ShantanuT01/DACTYL-Pretraining huggingface dataset:
We forecast constraints on primordial non-Gaussianity achievable from forthcoming surveys by exploiting the scale-dependent halo bias introduced on large scales by non-Gaussian initial conditions. We explore the performance of exploiting both the shape of the galaxy power-spectrum on large scales and the cross-correlation of galaxies with Cosmic Microwave Background maps through the Integrated Sachs Wolfe effect. We find that future surveys can detect primordial non-Gaussianity of the local form with a non-Gaussianity parameter $|f_{\rm NL}|$ of order unity. This is particularly exciting because, while the simplest single-field slow-roll models of inflation predict a primordial $|f_{\rm NL}|\ll 1$, this signal sources extra contributions to the effective $f_{\rm NL}$ of large-scale structures that are expected to be above our predicted detection threshold.
We obtain Schauder estimates for a general class of linear integro-differential equations. The estimates are applied to a scalar non-local Burgers equation and complete the global well-posedness results obtained in \cite{ISV}.
We consider multidimensional SDEs with singular drift $b$ and Sobolev diffusion coefficients $\sigma$, satisfying Krylov--R\"ockner type assumptions. We prove several stability estimates, comparing solutions driven by different $(b^i,\sigma^i)$, both for It\^o and Stratonovich SDEs, possibly depending on negative Sobolev norms of the difference $b^1-b^2$. We then discuss several applications of these results to McKean--Vlasov SDEs, criteria for strong compactness of solutions and Wong--Zakai type theorems.
We present bijections for the planar cases of two counting formulas on maps that arise from the KP hierarchy (Goulden-Jackson and Carrell-Chapuy formulas), relying on a "cut-and-slide" operation. This is the first time a bijective proof is given for quadratic map-counting formulas derived from the KP hierarchy. Up to now, only the linear one-faced case was known (Harer-Zagier recurrence and Chapuy-F\'eray-Fusy bijection). As far as we know, this bijection is new and not equivalent to any of the well-known bijections between planar maps and tree-like objects.
The high accuracy of space data increased the number of the periodicities determined for pulsating variable stars, but the mode identification is still a critical point in the non-asymptotic regime. We use regularities in frequency spacings for identifying the pulsation modes of the recently discovered delta Sct star ID 102749568. In addition to analysing CoRoT light curves (15252 datapoints spanning 131 days), we obtained and analysed both spectroscopic and extended multi-colour photometric data. We applied standard tools (MUFRAN, Period04, SigSpec, and FAMIAS) for time-series analysis. A satisfactory light-curve fit was obtaining by means of 52 independent modes and 15 combination terms. The frequency spacing revealed distinct peaks around large (25.55-31.43 microHz), intermediate (9.80, 7.66 microHz), and low (2.35 microHz) separations. We directly identified 9 modes, and the l and n values of other three modes were extrapolated. The combined application of spectroscopy, multi-colour photometry, and modelling yielded the precise physical parameters and confirmed the observational mode identification. The large separation constrained the log g and related quantities. The dominant mode is the radial first overtone.
Aims. We aim to infer the sub-surface distribution of the Sun's non-axisymmetric azimuthal magnetic flux from observable quantities, such as the surface magnetic field and the large scale plasma flows.   Methods. We have built a kinematic flux transport model of the solar dynamo based on the Babcock-Leighton framework. We constructed the source term for the poloidal field using SOLIS magnetograms spanning three solar cycles. Based on this source we calculated the azimuthal flux below the surface. The flux transport model has two free parameters which we constrain using sunspot observations from cycle 22. We compared the model results with observations from cycle 23.   Results. The structure of the azimuthal field is mainly axisymmetric. The departures from axisymmetry represent, on average, ~3% of the total azimuthal flux. Owing to its relative weakness, the non-axisymmetric structure of the azimuthal field does not have a significant impact on the location in which the emergences appear or on the amount of flux contained in them. We find that the probability of emergence is a function of the ratio between the flux content of an active region and the underlying azimuthal flux.
We derive a model-independent expression for the minimum line-of-sight extent of the hot plasma in a cluster of galaxies. The only inputs are the 1-5 keV X-ray surface brightness and the Comptonization from Sunyaev-Zel'dovich (SZ) data. No a priori assumptions regarding equilibrium or geometry are required. The method applies when the X-ray emitting material has temperatures anywhere between 0.3 keV and 20 keV and metallicities between 0 and twice solar---conditions fulfilled by nearly all intracluster plasma. Using this method, joint APEX-SZ and Chandra X-ray Observatory data on the Bullet Cluster yield a lower limit of 400 +/- 56 kpc on the half-pressure depth of the main component, limiting it to being at least spherical, if not cigar-shaped primarily along the line of sight.
We consider weighted random balls in $\real^d$ distributed according to a random Poisson measure with heavy-tailed intensity and study the asymptotic behaviour of the total weight of some configurations in $\real^d$. This procedure amounts to be very rich and several regimes appear in the limit, depending on the intensity of the balls, the zooming factor, the tail parameters of the radii and of the weights. Statistical properties of the limit fields are also evidenced, such as isotropy, self-similarity or dependence. One regime is of particular interest and yields $\alpha$-stable stationary isotropic self-similar generalized random fields which recovers Takenaka fields, Telecom process or fractional Brownian motion.
The availability of continuous helioseismic data for two consecutive solar minima has provided a unique opportunity to study the changes in the solar interior that might have led to this unusual minimum. We present preliminary analysis of inter mediate-degree mode frequencies in the 3 mHz band during the current period of minimal solar activity and show that the mode frequencies are significantly lower than those during the previous activity minimum. Our analysis do not show any signature of the beginning of cycle 24 till the end of 2008. In addition, the zonal and meridional flow patterns inferred from inverting frequencies also hint for a delayed onset of a new cycle. The estimates of travel time are higher than the previous minimum confirming a relatively weak solar activity during the current minimum.
The unconventional Si-compatible ferroelectricity in hafnia-based systems, which becomes robust only at nanoscopic sizes, has attracted a lot of interest. While a metastable polar orthorhombic (o-) phase (Pca21) is widely regarded as the responsible phase for ferroelectricity, a higher energy polar rhombohedral (r-) phase is recently reported on epitaxial HfZrO4 (HZO) films grown on (001) SrTiO3 (R3m or R3), (0001) GaN (R3), and Si (111). Armed with results on these systems, here we report a systematic study leading towards identifying comprehensive global trends for stabilizing r-phase polymorphs in epitaxially grown HZO thin films (6 nm) on various substrates (perovskites, hexagonal and Si).
Leading order study of direct photon production from proton-proton collisions, in the framework of Minimal (Seiberg-Witten) Non-Commutative Standard Model (NCSM), taking into account the Earth-rotation effects. We found that relative non-commutative contributions increase significantly at very high photon transverse momentum. Therefore, using Run-1 (\sqrt{s}= 8 TeV) and Run-2 (\sqrt{s}= 13 TeV) ATLAS experimental data of inclusive isolated prompt photon cross-section, TeV-Scale bounds of the non-commutativity (NC) parameter are obtained. For space-space non-commutativity, we obtain: {\Lambda}b=1.145 \pm 0.015 TeV , and for space-time non-commutativity, we obtain : {\Lambda}e=1.125 \pm 0.035 TeV.
We present arguments which suggest that the bulk higher-spin gravity duals of weakly-coupled conformal field theories obey some refined notion of locality. In particular, we discuss the Mellin amplitude programme in this context. We focus on the $O(N)$ vector model and minimal higher-spin gravity as a paradigmatic example of such holographic dual pairs. We restrict ourselves to three- and four-point functions of scalar primary operators, but the qualitative conclusions are expected to hold for the generic case.
In this paper we explore the fundamentals of the Martingale Representation Theorem (MRT) and a closely related result, the Clark-Ocone formula. We also investigate how far these theorems can be taken, notably beyond the regular Sobolev spaces, through changes of measures and enlargement of filtrations. We look at Brownian motion (B.M.) driven continuous martingales as well as Jump and Levy process-driven martingales.
We report on a simple but highly efficient source of polarization-entangled photon pairs at non-degenerate wavelengths. The fully collinear configuration of the source enables very high coupling efficiency into a single optical mode and allows the use of long nonlinear crystals. With optimized dispersion compensation it is possible to use a free-running laser diode as pump source and to reach an entanglement fidelity of 99.4 % at rates as high as 27000 pairs/s per mW of pump power. This greatly enhances the practicality of the source for applications in quantum communication and metrology.
This work is divided into two main parts. The first part is devoted to exploring the connectivity of random subgraphs of cartesian products of $K_1$, $K_2$, and $P_3$. In the second part, the author presents a short review of the results about network reliability.
A non-technical description of the Operator Product Expansion and Renormalization Group techniques as applied to weak decays of mesons is presented. We use this opportunity to summarize briefly the present status of the next-to-leading QCD corrections to weak decays and their implications for the unitarity triangle, the ratio epsilon prime/epsilon, the radiative decay B-> s gamma, and the rare decays K^+ -> pi^+ nu barnu and K_L to pi^0 nu barnu.
Embodied perception refers to the ability of an autonomous agent to perceive its environment so that it can (re)act. The responsiveness of the agent is largely governed by latency of its processing pipeline. While past work has studied the algorithmic trade-off between latency and accuracy, there has not been a clear metric to compare different methods along the Pareto optimal latency-accuracy curve. We point out a discrepancy between standard offline evaluation and real-time applications: by the time an algorithm finishes processing a particular frame, the surrounding world has changed. To these ends, we present an approach that coherently integrates latency and accuracy into a single metric for real-time online perception, which we refer to as "streaming accuracy". The key insight behind this metric is to jointly evaluate the output of the entire perception stack at every time instant, forcing the stack to consider the amount of streaming data that should be ignored while computation is occurring. More broadly, building upon this metric, we introduce a meta-benchmark that systematically converts any single-frame task into a streaming perception task. We focus on the illustrative tasks of object detection and instance segmentation in urban video streams, and contribute a novel dataset with high-quality and temporally-dense annotations. Our proposed solutions and their empirical analysis demonstrate a number of surprising conclusions: (1) there exists an optimal "sweet spot" that maximizes streaming accuracy along the Pareto optimal latency-accuracy curve, (2) asynchronous tracking and future forecasting naturally emerge as internal representations that enable streaming perception, and (3) dynamic scheduling can be used to overcome temporal aliasing, yielding the paradoxical result that latency is sometimes minimized by sitting idle and "doing nothing".
Two laterally adjacent quantum Hall systems separated by an extended barrier of a thickness on the order of the magnetic length possess a complex Landau band structure in the vicinity of the line junction. The energy dispersion is obtained from an exact quantum-mechanical calculation of the single electron eigenstates for the coupled system by representing the wave functions as a superposition of parabolic cylinder functions. For orbit centers approaching the barrier, the separation of two subsequent Landau levels is reduced from the cyclotron energy to gaps which are much smaller. The position of the anticrossings increases on the scale of the cyclotron energy as the magnetic field is raised. In order to experimentally investigate a particular gap at different field strengths but under constant filling factor, a GaAs/AlGaAs heterostructure with a 52 Angstrom thick tunneling barrier and a gate electrode for inducing the two-dimensional electron systems was fabricated by the cleaved edge overgrowth method. The shift of the gaps is observed as a displacement of the conductance peaks on the scale of the filling factor. Besides this effect, which is explained within the picture of Landau level mixing for an ideal barrier, we report on signatures of quantum interferences at imperfections of the barrier which act as tunneling centers. The main features of the recent experiment of Yang, Kang et al. are reproduced and discussed for different gate voltages. Quasiperiodic oscillations, similar to the Aharonov Bohm effect at the quenched peak, are revealed for low magnetic fields before the onset of the regular conductance peaks.
A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects:   (a) a non-null (non-isotropic) vector field,   (b) the orthogonal to the vector field sub space,   (c) an affine connection and the related to it covariant differential operator determining a transport along the given non-null vector filed.   On the grounds of this definition other definitions related to the notions of accelerated, inertial, proper accelerated and proper inertial frames of reference are introduced and applied to some mathematical models for the space-time. The auto-parallel equation is obtained as an Euler-Lagrange's equation. Einstein's theory of gravitation appears as a theory for determination of a special frame of reference (with the gravitational force as inertial force) by means of the metrics and the characteristics of a material distribution.   PACS numbers: 0490, 0450, 1210G, 0240V
Let $C$ be a curve defined over a number field $k$. We say a closed point $x\in C$ of degree $d$ is isolated if it does not belong to an infinite family of degree $d$ points parametrized by the projective line or a positive rank abelian subvariety of the curve's Jacobian. Building on work of Bourdon, Ejder, Liu, Odumodu, and Viray, we characterize elliptic curves with rational $j$-invariant which give rise to an isolated point of odd degree on $X_1(N)/\mathbb{Q}$ for some positive integer $N$.
We propose a system of two coupled parabolic equations that have degenerate diffusion constants depending on the energy-like variable. The dissipation of the velocity-like variable is fed as a source term into the energy equation leading to conservation of the total energy. Because of the degeneracies there are solutions with nontrivial support that may grow in time like in the porous medium equation, which is contained in our system as a special case. The motion of the free boundary may be driven by either self-diffusion of the energy-like variable or by dissipation of the velocity-like variable. We discuss the cross-over of these two phenomena in terms of the associated planar traveling waves. Moreover, we provide existence of suitably defined weak and very weak solutions. After providing a thermodynamically motivated gradient structure we also establish convergence into steady state for bounded domains.
We have investigated a highly energetic H-ingestion event during shell He burning leading to H-burning luminosities of $\log(L_\mathrm{H}/\mathrm{\Lsun}) \sim 13$ in a $45 \Msun$ Pop III massive stellar model. In order to track the nucleosynthesis which may occur in such an event, we run a series of single-zone nucleosynthesis models for typical conditions found in the stellar evolution model. Such nucleosynthesis conditions may lead to $\textit{i}-$process neutron densities of up to $ \sim 10^{13} \mathrm{cm}^{-3}$. The resulting simulation abundance pattern, where Mg comes from He burning and Ca from the $\textit{i}$ process, agrees with the general observed pattern of the most iron-poor star currently known, SMSS J031300.36-670839.3. However, Na is also efficiently produced in these $i$ process conditions, and the prediction exceeds observations by $\sim 2.5 \unitstyle{dex}$. While this probably rules out this model for SMSS J031300.36-670839.3, the typical $\textit{i}-$process signature of combined He burning and $\textit{i}$ process of higher than solar [Na/Mg], [Mg/Al] and low [Ca/Mg] is reproducing abundance features of the two next most iron-poor stars HE\,1017-5240 and HE\,1327-2326 very well. The $i$ process does not reach Fe which would have to come from a low level of additional enrichment. $\textit{i}$ process in hyper-metal poor or Pop III massive stars may be able to explain certain abundance patterns observed in some of the most-metal poor CEMP-no stars.
We study the predictions for BR(mu-> e+gamma) and BR(tau-> e,mu+gamma) in a class of recently proposed horizontal SU(2) model that leads to a 3 X 2 seesaw model for neutrino masses. We consider two such models and obtain the correct bi-large mixing pattern for neutrinos. In these models, the effective low energy theory below the SU(2)_H scale is the MSSM. Assuming a supersymmetry breaking pattern as in the minimal SUGRA models, we find that consistent with present g-2, b->s+gamma and WMAP dark matter constraints on the parameters of the model, the BR(mu-> e+gamma) prediction is accessible to the proposed MEG experiment at PSI making this class of models testable in the near future.
Averbouch, Godlin and Makowsky define the edge elimination polynomial of a graph by a recurrence relation with respect to the deletion, contraction and extraction of an edge. It generalizes some well-known graph polynomials such as the chromatic polynomial and the matching polynomial. By introducing two equivalent graph polynomials, one enumerating subgraphs and the other enumerating colorings, we show that the edge elimination polynomial of a simple graph is reconstructible from its polynomial deck and that it encodes the degree sequence of an arbitrary graph.
Spinons are among the generic excitations in one-dimensional spin systems, they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show that a representation in terms of hopping and Bogoliubov spinon processes, which we call "spinon-pair" operators, and their combination is possible. We refer to such a representation as second quantized form. Neglecting terms which change the number of spinons yields the variational results. Treating the bilinear and quartic terms by continuous unitary transformations leads to considerably improved results. Thus, we provide the proof-of-principle that systems displaying massive spinons as elementary excitations can be treated in second quantization based on spinon-pair representation.
Hipparcos astrometric binaries were observed with the NICI adaptive optics system at Gemini-S, completing the work of Paper I (Tokovinin et al. 2012). Among the 65 F, G, K dwarfs within 67pc of the Sun studied here, we resolve 18 new sub-arcsecond companions, re-measure 7 known astrometric pairs, and establish the physical nature of yet another three wider companions. The 107 astrometric binaries targeted at Gemini so far have 38 resolved companions with separations under 3". Modeling shows that bright enough companions with separations on the order of an arcsecond can perturb the Hipparcos astrometry when they are not accounted for in the data reduction. However, the resulting bias of parallax and proper motion is generally below formal errors and such companions cannot produce fake acceleration. This work contributes to the multiplicity statistics of nearby dwarfs by bridging the gap between spectroscopic and visual binaries and by providing estimates of periods and mass ratios for many astrometric binaries.
We investigate an integrated optical circuit on lithium niobate designed to implement the teleportation-based quantum relay scheme for one-way quantum communication at a telecom wavelength. Such an advanced quantum circuit merges for the first time, both optical-optical and electro-optical non-linear functions necessary to implement the desired on-chip single qubit teleportation. On one hand, spontaneous parametric down-conversion is used to produce entangled photon-pairs. On the other hand, we take advantage of two photon routers, consisting of electro-optically controllable couplers, to separate the paired photons and to perform a Bell state measurement, respectively. After having validated all the individual functions in the classical regime, we have performed a Hong-Ou-Mandel (HOM) experiment to mimic a one-way quantum communication link. Such a quantum effect, seen as a prerequisite towards achieving teleportation, has been obtained, at one of the routers, when the chip was coupled to an external single photon source. The two-photon interference pattern shows a net visibility of 80%, which validates the proof of principle of a "quantum relay circuit" for qubits carried by telecom photons. In case of optimized losses, such a chip could increase the maximal achievable distance of one-way quantum key distribution links by a factor 1.8. Our approach and results emphasize the high potential of integrated optics on lithium niobate as a key technology for future reconfigurable quantum information manipulation.
Anomaly driving detection is an important problem in advanced driver assistance systems (ADAS). It is important to identify potential hazard scenarios as early as possible to avoid potential accidents. This study proposes an unsupervised method to quantify driving anomalies using a conditional generative adversarial network (GAN). The approach predicts upcoming driving scenarios by conditioning the models on the previously observed signals. The system uses the difference of the output from the discriminator between the predicted and actual signals as a metric to quantify the anomaly degree of a driving segment. We take a driver-centric approach, considering physiological signals from the driver and controller area network-Bus (CAN-Bus) signals from the vehicle. The approach is implemented with convolutional neural networks (CNNs) to extract discriminative feature representations, and with long short-term memory (LSTM) cells to capture temporal information. The study is implemented and evaluated with the driving anomaly dataset (DAD), which includes 250 hours of naturalistic recordings manually annotated with driving events. The experimental results reveal that recordings annotated with events that are likely to be anomalous, such as avoiding on-road pedestrians and traffic rule violations, have higher anomaly scores than recordings without any event annotation. The results are validated with perceptual evaluations, where annotators are asked to assess the risk and familiarity of the videos detected with high anomaly scores. The results indicate that the driving segments with higher anomaly scores are more risky and less regularly seen on the road than other driving segments, validating the proposed unsupervised approach.