ShantanuT01/DACTYL-Pretraining huggingface dataset:
A proposed phase-estimation protocol based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that the Cram\'{e}r-Rao sensitivity is sub-Heisenberg [Phys.\ Rev.\ Lett.\ {\bf104}, 103602 (2010)]. However, these measurements are problematic, making it unclear if this sensitivity can be obtained with a finite number of measurements. This sensitivity is only for phase near zero, and in this region there is a problem with ambiguity because measurements cannot distinguish the sign of the phase. Here, we consider a finite number of parity measurements, and show that an adaptive technique gives a highly accurate phase estimate regardless of the phase. We show that the Heisenberg limit is reachable, where the number of trials needed for mean photon number $\bar{n}=1$ is approximately one hundred. We show that the Cram\'{e}r-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval ($-\pi/2, \pi/2$).
Let $p=3n+1$ be a prime with $n\in\mathbb{N}=\{0,1,\cdots\}$, and let $g\in\mathbb{Z}$ be a primitive root modulo $p$. Let $0<a_1<\cdots<a_n<p$ be all the cubic residues modulo $p$ in the interval $(0,p)$. Then clearly the sequence $$a_1\ {\rm mod}\ p,\ a_2\ {\rm mod}\ p,\cdots, a_n\ {\rm mod}\ p$$ is a permutation $s_p(g)$ of the sequence $$g^3\ {\rm mod}\ p,\ g^6\ {\rm mod}\ p,\cdots, g^{3n}\ {\rm mod}\ p.$$ In this paper, we shall determine the sign of this permutation.
The subsurface properties of active regions prior to their appearance at the solar surface may shed light on the process of active region formation. Helioseismic holography has been applied to samples taken from two populations of regions on the Sun (pre-emergence and without emergence), each sample having over 100 members, that were selected to minimize systematic bias, as described in Paper I (Leka et al., 2012). Paper II (Birch et al., 2012) showed that there are statistically significant signatures in the average helioseismic properties that precede the formation of an active region. This paper describes a more detailed analysis of the samples of pre-emergence regions and regions without emergence, based on discriminant analysis. The property that is best able to distinguish the populations is found to be the surface magnetic field, even a day before the emergence time. However, after accounting for the correlations between the surface field and the quantities derived from helioseismology, there is still evidence of a helioseismic precursor to active region emergence that is present for at least a day prior to emergence.
In 1978 E. De Giorgi formulated a conjecture concerning the one-dimensional symmetry of bounded solutions to the elliptic equation \Delta u=F'(u), which are monotone in some direction. In this paper we prove the analogous statement for the equation \Delta u - <x, Du> =F'(u), where the Laplacian is replaced by the Ornstein-Uhlenbeck operator. Our theorem holds without any restriction on the dimension of the ambient space, and this allows us to obtain an similar result in infinite dimensions by a limit procedure.
Simulation techniques are providing with each passing day a deeper insight into the structure and properties of materials. Two main obstacles appear for the cooperation of simulation and experiment: on the one hand, the frequent lack of a degree of uncertainty associated with calculated data. On the other, the concomitant underlying feeling that calculation parameters can be tuned with the explicit aim of matching the experimental results, even at the expense of the quality of the simulation. Without the definition of an error bar for estimating the precision of the calculation, direct comparison of calculated and experimental data can lack physical significance. In this contribution, we employ the well known delocalization error of DFT and HF to develop a simple and robust procedure to quickly estimate an error bar for calculated quantities in the field of solid state chemistry. First, we validate our model on one of the simplest properties of a solid, the geometry of its unit cell, which can be determined experimentally with high accuracy. In this case, our computational window is too large to provide a useful error bar. However, it provides computational material scientists with a pointer on how much a given system is affected by the method of choice, i.e. how much it is sensible to parameter tuning and how much care should be taken in doing it. Then, we move to another quantity which has a greater experimental uncertainty, namely transition pressure, and show that our approach can lead to error bars comparable to experiment. Hence, both experiment and theory can be compared on an even basis taking into account the uncertainty introduced by the scientist, both in the measuring conditions and the tuning of computational parameters.
Ohya and Volovich have been proposed a new quantum computation model with chaos amplification to solve the SAT problem, which went beyond usual quantum algorithm. In this paper we study the complexity of the SAT algorithm by counting the steps of computation algorithm rigorously, which was mentioned in the paper [1,2,3,5,7]For this purpose, we refine the quantum gates treating the SAT problem step by step.
We report first results of an implementation of a chemical model in a cosmological code, based on the Smoothed Particle Hydrodynamics (SPH) technique. We show that chemical SPH simulations are a promising tool to provide clues for the understanding of the chemical properties of galaxies in relation to their formation and evolution in a cosmological framework.
Baker's method, relying on estimates on linear forms in logarithms of algebraic numbers, allows one to prove in several situations the effective finiteness of integral points on varieties. In this article, we give a generalisation of results of Levin regarding Baker's method for varieties, and explain how, quite surprisingly, it mixes (under additional hypotheses) with Runge's method to improve some known estimates in the case of curves by bypassing (or more generally reducing) the need for linear forms in $p$-adic logarithms.
We present observations of a new phenomenon in pulsating white dwarf stars: large-amplitude outbursts at timescales much longer than the pulsation periods. The cool (Teff = 11,010 K), hydrogen-atmosphere pulsating white dwarf PG 1149+057 was observed nearly continuously for more than 78.8 d by the extended Kepler mission in K2 Campaign 1. The target showed 10 outburst events, recurring roughly every 8 d and lasting roughly 15 hr, with maximum flux excursions up to 45% in the Kepler bandpass. We demonstrate that the outbursts affect the pulsations and therefore must come from the white dwarf. Additionally, we argue that these events are not magnetic reconnection flares, and are most likely connected to the stellar pulsations and the relatively deep surface convection zone. PG 1149+057 is now the second cool pulsating white dwarf to show this outburst phenomenon, after the first variable white dwarf observed in the Kepler mission, KIC 4552982. Both stars have the same effective temperature, within the uncertainties, and are among the coolest known pulsating white dwarfs of typical mass. These outbursts provide fresh observational insight into the red edge of the DAV instability strip and the eventual cessation of pulsations in cool white dwarfs.
We describe the space of projective planes of complex skew-symmetric matrices of order six and constant rank four. We prove that it has four connected components, all of dimension 26 and homogeneous under the action of PGL_6.
The probability of observing "supernova - gamma-ray burst" (GRB) pair events and recurrent GRBs from one galaxy in a time interval of several years has been estimated. Supernova explosions in binary systems accompanied by the formation of a short-lived pair of compact objects can be the sources of such events. If a short GRB is generated during the collision of a pair, then approximately each of ~300 short GRBs with redshift z must have an optical precursor - a supernova in the observer's time interval <2(1+z)yr. If the supernova explosion has the pattern of a hypernova, then a successive observation of long and short GRBs is possible. The scenario for the generation of multiple GRBs in collapsing galactic nuclei is also discussed.
Here we consider a non-perturbative description of the non-interacting resonant model using a scattering approach employed in JCP 152(24) 244126 (2020). We showed that such description coincides with the standard NEGF and Landauer-Buttiker approaches.
We prove that the height function associated with the uniform six-vertex model (or equivalently, the uniform homomorphism height function from $\mathbb Z^2$ to $\mathbb Z$) satisfies a central limit theorem, upon some logarithmic rescaling.
We study a derivative nonlinear Schr\"{o}dinger equation, allowing non-integer powers in the nonlinearity, $|u|^{2\sigma} u_x$. Making careful use of the energy method, we are able to establish short-time existence of solutions with initial data in the energy space, $H^1$. For more regular initial data, we establish not just existence of solutions, but also well-posedness of the initial value problem. These results hold for real-valued $\sigma\geq 1,$ while prior existence results in the literature require integer-valued $\sigma$ or $\sigma$ sufficiently large ($\sigma \geq 5/2$), or use higher-regularity function spaces.
We present the discovery of long-period, low-amplitude, g-mode pulsations in the intermediate He-rich hot subdwarf (sdOB) star Feige 46. Up until now only one other He-enriched sdOB star (LS IV -14116) was known to exhibit such pulsations. From our ground-based light curves of Feige 46, we extracted five independent periodicities ranging from 2294 s to 3400 s. We fitted our low-resolution, high signal-to-noise optical spectrum of the star with our grid of non-LTE model atmospheres and derived the following atmospheric parameters: Teff = 36120 $\pm$ 230 K, log g = 5.93 $\pm$ 0.04 and log N(He)/N(H) = -0.32 $\pm$ 0.03 (formal fitting errors only). These parameters are very similar to those of LS IV -14116 and place Feige 46 well outside of the instability strip where the hydrogen-rich g-mode sdB pulsators are found. We used the Gaia parallax and proper motion of Feige 46 to perform a kinematic analysis of this star and found that it likely belongs to the Galactic halo population. This is most certainly an intriguing and interesting result given that LS IV -14116 is also a halo object. The mechanism responsible for the pulsations in these two peculiar objects remains unclear but a possible scenario involves the $\epsilon$-mechanism. Although they are the only two members in their class of variable stars, these pulsators appear to have more in common than just their pulsation properties.
Broad band spectra of total and compact--scale radio emission from blazars, used in combination with kinematic information inferred from VLBI monitoring programs, can be applied successfully to better constrain the models of compact jets. We discuss here a ``hands-on'' approach for tying together the kinematic and spectral properties of radio emission from blazars.
We consider a simple, physical approach to the problem of marginally trapped surfaces in the Nonsymmetric Gravitational Theory (NGT). We apply this approach to a particular spherically symmetric, Wyman sector gravitational field, consisting of a pulse in the antisymmetric field variable. We demonstrate that marginally trapped surfaces do exist for this choice of initial data.
We report the discovery of the second compact elliptical (cE) galaxy SDSSJ150634.27+013331.6 in the nearby NGC5846 group by the Virtual Observatory (VO) workflow . This object (M_B = -15.98 mag, R_e = 0.24 kpc) becomes the fifth cE where the spatially-resolved kinematics and stellar populations can be obtained. We used archival HST WFPC2 images to demonstrate that its light profile has a two-component structure, and integrated photometry from GALEX, SDSS, UKIDSS, and Spitzer to build the multi-wavelength SED to constraint the star formation history (SFH). We observed this galaxy with the PMAS IFU spectrograph at the Calar-Alto 3.5m telescope and obtained two-dimensional maps of its kinematics and stellar population properties using the full-spectral fitting technique. Its structural, dynamical and stellar population properties suggest that it had a massive progenitor heavily tidally stripped by NGC5846.
We explain how stochastic TQFT supersymmetry can be made compatible with space supersymmetry. Taking the case of N=2 supersymmetric quantum mechanics, (the proof would be the same for the Wess-Zumino model), we determine the kernels that ensure the convergence of the stochastic process toward the standard path integral, under the condition that they are covariant under supersymmetry. They depend on a massive parameter M that can be chosen at will and modifies the course of the stochastic evolution, but the infinite stochastic time limit of the correlation functions is in fact independent on the choice of M.
As holographic description of BPS Wilson loops in ${\cal N}=3$ flavored ABJM theory with $N_f=k=1$, BPS M2-branes in $AdS_4\times N(1, 1)$ are studied in details. Two $1/3$-BPS membrane configurations are found. One of them is dual to the $1/3$-BPS Wilson loop of Gaiotto-Yin type. The regulated membrane action captures precisely the leading exponential behavior of the vacuum expectation values of $1/3$-BPS Wilson loops in the strong coupling limit, which was computed before using supersymmetric localization technique. Moreover, there is no BPS membrane with more supersymmetries in the background, under quite natural assumption on the membrane worldvolume. This suggests that there is no Wilson loop preserving more than 1/3 supersymmetries in such flavored ABJM theory.
In this paper, we study the surjectivity of adelic Galois representation associated to Drinfeld $\mathbb{F}_q[T]$-modules over $\mathbb{F}_q(T)$ of rank $2$ in the cases when $q$ is even or $q=3$.
Single-particle resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory. Taking the neutron resonant state $\nu 1g_{9/2}$ in $^{60}$Ca as an example, we examine the analyticity of the eigenvalue and eigenfunction for the Dirac equation with respect to the coupling constant by means of a $\pade$ approximant of the second kind. The RMF-ACCC approach is then applied to $^{122}$Zr and, for the first time, this approach is employed to investigate both the energies, widths and wave functions for $l\ne 0$ resonant states close to the continuum threshold. Predictions are also compared with corresponding results obtained from the scattering phase shift method.
A vector bundle on a projective variety has a natural cohomology if for every twist its cohomology is concentrated in a single degree. Eisenbud and Schreyer conjectured there should be vector bundles on $\mathbb{P}^1 \times \mathbb{P}^1$ with natural cohomology with respect to bundles $\mathcal{O}(1,0),\mathcal{O}(0,1)$ with prescribed Hilbert polynomial. We prove this conjecture.
Lov\'asz and Cherkassky discovered in the 1970s independently that if $ G $ is a finite graph with a given set $ T $ of terminal vertices such that $ G $ is inner Eulerian, then the maximal number of edge-disjoint paths connecting distinct vertices in $ T $ is $ \sum_{t\in T}\lambda(t, T-t) $ where $\lambda $ is the local edge-connectivity function. The optimality of a system of edge-disjoint $ T $-paths in the Lov\'asz-Cherkassky theorem is witnessed by the existence of certain cuts by Menger's theorem. The infinite generalisation of Menger's theorem by Aharoni and Berger (earlier known as the Erd\H{o}s-Menger Conjecture) together with the characterization of infinite Eulerian graphs due to Nash-Williams makes it possible to generalise the theorem for infinite graphs in a structural way. The aim of this paper is to formulate this generalisation and prove it for countable graphs.
We present an analysis of the clustering evolution of dark matter in four cold dark matter (CDM) cosmologies. We use a suite of high resolution, 17-million particle, N-body simulations which sample volumes large enough to give clustering statistics with unprecedented accuracy. We investigate both a flat and an open model with Omega_0=0.3, and two models with Omega=1, one with the standard CDM power spectrum and the other with the same power spectrum as the Omega_0=0.3 models. The amplitude of primordial fluctuations is set so that the models reproduce the observed abundance of rich galaxy clusters by the present day. The mass 2-point correlation function and power spectrum of all the simulations differ significantly from those of the observed galaxy distribution, in both shape and amplitude. Thus, for any of these models to provide an acceptable representation of reality, the distribution of galaxies must be biased relative to the mass in a non-trivial, scale-dependent, fashion. In the Omega=1 models the required bias is always greater than unity, but in the Omega_0=0.3 models an "antibias" is required on scales smaller than \sim 5\hmpc. The mass correlation functions in the simulations are well fit by recently published analytic models. The velocity fields are remarkably similar in all the models, whether they be characterised as bulk flows, 1-particle or pairwise velocity dispersions. This similarity is a direct consequence of our adopted normalisation. The small-scale pairwise velocity dispersion of the dark matter is somewhat larger than recent determinations from galaxy redshift surveys, but the bulk-flows predicted by our models are broadly in agreement with most available data.
The paper presents a dictionary integration algorithm using 3D morphable face models (3DMM) for pose-invariant collaborative-representation-based face classification. To this end, we first fit a 3DMM to the 2D face images of a dictionary to reconstruct the 3D shape and texture of each image. The 3D faces are used to render a number of virtual 2D face images with arbitrary pose variations to augment the training data, by merging the original and rendered virtual samples to create an extended dictionary. Second, to reduce the information redundancy of the extended dictionary and improve the sparsity of reconstruction coefficient vectors using collaborative-representation-based classification (CRC), we exploit an on-line elimination scheme to optimise the extended dictionary by identifying the most representative training samples for a given query. The final goal is to perform pose-invariant face classification using the proposed dictionary integration method and the on-line pruning strategy under the CRC framework. Experimental results obtained for a set of well-known face datasets demonstrate the merits of the proposed method, especially its robustness to pose variations.
A model of dark matter (DM) that communicates with the Standard Model (SM) exclusively through suppressed dimension five operator is discussed. The SM is augmented with a symmetry $U(1)_X \otimes Z_2$, where $U(1)_X$ is gauged and broken spontaneously by a very heavy decoupled scalar. The massive $U(1)_X$ vector boson ($X^\mu$) is stabilized being odd under unbroken $Z_2$ and therefore may contribute as the DM component of the universe. Dark sector field strength tensor $X^{\mu\nu}$ couples to the SM hypercharge tensor $B^{\mu\nu}$ via the presence of a heavier $Z_2$ odd real scalar $\Phi$, i.e. $1/\Lambda \; X^{\mu\nu}B_{\mu\nu}\Phi$, with $\Lambda$ being a scale of new physics. The freeze-in production of the vector boson dark matter feebly coupled to the SM is advocated in this analysis. Limitations of the so-called UV freeze-in mechanism that emerge when the maximum reheat temperature $T_\text{RH}$ drops down close to the scale of DM mass are discussed. The parameter space of the model consistent with the observed DM abundance is determined. The model easily and naturally avoids both direct and indirect DM searches. Possibility for detection at the Large Hadron Collider (LHC) is also considered. A Stueckelberg formulation of the model is derived.
In this paper we introduce a unified approach to deal with incidence problems between points and varieties over finite fields. More precisely, we prove that the number of incidences $I(\mathcal{P}, \mathcal{V})$ between a set $\mathcal{P}$ of points and a set $\mathcal{V}$ of varieties of a certain form satisfies $$\left\vert I(\mathcal{P},\mathcal{V})-\frac{|\mathcal{P}||\mathcal{V}|}{q^k}\right\vert\le q^{dk/2}\sqrt{|\mathcal{P}||\mathcal{V}|}.$$   This result is a generalization of the results of Vinh (2011), Bennett et al. (2014), and Cilleruelo et al. (2015). As applications of our incidence bounds, we obtain results on the pinned value problem and the Beck type theorem for points and spheres.   Using the approach introduced, we also obtain a result on the number of distinct distances between points and lines in $\mathbb{F}_q^2$, which is the finite field analogous of a recent result of Sharir et al. (2015).
We generate $\sim$ 100,000 model spectra of Type Ia Supernovae (SNIa) to form a spectral library for the purpose of building an Artificial Intelligence Assisted Inversion (AIAI) algorithm for theoretical models. As a first attempt, we restrict our studies to time around $B$-band maximum and compute theoretical spectra with a broad spectral wavelength coverage from 2000 $-$ 10000 ${\rm \AA}$ using the code TARDIS. Based on the library of theoretically calculated spectra, we construct the AIAI algorithm with a Multi-Residual Convolutional Neural Network (MRNN) to retrieve the contributions of different ionic species to the heavily blended spectral profiles of the theoretical spectra. The AIAI is found to be very powerful in distinguishing spectral patterns due to coupled atomic transitions and has the capacity of quantitatively measuring the contributions from different ionic species. By applying the AIAI algorithm to a set of well observed SNIa spectra, we demonstrate that the model can yield powerful constraints on the chemical structures of these SNIa. Using the chemical structures deduced from AIAI, we successfully reconstructed the observed data, thus confirming the validity of the method. We show that the light curve decline rate of SNIa is correlated with the amount of $^{56}$Ni above the photosphere in the ejecta. We detect a clear decrease of $^{56}$Ni mass with time that can be attributed to its radioactive decay. Our Code and model spectra are made available on the website \href{https://github.com/GeronimoChen/AIAI-Supernova}{https://github.com/GeronimoChen/AIAI-Supernova}.
The strong geodetic number, $\text{sg}(G),$ of a graph $G$ is the smallest number of vertices such that by fixing one geodesic between each pair of selected vertices, all vertices of the graph are covered. In this paper, the study of the strong geodetic number of complete bipartite graphs is continued. The formula for $\text{sg}(K_{n,m})$ is given, as well as a formula for the crown graphs $S_n^0$. Bounds on $\text{sg}(Q_n)$ are also discussed.
In this paper we study the complementarity spectrum of digraphs, with special attention to the problem of digraph characterization through this complementarity spectrum. That is, whether two non-isomorphic digraphs with the same number of vertices can have the same complementarity eigenvalues. The complementarity eigenvalues of matrices, also called Pareto eigenvalues, has led to the study of the complementarity spectrum of (undirected) graphs and, in particular, the characterization of undirected graphs through these eigenvalues is an open problem. We characterize the digraphs with one and two complementarity eigenvalues, and we give examples of non-isomorphic digraphs with the same complementarity spectrum.