ShantanuT01/DACTYL-Pretraining huggingface dataset:
We develop a long wavelength approximation in order to describe the low-energy states of carbon nanotubes in a transverse magnetic field. We show that, in the limit where the square of the magnetic length $l = \sqrt{\hbar c /e B}$ is much larger than the $C$-$C$ distance times the nanotube radius $R$, the low-energy theory is given by the linear coupling of a two-component Dirac spinor to the corresponding vector potential. We investigate in this regime the evolution of the band structure of zig-zag nanotubes for values of $R/l > 1$, showing that for radius $R \approx 20$ nm a clear pattern of Landau levels start to develop for magnetic field strength $B \gtrsim 10$ T. The levels tend to be four-fold degenerate, and we clarify the transition to the typical two-fold degeneracy of graphene as the nanotube is unrolled to form a curved strip. We show that the dynamics of the Dirac fermions leads to states which are localized at the flanks of the nanotube and that carry chiral currents in the longitudinal direction. We discuss the possibility to observe the quantization of the Hall conductivity in thick carbon nanotubes, which should display steps at even multiples of $2 e^2/h$, with values doubled with respect to those in the odd-integer quantization of graphene.
The accurate localization of facial landmarks is at the core of face analysis tasks, such as face recognition and facial expression analysis, to name a few. In this work, we propose a novel localization approach based on a deep learning architecture that utilizes cascaded subnetworks with convolutional neural network units. The cascaded units of the first subnetwork estimate heatmap-based encodings of the landmarks locations, while the cascaded units of the second subnetwork receive as input the output of the corresponding heatmap estimation units, and refine them through regression. The proposed scheme is experimentally shown to compare favorably with contemporary state-of-the-art schemes, especially when applied to images depicting challenging localization conditions.
We prove an inequality of the form $\gamma_n\geq C_n(\gamma_{n-1})$ giving a lower bound for the Hermite constant $\gamma_n$ in dimension $n$ in terms of $\gamma_{n-1}$. Iterating this inequality yields a new proof of the Minkowski-Hlawka bound.
We show how two topologically distinct spaces - the Kahler K3 x T^2 and the non-Kahler T^2 bundle over K3 - can be smoothly connected in heterotic string theory. The transition occurs when the base K3 is deformed to the T^4/Z_2 orbifold limit. The orbifold theory can be mapped via duality to M-theory on K3 x K3 where the transition corresponds to an exchange of the two K3's.
We give the full supersymmetric and kappa-symmetric actions for the Dirichlet p-branes, including their coupling to background superfields of ten-dimensional type IIA and IIB supergravity.
We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by agreement algorithm defined on elements of a group and prove that equivariance of output pose vectors, as well as invariance of output activations, hold under certain conditions. Second, we connect the resulting equivariant capsule networks with work from the field of group convolutional networks. Through this connection, we provide intuitions of how both methods relate and are able to combine the strengths of both approaches in one deep neural network architecture. The resulting framework allows sparse evaluation of the group convolution operator, provides control over specific equivariance and invariance properties, and can use routing by agreement instead of pooling operations. In addition, it is able to provide interpretable and equivariant representation vectors as output capsules, which disentangle evidence of object existence from its pose.
Far-infrared observations provide crucial data for the investigation and characterisation of the properties of dusty material in the Interstellar Medium (ISM), since most of its energy is emitted between ~100 and 200 um. We present the first all-sky image from a sensitive all-sky survey using the Japanese AKARI satellite, in the wavelength range 50 -- 180 um. Covering >99% of the sky in four photometric bands with four filters centred at 65 um, 90 um, 140 um, and 160 um wavelengths, this achieved spatial resolutions from 1 to 2 arcmin and a detection limit of <10 MJy sr-1, with absolute and relative photometric accuracies of <20%. All-sky images of the Galactic dust continuum emission enable astronomers to map the large-scale distribution of the diffuse ISM cirrus, to study its thermal dust temperature, emissivity and column density, and to measure the interaction of the Galactic radiation field and embedded objects with the surrounding ISM. In addition to the point source population of stars, protostars, star-forming regions, and galaxies, the high Galactic latitude sky is shown to be covered with a diffuse filamentary-web of dusty emission that traces the potential sites of high latitude star formation. We show that the temperature of dust particles in thermal equilibrium with the ambient interstellar radiation field can be estimated by using 90 um, 140 um, and 160 um data. The FIR AKARI full-sky maps provide a rich new data set within which astronomers can investigate the distribution of interstellar matter throughout our Galaxy, and beyond.
A theoretical model of one-body nuclear friction which was developed earlier, namely the chaos-weighted wall formula, is applied to a dynamical description of compound nuclear decay in the framework of the Langevin equation coupled with statistical evaporation of light particles and photons. We have used both the usual wall formula friction and its chaos-weighted version in the Langevin equation to calculate the fission probability and prescission neutron multiplicity for the compound nuclei $^{178}$W, $^{188}$Pt, $^{200}$Pb, $^{213}$Fr, $^{224}$Th, and $^{251}$Es. We have also obtained the contributions of the presaddle and postsaddle neutrons to the total prescission multiplicity. A detailed analysis of our results leads us to conclude that the chaos-weighted wall formula friction can adequately describe the fission dynamics in the presaddle region. This friction, however, turns out to be too weak to describe the postsaddle dynamics properly. This points to the need for a suitable explanation for the enhanced neutron emission in the postsaddle stage of nuclear fission.
We present the Planck likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations. We use this likelihood to derive the Planck CMB power spectrum over three decades in l, covering 2 <= l <= 2500. The main source of error at l <= 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher l's. For l < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz through a physically motivated Bayesian component separation technique. At l >= 50, we employ a correlated Gaussian likelihood approximation based on angular cross-spectra derived from the 100, 143 and 217 GHz channels. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on cosmological parameters. We find good internal agreement among the high-l cross-spectra with residuals of a few uK^2 at l <= 1000. We compare our results with foreground-cleaned CMB maps, and with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. The best-fit LCDM cosmology is in excellent agreement with preliminary Planck polarisation spectra. The standard LCDM cosmology is well constrained by Planck by l <= 1500. For example, we report a 5.4 sigma deviation from n_s /= 1. Considering various extensions beyond the standard model, we find no indication of significant departures from the LCDM framework. Finally, we report a tension between the best-fit LCDM model and the low-l spectrum in the form of a power deficit of 5-10% at l <~ 40, significant at 2.5-3 sigma. We do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent dataset. (Abridged)
New red and violet system line lists for the CN isotopologues 13C14N and 12C15N have been generated. These new transition data are combined with those previously derived for 12C14N, and applied to the determination of CNO abundances in the solar photosphere and in four red giant stars: Arcturus, the bright very low-metallicity star HD 122563, and carbon-enhanced metal-poor stars HD 196944 and HD 201626. When lines of both red and violet system lines are detectable in a star, their derived N abundances are in good agreement. The mean N abundances determined in this work generally are also in accord with published values.
We study the effects of various symmetry-breaking perturbations on the experimentally measurable signatures (such as conductance and Josephson response) of quasi-one-dimensional (quasi-1D) spin-triplet superconductors. In the first part of the paper, we numerically compute the zero and nonzero temperature conductances of the quasi-1D nanowires that host multiple Majorana zero modes. Following the discussion of the case of s-wave Rashba nanowires, we shift to the main focus, i.e., multichannel spin-triplet superconductors. Applying gate voltages (which changes the symmetry of the spin-orbit coupling) as well as magnetic fields to the nanowire, tunes the system between different symmetry classes by splitting the multiple Majorana zero modes. We study how the conductance tracks the topological invariants and the spectra in all these cases. In the second part of the paper, we study the effects of the symmetry-induced spectrum-breaking on the Andreev spectra of Josephson junctions. Similar to the case of the conductance studies, we find that the spectrum shows multiple zero-energy Andreev bound states in the highly symmetric case with mirror and chiral symmetries.
The effect of narrow dibaryon resonances to nuclear matter and structure of neutron stars is investigated in the mean-field theory (MFT) and in the relativistic Hartree approximation (RHA). The existence of massive neutron stars imposes constraints to the coupling constants of the omega- and sigma-mesons with dibaryons. We conclude that the experimental candidates to dibaryons d1(1920) and d'(2060) if exist form in nuclear matter a Bose condensate stable against compression. This proves stability of the ground state for nuclear matter with a Bose condensate of the light dibaryons.
Given a graph $G$ and a subset of vertices $D\subseteq V(G)$, the external neighbourhood of $D$ is defined as $N_e(D)=\{u\in V(G)\setminus D:\, N(u)\cap D\ne \varnothing\}$, where $N(u)$ denotes the open neighbourhood of $u$. Now, given a subset $D\subseteq V(G)$ and a vertex $v\in D$, the external private neighbourhood of $v$ with respect to $D$ is defined to be $epn(v,D)=\{u\in V(G)\setminus D: N(u)\cap D=\{v\}\}.$ The strong differential of a set $D\subseteq V(G)$ is defined as $\partial_s(D)=|N_e(D)|-|D_w|,$ where $D_w=\{v\in D: epn(v,D)\neq \varnothing\}$. In this paper we focus on the study of the strong differential of a graph, which is defined as $$\partial_s(G)=\max \{\partial_s(D): D\subseteq V(G)\}.$$ Among other results, we obtain general bounds on $\partial_s(G)$ and we prove a Gallai-type theorem, which states that $\partial_s(G)+\gamma_{I}(G)=n(G)$, where $\gamma_{I}G)$ denotes the Italian domination number of $G$. Therefore, we can see the theory of strong differential in graphs as a new approach to the theory of Italian domination. One of the advantages of this approach is that it allows us to study the Italian domination number without the use of functions. As we can expect, we derive new results on the Italian domination number of a graph.
We construct in a Sonine Space of entire functions a subspace related to the Riemann zeta function and we show that the quotient contains vectors intrinsically attached to the non-trivial zeros and their multiplicities.
We introduce FigureQA, a visual reasoning corpus of over one million question-answer pairs grounded in over 100,000 images. The images are synthetic, scientific-style figures from five classes: line plots, dot-line plots, vertical and horizontal bar graphs, and pie charts. We formulate our reasoning task by generating questions from 15 templates; questions concern various relationships between plot elements and examine characteristics like the maximum, the minimum, area-under-the-curve, smoothness, and intersection. To resolve, such questions often require reference to multiple plot elements and synthesis of information distributed spatially throughout a figure. To facilitate the training of machine learning systems, the corpus also includes side data that can be used to formulate auxiliary objectives. In particular, we provide the numerical data used to generate each figure as well as bounding-box annotations for all plot elements. We study the proposed visual reasoning task by training several models, including the recently proposed Relation Network as a strong baseline. Preliminary results indicate that the task poses a significant machine learning challenge. We envision FigureQA as a first step towards developing models that can intuitively recognize patterns from visual representations of data.
Robust visual localization under a wide range of viewing conditions is a fundamental problem in computer vision. Handling the difficult cases of this problem is not only very challenging but also of high practical relevance, e.g., in the context of life-long localization for augmented reality or autonomous robots. In this paper, we propose a novel approach based on a joint 3D geometric and semantic understanding of the world, enabling it to succeed under conditions where previous approaches failed. Our method leverages a novel generative model for descriptor learning, trained on semantic scene completion as an auxiliary task. The resulting 3D descriptors are robust to missing observations by encoding high-level 3D geometric and semantic information. Experiments on several challenging large-scale localization datasets demonstrate reliable localization under extreme viewpoint, illumination, and geometry changes.
An $m=1$ lopsided asymmetry is common in disc galaxies. Here, we investigate the excitation of an $m=1$ lopsidedness in host galaxies during minor mergers while choosing a set of 1:10 merger models (with varying orbital configurations, morphology of the host galaxy) from the GalMer galaxy merger library. We show that a minor merger triggers a prominent $m=1$ lopsidedness in stars of the host galaxy. The strength of the $m=1$ lopsidedness undergoes a transient amplification phase after each pericenter passage of the satellite, in concordance with past findings of exciting an $m=1$ lopsidedness by tidal encounters. However, once the merger happens, and the post-merger remnant readjusts itself, the lopsidedness disappears in short time-scale ($\sim$ 500-850 Myr). Furthermore, a delayed merger can drive a prolonged ($\sim$2 Gyr) lopsidedness in the host galaxy. We demonstrate that the $m=1$ lopsidedness rotates with a well-defined pattern speed which is much slower than the $m=2$ bar pattern speed, and is retrograde with respect to the bar. This gives rise to a dynamical scenario where the Inner Lindblad resonance of the $m=1$ lopsidedness falls in between the corotation and the Outer Lindblad resonance of the $m=2$ bar mode. A kinematic lopsidedness also arises in the host galaxy; the resulting temporal variation closely follows that of the density lopsidedness. The minor merger also triggers a transient off-centred stellar disc-dark matter halo configuration due to the tidal encounter with the satellite.
A careful renormalization group analysis of the electroweak Standard Model, considered as a low energy effective theory, reveals that there is no hierarchy problem in the broken phase of the SM. In the broken phase a light Higgs turns out to be natural as it appears self-protected and self-tuned by the spontaneous symmetry breaking. It means that the scalar Higgs needs not be protected by any extra symmetry, specifically super symmetry, in order not to be much heavier than the other SM particles, which are protected by gauge- or chiral-symmetry. Thus the existence of quadratic cutoff effects in the SM cannot motivate the need for a super symmetric extensions of the SM, but in contrast plays an important role in triggering the electroweak phase transition at a scale about 10^{17} GeV and in shaping the Higgs potential in the early universe to drive inflation as supported by observation. The impact on the inflation profile of the quadratically enhanced bare Higgs mass term in the unbroken phase is discussed in some detail. My analysis suggests that inflation in the early universe is a direct consequence of the SM Higgs sector with its quadratic enhancement of the bare Higgs mass term
We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and covariances of the random variables in question. These include the total rate of change of the entropy, the entropy production rate, the entropy flux rate and the three components of the entropy production. All equations are cast in a way suitable for large-scale analysis of linear Langevin systems. Our results are also applied to different types of electrical circuits, which suitably illustrate the most relevant aspects of the problem.
Joint analysis of Cosmic Microwave Background, Baryon Acoustic Oscillation, and supernova data has enabled precision estimation of cosmological parameters. New programs will push to 1% uncertainty in the dark energy equation of state and tightened constraint on curvature, requiring close attention to systematics. Direct 1% measurement of the Hubble constant (H0) would provide a new constraint. It can be obtained without overlapping systematics directly from recessional velocities and geometric distance estimates for galaxies via the mapping of water maser emission that traces the accretion disks of nuclear black holes. We identify redshifts 0.02<z<0.06 as best for small samples, e.g., 10 widely distributed galaxies, each with 3% distance uncertainty. Knowledge of peculiar radial motion is also required. Mapping requires very long baseline interferometry (VLBI) with the finest angular resolution, sensitivity to individual lines of a few mJy-km/s, and baselines that can detect a complex of ~10 mJy lines (peak) in < 1 min. For 2010-2020, large ground apertures (50-100m diameter) augmenting the VLBA are critical, such as EVLA, GBT, Effelsberg, and the Large Millimeter Telescope, for which we propose a 22 GHz receiver and VLBI instrumentation. A space-VLBI aperture may be required, thus motivating US participation in the Japanese VSOP-2 mission (launch c.2013). This will provide 3-4x longer baselines and ~5x improvement in distance uncertainty. There are now 5 good targets at z>0.02, out of ~100 known masers. A single-dish discovery survey of >10,000 nuclei (>2500 hours on the GBT) would build a sample of tens of potential distance anchors. Beyond 2020, a high-frequency SKA could provide larger maser samples, enabling estimation of H0 from individually less accurate distances, and possibly without the need for peculiar motion corrections.
We study, in the semi-classical approximation, the convergence of the quantum density and the quantum action, solutions to the Madelung equations, when the Planck constant h tends to 0. We find two different solutions which depend to the initial density . In the first case where the initial quantum density is a classical density rho_0(x), the quantum density and the quantum action converge to a classical action and a classical density which satisfy the statistical Hamilton-Jacobi equations. These are the equations of a set of classical particles whose initial positions are known only by the density rho_0(x). In the second case where initial density
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with small average graph distance between vertices, but adding an edge comes at a cost measured according to the geometry of the ambient physical space. In most cases, we identify the order of magnitude of the average graph distance as a function of the parameters of the model. As the proofs reveal, hierarchical structures naturally emerge from our simple modeling assumptions. Moreover, a critical regime exhibits an infinite number of discontinuous phase transitions.
We study the following interacting particle system. There are $\rho n$ particles, $\rho < 1$, moving clockwise ("right"), in discrete time, on $n$ sites arranged in a circle. Each site may contain at most one particle. At each time, a particle may move to the right-neighbor site according to the following rules. If its right-neighbor site is occupied by another particle, the particle does not move. If the particle has unoccupied sites ("holes") as neighbors on both sides, it moves right with probability $1$. If the particle has a hole as the right-neighbor and an occupied site as the left-neighbor, it moves right with probability $0<p<1$. (We refer to the latter rule as a "holdback" property.) The main question we address is: what is the system steady-state flux (or throughput) when $n$ is large, as a function of density $\rho$? The most interesting range of densities is $0\le \rho < 1/2$. We define the system {\em typical flux} as the limit in $n\to\infty$ of the steady-state flux in a system subject to additional random perturbations, when the perturbation rate vanishes. Our main results show that: (a) the typical flux is different from the formal flux, defined as the limit in $n\to\infty$ of the steady-state flux in the system without perturbations, and (b) there is a phase transition at density $h=p/(1+p)$. If $\rho<h$, the typical flux is equal to $\rho$, which coincides with the formal flux. If $\rho>h$, a {\em condensation} phenomenon occurs, namely the formation and persistence of large particle clusters; in particular, the typical flux in this case is $p(1-\rho) < h < \rho$, which differs from the formal flux when $h < \rho < 1/2$. Our results include both steady-state and transient analysis. In particular, we derive a version of the Ballot Theorem, and show that the key "reason" for large cluster formation for densities $\rho > h$ is described by this theorem.
In order to obtain the properties of compact stellar objects, appropriate equations of state have to be used. In the literature, strange meson fields, namely the scalar meson field ${\sigma}^*(975)$ and the vector meson field $\phi(1020)$, had to be considered in order to reproduce the observed strongly attractive $\Lambda\Lambda$ interaction. The introduction of these strange mesons makes the equations of state harder (EOS) due to the repulsive effect of the $\phi(1020)$ meson. In this work the inclusion of these mesons in the equation of state and their influence on the properties of the neutron stars are investigated.
Using data from our Parkes & ATCA HI survey of six groups analogous to the Local Group, we find that the HI mass function and velocity distribution function for loose groups are the same as those for the Local Group. Both mass functions confirm that the "missing satellite" problem exists in other galaxy groups.