ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let X be an irreducible smooth projective curve of genus at least two over an algebraically closed field k of characteristic p>0. In this paper we study the natural stratification, defined using the absolute Frobenius of X, on the moduli space of vector bundles on X of suitable rank. In characteristic two we provide a complete classification of rank two semi-stable vector bundles whose Frobenius pull-back is not semi-stable. We also obtain fairly good information about the strata of the Frobenius stratification, including the irreducibility and the dimension of each non-empty Frobenius stratum. In particular we show that the locus of Frobenius destabilized bundles has dimension 3g-4 in the moduli space of semi-stable bundles of rank two. We also construct stable bundles that are destabilized by Frobenius in the following situations: characteristic p=2 and rank four, (2) characteristic p=rank=3, (3) characteristic p=rank=5 and g at least three.   We also explore (in any characteristic) the connection between Frobenius destabilized bundles and (pre)-opers, this approach allows us to reinterpret some of our results in terms of pre-opers and also allows us to construct Frobenius destablised bundles from certain pre-opers (or opers).   The other result we obtain is (for characteristic two): we show that the Gunning bundle descends under Frobenius when genus g is even. If g is odd, then the Gunning bundle twisted by any odd degree line bundle also descends.
A model is presented in which O(10 TeV) stop masses, typically required by the Higgs boson mass in supersymmetric models, do not originate from soft supersymmetry breaking terms that would drive the Higgs mass squared parameter to large negative values but rather from the mixing with vectorlike partners. Their contribution to the Higgs mass squared parameter is reduced to threshold corrections and, thus, it is one loop suppressed compared to usual scenarios. New fermion and scalar partners of the top quark with O(10 TeV) masses are predicted.
Continuous-variable quantum key distribution (CV-QKD) has many practical advantages including compatibility with current optical communication technology. Implementation using heterodyne measurements is particularly attractive since it eliminates the need for active phase locking of the remote pair of local oscillators, but the full security of CV QKD with discrete modulation was only proved for a protocol using homodyne measurements. Here we propose an all-heterodyne CV-QKD protocol with binary modulation and prove its security against general attacks in the finite-key regime. Although replacing a homodyne measurement with a heterodyne measurement would be naively expected to incur a 3-dB penalty in the rate-distance curve, our proof achieves a key rate with only a 1-dB penalty.
In this paper we prove existence and uniqueness of solutions to a nonlocal parabolic problem which generalizes the electric heating problem of a conducting body.
The properties of 1^-_1 two-phonon states and the characteristics of E1 transition probabilities between low-lying collective states in spherical nuclei are analysed within the Q-phonon approach to the description of collective states. Several relations between observables are obtained. Microscopic calculations of the E1 0^+_1 -> 1^-_1 transition matrix elements are performed on the basis of the RPA. A satisfactory description of the experimental data is obtained.
We prove that every graph with sufficiently large minimum degree $d$ contains a spanning forest in which every component is a star of size at least $\sqrt{d} - \tilde O(d^{1/4})$. This improves the result of Alon and Wormald and is optimal up to the lower order term.
We search the literature for reports on the spectral properties of neutron-star low-mass X-ray binaries when they have accretion luminosities between 1E34 and 1E36 ergs/s. We found that in this luminosity range the photon index (obtained from fitting a simple absorbed power-law in the 0.5-10 keV range) increases with decreasing 0.5-10 keV X-ray luminosity (i.e., the spectrum softens). Such behaviour has been reported before for individual sources, but here we demonstrate that very likely most (if not all) neutron-star systems behave in a similar manner and possibly even follow a universal relation. When comparing the neutron-star systems with black-hole systems, it is clear that most black-hole binaries have significantly harder spectra at luminosities of 1E34 - 1E35 erg/s. Despite a limited number of data points, there are indications that these spectral differences also extend to the 1E35 - 1E36 erg/s range. This observed difference between the neutron-star binaries and black-hole ones suggests that the spectral properties (between 0.5-10 keV) at 1E34 - 1E35 erg/s can be used to tentatively determine the nature of the accretor in unclassified X-ray binaries. We discuss our results in the context of properties of the accretion flow at low luminosities and we suggest that the observed spectral differences likely arise from the neutron-star surface becoming dominantly visible in the X-ray spectra. We also suggest that both the thermal component and the non-thermal component might be caused by low-level accretion onto the neutron-star surface for luminosities below a few times 1E34 erg/s.
We study the pump current and noise properties in an adiabatically modulated magnetic nanowire with double domain walls (DW). The modulation is brought about by applying a slowly oscillating magnetic and electric fields with a controllable phase difference. The pumping mechanism resembles the case of the quantum dot pump with two-oscillating gates. The pump current, shot noise, and heat flow show peaks when the Fermi energy matches with the spin-split resonant levels localized between the DWs. The peak height of the pump current is an indicator for the lifetime of the spin-split quasistationary states between the DWs. For sharp DWs, the energy absorption from the oscillating fields results in side-band formations observable in the pump current. The pump noise carries information on the correlation properties between the nonequilibrium electrons and the quasi-holes created by the oscillating scatterer. The ratio between the pump shot noise and the heat flow serves as an indicator for quasi-particle correlation.
Ballistic spin transport is studied through electronic tuners with double stubs attached to them. The spins precess due to the spin-orbit interaction. Injected polarized spins can exit the structure polarized in the opposite direction. A nearly square-wave spin transmission, with values 1 and 0, can be obtained using a periodic system of symmetric stubs and changing their length or width. The gaps in the transmission can be widened using asymmetric stubs. An additional modulation is obtained upon combining stub structures with different values of the spin-orbit strength.
We measure how the properties of star-forming central galaxies correlate with large-scale environment, $\delta$, measured on $10$Mpc/h scales. We use group catalogs to isolate a robust sample of central galaxies with high purity and completeness. The properties we investigate are star formation rate (SFR), exponential disk scale length $R_{\rm exp}$, and Sersic index of the light profile, $n$. We find that, at all stellar masses, there is an inverse correlation between SFR and $\delta$, meaning that above-average star forming centrals live in underdense regions. For $n$ and $R_{\rm exp}$, there is no correlation with $\delta$ at $M_{\rm star}\lesssim 10^{10.5}$ $M_\odot$, but at higher masses there are positive correlations; a weak correlation with $R_{\rm exp}$ and a strong correlation with $n$. These data are evidence of assembly bias within the star-forming population. The results for SFR are consistent with a model in which SFR correlates with present-day halo accretion rate, $\dot{M}_h$. In this model, galaxies are assigned to halos using the abundance matching ansatz, which maps galaxy stellar mass onto halo mass. At fixed halo mass, SFR is assigned to galaxies using the same approach,but $\dot{M}_h$ is used to map onto SFR. The best-fit model requires some scatter in the $\dot{M}_h$-SFR relation. The $R_{\rm exp}$ and $n$ measurements are consistent with a model in which these quantities are correlated with the spin parameter of the halo, $\lambda$. Halo spin does not correlate with $\delta$ at low halo masses, but for higher mass halos, high-spin halos live in higher density environments at fixed $M_h$. Put together with the earlier installments of this series, these data demonstrate that quenching processes have limited correlation with halo formation history, but the growth of active galaxies, as well as other detailed properties, are influenced by the details of halo assembly.
We consider a generalization of the parabolic Anderson model driven by space-time white noise, also called the stochastic heat equation, on the real line. High peaks of solutions have been extensively studied under the name of intermittency, but less is known about spatial regions between peaks, which may loosely refer to as valleys. We present two results about the valleys of the solution.   Our first theorem provides information about the size of valleys and the supremum of the solution over a valley. More precisely, we show that the supremum of the solution over a valley vanishes as $t\to\infty$, and we establish an upper bound of $\exp\{-\text{const}\cdot t^{1/3}\}$ for the rate of decay. We demonstrate also that the length of a valley grows at least as $\exp\{+\text{const}\cdot t^{1/3}\}$ as $t\to\infty$.   Our second theorem asserts that the length of the valleys are eventually infinite when the initial data has subgaussian tails.
A generalization of the McVittie solution, representing spacetime of a mass particle placed in (n+2) dimensional Robertson-Walker universe is reported.
We present a new efficient method to compute Uehling-Uhlenbeck collision integral for all two-particle interactions in relativistic plasma with drastic improvement in computation time with respect to existing methods. Plasma is assumed isotropic in momentum space. The set of reactions consists of: Moeller and Bhabha scattering, Compton scattering, two-photon pair annihilation, and two-photon pair production, which are described by QED matrix elements. In our method exact energy and particle number conservation laws are satisfied. Reaction rates are compared, where possible, with the corresponding analytical expressions and convergence of numerical rates is demonstrated.
A simple graph more often than not contains adjacent vertices with equal degrees. This in particular holds for all pairs of neighbours in regular graphs, while a lot such pairs can be expected e.g. in many random models. Is there a universal constant $K$, say $K=3$, such that one may always dispose of such pairs from any given connected graph with at least three vertices by blowing its selected edges into at most $K$ parallel edges? This question was first posed in 2004 by Karo\'nski, {\L}uczak and Thomason, who equivalently asked if one may assign weights $1,2,3$ to the edges of every such graph so that adjacent vertices receive distinct weighted degrees - the sums of their incident weights. This basic problem is commonly referred to as the 1-2-3 Conjecture nowadays, and has been addressed in multiple papers. Thus far it is known that weights $1,2,3,4,5$ are sufficient [J. Combin. Theory Ser. B 100 (2010) 347-349]. We show that this conjecture holds if only the minimum degree $\delta$ of a graph is large enough, i.e. when $\delta = \Omega(\log\Delta)$, where $\Delta$ denotes the maximum degree of the graph. The principle idea behind our probabilistic proof relies on associating random variables with a special and carefully designed distribution to most of the vertices of a given graph, and then choosing weights for major part of the edges depending on the values of these variables in a deterministic or random manner.
What is a good visual representation for autonomous agents? We address this question in the context of semantic visual navigation, which is the problem of a robot finding its way through a complex environment to a target object, e.g. go to the refrigerator. Instead of acquiring a metric semantic map of an environment and using planning for navigation, our approach learns navigation policies on top of representations that capture spatial layout and semantic contextual cues. We propose to using high level semantic and contextual features including segmentation and detection masks obtained by off-the-shelf state-of-the-art vision as observations and use deep network to learn the navigation policy. This choice allows using additional data, from orthogonal sources, to better train different parts of the model the representation extraction is trained on large standard vision datasets while the navigation component leverages large synthetic environments for training. This combination of real and synthetic is possible because equitable feature representations are available in both (e.g., segmentation and detection masks), which alleviates the need for domain adaptation. Both the representation and the navigation policy can be readily applied to real non-synthetic environments as demonstrated on the Active Vision Dataset [1]. Our approach gets successfully to the target in 54% of the cases in unexplored environments, compared to 46% for non-learning based approach, and 28% for the learning-based baseline.
We deal with the problem of determining an inclusion within an electrical conductor from electrical boundary measurements. Under mild a priori assumptions we establish an optimal stability estimate.
Topological insulators (TI) are a phase of matter that host unusual metallic states on their surfaces. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photo-emission spectroscopy and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI Bi2Se3 loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that there is a change in topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically-protected surface states, and will provoke new studies as to the fundamental nature of topological phase of matter in the presence of disorder.
The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we describe the structure of timelike boundary conditions; the matching problem across null hypersurfaces; and the propagation of gravitational shocks.
We present observational evidence for the inhibition of bar formation in dispersion-dominated (dynamically hot) galaxies by studying the relationship between galactic structure and host galaxy kinematics in a sample of 257 galaxies between 0.1 $<$ z $\leq$ 0.84 from the All-Wavelength Extended Groth Strip International Survey (AEGIS) and the Deep Extragalactic Evolutionary Probe 2 (DEEP2) survey. We find that bars are preferentially found in galaxies that are massive and dynamically cold (rotation-dominated) and on the stellar Tully-Fisher relationship, as is the case for barred spirals in the local Universe. The data provide at least one explanation for the steep ($\times$3) decline in the overall bar fraction from z=0 to z=0.84 in L$^*$ and brighter disks seen in previous studies. The decline in the bar fraction at high redshift is almost exclusively in the lower mass (10 $<$ log M$_{*}$(\Msun)$<$ 11), later-type and bluer galaxies. A proposed explanation for this "downsizing" of the bar formation / stellar structure formation is that the lower mass galaxies may not form bars because they could be dynamically hotter than more massive systems from the increased turbulence of accreting gas, elevated star formation, and/or increased interaction/merger rate at higher redshifts. The evidence presented here provides observational support for this hypothesis. However, the data also show that not every disk galaxy that is massive and cold has a stellar bar, suggesting that mass and dynamic coldness of a disk are necessary but not sufficient conditions for bar formation -- a secondary process, perhaps the interaction history between the dark matter halo and the baryonic matter, may play an important role in bar formation.
In [G. Baker et al., Phys. Rev. Lett. 81, 554 (1998)] a number of supposedly novel and surprising features were observed in a system composed of two periodically driven and asymmetrically coupled pendula. In particular it was claimed that `permanent synchronization ... does not occur except as a numerical artifact'. It was suggested that this might be related to the particular type of coupling. In this comment I want to point out that some of these claims cannot be maintained. The synchronization in this system is precisely of standard blow-out type. The observed intermittency is exactly the on-off intermittency well known from the synchronization of multifractal chaotic attractors.
This paper presents a novel framework for human trajectory prediction based on multimodal data (video and radar). Motivated by recent neuroscience discoveries, we propose incorporating a structured memory component in the human trajectory prediction pipeline to capture historical information to improve performance. We introduce structured LSTM cells for modelling the memory content hierarchically, preserving the spatiotemporal structure of the information and enabling us to capture both short-term and long-term context. We demonstrate how this architecture can be extended to integrate salient information from multiple modalities to automatically store and retrieve important information for decision making without any supervision. We evaluate the effectiveness of the proposed models on a novel multimodal dataset that we introduce, consisting of 40,000 pedestrian trajectories, acquired jointly from a radar system and a CCTV camera system installed in a public place. The performance is also evaluated on the publicly available New York Grand Central pedestrian database. In both settings, the proposed models demonstrate their capability to better anticipate future pedestrian motion compared to existing state of the art.
The model of point particle in general external fields is considered and the generalized equivalence principle is suggested identifying all backgrounds which give rise to equivalent particle dynamics. The equivalence transformations for external fields are interpreted as gauge ones. The gauge group appears to be a semidirect product of all phase space canonical transformations to an abelian ideal of "hyperWeyl" transformations and includes U(1) and general coordinate symmetries as a subgroup. The implications of this gauge symmetry are considered and a connection of general backgrounds to the infinite collection of Fronsdal gauge fields is studied. Although the result is negative and no direct connection arises, it is discussed how higher spin fields could be found among general external fields if one relaxes somehow the equivalence principle. Besides, the particle action in general backgrounds is shown to reproduce the De Wit-Freedman point particle -- symmetric tensors first order interaction suggested many years ago, and generalizes their result to all orders in interaction.
We study the time evolution of a qubit linearly coupled with a quantum environment under a sequence of short pi pulses. Our attention is focused on the case where qubit-environment interactions induce the decoherence with population decay. We assume that the environment consists of a set of bosonic excitations. The time evolution of the reduced density matrix for the qubit is calculated in the presence of periodic short pi pulses. We confirm that the decoherence is suppressed if the pulse interval is shorter than the correlation time for qubit-environment interactions.
We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for all intersection numbers on the hyperelliptic locus with one $\lambda$-class, and powers of a $\psi$-class pulled back along the branch map. This is achieved by using Atiyah-Bott localization on a stack of stable maps into the orbifold $[\mathbb{P}^1/\mathbb{Z}_2]$.
We are dealing with the validity of a large deviation principle for a class of reaction-diffusion equations with polynomial nonlinearity, perturbed by a Gaussian random forcing. We are here interested in the regime where both the strength of the noise and its correlation are vanishing, on a length scale $\epsilon$ and $\delta(\epsilon)$, respectively, with $0<\epsilon,\delta(\epsilon)<<1$. We prove that, under the assumption that $\epsilon$ and $\delta(\epsilon)$ satisfy a suitable scaling limit, a large deviation principle holds in the space of continuous trajectories with values both in the space of square-integrable functions and in Sobolev spaces of negative exponent. Our result is valid, without any restriction on the degree of the polynomial nor on the space dimension.
Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases. Several mathematical studies proposed to approximate the pdf in a quite general framework or even to simulate this hitting time using a discrete time approximation of the Brownian motion. The authors study a new algorithm which permits to simulate the first-passage time using an iterating procedure. The convergence rate presented in this paper suggests that the method is very efficient.
Solar magnetic fields leave their fingerprints in the polarization signatures of the emergent spectral line radiation. This occurs through a variety of rather unfamiliar physical mechanisms, not only via the Zeeman effect. In particular, magnetic fields modify the atomic level polarization (population imbalances and quantum coherences) that anisotropic radiative pumping processes induce in the atoms and molecules of the solar atmosphere. Interestingly, this so-called Hanle effect allows us to "see" magnetic fields to which the Zeeman effect is blind within the limitations of the available instrumentation. Here I argue that the IR triplet of Ca II and the He I 10830 \AA multiplet would be very suitable choices for investigating the magnetism of the solar chromosphere via spectropolarimetric observations from a future space telescope, such as JAXA's SOLAR-C mission.
We assess the multi-wavelength observable properties of the bow shock around a runaway early type star using a combination of hydrodynamical modelling, radiative transfer calculations and synthetic imaging. Instabilities associated with the forward shock produce dense knots of material which are warm, ionised and contain dust. These knots of material are responsible for the majority of emission at far infra-red, H alpha and radio wavelengths. The large scale bow shock morphology is very similar and differences are primarily due to variations in the assumed spatial resolution. However infra-red intensity slices (at 22 microns and 12 microns) show that the effects of a temperature gradient can be resolved at a realistic spatial resolution for an object at a distance of 1 kpc.