ShantanuT01/DACTYL-Pretraining huggingface dataset:
We define a new statistic on any Weyl group which we call the odd length and which reduces, for Weyl groups of types $A$, $B$, and $D$, the the statistics by the same name that have already been defined and studied in [10], [13], [14], and [3]. We show that the signed (by length) generating function of the odd length always factors nicely except possibly in type $E_8$, and we obtain multivariate analogues of these factorizations in types $B$ and $D$.
In this paper we define the fractional Cox-Ingersoll-Ross process as $X_t:=Y_t^2\mathbf{1}_{\{t<\inf\{s>0:Y_s=0\}\}}$, where the process $Y=\{Y_t,t\ge0\}$ satisfies the SDE of the form $dY_t=\frac{1}{2}(\frac{k}{Y_t}-aY_t)dt+\frac{\sigma}{2}dB_t^H$, $\{B^H_t,t\ge0\}$ is a fractional Brownian motion with an arbitrary Hurst parameter $H\in(0,1)$. We prove that $X_t$ satisfies the stochastic differential equation of the form $dX_t=(k-aX_t)dt+\sigma\sqrt{X_t}\circ dB_t^H$, where the integral with respect to fractional Brownian motion is considered as the pathwise Stratonovich integral. We also show that for $k>0$, $H>1/2$ the process is strictly positive and never hits zero, so that actually $X_t=Y_t^2$. Finally, we prove that in the case of $H<1/2$ the probability of not hitting zero on any fixed finite interval by the fractional Cox-Ingersoll-Ross process tends to 1 as $k\rightarrow\infty$.
We investigate a quasi-local energy naturally introduced by Kodama's prescription for a spherically symmetric space-time with a positive cosmological constant $\Lambda$. We find that this quasi-local energy is well behaved inside a cosmological horizon. However, when there is a scalar field with a long enough Compton wavelength, the quasi-local energy diverges in the course of its time evolution outside the cosmological horizon. This means that the quasi-local energy has a meaning only inside the cosmological horizon.
The objective of this work is to numerically integrate in space and time the effective-mass Schrodinger equation for an excitonic wave packet in a coupled quantum-well system under a time-dependent electric field. Taking as a starting point a time-dependent Hartree potential, we derive the nonlinear dynamical evolution of the excitonic wave function. We found that the system resonant condition can be modified owing to the reaction field generated by a charge dynamically trapped in the quantum-well pair. As a result, this study raises a broader question: is it possible to create an electrostatic trap for indirect excitons at high ac frequencies? We conclude there is a possibility of having another kind of terahertz electromagnetic radiation emerging from an excitonic trap.
We analyze deep g' and r' band data of 97 galaxy clusters imaged with MegaCam on the Canada-France-Hawaii telescope. We compute the number of luminous (giant) and faint (dwarf) galaxies using criteria based on the definitions of de Lucia et al. (2007). Due to excellent image quality and uniformity of the data and analysis, we probe the giant-to-dwarf ratio (GDR) out to z ~ 0.55. With X-ray temperature (Tx) information for the majority of our clusters, we constrain, for the first time, the Tx-corrected giant and dwarf evolution separately. Our measurements support an evolving GDR over the redshift range 0.05 < z < 0.55. We show that modifying the (g'-r'), m_r' and K-correction used to define dwarf and giant selection do not alter the conclusion regarding the presence of evolution. We parameterize the GDR evolution using a linear function of redshift (GDR = alpha * z + beta) with a best fit slope of alpha = 0.88 +/- 0.15 and normalization beta = 0.44 +/- 0.03. Contrary to claims of a large intrinsic scatter, we find that the GDR data can be fully accounted for using observational errors alone. Consistently, we find no evidence for a correlation between GDR and cluster mass (via Tx or weak lensing). Lastly, the data suggest that the evolution of the GDR at z < 0.2 is driven primarily by dry merging of the massive giant galaxies, which when considered with previous results at higher redshift, suggests a change in the dominant mechanism that mediates the GDR.
We consider three types of set-systems that have interesting applications in algebraic combinatorics and representation theory: maximal collections of the so-called strongly separated, weakly separated, and chord separated subsets of a set $[n]=\{1,2,\ldots,n\}$. These collections are known to admit nice geometric interpretations; namely, they are bijective, respectively, to rhombus tilings on the zonogon $Z(n,2)$, combined tilings on $Z(n,2)$, and fine zonotopal tilings (or `cubillages') on the 3-dimensional zonotope $Z(n,3)$. We describe interrelations between these three types of set-systems in $2^{[n]}$, by studying interrelations between their geometric models. In particular, we completely characterize the sets of rhombus and combined tilings properly embeddable in a fixed cubillage, explain that they form distributive lattices, give efficient methods of extending a given rhombus or combined tiling to a cubillage, and etc.
We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics. It asserts that if a set of states can be distinguished with high probability, they can be distinguished by a measurement that leaves the states almost invariant, including correlation with a reference system. While GMP is satisfied in both classical and quantum theories, we show, within the framework of general probabilistic theories, that it imposes strong restrictions on the law of physics. First, the measurement uncertainty of a pair of observables cannot be significantly larger than the preparation uncertainty. Consequently, the strength of the CHSH nonlocality cannot be maximal. The parameter in the stretched quantum theory, a family of general probabilistic theories that includes the quantum theory, is also limited. Second, the conditional entropy defined in terms of a data compression theorem satisfies the chain inequality. Not only does it imply information causality and Tsirelson's bound, but it singles out the quantum theory from the stretched one. All these results show that GMP would be one of the principles at the heart of quantum mechanics.
We study the stability in the inverse problem of determining the time dependent zeroth-order coefficient $q(t,x)$ arising in the wave equation, from boundary observations. We derive, in dimension $n\geq 2$, a log-type stability estimate in the determination of $q$ from the Dirichlet-to-Neumann map, in a subset of our domain assuming that it is known outside this subset. Moreover, we prove that we can extend this result to the determination of $q$ in a larger region, and then in the whole domain provided that we have much more data.
By use of the resonating group method, the Delta K, Lambda K, and Sigma K states are further dynamically studied in the extended chiral SU(3) quark model based on our previous work. Similar to the results given by the original chiral SU(3) quark model, the calculated results here still show that the interactions of Delta K with isospin I=1 and Sigma K with isospin I=1/2 are attractive, which can consequently lead to Delta K and Sigma K quasibound states. When the channel coupling of Lambda K and Sigma K is considered, the calculated phase shifts show a sharp resonance between the thresholds of these two channels with spin-parity J^P=1/2^-.
In this work, we explore the problem of generating fantastic special-effects for the typography. It is quite challenging due to the model diversities to illustrate varied text effects for different characters. To address this issue, our key idea is to exploit the analytics on the high regularity of the spatial distribution for text effects to guide the synthesis process. Specifically, we characterize the stylized patches by their normalized positions and the optimal scales to depict their style elements. Our method first estimates these two features and derives their correlation statistically. They are then converted into soft constraints for texture transfer to accomplish adaptive multi-scale texture synthesis and to make style element distribution uniform. It allows our algorithm to produce artistic typography that fits for both local texture patterns and the global spatial distribution in the example. Experimental results demonstrate the superiority of our method for various text effects over conventional style transfer methods. In addition, we validate the effectiveness of our algorithm with extensive artistic typography library generation.
I discuss the validity of a result put forward recently by Chomaz and Gulminelli [Physica A 330 (2003) 451] concerning the equivalence of two definitions of first-order phase transitions. I show that distributions of zeros of the partition function fulfilling the conditions of the Yang-Lee Theorem are not necessarily associated with nonconcave microcanonical entropy functions or, equivalently, with canonical distributions of the mean energy having a bimodal shape, as claimed by Chomaz and Gulminelli. In fact, such distributions of zeros can also be associated with concave entropy functions and unimodal canonical distributions having affine parts. A simple example is worked out in detail to illustrate this subtlety.
We compute the holographic entanglement entropy and subregion complexity of spherical boundary subregions in the uncharged and charged AdS black hole backgrounds, with the \textbf{change} in these quantities being defined with respect to the pure AdS result. This calculation is done perturbatively in the parameter $\frac{R}{z_{\rm h}}$, where $z_{\rm h}$ is the black hole horizon and $R$ is the radius of the entangling region. We provide analytic formulae for these quantities as functions of the boundary spacetime dimension $d$ including several orders higher than previously computed. We observe that the change in entanglement entropy has definite sign at each order and subregion complexity has a negative sign relative to entanglement entropy at each of those orders (except at first order or in three spacetime dimensions, where it vanishes identically).   We combine pre-existing work on the "complexity equals volume" conjecture and the conjectured relationship between Fisher information and bulk entanglement to suggest a refinement of the so-called first law of entanglement thermodynamics by introducing a work term associated with complexity. This extends the previously proposed first law, which held to first order, to one which holds to second order. We note that the proposed relation does not hold to third order and speculate on the existence of additional information-theoretic quantities that may also play a role.
Non-trivial spin structures in itinerant magnets can give rise to topological Hall effect (THE) due to the interacting local magnetic moments and conductive electrons. While, in series of materials, THE has mostly been observed at low temperatures far below room temperature (RT) limiting its potential applications. Here, we report the anisotropic anomalous Hall effect (AHE) near RT in LaMn2Ge2, a noncollinear ferromagnetic (FM) with Curie temperature TC=325 K. Large topological Hall resistivity of ~1.0 10-6 ohmcm in broad temperature range (190 K <T< 300 K) is realized as field (H) parallel to the ab-plane (H // ab) and current along c axis (I // c), in contrast to the conventional AHE for H // c and I // ab. The emergence of THE is attributed to the spin chirality of noncoplanar spin configurations stabilized by thermal fluctuation during spin flop process. Moreover, the constructed temperature-field (H-T) phase diagrams based on the isothermal topological Hall resistivity reveal a field-induced transition from the noncoplanar spin configuration to polarized ferromagnetic states. Our experimental realization of large THE near RT highlights LaMn2Ge2 as a promising system for functional applications in novel spintronic devices.
We prove the existence of positive solutions to a sys- tem of k non-linear elliptic equations corresponding to standing- wave k-uples solutions to a system of non-linear Klein-Gordon equations. Our solutions are characterised by a small energy/charge ratio, appropriately defined.
The probability distribution of the velocity of gas molecules in a closed container is described by the kinetic theory of gases. When molecules collide or impact the walls of a container, they exchange energy and momentum in accordance with Newton's laws of motion. Between collisions, the trajectory of individual molecules is a straight line, neglecting gravity. During the formation of a galaxy, the stars are constrained to a region of space and exchange energy and momentum in a manner similar to molecules. In this paper, an exact model of an ideal gas is derived and analyzed to determine the probability distribution of the molecular velocities, which are then compared with the probability distribution of velocities associated with stars during galaxy formation.
Inertia effects in magnetization dynamics are theoretically shown to result in a different type of spin waves, i.e. nutation surface spin waves, which propagate at terahertz frequencies in in-plane magnetized ferromagnetic thin films. Considering the magnetostatic limit, i.e. neglecting exchange coupling, we calculate dispersion relation and group velocity, which we find to be slower than the velocity of conventional (precession) spin waves. In addition, we find that the nutation surface spin waves are backward spin waves. Furthermore, we show that inertia causes a decrease of the frequency of the precession spin waves, namely magnetostatic surface spin waves and backward volume magnetostatic spin waves. The magnitude of the decrease depends on the magnetic properties of the film and its geometry.
Based on the Liouville-von Neumann equation, we obtain closed system of equations for the description of a qutrit or coupled qutrits in arbitrary time-dependent external magnetic field. The dependence of the dynamics on the initial states and magnetic field modulation is studied analytically and numerically. We compare the relative entanglement measure's dynamics in the bi-qutrit system with permutation particle symmetry. We find the magnetic field modulation which retains the entanglement in the system of two coupled qutrits. Analytical formulas for entanglement measures in the chain from 2 to 6 qutrits are presented.
Although commercial and open-source software exist to reconstruct a static object from a sequence recorded with an RGB-D sensor, there is a lack of tools that build rigged models of articulated objects that deform realistically and can be used for tracking or animation. In this work, we fill this gap and propose a method that creates a fully rigged model of an articulated object from depth data of a single sensor. To this end, we combine deformable mesh tracking, motion segmentation based on spectral clustering and skeletonization based on mean curvature flow. The fully rigged model then consists of a watertight mesh, embedded skeleton, and skinning weights.
We investigate the charged Higgs boson signal at the LHC using its dominant production and decay modes with triple b-tagging, i.e. $tH^- \to t\bar tb \to b\bar bb W^+ W^-$, followed by leptonic decay of one W and hadronic decay of the other. We consider the continuum background from the associated production of $t\bar t$ with a b- or a light quark or gluon jet, which can be mis-tagged as b-jet. We reconstruct the top quark masses to identify the 3rd b-jet accompanying the $t\bar t$ pair, and use its p_T distribution to distinguish the signal from the background. Combining this with the reconstruction of the $H^\pm$ mass gives a viable signature over two interesting regions of the parameter space - i.e. $\tan\beta \sim 1$ and $\sim m_t/m_b$.
We investigated narrow line Seyfert 1 galaxies (NLS1s) at optical, mid-infrared (MIR) and X-ray wavelengths, comparing them to the broad line active galactic nuclei (BLAGNs). We found that black hole mass, coronal line luminosities, X-ray hardness ratio and X-ray, optical and MIR luminosities are higher for the BLAGNs than for NLS1s, while policyclic aromatic hydrocarbon (PAH) contribution and the accretion rates are higher for the NLS1s. Furthermore, we found some trends among spectral parameters that NLS1s have and BLAGNs do not have. The evolution of FWHM(H$\beta$) with the luminosities of MIR and coronal lines, continuum luminosities, PAH contribution, H$\beta$ broad line luminosity, FWHM[O\,III] and EW(H$\beta$NLR), are important trends found for NLS1s. That may contribute to the insight that NLS1s are developing AGNs, growing their black holes, while their luminosities and FWHM(H$\beta$) consequently grow, and that BLAGNs are mature, larger objects of slower and/or different evolution. Black hole mass is related to PAH contribution only for NLS1s, which may suggest that PAHs are more efficiently destroyed in NLS1s.
The mechanism of particle mass generation in the Standard Model is discussed. It is shown that non-zero vacuum expectation value of a scalar field together with the proper symmetry of the Lagrangian allow a certain class of scalar field potentials providing generation of gauge boson and fermion masses and keeping the electroweak sector of the model unchanged. Applying the minimality principle and certain additional conditions one can reduce the number of free parameters in the model. Possible phenomenological consequences in the scalar sector for different choices of the potential are discussed.
Observations of multi-wavelength and therefore height-dependent information following events throughout the solar atmosphere and unambiguously assigning a relation between these rapidly evolving layers are rare and difficult to obtain. Yet, they are crucial for our understanding of the physical processes that couple the different regimes in the solar atmosphere. We characterize the exploding granule event with simultaneous observations of Hinode spectroplarimetric data in the solar photosphere and Hinode broadband CaIIH images combined with Interface Region Imaging Spectrograph (IRIS) slit spectra. We follow the evolution of an exploding granule and its connectivity throughout the atmosphere and analyze the dynamics of a magnetic element that has been affected by the abnormal granule. In addition to magnetic flux maps we use a local correlation tracking method to infer the horizontal velocity flows in the photosphere and apply a wavelet analysis on several IRIS chromospheric emission features such as MgIIk2v and MgIIk3 to detect oscillatory phenomena indicating wave propagation. During the vigorous expansion of the abnormal granule we detect radially outward horizontal flows, causing, together with the horizontal flows from the surrounding granules, the magnetic elements in the bordering intergranular lanes to be squeezed and elongated. In reaction to the squeezing, we detect a chromospheric intensity and velocity oscillation pulse which we identify as an upward traveling hot shock front propagating clearly through the IRIS spectral line diagnostics of MgIIh&k. Conclusion: Exploding granules can trigger upward-propagating shock fronts that dissipate in the chromosphere.
The mm to sub-mm spectrum of Sgr A* at the Galactic center, as well as its polarization characteristics, are consistent with the inner 10 Schwarzschild radii of a tight Keplerian emitting region of hot, magnetized, orbiting gas. This plasma may also be the source through self-Comptonization of the X-rays detected by Chandra. It has long been suspected that the circularization region between the quasi-spherical infall at large radii, and this inner zone, is responsible for producing the rest of Sgr A*'s spectrum. In this paper, we report the results of a detailed study of this region. First, the combination of existing cm and X-ray data preclude the possibility of producing the observed strong 1.36 GHz radio flux via thermal synchrotron within a bounded flow. If Sgr A*'s radio spectrum is produced by accreting gas, it appears that a non-thermal particle distribution is a necessity. Second, if this is the correct picture for how Sgr A*'s spectrum is produced, it appears that the Chandra-detected X-rays may originate either from self-Comptonization in the inner Keplerian region, or from optically-thin nonthermal synchrotron emission in the much larger, circularization zone, extending up to 500 Schwarzschild radii or more. This is a question that should be answered by upcoming broadband observations, since the mm-bump and X-rays are strongly correlated in the former case, whereas the X-rays are strongly correlated to the cm-radio flux in the latter. In addition, X-rays produced in the circularized gas could show periodic or quasi-periodic variations, but not those produced via nonthermal synchrotron emission much farther out.
This paper proposes the Parallel WiSARD Object Tracker (PWOT), a new object tracker based on the WiSARD weightless neural network that is robust against quantization errors. Object tracking in video is an important and challenging task in many applications. Difficulties can arise due to weather conditions, target trajectory and appearance, occlusions, lighting conditions and noise. Tracking is a high-level application and requires the object location frame by frame in real time. This paper proposes a fast hybrid image segmentation (threshold and edge detection) in YcbCr color model and a parallel RAM based discriminator that improves efficiency when quantization errors occur. The original WiSARD training algorithm was changed to allow the tracking.
We look at solutions (both BPS and non-BPS) of the $\mathbb{CP}^{N-1}$ model on $\mathbb{R} \times S^1$ (with twisted boundary conditions), in particular by using a conformal mapping technique, and we show how to interpret these solutions by decomposing them into expressions describing constituent solitons. We point out the problems that may arise (for non-BPS solutions) when one naively looks at the clustering properties of these solutions. This could lead to misunderstandings when studying extrapolations between small and large compactification radii.
Lectures Given at the Nato Advanced Study Institute-Particle Production in Highly Excited Matter Il Ciocco, Italy July 1992 figure available on request. Input harvmac.tex
Diffuse interstellar bands (DIBs) can trace different conditions of the ISM along the sightline toward the observed stars. A small survey was made in optical wavelengths, producing high resolution and high signal to noise spectra. We present measurements of 19 DIBs' properties in 50 sightlines towards hot stars, distributed at a variety of galactic coordinates and interstellar reddening. Equivalent widths were obtained by fitting asymmetric Gaussian and variable continuum to DIBs. Conditions of the ISM were calculated from 8 atomic and molecular interstellar lines. Two distinctively different types of DIBs were identified, by carefully comparing correlation coefficients between DIBs and reddening and by different behaviour in UV shielded ($\zeta$) and non-shielded ($\sigma$) sightlines. A ratio of DIBs at 5780 \AA\ and~5797 \AA\ proved to be reliable enough to distinguish between two different sightline types. Based on linear relations between DIB equivalent width and reddening for $\sigma$ and $\zeta$ sightlines, we divide DIBs into type {\sc i} (where both linear relations are similar) and type {\sc ii} (where they are significantly different). Linear relation for $\zeta$ type sightlines always show a higher slope and larger x-intercept parameter than the relation for $\sigma$ sightlines. Scatter around the linear relation is reduced after the separation, but it does not vanish completely. This means that UV shielding is the dominant factor of the DIB equivalent width vs.\ reddening relation shape for $\zeta$ sightlines, but in $\sigma$ sightlines other physical parameters play a major role. No similar dependency on gas density, electron density or turbulence was observed. A catalog of all observed interstellar lines is made public.