ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present the first galaxy-galaxy weak lensing results using early data from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). These results are based on ~22 sq. deg. of i' data. From this data, we estimate the average velocity dispersion for an L* galaxy at a redshift of 0.3 to be 137 +- 11 km/s, with a virial mass, M_{200}, of 1.1 +- 0.2 \times 10^{12} h^{-1} Msun and a rest frame R-band mass-to-light ratio of 173 +- 34 h Msun/Lsun. We also investigate various possible sources of systematic error in detail. Additionally, we separate our lens sample into two sub-samples, divided by apparent magnitude, thus average redshift. From this early data we do not detect significant evolution in galaxy dark matter halo mass-to-light ratios from a redshift of 0.45 to 0.27. Finally, we test for non-spherical galaxy dark matter halos. Our results favor a dark matter halo with an ellipticity of ~0.3 at the 2-sigma level when averaged over all galaxies. If the sample of foreground lens galaxies is selected to favor ellipticals, the mean halo ellipticity and significance of this result increase.
The recent detections of the binary black hole mergers GW150914 and GW151226 have inaugurated the field of gravitational-wave astronomy. For the two main formation channels that have been proposed for these sources, isolated binary evolution in galactic fields and dynamical formation in dense star clusters, the predicted masses and merger rates overlap significantly, complicating any astrophysical claims that rely on measured masses alone. Here, we examine the distribution of spin- orbit misalignments expected for binaries from the field and from dense star clusters. Under standard assumptions for black-hole natal kicks, we find that black-hole binaries similar to GW150914 could be formed with significant spin-orbit misalignment only through dynamical processes. In particular, these heavy-black-hole binaries can only form with a significant spin-orbit anti-alignment in the dynamical channel. Our results suggest that future detections of merging black hole binaries with measurable spins will allow us to identify the main formation channel for these systems.
A cyclic quadrilateral is called a Brahmagupta quadrilateral if its four sides, the two diagonals and the area are all given by integers. In this paper we consider the hitherto unsolved problem of finding two Brahmagupta quadrilaterals with equal perimeters and equal areas. We obtain two parametric solutions of the problem -- the first solution generates examples in which each quadrilateral has two equal sides while the second solution gives quadrilaterals all of whose sides are unequal. We also show how more parametric solutions of the problem may be obtained.
The discrete-time quantum walk (QW) is a quantum version of the random walk (RW) and has been widely investigated for the last two decades. Some remarkable properties of QW are well known. For example, QW has a ballistic spreading, i.e., QW is quadratically faster than RW. For some cases, localization occurs: a walker stays at the starting position forever. In this paper, we consider stationary measures of two-state QWs on the line. It was shown that for any space-homogeneous model, the uniform measure becomes the stationary measure. However, the corresponding result for space-inhomogeneous model is not known. Here, we present a class of space-inhomogeneous QWs on the line and cycles in which the uniform measure is stationary. Furthermore, we briefly discuss a difference between QWs and RWs.
We investigate the properties of persistent charge current driven by magnetic flux in a quasi-periodic mesoscopic Fibonacci ring with Rashba and Dresselhaus spin-orbit interactions. Within a tight-binding framework we work out individual state currents together with net current based on second-quantized approach. A significant enhancement of current is observed in presence of spin-orbit coupling and sometimes it becomes orders of magnitude higher compared to the spin-orbit interaction free Fibonacci ring. We also establish a scaling relation of persistent current with ring size, associated with the Fibonacci generation, from which one can directly estimate current for any arbitrary flux, even in presence of spin-orbit interaction, without doing numerical simulation. The present analysis indeed gives a unique opportunity of determining persistent current and has not been discussed so far.
Magic-angle spinning (MAS) solid state nuclear magnetic resonance (NMR) spectroscopy is shown to be a promising technique for implementing quantum computing. The theory underlying the principles of quantum computing with nuclear spin systems undergoing MAS is formulated in the framework of formalized quantum Floquet theory. The procedures for realizing state labeling, state transformation and coherence selection in Floquet space are given. It suggests that by this method, the largest number of qubits can easily surpass that achievable with other techniques. Unlike other modalities proposed for quantum computing, this method enables one to adjust the dimension of the working state space, meaning the number of qubits can be readily varied. The universality of quantum computing in Floquet space with solid state NMR is discussed and a demonstrative experimental implementation of Grover's search is given.
Recently, Hawking radiation from a $4-$dimensional linear dilaton black hole solution to Einstein-Maxwell-Dilaton (EMD) theory, via a method of computing exactly the semi-classical radiation, has been derived by Cl\U{e9}ment, et al. Their results show that, whenever solution is available to the massless scalar wave equation, an exact computation of the radiation spectrum leads to the Hawking temperature $T_{H}$. We apply the same method to derive Hawking radiation spectrum for higher dimensional linear dilaton black holes in the Einstein-Yang-Mills-Dilaton (EYMD) and Einstein-Maxwell-Dilaton (EMD) theories. Our results show that the radiation with high frequencies for these massive black holes reveal some remarkable information about the $T_{H}$.
We count various classes of algebraic integers of fixed degree by their largest absolute value. The classes of integers considered include all algebraic integers, Perron numbers, totally real integers, and totally complex integers. We give qualitative and quantitative results concerning the distribution of Perron numbers, answering in part a question of W. Thurston.
A search for anisotropy at different scales in the arrival directions of cosmic rays with energies above 1 PeV is performed with data of the Tunka-133 array. A number of regions with angular sizes up to approximately 30 degrees that deviate from the uniform background with a statistical significance greater than three standard deviations are found using the shuffling technique both in the complete data set and its subsets in different energy ranges. Some regions with an excess of cosmic rays correlate with the distribution of possible cosmic ray sources. A comparison of the results with a similar analysis of the legacy data of the EAS MSU array is presented.
Some of the most popular ways to treat quantum critical materials, that is, materials close to a magnetic instability, are based on the Landau functional. The central quantity of such approaches is the average magnitude of spin fluctuations, which is very difficult to measure experimentally or compute directly from the first principles. We calculate the parameters of the Landau functional for Pd and use these to connect the critical fluctuations beyond the local-density approximation and the band structure.
We prove that there is no circulant Hadamard matrix $H$ with first row $[h_{1},\ldots,h_{n}]$ of order $n>4$, under a condition about a sum of scalar products of rows of two other circulant matrices of size $n/2$ associated to $H.$
We provide a construction of examples of semistable degeneration via toric geometry. The applications include a higher dimensional generalization of classical degeneration of K3 surface into 4 rational components, an algebraic geometric version of decomposing K3 as the fiber sum of two E(1)'s as well as it's higher dimensional generalizations, and many other new examples.
Unlike widely explored complex oxide heterostructures grown along [001], the study of [111]-oriented heterointerfaces are very limited thus far. One of the main challenges is to overcome the polar discontinuity that hinders the epitaxy of atomically sharp interfaces. Here, by taking the LaCoO3/SrTiO3(111) as a prototype, we show that the reconstruction, which effectively compensates the surface polarity, can stabilize the epitaxy of the heterostructure with polar discontinuity. Reconstructed substrate surface is prepared, while the growth is controlled to form reconstruction on the film surface. To suppress the chemical diffusion across the interface, the growth is interrupted between each unit cell layer to allow the lattice relaxation at a lowered temperature. In this way, high quality two-dimensional growth is realized and the heterointerfaces exhibit sharpness at the atomic scale. Our work provides a path to precisely control the growth of complex oxide heterostructures along polar orientations that exhibit emergent quantum phenomena.
Recently, Andreatta, Iovita and Pilloni have constructed spaces of overconvergent modular forms in characteristic p, together with a natural extension of the Coleman-Mazur eigencurve over a compactified (adic) weight space. Similar ideas have also been used by Liu, Wan and Xiao to study the boundary of the eigencurve. This all goes back to an idea of Coleman.   In this article, we construct natural extensions of eigenvarieties for arbitrary reductive groups G over a number field which are split at all places above p. If G is GL(2)/Q, then we obtain a new construction of the extended eigencurve of Andreatta-Iovita-Pilloni. If G is an inner form of GL(2) associated to a definite quaternion algebra, our work gives a new perspective on some of the results of Liu-Wan-Xiao.   We build our extended eigenvarieties following Hansen's construction using overconvergent cohomology. One key ingredient is a definition of locally analytic distribution modules which permits coefficients of characteristic p (and mixed characteristic). When G is GL(n) over a totally real or CM number field, we also construct a family of Galois representations over the reduced extended eigenvariety.
We give elementary proofs of the main theorems about (small) quantum cohomology of Grassmannians, including the quantum Giambelli and quantum Pieri formulas, the rim-hook algorithm, Siebert and Tian's presentation, and a recent theorem of Fulton and Woodward about the minimal q-power which appears in a product of two Schubert classes.
Person re-identification has seen significant advancement in recent years. However, the ability of learned models to generalize to unknown target domains still remains limited. One possible reason for this is the lack of large-scale and diverse source training data, since manually labeling such a dataset is very expensive and privacy sensitive. To address this, we propose to automatically synthesize a large-scale person re-identification dataset following a set-up similar to real surveillance but with virtual environments, and then use the synthesized person images to train a generalizable person re-identification model. Specifically, we design a method to generate a large number of random UV texture maps and use them to create different 3D clothing models. Then, an automatic code is developed to randomly generate various different 3D characters with diverse clothes, races and attributes. Next, we simulate a number of different virtual environments using Unity3D, with customized camera networks similar to real surveillance systems, and import multiple 3D characters at the same time, with various movements and interactions along different paths through the camera networks. As a result, we obtain a virtual dataset, called RandPerson, with 1,801,816 person images of 8,000 identities. By training person re-identification models on these synthesized person images, we demonstrate, for the first time, that models trained on virtual data can generalize well to unseen target images, surpassing the models trained on various real-world datasets, including CUHK03, Market-1501, DukeMTMC-reID, and almost MSMT17. The RandPerson dataset is available at https://github.com/VideoObjectSearch/RandPerson.
Let $G$ be a connected graph. If $G$ contains a matching of size $k$, and every matching of size $k$ is contained in a perfect matching of $G$, then $G$ is said to be \emph{$k$-extendable}. A $k$-regular spanning subgraph of $G$ is called a \textit{$k$-factor}. In this paper, we provide spectral conditions for a (balanced bipartite) graph with minimum degree $\delta$ to be $k$-extendable, and for the existence of a $k$-factor in a balanced bipartite graph, respectively. Our results generalize some previous results on perfect matchings of graphs, and extend the results in \cite{D.F} and \cite{W.L} to $k$-extendable graphs. Furthermore, our results generalize the result of Lu, Liu and Tian \cite{Lu-Liu} to general regular factors. Additionally, using the equivalence of $k$ edge-disjoint perfect matchings and $k$-factors in balanced bipartite graphs, our results can derive a spectral condition for the existence of $k$ edge-disjoint perfect matchings in balanced bipartite graphs.
Next-generation spectroscopic surveys will map the large-scale structure of the observable universe, using emission line galaxies as tracers. While each survey will map the sky with a specific emission line, interloping emission lines can masquerade as the survey's intended emission line at different redshifts. Interloping lines from galaxies that are not removed can contaminate the power spectrum measurement, mixing correlations from various redshifts and diluting the true signal. We assess the potential for power spectrum contamination, finding that an interloper fraction worse than 0.2% could bias power spectrum measurements for future surveys by more than 10% of statistical errors, while also biasing power spectrum inferences. We also construct a formalism for predicting cosmological parameter bias, demonstrating that a 0.15%-0.3% interloper fraction could bias the growth rate by more than 10% of the error, which can affect constraints on gravity upcoming surveys. We use the COSMOS Mock Catalog (CMC), with the emission lines re-scaled to better reproduce recent data, to predict potential interloper fractions for the Prime Focus Spectrograph (PFS) and the Wide-Field InfraRed Survey Telescope (WFIRST). We find that secondary line identification, or confirming galaxy redshifts by finding correlated emission lines, can remove interlopers for PFS. For WFIRST, we use the CMC to predict that the 0.2% target can be reached for the WFIRST H$\alpha$ survey, but sensitive optical and near-infrared photometry will be required. For the WFIRST [OIII] survey, the predicted interloper fractions reach several percent and their effects will have to be estimated and removed statistically (e.g. with deep training samples). (Abridged)
In arxiv:1108.5354 the Kolmogorov-Smirnov (K-S) test and Kolmogorov stochasticity parameter (KSP) is applied to CMB data. Their interpretation of the KSP method, however, lacks essential elements. In addition, their main result on the Gaussianity of CMB was not a matter of debate in previous KSP-CMB studies which also included predictions on cold spots, point sources.
We use a new idea to construct a theory of iterated Coleman functions in higher dimensions than 1. A Coleman function in this theory consists of a unipotent differential equation, a section on the underlying bundle and a solution to the equation on a residue disc. The new idea is to use the theory of Tannakian categories and the action of Frobenius to anlytically continue solutions of the differential equation to all residue discs.
Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach.
First-principles calculations of work function tuning induced by different chemical terminations on Si(100) surface are presented and discussed. We find that the presence of halogen atoms (I, Br, Cl, and F) leads to an increase of the work function if compared to the fully hydrogenated surface. This is a quite general effect and is directly linked to the chemisorbed atoms electronegativity as well as to the charge redistribution at the interface. All these results are examined with respect to previous theoretical works and experimental data obtained for the (100) as well as other Si surface orientations. Based on this analysis, we argue that the changes in the electronic properties caused by variations of the interfacial chemistry strongly depend on the chemisorbed species and much less on the surface crystal orientation.
The demand for petroleum dependent chemicals and materials has been increasing despite the dwindling of their fossil resources. As the dead-end of petroleum based industry has started to appear, today's modern society has to implement alternative energy and valuable chemical resources immediately. Owing to the importance of lignocellulosic biomass being the most abundant and bio-renewable biomass on earth, this critical review provides insights into the potential of lignocellulosic biomass as an alternative platform to fossil resources. In this context, over 200 value-added compounds, which can be derived from lignocellulosic biomass by various treatment methods, are presented with their references. Lignocellulosic biomass based polymers and their commercial importance are also reported mainly in the frame of these compounds. This review article aims to draw the map of lignocellulosic biomass derived chemicals and their synthetic polymers, and to reveal the scope of this map in today's modern chemical and polymer industry.
We provide a weaker version of the generalized lifting property which holds in complete generality for all finite Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also describe some combinatorial properties of the associated polytopes.
Recent observations of the rotation curve of M31 show a rise of the outer part that can not be understood in terms of standard dark matter models or perturbations of the galactic disc by M31's satellites. Here, we propose an explanation of this dynamical feature based on the influence of the magnetic field within the thin disc. We have considered standard mass models for the luminous mass distribution, a NFW model to describe the dark halo, and we have added up the contribution to the rotation curve of a magnetic field in the disc, which is described by an axisymmetric pattern. Our conclusion is that a significant improvement of the fit in the outer part is obtained when magnetic effects are considered. The best-fit solution requires an amplitude of ~4 microG with a weak radial dependence between 10 and 38 kpc.
We give bounds on the degree of generators for the ideal of relations of the graded algebras of modular forms with coefficients in $\mathbb{Q}$ over congruence subgroups $\Gamma_0(N)$ for $N$ satisfying some congruence conditions and for $\Gamma_1(N)$. We give similar bounds for the graded $\mathbb{Z}[\frac{1}{N}]$-algebra of modular forms on $\Gamma_1(N)$ with coefficients in $\mathbb{Z}[\frac{1}{N}]$. For a prime $p \geq 5$, we give a lower bound on the highest weight appearing in a minimal list of generators for $\Gamma_0(p)$, and we identify a set of generators for the graded algebra $M(\Gamma_0(p),\mathbb{Z})$ of modular forms over $\Gamma_0(p)$ with coefficients in $\mathbb{Z}$, showing that this weight is unbounded. We generalize a result of Serre concerning congruences between modular forms over $\Gamma_0(p)$ and $SL_2(\mathbb{Z})$, and use it to identify a set of generators for $M(\Gamma_0(p),\mathbb{Z})$, and we state two conjectures detailing further the structure of this algebra. Finally we provide computations concerning the number of generators and relations for each of these algebras, as well as computational evidence for these conjectures.
Consider a Wiener process $W$ on a circle of circumference $L$. We prove the rather surprising result that the Laplace transform of the distribution of the first time, $\theta_L$, when the Wiener process has visited every point of the circle can be solved in closed form using a continuous recurrence approach.
We study, on the basis of the general entangled-plaquette variational ansatz, the ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice. Our numerical estimates are in good agreement with available exact results and comparable, for large system sizes, to those computed via the best alternative numerical approaches, or by means of variational schemes based on specific (i.e., incorporating problem dependent terms) trial wave functions. The extrapolation to the thermodynamic limit of our results for lattices comprising up to N=324 spins yields an upper bound of the ground-state energy per site (in units of the exchange coupling) of $-0.5458(2)$ [$-0.4074(1)$ for the XX model], while the estimated infinite-lattice order parameter is $0.3178(5)$ (i.e., approximately 64% of the classical value).
Deterministic quantum computation with one quantum bit (DQC1), or the one clean qubit model, [E. Knill and R. Laflamme, Phys. Rev. Lett. {\bf81}, 5672 (1998)] is a model of quantum computing where the input is the tensor product of a single pure qubit and many completely-mixed states, and only the single qubit is measured at the end of the computation. In spite of its naive appearance, the DQC1 model can efficiently solve some problems for which no classical efficient algorithms are known, and therefore it has been conjectured that the DQC1 model is more powerful than classical computing (under the assumption of $\mbox{BPP}\subsetneq\mbox{BQP}$). Here we show that the output probability distribution of the DQC1 model cannot be classically efficiently approximated (exactly within a polynomial bit length or in the fully polynomial randomized approximation scheme (FPRAS) with at most a constant error) unless $\mbox{BQP}\subseteq\mbox{BPP}$.
YMnO3 thin films have been grown on n - type Si substrates by nebulized spray pyrolysis in the Metal - Ferroelectric - Semiconductor (MFS) configuration. The C-V characteristics of the film in MFS structure exhibit hysteretic behavior consistent with the polarization charge switching direction, with the memory window decreasing with increase in temperature. The density of interface states decreases with the increase in the annealing temperature. Mapping of the silicon energy band gap with the interface states has been carried out. The leakage current measured in the accumulation region, is lower in well-crystallized thin films and obeys a space- charge limited conduction mechanism.