ShantanuT01/DACTYL-Pretraining huggingface dataset:
We report on measurements of the cosmic microwave background (CMB) and celestial polarization at 146 GHz made with the Atacama Cosmology Telescope Polarimeter (ACTPol) in its first three months of observing. Four regions of sky covering a total of 270 square degrees were mapped with an angular resolution of $1.3'$. The map noise levels in the four regions are between 11 and 17 $\mu$K-arcmin. We present TT, TE, EE, TB, EB, and BB power spectra from three of these regions. The observed E-mode polarization power spectrum, displaying six acoustic peaks in the range $200<\ell<3000$, is an excellent fit to the prediction of the best-fit cosmological models from WMAP9+ACT and Planck data. The polarization power spectrum, which mainly reflects primordial plasma velocity perturbations, provides an independent determination of cosmological parameters consistent with those based on the temperature power spectrum, which results mostly from primordial density perturbations. We find that without masking any point sources in the EE data at $\ell<9000$, the Poisson tail of the EE power spectrum due to polarized point sources has an amplitude less than $2.4$ $\mu$K$^2$ at $\ell = 3000$ at 95\% confidence. Finally, we report that the Crab Nebula, an important polarization calibration source at microwave frequencies, has 8.7\% polarization with an angle of $150.7^\circ \pm 0.6^\circ$ when smoothed with a $5'$ Gaussian beam.
We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half.
Tropicalizations form a bridge between algebraic and convex geometry. We generalize basic results from tropical geometry which are well-known for special ground fields to arbitrary non-archimedean valued fields. To achieve this, we develop a theory of toric schemes over valuation rings of rank 1. As a basic tool, we use techniques from non-archimedean analysis.
We prove that there are infinitely many integers $n$ such that $n$ and $n+1$ have the same number of distinct prime divisors.
We use elementary methods to prove an incidence theorem for points and spheres in $\mathbb{F}_q^n$. As an application, we show that any point set of $P\subset \mathbb{F}_q^2$ with $|P|\geq 5q$ determines a positive proportion of all circles. The latter result is an analogue of Beck's Theorem for circles which is optimal up to multiplicative constants.
In this paper, for a family of second-order parabolic equation with rapidly oscillating and time-dependent periodic coefficients, we are interested in an approximate two-sphere one-cylinder inequality for these solutions in parabolic periodic homogenization, which implies an approximate quantitative propagation of smallness. The proof relies on the asymptotic behavior of fundamental solutions and the Lagrange interpolation technique.
Albertson, Berman, Hutchinson, and Thomassen showed in 1990 that there exist highly connected graphs in which every spanning tree contains vertices of degree 2. Using a result of Alon and Wormald, we show that there exists a natural number $d$ such that every graph of minimum degree at least $d$ contains a spanning tree without adjacent vertices of degree 2. Moreover, we prove that every graph with minimum degree at least 3 has a spanning tree without three consecutive vertices of degree 2.
Ground penetrating radar (GPR) target detection and classification is a challenging task. Here, we consider online dictionary learning (DL) methods to obtain sparse representations (SR) of the GPR data to enhance feature extraction for target classification via support vector machines. Online methods are preferred because traditional batch DL like K-SVD is not scalable to high-dimensional training sets and infeasible for real-time operation. We also develop Drop-Off MINi-batch Online Dictionary Learning (DOMINODL) which exploits the fact that a lot of the training data may be correlated. The DOMINODL algorithm iteratively considers elements of the training set in small batches and drops off samples which become less relevant. For the case of abandoned anti-personnel landmines classification, we compare the performance of K-SVD with three online algorithms: classical Online Dictionary Learning, its correlation-based variant, and DOMINODL. Our experiments with real data from L-band GPR show that online DL methods reduce learning time by 36-93% and increase mine detection by 4-28% over K-SVD. Our DOMINODL is the fastest and retains similar classification performance as the other two online DL approaches. We use a Kolmogorov-Smirnoff test distance and the Dvoretzky-Kiefer-Wolfowitz inequality for the selection of DL input parameters leading to enhanced classification results. To further compare with state-of-the-art classification approaches, we evaluate a convolutional neural network (CNN) classifier which performs worse than the proposed approach. Moreover, when the acquired samples are randomly reduced by 25%, 50% and 75%, sparse decomposition based classification with DL remains robust while the CNN accuracy is drastically compromised.
We present a study of the effects of the tensor-isospin term of the effective interaction in Hartree-Fock and Random Phase Approximation calculations. We used finite-range forces of Gogny type, and we added to them a tensor-isospin term which behaves, at large internucleonic distances, as the analogous term of the microscopic interactions. The strength of this tensor force has been chosen to reproduce the experimental energy of the lowest 0$^-$ excited state in $^{16}$O, which shows large sensitivity to this term of the interaction. With these finite-range interactions, we have studied the effects of the tensor-isospin force in ground and excited states of carbon, oxygen, calcium, nickel, zirconium, tin and lead isotopes. Our results show that the tensor force affects mainly the nucleon single particle energies. However, we found some interesting cases where also bulk nuclear properties are sensitive to the tensor interaction.
Dark matter density is formally infinite at the location of caustic surfaces, where dark matter sheet folds in phase space. The caustics separate multi-stream regions with different number of streams. Volume elements change the parity by turning inside out when passing through the caustic stage. Being measure-zero structures, identification of caustics via matter density fields is usually restricted to fine-grained simulations. Instead a generic purely geometric algorithm can be employed to identify caustics directly by using triangulation of Lagrangian sub-manifold x(q, t) where x and q are Eulerian and Lagrangian coordinates obtained in N-body simulations. The caustic surfaces are approximated by a set of triangles with vertices being the particles in the simulation. It is demonstrated that finding a dark matter halo is quite feasible by building its owtermost convex caustic. Neither more specific assumptions about the geometry of the boundary nor ad hoc parameters are needed. The halo boundary in our idealized but undoubtably generic simulation is neither spherical nor ellipsoidal but rather remarkably asymmetrical. The analysis of the kinetic and potential energies of individual particles and the halo as a whole along with an examination of the two-dimensional phase space has shown that the halo is gravitationally bound.
In this paper we study the existence and uniqueness of the $L_{\rho}^{2p}(\mathbb{R}^d;\mathbb{R}^1)\times L_{\rho}^2(\mathbb{R}^d;\mathbb{R}^d)$ valued solution of backward doubly stochastic differential equations with polynomial growth coefficients using week convergence, equivalence of norm principle and Wiener-Sobolev compactness arguments. Then we establish a new probabilistic representation of the weak solutions of SPDEs with polynomial growth coefficients through the solutions of the corresponding backward doubly stochastic differential equations (BDSDEs). This probabilistic representation is then used to prove the existence of stationary solution of SPDEs on $\mathbb{R}^d$ via infinite horizon BDSDEs. The convergence of the solution of BDSDE to the solution of infinite horizon BDSDEs is shown to be equivalent to the convergence of the pull-back of the solutions of SPDEs. With this we obtain the stability of the stationary solutions as well.
Some of the most interesting results on the global dynamics of solutions of the vacuum Einstein equations concern the Gowdy spacetimes whose spatial topology is that of a three-dimensional torus. In this paper certain of these ideas are extended to a wider class of vacuum spacetimes where the spatial topology is that of a non-trivial torus bundle over a circle. Compared to the case of the torus these are topologically twisted. They include inhomogeneous generalizations of the spatially homogeneous vacuum spacetimes of Bianchi types II and VI${}_0$. Using similar procedures it is shown that the vacuum solutions of Bianchi type VII${}_0$ are isometric to a class of Gowdy spacetimes, the circular loop spacetimes, thus establishing links between results in the literature which were not previously known to be related to each other.
We explore the structure of momentum distributions of Fermi liquids such as completely polarized 3He, unpolarized liquid 3He, and nuclear matter at nonzero temperatures. The study employs correlated density matrix theory and adapts the algorithm to deal with spin- and isospin-dependent correlations. The analysis is based on the factor decomposition of the one-body reduced density matrix. The decomposition permits to distinguish between statistical correlations and dynamic (direct) correlations. Together with the concept of renormalized fermions the formal results open the pathway to investigate the thermal boundaries of normal Fermi phases within correlated density matrix theory. We also discuss possible transitions from normal phases to anomalous fermion phases triggered by statistical correlations or by periodic phase-phase structures.
The All Sky Automated Survey (ASAS) data, covering nearly 70% of the whole sky south of declination +28 deg, were recently used to discover about 300 Beta Cephei stars brighter than V~11.5 mag. As this means a nearly fourfold increase in the number of known stars of this type, new possibilities in studying these pulsators open up, including statistical work. The homogeneity of the ASAS survey allows us to study their distribution in the local Galaxy. We discuss this distribution in the context of the location of nearby spiral arms. In addition, we show pulsational (periods, amplitudes) properties of the whole sample of known Beta Cephei stars. Some objects interesting from the point of view of asteroseismology are also indicated.
Olmez, in "Symmetric $1\frac{1}{2}$-Designs and $1\frac{1}{2}$-Difference Sets" (2014), introduced the concept of a partial geometric difference set (also referred to as a $1\frac{1}{2}$-design), and showed that partial geometric difference sets give partial geometric designs. Nowak et al., in "Partial Geometric Difference Families" (2014), introduced the concept of a partial difference family, and showed that these also give partial geometric designs. It was shown by Brouwer et al. in "Directed strongly regular graphs from $1\frac{1}{2}$-designs" (2012) that directed strongly regular graphs can be obtained from partial geometric designs. In this correspondence we construct several families of partial geometric difference sets and partial difference families with new parameters, thereby giving directed strongly regular graphs with new parameters. We also discuss some of the links between partially balanced designs, $2$-adesigns (which were recently coined by Cunsheng Ding in "Codes from Difference Sets" (2015)), and partial geometric designs, and make an investigation into when a $2$-adesign is partial geometric.
Context. Copper is an element whose interesting evolution with metallicity is not fully understood. Observations of copper abundances rely on a very limited number of lines, the strongest are the Cu I lines of Mult. 1 at 324.7 nm and 327.3 nm which can be measured even at extremely low metallicities. Aims. We investigate the quality of these lines as abundance indicators. Method. We measure these lines in two turn-off (TO) stars in the Globular Cluster NGC 6752 and two TO stars in the Globular Cluster NGC 6397 and derive abundances with 3D hydrodynamical model atmospheres computed with the CO5BOLD code. These abundances are compared to the Cu abundances measured in giant stars of the same clusters, using the lines of Mult. 2 at 510.5 nm and 578.2 nm. Results. The abundances derived from the lines of Mult. 1 in TO stars differ from the abundances of giants of the same clusters. This is true both using CO5BOLD models and using traditional 1D model atmospheres. The LTE 3D corrections for TO stars are large, while they are small for giant stars. Conclusions. The Cu I resonance lines of Mult. 1 are not reliable abundance indicators. It is likely that departures from LTE should be taken into account to properly describe these lines, although it is not clear if these alone can account for the observations. An investigation of these departures is indeed encouraged for both dwarfs and giants. Our recommendation to those interested in the study of the evolution of copper abundances is to rely on the measurements in giants, based on the lines of Mult. 2. We caution, however, that NLTE studies may imply a revision in all the Cu abundances, both in dwarfs and giants.
We study the enhanced diffusivity in the so called elephant random walk model with stops (ERWS) by including symmetric random walk steps at small probability $\epsilon$. At any $\epsilon > 0$, the large time behavior transitions from sub-diffusive at $\epsilon = 0$ to diffusive in a wedge shaped parameter regime where the diffusivity is strictly above that in the un-perturbed ERWS model in the $\epsilon \downarrow 0$ limit. The perturbed ERWS model is shown to be solvable with the first two moments and their asymptotics calculated exactly in both one and two space dimensions. The model provides a discrete analytical setting of the residual diffusion phenomenon known for the passive scalar transport in chaotic flows (e.g. generated by time periodic cellular flows and statistically sub-diffusive) as molecular diffusivity tends to zero.
When a quantum system is placed in thermal environments, we often assume that the system relaxes to the Gibbs state in which decoherence takes place in the system energy eigenbasis. However, when the coupling between the system and the environments is strong, the stationary state is not necessarily the Gibbs state due to environment-induced decoherence which can be interpreted as continuous measurement by the environments. Based on the einselection proposed by Zurek, we postulate that the Gibbs state is projected onto the pointer basis due to the continuous measurement. We justify the proposition by exact numerical simulation of a pair of coupled qubits interacting with boson gases. Furthermore, we demonstrate that heat conduction in non-equilibrium steady states can be suppressed in the strong coupling limit also by the environment-induced decoherence.
We characterize all position and momentum observables on R and on R^3. We study some of their operational properties and discuss their covariant joint observables.
It is known that in order for a supersymmetric gauge theory to be dynamically broken a necessary but not sufficient condition is that the Witten index $(-1)^F=n_b^0-n_f^0$ is zero. In the case the Witten index is zero it is in general hard to distinguish between theories with or without dynamical supersymmetry breaking. In this work we show that for a large class of theories the cancellation of the Witten index by itself signals the formation of a quark condensate and therefore produces dynamical supersymmetry breaking.
We propose a technique that propagates information forward through video data. The method is conceptually simple and can be applied to tasks that require the propagation of structured information, such as semantic labels, based on video content. We propose a 'Video Propagation Network' that processes video frames in an adaptive manner. The model is applied online: it propagates information forward without the need to access future frames. In particular we combine two components, a temporal bilateral network for dense and video adaptive filtering, followed by a spatial network to refine features and increased flexibility. We present experiments on video object segmentation and semantic video segmentation and show increased performance comparing to the best previous task-specific methods, while having favorable runtime. Additionally we demonstrate our approach on an example regression task of color propagation in a grayscale video.
Primordial black holes (PBHs) with mass $10^{16}-10^{17}$ g almost escape constraints from observations so could essentially contribute to dark matter density. Hawking evaporation of such PBHs produces with a steady rate $\gamma$- and $e^{\pm}$-radiations in MeV energy range, which can be absorbed by ordinary matter. Simplified estimates show that a small fraction of evaporated energy had to be absorbed by baryonic matter what can turn out to be enough to heat the matter so it is fully ionized at the redshift $z\sim 5... 10$. The result is found to be close to a borderline case where the effect appears, what makes it sensitive to the approximation used. In our approximation, degree of gas ionization reaches 50-100% by $z\sim 5$ for PBH mass $(3...7)\times 10^{16}$ g with their abundance corresponding to the upper limit.
The StarScan machine at the U.S. Naval Observatory (USNO) completed measuring photographic astrograph plates to allow determination of proper motions for the USNO CCD Astrograph Catalog (UCAC) program. All applicable 1940 AGK2 plates, about 2200 Hamburg Zone Astrograph plates, 900 Black Birch (USNO Twin Astrograph) plates, and 300 Lick Astrograph plates have been measured. StarScan comprises of a CCD camera, telecentric lens, air-bearing granite table, stepper motor screws, and Heidenhain scales to operate in a step-stare mode. The repeatability of StarScan measures is about 0.2 micrometer. The CCD mapping as well as the global table coordinate system has been calibrated using a special dot calibration plate and the overall accuracy of StarScan x,y data is derived to be 0.5 micrometer. Application to real photographic plate data shows that position information of at least 0.65 micrometer accuracy can be extracted from course grain 103a-type emulsion astrometric plates. Transformations between "direct" and "reverse" measures of fine grain emulsion plate measures are obtained on the 0.3 micrometer level per well exposed stellar image and coordinate, which is at the limit of the StarScan machine.
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent copies coincides in distribution with the rescaled original point process. These concepts makes sense in any convex cone, i.e. in a commutative semigroup equipped with multiplication by numbers, and lead to a construction of stable laws in general cones by means of the LePage series. The corresponding limit theorem shows that random samples (or binomial point processes) converge in distribution to the union-stable Poisson point process, and so yields a limit theorem for normalised sums of random elements with $\alpha$-stable limit for $\alpha\in(0,1)$.   By using the technique of harmonic analysis on semigroups we characterise distributions of $\alpha$-stable random elements and show how possible values of $\alpha$ relate to the properties of the semigroup and the corresponding scaling operation, in particular, their distributivity properties. The approach developed in the paper not only makes it possible to handle stable distributions in rather general cones (like spaces of sets or measures), but also provides an alternative way to prove classical limit theorems and deduce the LePage representation for strictly stable random vectors in Banach spaces.
We present de Haas-van Alphen and resistivity data on single crystals of the delafossite PdCoO2. At 295 K we measure an in-plane resistivity of 2.6 \mu{\Omega}-cm, making PdCoO2 the most conductive oxide known. The low-temperature in-plane resistivity has an activated rather than the usual T^5 temperature dependence, suggesting a gapping of effective scattering that is consistent with phonon drag. Below 10 K, the transport mean free path is 20 \mum, approximately 10^5 lattice spacings and an astoundingly high value for flux-grown crystals. We discuss the origin of these properties in light of our data.
We propose a model based on a generalized effective Hamiltonian for studying the effect of noise in quantum computations. The system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. Treating these fluctuations as Gaussian Markov processes with zero mean and delta function correlation times, we derive an exact equation of motion describing the dissipative dynamics for a system of n qubits. We then apply this model to study the effect of noise on the quantum teleportation and a generic quantum controlled-NOT (CNOT) gate. For the quantum CNOT gate, we study the effect of noise on a set of one- and two-qubit quantum gates, and show that the results can be assembled together to investigate the quality of a quantum CNOT gate operation. We compute the averaged gate fidelity and gate purity for the quantum CNOT gate, and investigate phase, bit-flip, and flip-flop errors during the CNOT gate operation. The effects of direct inter-qubit coupling and fluctuations on the control fields are also studied. We discuss the limitations and possible extensions of this model. In sum, we demonstrate a simple model that enables us to investigate the effect of noise in arbitrary quantum circuits under realistic device conditions.
We propose a new scenario for glassy dynamics in frustrated systems with no quenched-in randomness, based on jamming of extended dynamical structures near a critical point. This route to a glassy state is demonstrated in a lattice model of fluctuating lines. Numerical simulations of the model show non-exponential relaxations and diverging energy barriers in the vicinity of a thermodynamic phase transition. A master equation for the coarse grained dynamics is constructed. It shows how topological jamming leads to the observed glassy dynamics.
Recently, the first lithium detection outside of the Milky Way was made in low-metallicity gas of the Small Magellanic Cloud, which was at the level of the expected primordial value. Part of the observed lithium in any environment has primordial origin, but there is always some post-BBN (Big Bang Nucleosynthesis) contamination, since lithium can also be produced in cosmic-ray interactions with the interstellar medium. Using the fact that processes involving cosmic rays produce lithium, but also gamma rays through neutral pion decay, we use the Small Magellanic Cloud gamma-ray observations by Fermi-LAT to make predictions on the amount of lithium in this galaxy that was produced by galactic cosmic rays accelerated in supernova remnants. By including both fusion processes, as well as spallation of heavier nuclei, we find that galactic cosmic rays could produce a very small amount of lithium. In the case of 6Li isotope (which should only be produced by cosmic rays) we can only explain 0.16% of the measured abundance. If these cosmic rays are indeed responsible for such small lithium production, observed abundances could be the result of some other sources, which are discussed in the paper.