought as describing the role of anisotropy in the early stages of inflation. The concurrence of the cosmological constant and anisotropy are sufficient to produce a chaotic dynamics in the gravitational degrees of freedom, connected to the presence of a critical point of saddle-center type in the phase space of the system. The invariant character of chaos is guaranteed by the topology of the cylinders emanating from unstable periodic orbits in the neighborhood of the saddle-center. We discuss a possible mechanism for amplification of specific wavelengths of inhomogeneous fluctuations in the models. A geometrical interpretation is given for Wald's inequality in terms of invariant tori and their destruction by increasing values of the cosmological constant.
We analyze the impact of electric field and magnetic field fluctuations in the decoherence of the electronic spin associated with a single nitrogen-vacancy (NV) defect in diamond by engineering spin eigenstates protected either against magnetic noise or against electric noise. The competition between these noise sources is analyzed quantitatively by changing their relative strength through modifications of the environment. This study provides significant insights into the decoherence of the NV electronic spin, which is valuable for quantum metrology and sensing applications.
In this paper we extend the definition of time conditional G-expectations $\mathbb{\hat{E}}_{t}[\cdot]$ to a larger domain on which the dynamical consistency still holds. In fact we can consistently define, by taking the limit, the time conditional expectations for each random variable $X$ which is the downward limit (resp. upward limit) of a monotone sequence $\{X_{i}\}$ in $L_{G}^{1}(\Omega)$. To accomplish this procedure, some careful analysis is needed. Moreover, we give a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interesting properties for the extended conditional G-expectations.
We show that the condensate occupation of a superfluid Bose liquid quite generally exhibits anomalously large fluctuations at finite temperatures. In three dimensions, the variance scales like T^2 V^{4/3} at low T, generalizing the result obtained by Giorgini, Pitaevskii, and Stringari for a weakly interacting Bose gas. In two dimensions there is only a quasicondensate, and the fluctuations are of the same order as the mean value.
Zeros of the Riemann zeta function and its derivatives have been studied by many mathematicians. Among, the number of zeros and the distribution of the real part of non-real zeros of the derivatives of the Riemann zeta function have been investigated by Berndt, Levinson, Montgomery, Akatsuka, and the author. Berndt, Levinson, and Montgomery investigated the unconditional case, while Akatsuka and the author gave sharper estimates under the truth of the Riemann hypothesis. In this paper, we prove similar results related to the first derivative of the Dirichlet $L$-functions associated with primitive Dirichlet characters under the assumption of the generalized Riemann hypothesis.
We present a multi-wavelength observational study towards the high-mass young stellar object G8.68-0.37. A single massive gas-and-dust core is observed in the (sub)millimeter continuum and molecular line emissions. We fitted the spectral energy distribution (SED) from the dust continuum emission. The best-fit SED suggests the presence of two components with temperature of $T_{\rm d}=20$ K and 120 K, respectively. The core has a total mass of up to $1.5\times10^3$ $M_{\odot}$ and bolometric luminosity of $2.3\times10^4 L_{\odot}$. Both the mass and luminosity are dominated by the cold component ($T_{\rm d}=20$ K). The molecular lines of C$^{18}$O, C$^{34}$S, DCN, and thermally excited CH$_3$OH are detected in this core. Prominent infall signatures are observed in the $^{12}$CO $(1-0)$ and $(2-1)$. We estimated an infall velocity of 0.45 km s$^{-1}$ and mass infall rate of $7\times10^{-4} M_{\odot}$ year$^{-1}$. From the molecular lines, we have found a high DCN abundance and relative abundance ratio to HCN. The overabundant DCN may originate from a significant deuteration in the previous cold pre-protostellar phase. And the DCN should now be rapidly sublimated from the grain mantles to maintain the overabundance in the gas phase.
We construct complex projective schemes with Lyubeznik numbers of their cones depending on the choices of projective embeddings. This answers a question of G. Lyubeznik in the characteristic 0 case. It contrasts with a theorem of W. Zhang in the positive characteristic case where the Frobenius endomorphism is used. Reducibility of schemes is essential in our argument. B. Wang recently constructed examples of irreducible projective schemes (which are not normal) from our examples of reducible ones. So the question is still open in the normal singular case.
We study here what it means for the Universe to be nearly flat, as opposed to exactly flat. We give three definitions of nearly flat, based on density, geometry and dynamics; all three definitions are equivalent and depend on a single constant flatness parameter epsilon that quantifies the notion of nearly flat. Observations can only place an upper limit on epsilon, and always allow the possibility that the Universe is infinite with k=-1 or finite with k=1. We use current observational data to obtain a numerical upper limit on the flatness parameter and discuss its implications, in particular the "naturalness" of the nearly flat Universe.
Existing approaches for multi-view multi-person 3D pose estimation explicitly establish cross-view correspondences to group 2D pose detections from multiple camera views and solve for the 3D pose estimation for each person. Establishing cross-view correspondences is challenging in multi-person scenes, and incorrect correspondences will lead to sub-optimal performance for the multi-stage pipeline. In this work, we present our multi-view 3D pose estimation approach based on plane sweep stereo to jointly address the cross-view fusion and 3D pose reconstruction in a single shot. Specifically, we propose to perform depth regression for each joint of each 2D pose in a target camera view. Cross-view consistency constraints are implicitly enforced by multiple reference camera views via the plane sweep algorithm to facilitate accurate depth regression. We adopt a coarse-to-fine scheme to first regress the person-level depth followed by a per-person joint-level relative depth estimation. 3D poses are obtained from a simple back-projection given the estimated depths. We evaluate our approach on benchmark datasets where it outperforms previous state-of-the-arts while being remarkably efficient. Our code is available at https://github.com/jiahaoLjh/PlaneSweepPose.
Let $F$ be a number field unramified at an odd prime $p$ and $F_\infty$ be the $\mathbf{Z}_p$-cyclotomic extension of $F$. Generalizing Kobayashi plus/minus Selmer groups for elliptic curves, B\"uy\"ukboduk and Lei have defined modified Selmer groups, called signed Selmer groups, for certain non-ordinary $\mathrm{Gal}(\overline{F}/F)$-representations. In particular, their construction applies to abelian varieties defined over $F$ with good supersingular reduction at primes of $F$ dividing $p$. Assuming that these Selmer groups are cotorsion $\mathbf{Z}_p[[\mathrm{Gal}(F_\infty/F)]]$-modules, we show that they have no proper sub-$\mathbf{Z}_p[[\mathrm{Gal}(F_\infty/F)]]$-module of finite index. We deduce from this a number of arithmetic applications. On studying the Euler-Poincar\'e characteristic of these Selmer groups, we obtain an explicit formula on the size of the Bloch-Kato Selmer group attached to these representations. Furthermore, for two such representations that are isomorphic modulo $p$, we compare the Iwasawa-invariants of their signed Selmer groups.
In this work, gravitational phase transition emerging from anti de-Sitter (AdS) to de-Sitter (dS) vacua in Einstein-Gauss-Bonnet-massive gravity (EGBMG) is considered. We determine the location of thermalon (a static bubble solution in Euclidean space) which exists in casually connected two regions of the spacetime. The thermalon plays a major role in gravitational phase transition by inducing the decay of the negative effective cosmological constant to the positive one due to the higher-order gravity effects. The thermodynamics phase space of the Hawking temperature and free energy is investigated in details. We find that the free energy of the thermalon is always negative at the maximum of Hawking temperature for all possible values of the Gauss-Bonnet couplings. This means that the phase transition mediated by thermalon from AdS to dS asymptotics is inevitable according to the presence of the massive gravity. More importantly, the parameters of the massive gravity behave similarly to the order parameters in the phase transition instead of the Gauss-Bonnet coupling.
We investigate the effect of a quantised vibrational mode on electron tunneling through a chain of three quantum dots. The outer dots are coupled to voltage leads, but the position of the central dot is not rigidly fixed. Motion of the central dot modulates the size of the tunneling barriers in opposite ways so that electron tunneling is correlated with the position of the oscillator. We treat the electronic part of the problem using a simple Coulomb-blockade picture, and model the vibration of the central dot as a quantum oscillator. We calculate the eigenspectrum of the system as a function of the energy level shift between the outer dots. Using a density matrix method, we include couplings to external leads and calculate the steady-state current through the device. The current shows marked resonances which correspond to avoided-level crossings in the eigenvalue spectrum. When the tunneling length of the electrons is of order the zero-point position uncertainty of the quantum oscillator, current far from the electronic resonance is dominated by electrons hopping on and off the central dot sequentially; the oscillator can be regarded as shuttling electrons across the system [L.Y. Gorelik, et al., Phys. Rev. Lett. 80, 4526 (1998)]. Damping of the oscillator can increase the current by preventing electrons from hopping `backwards'.
Exquisite sensitivities are a prominent advantage of quantum sensors. Ramsey sequences allow precise measurement of direct current fields, while Hahn-echo-like sequences measure alternating current fields. However, the latter are restrained for use with high-frequency fields (above approximately $1$ kHz) due to finite coherence times, leaving less-sensitive noncoherent methods for the low-frequency range. In this paper, we propose to bridge the gap with a fitting-based algorithm with a frequency-independent sensitivity to coherently measure low-frequency fields. As the algorithm benefits from coherence-based measurements, its demonstration with a single nitrogen-vacancy center gives a sensitivity of $9.4$ nT Hz$^{-0.5}$ for frequencies below about $0.6$ kHz down to near-constant fields. To inspect the potential in various scenarios, we apply the algorithm at a background field of tens of nTs, and we measure low-frequency signals via synchronization.
The phenomenon of the electromagnetic absorption by arbitrarily distributed discrete absorbers is analyzed from the photon point of view. It is shown that apart from the decrease in the intensity of the signal the net effect of absorption includes a relative increase in the photon bunching.
In this paper, we study the inner and outer boundary densities of some sets with self-similar boundary having Minkowski dimension $s\textgreater{}d-1$ in $\mathbb{R}^{d}$. These quantities turn out to be crucial in some problems of set estimation theory, as we show here for the Voronoi approximation of the set with a random input constituted by $n$ iid points in some larger bounded domain. We prove that some classes of such sets have positive inner and outer boundary density, and therefore satisfy Berry-Essen bounds in $n^{-s/2d}$ for Kolmogorov distance. The Von Koch flake serves as an example, and a set with Cantor boundary as a counter-example. We also give the almost sure rate of convergence of Hausdorff distance between the set and its approximation.
2S 0921$-$630 is an eclipsing low-mass X-ray binary (LMXB) with an orbital period of $\sim$ 9 days. Past X-ray observations have revealed that 2S 0921$-$630 has an extended accretion disk corona (ADC), from which most of the X-rays from the system are emitted. We report the result of our Suzaku archival data analysis of 2S 0921$-$630. The average X-ray spectrum is reproduced with a blackbody emission ($kT_{\rm bb} \sim 0.3$ keV) Comptonized by optically-thick gas (``Compton cloud''; optical depth $\tau \sim 21$) with a temperature of $\sim 2$ keV, combined with thirteen emission lines. We find that most of the emission lines correspond to highly ionized atoms: O, Ne, Mg, Si, S, Ar, and Fe. A K$\alpha$ emission line and an absorption edge of semi-neutral iron (Fe I -- XVII) are also detected. The semi-neutral iron K$\alpha$ line is significantly broad with a width of $0.11 \pm 0.02$ keV in sigma, which corresponds to the Doppler broadening by the Kepler motion at a radius of $\sim 10^9$ cm. We suggest that the observed semi-neutral iron line originates at the inner part of the accretion disk in the immediate outside of the Compton cloud, i.e., the Compton cloud may have a radius of $\sim 10^9$ cm.
Two-dimensional (2D) topological insulator (TI) have been recognized as a new class of quantum state of matter. They are distinguished from normal 2D insulators with their nontrivial band-structure topology identified by the $Z_2$ number as protected by time-reversal symmetry (TRS). 2D TIs have intriguing spin-velocity locked conducting edge states and insulating properties in the bulk. In the edge states, the electrons with opposite spins propagate in opposite directions and the backscattering is fully prohibited when the TRS is conserved. This leads to quantized dissipationless "two-lane highway" for charge and spin transportation and promises potential applications. Up to now, only very few 2D systems have been discovered to possess this property. The lack of suitable material obstructs the further study and application. Here, by using first-principles calculations, we propose that the functionalized MXene with oxygen, M$_2$CO$_2$ (M=W, Mo and Cr), are 2D TIs with the largest gap of 0.194 eV in W case. They are dynamically stable and natively antioxidant. Most importantly, they are very likely to be easily synthesized by recent developed selective chemical etching of transition-metal carbides (MAX phase). This will pave the way to tremendous applications of 2D TIs, such as "ideal" conducting wire, multifunctional spintronic device, and the realization of topological superconductivity and Majorana modes for quantum computing.
We present the results of an optical spectroscopic survey of 46 heavily obscured quasar candidates. Objects are selected using their mid-infrared (mid-IR) colours and magnitudes from the Wide-Field Infrared Survey Explorer (WISE) and their optical magnitudes from the Sloan Digital Sky Survey (SDSS). Candidate Active Galactic Nuclei (AGNs) are selected to have mid-IR colours indicative of quasar activity and lie in a region of mid-IR colour space outside previously published X-ray based selection regions. We obtain optical spectra for our sample using the Robert Stobie Spectrograph on the Southern African Large Telescope. Thirty objects (65%) have identifiable emission lines, allowing for the determination of spectroscopic redshifts. Other than one object at $z\sim2.6$, candidates have moderate redshifts ranging from $z=0.1$ to $0.8$ with a median of 0.3. Twenty-one (70%) of our objects with identified redshift (46% of the whole sample) are identified as AGNs through common optical diagnostics. We model the spectral energy distributions of our sample and found that all require a strong AGN component, with an average intrinsic AGN fraction at 8$\,\mu$m of 0.91. Additionally, the fits require large extinction coefficients with an average $E(B-V)_\textrm{AGN} = 17.8$ (average $A(V)_\textrm{AGN} = 53.4$). By focusing on the area outside traditional mid-IR photometric cuts, we are able to capture and characterise a population of deeply buried quasars that were previously unattainable through X-ray surveys alone.
This paper is concerned with equilibrium configurations of one-dimensional particle system with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness results for a $\Gamma$-development of the energy with the novelty that external forces are allowed. In particular, the forces may depend on Lagrangian or Eulerian coordinates. Our result is based on a new technique for deriving compactness results which are required for calculating the first-order $\Gamma$-limit: instead of comparing a configuration of $n$ atoms to a global minimizer of the $\Gamma$-limit, we compare the configuration to a minimizer in some subclass of functions which in some sense are "close to" the configuration. This new technique is required due to the additional presence of forces with non-convex potentials. The paper is complemented with the study of the minimizers of the $\Gamma$-limit.
Active galactic nuclei (AGNs) have been one of the most widely discussed sources of ultrahigh-energy cosmic rays (UHECRs). The recent results of Pierre Auger observatory (PAO) have indicated a possible composition change of UHECRs above ~10^{18.5} eV towards heavy nuclei. We show here that if indeed UHECRs are largely heavy nuclei, then nearby radio quiet AGNs can also be viable sources of UHECRs. We derive constraints on the acceleration sites which enable acceleration of UHECRs to 10^{20} eV without suffering losses. We show that the acceleration of UHECRs and the survival of energetic heavy nuclei are possible in the parsec scale weak jets that are typically observed in these objects, the main energy loss channel being photodisintegration. On this scale, energy dissipation by shock waves resulting from interactions inside a jet or of the jet with surrounding material are expected, which may accelerate the particles up to very high energies. We discuss the possible contribution of radio-quiet AGNs to the observed UHECR flux, and show that the required energy production rate in UHECRs by a single object could be as low as ~ 3*10^{39} erg/s, which is less than a percent of the bolometric luminosity, and thus energetically consistent. We discuss consequences of this model, the main one being the difficulty in detecting energetic secondaries (\gamma-rays and neutrinos) from the same sources.
We present the theoretical results for the Majorana band structure and thermal transport properties in the Kitaev honeycomb model under a staggered magnetic field in addition to a uniform one. The Majorana band structure is asymmetrically modulated in momentum space, and the valley degree of freedom is activated and controlled by the magnitudes and directions of the uniform and staggered magnetic fields; as a result, the Majorana excitation is either gapped or gapless, the latter of which in general has Majorana Fermi surfaces, in contrast to the point nodes in the absence of the fields. We show that the asymmetric deformation of the Majorana band induces a nonlinear (nonreciprocal) thermal transport, in addition to the linear one. The field dependence of the linear thermal current is correlated with the magnitude of the Majorana gap, while that of the nonlinear thermal current is associated with the asymmetry of the Majorana excitation spectra. We show the estimates of the thermal currents and discuss that the linear response is experimentally measurable, whereas future improvement is required for the observation of the nonlinear one. We also discuss how the thermal currents are modulated by other additional effects of the magnetic field and contributions from conventional magnons, latter of which are expected in heterostructures to realize an internal staggered magnetic field.