ShantanuT01/DACTYL-Pretraining huggingface dataset:
A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau column-standard. An $i$-inverted Young tableau is a row-standard tableau with precisely $i$ inversion pairs, and may be interpreted as a generalization of (column-standard) Young tableau. Inverted Young tableau that lack repeated entries were introduced by Fresse to calculate the Betti numbers of Springer fibers in Type A, and were later developed as combinatorial objects in their own right by Beagley and Drube. This paper generalizes earlier notions of tableau inversions to row-standard tableaux with repeated entries, yielding an interesting new generalization of semistandard (as opposed to merely standard) Young tableaux. We develop a closed formula for the maximum numbers of inversion pairs for a row-standard tableau with a specific shape and content, and show that the number of $i$-inverted tableaux of a given shape is invariant under permutation of content. We then enumerate $i$-inverted Young tableaux for a variety of shapes and contents, and generalize an earlier result that places $1$-inverted Young tableaux of a general shape in bijection with $0$-inverted Young tableaux of a variety of related shapes.
Motion capture is the process of recording the movement of objects or people. It is used in military, entertainment, sports, and medical applications, and for validation of computer vision[2] and robotics. In filmmaking and video game development, it refers to recording actions of human actors, and using that information to animate digital character models in 2D or 3D computer animation. When it includes face and fingers or captures subtle
In this paper we construct super Yang-Mills theory in 10+2 dimensions, a number of dimensions that was not reached before in a unitary supersymmetric field theory, and show that this is the 2T-physics source of some cherished lower dimensional field theories. The much studied conformally exact N=4 Super Yang-Mills field theory in 3+1 dimensions is known to be a compactified version of N=1 SYM in 9+1 dimensions, while M(atrix) theory is obtained by compactifications of the 9+1 theory to 0 dimensions (also 0+1 and others). We show that there is a deeper origin of these theories in two higher dimensions as they emerge from the new theory with two times. Pursuing various alternatives of gauge choices, solving kinematic equations and/or dimensional reductions of the 10+2 theory, we suggest a web of connections that include those mentioned above and a host of new theories that relate 2T-physics and 1T-physics field theories, all of which have the 10+2 theory as the parent. In addition to establishing the higher spacetime underpinnings of these theories, a side benefit could be that in principle our approach can be used to develop new computational techniques.
Here we apply the full Will-Nordtvedt version of the Parameterized Post-Newtonian (PPN) formalism to a class of General Relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant $G$ is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the External Potential Effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales, for any of them the Solar System bounds need to be considered.
It is well known that the flat radio spectrum is a common property in the spectral energy distribution of blazars. Although the one-zone leptonic models are generally successful in explaining the multi-wave band emission, they are problematic in reproducing the radio spectrum. In the study of Mrk 421, one-zone models suggest that in order to avoid overproducing the radio flux, the minimum electron Lorentz factor should be larger than a few hundred at least, even considering the synchrotron self-absorption effect. This result suggests that the model predicted spectral index in the radio band of Mrk 421 should be -1/3. On the basis of this result, by assuming there is a neglected region that will also contribute the radio emission and its electron energy index is naturally originate from the simplest first-order Fermi acceleration mechanism, we can get a superimposed flat radio spectrum. In this paper, a two-zone model is proposed to reproduce the quiescent state spectral energy distribution of Mrk 421. In addition to taking into account the emission from a conventional radiation zone, we further consider the emission from the acceleration zone in which particles are accelerated at a shock front. With the present model, our fitting result suggests that the low frequency flat radio spectrum of Mrk 421 might be explained as a superposition of the synchrotron emission from acceleration zone and radiation zone.
Cuspy triaxial potentials admit a large number of chaotic orbits, which moreover exhibit extreme "stickiness" that makes the process of chaotic mixing surprisingly inefficient. Environmental effects, modeled as noise and/or periodic driving, help accelerate phase space transport but probably not as much as in simpler potentials. This could mean that cuspy triaxial ellipticals cannot exist as time-independent systems.
The interplay between different orders is of fundamental importance in physics. The spontaneous, symmetry-breaking charge order, responsible for the stripe or the nematic phase, has been of great interest in many contexts where strong correlations are present, such as high-temperature superconductivity and quantum Hall effect. In this article we show the unexpected result that in an interacting two-dimensional electron system, the robustness of the nematic phase, which represents an order in the charge degree of freedom, not only depends on the orbital index of the topmost, half-filled Landau level, but it is also strongly correlated with the magnetic order of the system. Intriguingly, when the system is fully magnetized, the nematic phase is particularly robust and persists to much higher temperatures compared to the nematic phases observed previously in quantum Hall systems. Our results give fundamental new insight into the role of magnetization in stabilizing the nematic phase, while also providing a new knob with which it can be effectively tuned.
This paper is a review of previous works on the stochastic background of gravitational waves (SBGWs) which has been discussed in various peer-reviewed journals and international conferences. The SBGWs is analyzed with the aid of the Wilkinson Microwave Anisotropy Probe (WMAP) data. We emphasize that, in general, in previous works in the literature about the SBGWs, old Cosmic Background Explorer (COBE) data were used. After this, we want to face the problem of how the SBGWs and f(R) gravity (where f(R) is a function of the Ricci scalar R) can be related, showing, vice versa, that a revealed SBGWs could be a powerful probe for a given theory of gravity. In this way, it will also be shown that the conform treatment of SBGWs can be used to parametrize in a natural way f(R) theories. Some interesting examples which have been recently discussed in the literature will be also analysed. The presence and the potential detection of the SBGWs is quite important in the framework of the debate on high-frequency gravitational waves (HFGWs) too. Recently, the importance of HFGWs has been emphasized in some papers in the literature.
In this note, we extend work of Farkas and Rim\'anyi on applying quadric rank loci to finding divisors of small slope on the moduli space of curves by instead considering all divisorial conditions on the hypersurfaces of a fixed degree containing a projective curve. This gives rise to a large family of virtual divisors on $\overline{\mathcal{M}_g}$. We determine explicitly which of these divisors are candidate counterexamples to the Slope Conjecture. The potential counterexamples exist on $\overline{\mathcal{M}_g}$, where the set of possible values of $g\in \{1,\ldots,N\}$ has density $\Omega(\log(N)^{-0.087})$ for $N>>0$. Furthermore, no divisorial condition defined using hypersurfaces of degree greater than 2 give counterexamples to the Slope Conjecture, and every divisor in our family has slope at least $6+\frac{8}{g+1}$.
Solutions SP00, SM00 and FA00 of nucleon-nucleon (NN) phase shift analyzes by Arndt et al. are used in optical model studies. The partial waves, single channels J.leq.7 and coupled channels J.leq.6, are scrutinized. The radial probability distributions and losses of flux are used to identify the known Delta and N* resonances as well as anticipated other structures. The energy interval extends to 3 GeV.
In the first part of this article I determine the geometry of a slowly rotating black hole deformed by generic tidal forces created by a remote distribution of matter. The metric of the deformed black hole is obtained by integrating the Einstein field equations in a vacuum region of spacetime bounded by r < r_max, with r_max a maximum radius taken to be much smaller than the distance to the remote matter. The tidal forces are assumed to be weak and to vary slowly in time, and the metric is expressed in terms of generic tidal quadrupole moments E_{ab} and B_{ab} that characterize the tidal environment. The metric incorporates couplings between the black hole's spin vector and the tidal moments, and captures all effects associated with the dragging of inertial frames. In the second part of the article I determine the tidal moments by immersing the black hole in a larger post-Newtonian system that includes an external distribution of matter; while the black hole's internal gravity is allowed to be strong, the mutual gravity between the black hole and the external matter is assumed to be weak. The post-Newtonian metric that describes the entire system is valid when r > r_min, where r_min is a minimum distance that must be much larger than the black hole's radius. The black-hole and post-Newtonian metrics provide alternative descriptions of the same gravitational field in an overlap r_min < r < r_max, and matching the metrics determine the tidal moments, which are expressed as post-Newtonian expansions carried out through one-and-a-half post-Newtonian order. Explicit expressions are obtained in the specific case in which the black hole is a member of a post-Newtonian two-body system.
We present the first observational limits to the ultra-high energy (UHE) neutrino flux from the Galactic Center, and from Centaurus A which is the nearest active galactic nucleus (AGN). These results are based on our "Lunar UHE Neutrino Astrophysics using the Square Kilometer Array" (LUNASKA) project experiments at the Australia Telescope Compact Array (ATCA). We also derive limits for the previous experiments and compare these limits with expectations for acceleration and super-heavy dark matter models of the origin of UHE cosmic rays.
We present results for the QUEST RR Lyrae Survey at low galactic latitude, conducted entirely with observations obtained with the QUEST mosaic camera and the 1.0/1.5m J\"urgen Stock Schmidt telescope at the National Observatory of Venezuela. The survey spans an area of 476 sq. deg on the sky, with multi-epoch observations in the V, R and I photometric bands for 6.5x10^6 stars in the galactic latitude range 30<= b(deg) <=+25, in a direction close to the Galactic Anticenter 190<= l(deg)<= 230. The variability survey has a typical number of 30 observations per object in V and I and ~25 in R, with up to ~120-150 epochs in V and I and up to ~100 in R in the best sampled regions. The completeness magnitudes of the survey are V=R=18.5 mag, and I=18.0 mag. We identified 211 RR Lyrae stars, 160 bona fide stars of type ab and 51 candidates of type c, ours being the first deep RR Lyrae survey conducted at low galactic latitude.The completeness of the RR Lyrae survey was estimated in >95 per cent and ~85 per cent for RRab and RRc stars respectively. Photometric metallicities were computed based on the light curves and individual extinctions calculated from minimum light colours for each RRab star. Distances were obtained with typical errors ~7 per cent. The RR Lyrae survey simultaneously spans a large range of heliocentric distances 0.5<= R_hel(kpc)<=40 and heights above the plane -15<=z(kpc)<=+20, with well known completeness across the survey area, making it an ideal set for studying the struc ture of the Galactic thick disk.
In this paper we make a series of numerical experiments to support Greenberg's $p$-rationality conjecture, we present a family of $p$-rational biquadratic fields and we find new examples of $p$-rational multiquadratic fields. In the case of multiquadratic and multicubic fields we show that the conjecture is a consequence of the Cohen-Lenstra-Martinet heuristic and of the conjecture of Hofmann and Zhang on the $p$-adic regulator, and we bring new numerical data to support the extensions of these conjectures. We compare the known algorithmic tools and propose some improvements.
We present a map of the Cosmic Microwave Background (CMB) anisotropies induced by the late Integrated Sachs Wolfe effect. The map is constructed by combining the information of the WMAP 7-yr CMB data and the NRAO VLA Sky Survey (NVSS) through a linear filter. This combination improves the quality of the map that would be obtained using information only from the Large Scale Structure data. In order to apply the filter, a given cosmological model needs to be assumed. In particular, we consider the standard LCDM model. As a test of consistency, we show that the reconstructed map is in agreemet with the assumed model, which is also favoured against a scenario where no correlation between the CMB and NVSS catalogue is considered.
Oscillation frequency of spin torque oscillator with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer is theoretically investigated by taking into account the field-like torque. It is shown that the field-like torque plays an important role in finding the balance between the energy supplied by the spin torque and the dissipation due to the damping, which results in a steady precession. The validity of the developed theory is confirmed by performing numerical simulations based on the Landau-Lifshitz-Gilbert equation.
The author constructs the moduli of representations whose images generate the subalgebra of upper triangular matrices (up to inner automorphisms) of the full matrix ring for any groups and any monoids.
The Sagdeev-Zaslavski (SZ) equation for wave turbulence is analytically derived, both in terms of generating function and of multi-point pdf, for weakly interacting waves with initial random phases. When also initial amplitudes are random, the one-point pdf equation is derived. Such analytical calculations remarkably agree with results obtained in totally different fashions. Numerical investigations of the two-dimensional nonlinear Schroedinger equation (NLSE) and of a vibrating plate prove that: (i) generic Hamiltonian 4-wave systems rapidly attain a random distribution of phases independently of the slower dynamics of the amplitudes, vindicating the hypothesis of initially random phases; (ii) relaxation of the Fourier amplitudes to the predicted stationary distribution (exponential) happens on a faster timescale than relaxation of the spectrum (Rayleigh-Jeans distribution); (iii) the pdf equation correctly describes dynamics under different forcings: the NLSE has an exponential pdf corresponding to a quasi-gaussian solution, like the vibrating plates, that also show some intermittency at very strong forcings.
The electromagnetic (EM) follow-up of a gravitational wave (GW) event requires to scan a wide sky region, defined by the so called "skymap", for the detection and identification of a transient counterpart. We propose a novel method that exploits information encoded in the GW signal to construct a "detectability map", which represents the time-dependent ("when") probability to detect the transient at each position of the skymap ("where"). Focusing on the case of a neutron star binary inspiral, we model the associated short gamma-ray burst afterglow and macronova emission, using the probability distributions of binary parameters (sky position, distance, orbit inclination, mass ratio) extracted from the GW signal as inputs. The resulting family of possible lightcurves is the basis to construct the detectability map. As a practical example, we apply the method to a simulated GW signal produced by a neutron star merger at 75 Mpc whose localization uncertainty is very large (about 1500 square degrees). We construct observing strategies based on the detectability maps for optical, infrared and radio facilities, taking VST, VISTA and MeerKAT as prototypes. Assuming limiting fluxes of r ~ 24.5, J ~ 22.4 (AB magnitudes) and 500 uJy @ 1.4 GHz for ~ 1000 s of exposure each, the afterglow and macronova emissions are successfully detected with a minimum observing time of 7, 15 and 5 hours respectively.
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture, where some portions are made time-dependent. This can provide a favorable complexity trade-off as the algorithm scales exponentially better with derivatives of the time-dependent component than the original Hamiltonian. We show that this leads to an exponential improvement in gate complexity for simulating some classes of diagonally dominant Hamiltonian. Additionally we show that this can reduce the gate-complexity scaling for simulating $N$-site Hubbard models for time $t$ with arbitrary long-range interactions as well as reduce the cost of quantum chemistry simulations within a similar-sized plane-wave basis to $\widetilde{\mathcal{O}}(N^2t)$ from $\widetilde{\mathcal{O}}(N^{11/3}t)$. We also show a quadratic improvement in query complexity for simulating sparse time-dependent Hamiltonians, which may be of independent interest.
We study one-dimensional spinless fermions at zero and finite temperature T using the density matrix renormalization group. We consider nearest as well as next-nearest neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system alogrithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power law suppression of the momentum distribution n(k) function at T=0 can be directly observed over several orders of magnitude. At finite temperature, we show that n(k) obeys a scaling relation. The Luttinger liquid parameter and the renormalized Fermi velocity can be extracted from the density response function, the specific heat, and/or the susceptibility without the need to carry out any finite-size analysis. We illustrate that the energy scale below which Luttinger liquid power laws manifest vanishes as the half-filled system is driven into a gapped phase by large interactions.
Matched-filtering for the identification of compact object mergers in gravitational-wave antenna data involves the comparison of the data stream to a bank of template gravitational waveforms. Typically the template bank is constructed from phenomenological waveform models since these can be evaluated for an arbitrary choice of physical parameters. Recently it has been proposed that singular value decomposition (SVD) can be used to reduce the number of templates required for detection. As we show here, another benefit of SVD is its removal of biases from the phenomenological templates along with a corresponding improvement in their ability to represent waveform signals obtained from numerical relativity (NR) simulations. Using these ideas, we present a method that calibrates a reduced SVD basis of phenomenological waveforms against NR waveforms in order to construct a new waveform approximant with improved accuracy and faithfulness compared to the original phenomenological model. The new waveform family is given numerically through the interpolation of the projection coefficients of NR waveforms expanded onto the reduced basis and provides a generalized scheme for enhancing phenomenological models.
We compute the O(alpha_s) QCD corrections to charged triple vector boson production at a hadron collider, i.e. the processes pp -> ZZW + X and pp -> WWW + X. Intermediate Higgs boson exchange effects, spin correlations from leptonic vector boson decays, and off-shell contributions are all taken into account. Results are implemented in a fully flexible Monte Carlo program that allows for an easy customization of kinematical cuts and variation of the factorization and renormalization scales. We analyze the dependence of the differential cross sections under scale variations and present distributions where the QCD corrections strongly modify the leading-order results.
Optimal estimates on the asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations \[-\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\,x\in \mathbb{R}^{N},\] where $1<p<N, 0\leq\mu<\left({(N-p)}/{p}\right)^{p}$ and $Q\in L^{\infty}(\mathbb{R}^{N})$.
Recent developments in the chemical modelling of cometary comae are described. We discuss the cyanide chemistry and present new HCN observations of the recent comet C/2002 C1 (Ikeya-Zhang). The connection between interstellar and cometary organic molecules is discussed from the perspective of recent theories of interstellar gas-grain chemistry.
We implement the mechanism of spontaneous CP violation in the 3-3-1 model with right-handed neutrinos and recognize their sources of CP violation. Our main result is that the mechanism works already in the minimal version of the model and new sources of CP violation emerges as an effect of new physics at energies higher than the electroweak scale.
We present a generative model which can automatically summarize the stroke composition of free-hand sketches of a given category. When our model is fit to a collection of sketches with similar poses, it discovers and learns the structure and appearance of a set of coherent parts, with each part represented by a group of strokes. It represents both consistent (topology) as well as diverse aspects (structure and appearance variations) of each sketch category. Key to the success of our model are important insights learned from a comprehensive study performed on human stroke data. By fitting this model to images, we are able to synthesize visually similar and pleasant free-hand sketches.
The expectation of explaining cosmological observations without requiring new energy sources is forsooth worthy of investigation. In this letter, a new kind of Cardassian models, called exponential Cardassian models, for the late-time universe are investigated in the context of the spatially flat FRW universe scenario. We fit the exponential Cardassian models to current type Ia supernovae data and find they are consistent with the observations. Furthermore, we point out that the equation-of-state parameter for the effective dark fluid component in exponential Cardassian models can naturally cross the cosmological constant divide $w=-1$ that observations favor mildly without introducing exotic material that destroy the weak energy condition.