ShantanuT01/DACTYL-Pretraining huggingface dataset:
The embedding of a torus into an inner form of PGL(2) defines an adelic toric period. A general version of Duke's theorem states that this period equidistributes as the discriminant of the splitting field tends to infinity. In this paper we consider a torus embedded diagonally into two distinct inner forms of PGL(2). Assuming the Generalized Riemann Hypothesis (and some additional technical assumptions), we show simultaneous equidistribution as the discriminant tends to infinity, with an effective logarithmic rate. Our proof is based on a probabilistic approach to estimating fractional moments of L-functions twisted by extended class group characters.
We discuss two types of instabilities which may arise in string theory compactified to asymptotically AdS spaces: perturbative, due to discrete modes in the spectrum of the Laplacian, and non-perturbative, due to brane nucleation. In the case of three dimensional Einstein manifolds, we completely characterize the presence of these instabilities, and in higher dimensions we provide a partial classification. The analysis may be viewed as an extension of the Breitenlohner-Freedman bound. One interesting result is that, apart from a very special class of exceptions, all Euclidean asymptotically AdS spaces with more than one conformal boundary component are unstable, if the compactification admits BPS branes or scalars saturating the Breitenlohner-Freedman bound. As examples, we analyze quotients of AdS in any dimension and AdS Taub-NUT spaces, and show a space which was previously discussed in the context of AdS/CFT is unstable both perturbatively and non-perturbatively.
The NMR measurements performed on a single orthorhombic crystal of superconducting ferromagnet UCoGe (Y.Ihara et al, Phys. Rev. Lett. v.105, 206403 (2010)) demonstrate strongly anisotropic magnetic properties of this material. The presented calculations allow to establish the dependence of longitudinal spin-lattice relaxation rate from temperature and magnetic field. The value 1/T_1T in field perpendicular to spontaneous magnetisation directed along c-axis has maximum in vicinity of Curie temperature whereas it does not reveal similar behaviour in field parallel to the direction of spontaneous magnetisation. Also there was shown that the longitudinal spin-lattice relaxation rate is strongly field dependent when the field directed in b-crystallographic direction but field independent if magnetic field is oriented along a-axis.
Standard solar models (SSM) constructed in accord with low metal abundances disagree with the seismically inferred results. We constructed rotating solar models with low metal abundances that included enhanced settling and convection overshoot. In one of our rotating models, \textbf{AGSSr2a}, the convection overshoot allowed us to recover the radius of the base of convection zone (CZ) at a level of $1\sigma$. The rotational mixing almost completely counteracts the enhanced settling for the surface helium abundance, but only partially for the surface heavy-element abundance. At the level of $1\sigma$, the combination of rotation and enhanced settling brings the surface helium abundance into agreement with the seismically inferred value of $0.2485\pm0.0035$, and makes the model have better sound-speed and density profiles than SSM constructed in accordance with high metal abundances. The radius of the base of the CZ and the surface helium abundance of \textbf{AGSSr2a} are $0.713$ $R_{\odot}$ and $0.2472$, respectively; the absolute values of the relative differences in sound speed and density between it and the Sun are less than $0.0025$ and $0.015$, respectively. Moreover, predicted neutrino fluxes of our model are comparable with the predictions of previous research works.
The symbiotic system HM Sagittae consists of a Mira star and a secondary White Dwarf component. The dust content of the system was severely affected by the nova outburst in 1975, which is still ongoing. The capabilities of optical interferometry operating in the mid-IR allow us to investigate the current geometry of the dust envelope. We test our previous spectro-interferometric study of this system with new interferometric configurations, increasing the uv coverage and allowing us to ascertain the appearance of the source between 8 and 13micron. We used the MIDI instrument of the VLTI with the unit telescopes (UTs) and auxiliary telescopes (ATs) providing baselines oriented from PA=42degrees to 127 degrees. The data are interpreted by means of an elliptical Gaussian model and the spherical radiative transfer code DUSTY. We demonstrate that the data can be reproduced well by an optically thick dust shell of amorphous silicate, typical of those encountered around Mira stars, whose measured dimension increases from 8 to 13micron. We confirm that the envelope is more extended in a direction perpendicular to the binary axis. The level of elongation increases with wavelength in contrast to our claim in a previous study. The wider uv coverage allows us to deepen our previous investigations of the close circumstellar structure of this object.
We discuss experimentally realizable situations in which surface effects may "screen out" the dipolar interactions in an assembly of nanomagnets, which then behaves as a noninteracting system. We consider three examples of physical observables, equilibrium magnetization, ac susceptibility and ferromagnetic resonance spectrum, to illustrate this screening effect. For this purpose, we summarize the formalism that accounts for both the intrinsic features of the nanomagnets and their collective effects within an assembly the condition for screening.
Radio galaxies can be seen out to very high redshifts, where in principle they can serve as probes of the early evolution of the Universe. Here we show that for any model of radio-galaxy evolution in which the luminosity decreases with time after an initial rapid increase (that is, essentially all reasonable models), all observable high-redshift radio-galaxies must be seen when the lobes are less than 10^7 years old. This means that high-redshift radio galaxies can be used as a high-time-resolution probe of evolution in the early Universe. Moreover, this result helps to explain many observed trends of radio-galaxy properties with redshift [(i) the `alignment effect' of optical emission along radio-jet axes, (ii) the increased distortion in radio structure, (iii) the decrease in physical sizes, (iv) the increase in radio depolarisation, and (v) the increase in dust emission] without needing to invoke explanations based on cosmology or strong evolution of the surrounding intergalactic medium with cosmic time, thereby avoiding conflict with current theories of structure formation.
In the early 1990's, Billera and Sturmfels introduced the monotone path polytope (MPP), a special case of the general theory of fiber polytopes that associates a polytope to a pair $(P,\varphi)$ of a polytope $P$ and linear functional $\varphi$. In that same paper, they showed that MPPs of simplices and hyper-cubes are combinatorial cubes and permutahedra respectively. Their work has lead to many developments in combinatorics. Here we investigate the monotone paths for generic orientations of cross-polytopes. We show the face lattice of its MPP is isomorphic to the lattice of intervals in the sign poset from oriented matroid theory. We look at its $f$-vector, its realizations, and facets.
This paper introduces a novel oscillator that combines the tunability of spin Hall-driven nano oscillators with the high quality factor (Q) of high overtone bulk acoustic wave resonators (HBAR), integrating both reference and tunable oscillators on the same chip with CMOS. In such magneto acoustic spin Hall (MASH) oscillators, voltage oscillations across the magnetic tunnel junction (MTJ) that arise from a spin-orbit torque (SOT) are shaped by the transmission response of the HBAR that acts as a multiple peak-bandpass filter and a delay element due to its large time constant, providing delayed feedback. The filtered voltage oscillations can be fed back to the MTJ via a) strain, b) current, or c) magnetic field. We develop a SPICE-based circuit model by combining experimentally benchmarked models including the stochastic Landau-Lifshitz-Gilbert (sLLG) equation for magnetization dynamics and the Butterworth Van Dyke (BVD) circuit for the HBAR. Using the self-consistent model, we project up to $\sim$ 50X enhancement in the oscillator linewidth with Q reaching up to 52825 at 3 GHz, while preserving the tunability by locking the STNO to the nearest high Q peak of the HBAR. We expect that our results will inspire MEMS-based solutions to spintronic devices by combining attractive features of both fields for a variety of applications.
We report spectral fitting results for Rosat PSPC observations of the dipping source X 1755-338. These results are consistent with the two-component model that we previously proposed consisting of a blackbody point source plus an extended power law component. Remarkably, the low energy cut-off of the spectrum does not change appreciably in dips, and it can be seen that dipping takes place in the higher part of the PSPC band where the blackbody contributes to the spectrum. Thus dipping consists primarily of absorption of this component, whereas the low energy cut-off is determined by the power law. Thus, above 0.5 keV, the dipping is approximately independent of energy as seen in Exosat and 10 +/- 0.4% deep. Below 0.5 keV, there may be a small residual dipping effect of up to 3%; however dipping is certainly substantially reduced compared with the 20% seen by Exosat, and this is the first time that the effective cessation of dipping at low energies in such sources has been seen.
This paper reports the discovery of evidence for physical contact between the Galactic circumnuclear disk (CND) and an exterior giant molecular cloud. The central 10 pc of our Galaxy has been imaged in the HCN J=1-0, HCO+ J=1-0, CS J=2-1, H13CN J=1-0, SiO J=2-1, SO N_J=2_3-1_2, and HC3N J=11-10 lines using the Nobeyama Radio Observatory 45 m radio telescope. Based on our examination of the position-velocity maps of several high-density probe lines, we have found that an emission "bridge" may be connecting the +20 km/s cloud (M-0.13-0.08) and the negative-longitude extension of the CND. Analyses of line intensity ratios imply that the chemical property of the bridge is located between the +20 km/s cloud and the CND. We introduce a new interpretation that a part of the CND may be colliding with the 20 km/s cloud and the collision may be responsible for the formation of the bridge. Such collisional events could promote mass accretion onto the CND or into the inner ionized cavity, which may be further tested by proper motion studies.
Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic triple $(E_1,E_2,\phi)$ on $X$ consists of two holomorphic vector bundles $E_1$ and $E_2$ over $X$ and a holomorphic map $\phi:E_2 \to E_1$. There is a concept of stability for triples which depends on a real parameter $\sigma$. In this paper, we determine the Hodge polynomials of the moduli spaces of $\sigma$-stable triples with $\rk(E_1)=3$, $\rk(E_2)=1$, using the theory of mixed Hodge structures. This gives in particular the Poincar\'e polynomials of these moduli spaces. As a byproduct, we recover the Hodge polynomial of the moduli space of odd degree rank 3 stable vector bundles.
In preparation for the nuclear physics Long Range Plan exercise, a group of 104 neutrino physicists met in Seattle September 21-23 to discuss both the present state of the field and the new opportunities of the next decade. This report summarizes the conclusions of that meeting and presents its recommendations. Further information is available at the workshop's web site. This report will be further reviewed at the upcoming Oakland Town Meeting.
We prove that the states secretly chosen from a mixed state set can be perfectly discriminated if and only if these states are orthogonal. The sufficient and necessary condition when nonorthogonal quantum mixed states can be unambiguously discriminated is also presented. Furthermore, we derive a series of lower bounds on the inconclusive probability of unambiguous discrimination of states from a mixed state set with \textit{a prior} probabilities.
Let $Y$ be a submanifold of dimension $y$ of a polarized complex manifold $(X,A)$ of dimension $k\geq 3$, with $1\leq y\leq k-1$. We define and study two positivity conditions on $Y$ in $(X,A)$, called Seshadri $A$-bigness and (a stronger one) Seshadri $A$-ampleness. In this way we get the natural generalization of the theory initiated by Paoletti in \cite{Pao} (which corresponds to the case $(k,y)=(3,1)$) and subsequently generalized and completed in   \cite{BBF} (regarding curves in a polarized manifold of arbitrary dimension). The theory presented here, which is new even if $y=k-1$, is motivated by a reasonably large area of examples.
Scalar tensor theories of gravity can be formulated in the Einstein or in the Jordan frame, which are related by the conformal transformations. Although the two frames are describe the same physics, and are equivalent, the stability of the field equations in two frames are not the same. Here we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans Dicke theory, but the results can easily be generalized. Our analysis show that while there is one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in other frame , however stability of a critical points in one frame does not grantee the stability in other frame. Hence an unstable point in one frame may be mapped to a stable point in other frame. All trajectories between two critical points in phase space in one frame are different from their corresponds in other ones. This indicates that the dynamical behavior of variables and cosmological parameters are different in two frames. Hence for those features of the study which focus on observational measurements we must use the (JF) where experimental data have their usual interpretation
We formulate the problem of magnetic field dissipation during the accretion phase of low-mass star formation, and we carry out the first step of an iterative solution procedure by assuming that the gas is in free-fall along radial field lines. This so-called ``kinematic approximation'' ignores the back reaction of the Lorentz force on the accretion flow. In quasi steady-state, and assuming the resistivity coefficient to be spatially uniform, the problem is analytically soluble in terms of Legendre's polynomials and confluent hypergeometric functions. The dissipation of the magnetic field occurs inside a region of radius inversely proportional to the mass of the central star (the ``Ohm radius''), where the magnetic field becomes asymptotically straight and uniform. In our solution, the magnetic flux problem of star formation is avoided because the magnetic flux dragged in the accreting protostar is always zero. Our results imply that the effective resistivity of the infalling gas must be higher by several orders of magnitude than the microscopic electric resistivity, to avoid conflict with measurements of paleomagnetism in meteorites and with the observed luminosity of regions of low-mass star formation.
We consider the problem of the convergence of the so-called Le Page series in the Skohorod space $\bbD^d=\bbD([0,1],\bbR^d)$ and provide a simple criterion based on the moments of the increments of the random process involved in the series. This provides a simple sufficient condition for the existence of an $\alpha$-stable distribution on $\bbD^d$ with given spectral measure.
The main goal of this paper is to give a unified description for the structure of the small quantum cohomology rings for all homogeneous spaces of SL_n(C).
Following ideas of Nori, Biswas, ..., we show that given an integer r>0, a noetherian scheme X, and an effective Cartier divisor D on it, the parabolic vector bundles on (X,D) with weights multiples of 1/r (in the sense of Maruyama-Yokogawa) are equivalent to ordinary vector bundles on an orbifold, the stack of r-th roots associated to (X,D) (a twisted scheme in the sense of Abramovich-Vistoli). We use this fact to get some information on the finite parabolic bundles on the (pointed) projective line.
The near-term objectives of the research program at the Data Analysis Center are established within the context of the existing partial wave analyses available through the online suite of analysis and database codes accessible through SAID, the Scattering Analysis Interactive Database. This presentation reviews the efforts to determine a model independent method to obtain sets of partial wave amplitudes for strong and electromagnetic reactions, the interpretation of the amplitudes in terms of the excited states of the nucleon, the role of new precision unpolarized and polarized data, and new developments aimed at determining the photoproduction mulitpoles in a unitary, coupled-channel approach. The Chew-Mandelstam technique is discussed and applied to the problem of the S-wave pion- and eta-photoproduction amplitudes. The resulting eta production amplitudes exhibit the expected resonant behavior near the eta production threshold. Application of this method to a unified description of the hadro- and photoproduction amplitudes is discussed.
Analysis of over 36 years of time series data from the NSO/AFRL/Sac Peak K-line monitoring program elucidates five components of the variation of the seven measured chromospheric parameters: (a) the solar cycle (period ~ 11 years), (b) quasi-periodic variations (periods ~100 days), (c) a broad band stochastic process (wide range of periods), (d) rotational modulation, and (e) random observational errors, independent of (a)-(d). Correlation and power spectrum analyses elucidate periodic and aperiodic variation of these parameters. Time-frequency analysis illuminates periodic and quasi periodic signals, details of frequency modulation due to differential rotation, and in particular elucidates the rather complex harmonic structure (a) and (b) at time scales in the range ~0.1 - 10 years. These results using only full-disk data suggest that similar analyses will be useful at detecting and characterizing differential rotation in stars from stellar light-curves such as thosebeing produced by NASA's Kepler observatory. Component (c) consists of variations over a range of timescales, in the manner of a 1/f random process with a power-law slope index that varies in a systematic way. A time-dependent Wilson-Bappu effect appears to be present in the solar cycle variations (a), but not in the more rapid variations of the stochastic process (c). Component (d) characterizes differential rotation of the active regions. Component (e) is of course not characteristic of solar variability, but the fact that the observational errors are quite small greatly facilitates the analysis of the other components. The data analyzed in this paper can be found at the National Solar Observatory web site http://nsosp.nso.edu/cak_mon/, or by file transfer protocol at ftp://ftp.nso.edu/idl/cak.parameters
Rapid development in integrated optoelectronic devices and quantum photonic architectures creates a need for optical fiber to chip coupling with low losses. Here we present a fast and generic approach that allows temperature stable self-aligning connections of nanophotonic devices to optical fibers. We show that the attainable precision of our approach is equal to that of DRIE-process based couplings. Specifically, the initial alignment precision is $1.2\pm 0.4\mu m$, the average shift caused by mating $<0.5\mu m$, which is in the order of the precision of the concentricity of the employed fiber, and the thermal cycling stability is $<0.2\mu m$. From these values the expected overall alignment offset is calculated as $1.4 \pm 0.4\mu m$. These results show that our process offers an easy to implement, versatile, robust and DRIE-free method for coupling photonic devices to optical fibers. It can be fully automated and is therefore scalable for coupling to novel devices for quantum photonic systems.
Sampling occupies an important position in theories of various scientific fields, and Markov chain Monte Carlo (MCMC) provides the most common technique of sampling. In the progress of MCMC, a huge number of studies have aimed the acceleration of convergence to the target distribution. Hamiltonian Monte Carlo (HMC) is such a variant of MCMC. In the recent development of MCMC, another approach based on the violation of the detailed balance condition has attracted much attention. Historically, these two approaches have been proposed independently, and their relationship has not been clearly understood. In this paper, the two approaches are seamlessly understood in the framework of generalized Monte Carlo method that violates the detailed balance condition. Furthermore we propose an efficient Monte Carlo method based on our framework.
We analyse decoherence properties of entangled coherent states (ECSs) due to channel losses, and compare to the performance of bi-photon Bell states. By employing the concept of "entanglement of formation" (EOF), the degradation of fidelity and degree of entanglement are calculated. Two situations are considered: (1) asymmetric and (2) symmetric noise channel. In the first case, only the lower bound of EOF is given. However, in the latter case, we have obtained an explicit expression of concurrence (and then EOF) and found surprisingly our result is just incompatible with that of [Phys. Rev. A \textbf{82}, (2010) 062325] in the limit of $\alpha\rightarrow0$. We demonstrate that entangled coherent states with sufficient small amplitudes are more robust against channel decoherence than biphoton entangled states in both cases.
In this paper, we tackle the problem of online road network extraction from sparse 3D point clouds. Our method is inspired by how an annotator builds a lane graph, by first identifying how many lanes there are and then drawing each one in turn. We develop a hierarchical recurrent network that attends to initial regions of a lane boundary and traces them out completely by outputting a structured polyline. We also propose a novel differentiable loss function that measures the deviation of the edges of the ground truth polylines and their predictions. This is more suitable than distances on vertices, as there exists many ways to draw equivalent polylines. We demonstrate the effectiveness of our method on a 90 km stretch of highway, and show that we can recover the right topology 92\% of the time.
The diagram technique for the one-band Hubbard model is formulated for the case of moderate to strong Hubbard repulsion. The expansion in powers of the hopping constant is expressed in terms of site cumulants of electron creation and annihilation operators. For Green's function an equation of the Larkin type is derived and solved in a one-loop approximation for the case of two dimensions, nearest-neighbor hopping and half-filling. The obtained four-band structure of the spectrum and the shapes of the spectral function are close to those observed in Monte Carlo calculations. It is shown that the maxima forming the bands are of a dissimilar origin in different regions of the Brillouin zone.