ShantanuT01/DACTYL-Pretraining huggingface dataset:
Chen (quant-ph/0611126) has recently claimed ``exponential violation of local realism by separable states", in the sense that multi-partite separable quantum states are supposed to give rise to correlations and fluctuations that violate a Bell-type inequality that Chen takes to be satisfied by local realism. However, this can not be true since all predictions (including all correlations and fluctuations) that separable quantum states give rise to have a local realistic description and thus satisfy all Bell-type inequalities, and this holds for all number of parties. Since Chen claims otherwise by presenting a new inequality, claimed to be a Bell-type one, which separable states supposedly can violate, there must be a flaw in the argumentation. I will expose this flaw, not merely for clarification of this issue, but perhaps even more importantly since it re-teaches us an old lesson John Bell taught us over 40 years ago. I will argue that this lesson provides us with a new morale especially relevant to modern research in Bell-type inequalities.
We explore the possibility that radio loud gamma-ray bursts (GRBs) result from the collapse of massive stars in interacting binary systems, while radio quiet GRBs are produced by the collapse of single massive stars. A binary collapsar system can have the necessary angular momentum and energy budget to explain the longer prompt gamma-ray durations and higher isotropic energies seen in the the radio loud sub-sample of long GRBs. Additionally binary systems can lead to rich and extended circumstellar environments that allow for the presence of the long-lived radio afterglows seen in the radio loud systems. Finally, the relative fraction of stars in binary systems versus single star systems appears consistent with the fraction of radio loud versus radio quiet GRBs.
For a prime $p$ and a polynomial $F(X,Y)$ over a finite field $\mathbb{F}_p$ of $p$ elements, we give upper bounds on the number of solutions $$ F(x,y)=0, \quad x\in\mathcal{A}, \ y\in \mathcal{B}, $$ where $\mathcal{A}$ and $\mathcal{B}$ are very small intervals or subgroups. These bounds can be considered as positive characteristic analogues of the result of Bombieri and Pila (1989) on sparsity of integral points on curves. As an application we prove that distinct consecutive elements in sequences generated compositions of several rational functions are not contained in any short intervals or small subgroups.
In weighted trees, all edges are endowed with positive integral weight. We enumerate weighted bicolored plane trees according to their weight and number of edges.
We show how to construct non-equilibrium thermodynamics for systems too small to be considered thermodynamically in a traditional sense. Through the use of a non-equilibrium ensemble of many replicas of the system which can be viewed as a large thermodynamic system, we discuss the validity of non-equilibrium thermodynamics relations and analyze the nature of dissipation in small systems through the entropy production rate. We show in particular that the Gibbs equation, when formulated in terms of average values of the extensive quantities, is still valid whereas the Gibbs-Duhem equation differs from the equation obtained for large systems due to the lack of the thermodynamic limit. Single-molecule stretching experiments are interpreted under the prism of this theory. The potentials of mean force and mean position, now introduced in these experiments in substitution of the thermodynamic potentials, correspond respectively to our Helmholtz and Gibbs energies. These results show that a thermodynamic formalism can indeed be applied at the single-molecule level.
We report the results of a $^{45}$Sc nuclear magnetic resonance (NMR) study on the quasi-one-dimensional compound Cu$_2$Sc$_2$Ge$_4$O$_{13}$ at temperatures between 4 and 300 K. This material has been a subject of current interest due to indications of spin gap behavior. The temperature-dependent NMR shift exhibits a character of low-dimensional magnetism with a negative broad maximum at $T_{max}$ $\simeq $ 170 K. Below $% T_{max}$, the NMR shifts and spin lattice relaxation rates clearly indicate activated responses, confirming the existence of a spin gap in Cu$_2$Sc$_2$Ge% $_4$O$_{13}$. The experimental NMR data can be well fitted to the spin dimer model, yielding a spin gap value of about 275 K which is close to the 25 meV peak found in the inelastic neutron scattering measurement. A detailed analysis further points out that the nearly isolated dimer picture is proper for the understanding of spin gap nature in Cu$_2$Sc$_2$Ge$_4$O$_{13}$.
In Combinatorial Game Theory, we study the set of games G, whose elements are mapped from positions of rulesets. In many case, given a ruleset, not all elements of G can be given as a position in the ruleset. It is an intriguing question what kind of ruleset would allow all of them to appear. In this paper, we introduce a ruleset named turning tiles and prove the ruleset is a universal partizan ruleset, that is, every element in G can occur as a position in the ruleset. This is the second universal partizan ruleset after generalized konane.
The ARIANNA detector is designed to detect neutrinos with energies above $10^{17}$eV. Due to the similarities in generated radio signals, cosmic rays are often used as test beams for neutrino detectors. Some ARIANNA detector stations are equipped with antennas capable of detecting air showers. Since the radio emission properties of air showers are well understood, and the polarization of the radio signal can be predicted from the arrival direction, cosmic rays can be used as a proxy to assess the reconstruction capabilities of the ARIANNA neutrino detector. We report on dedicated efforts of reconstructing the polarization of cosmic-ray radio pulses. After correcting for difference in hardware, the two stations used in this study showed similar performance in terms of event rate and agreed with simulation. Subselecting high quality cosmic rays, the polarizations of these cosmic rays were reconstructed with a resolution of $2.5^{\circ}$ (68% containment), which agrees with the expected value obtained from simulation. A large fraction of this resolution originates from uncertainties in the predicted polarization because of the contribution of the subdominant Askaryan effect in addition to the dominant geomagnetic emission. Subselecting events with a zenith angle greater than $70^{\circ}$ removes most influence of the Askaryan emission, and, with limited statistics, we found the polarization uncertainty is reduced to $1.3^{\circ}$ (68% containment).
Let $S$ be a noetherian scheme, and let $E$ be a coherent sheaf on it. We define a group-valued contravariant functor $GL_E$ on $S$-schemes by associating to any $S$-scheme $T$ the group $GL_E(T)$ of all linear automorphisms of the pullback of $E$ to $T$. This functor is clearly a sheaf in the fpqc topology. We prove that $GL_E$ is representable by a group-scheme over $S$ if and only if the sheaf $E$ is locally free.
Various jet observables in photoproduction are studied and compared to data from HERA. The feasibility of using a dijet sample for constraining the parton distributions in the photon is then studied. For the current data the experimental and theoretical uncertainties are comparable to the variation due to changing the photon parton distribution set.
The time-energy entanglement of down-converted photon pairs is particularly difficult to characterize because direct measurements of photon arrival times are limited by the temporal resolution of photon detection. Here, we explore an alternative possibility of characterizing the temporal coherence of two-photon wavefunctions using single photon interference with weak coherent light. Specifically, this method makes use of the fact that down-conversion generates a coherent superposition of vacuum and two-photon states, so that the coincidence count rates for photon pairs after interference with weak coherent light are given by a superposition of the two-photon wavefunction from the down-conversion with the product wavefunction defined by the weak coherent references. By observing the frequency dependent interference pattern, it is possible to reconstruct the amplitudes and the phases of the two-photon wavefunction within the bandwidth of the reference pulses used in the single photon interferences. The correlated single photon interferences therefore provide a direct map of the entangled two-photon wavefunction generated in the down-conversion process.
The asymptotic behaviour of the Neron-Tate height of Heegner points on a rational elliptic curve attached to an arithmetically normalized new cusp form f of weight 2, level N and trivial character is studied in this paper. By Gross-Zagier formula, this height is related to the special value at the critical point for the derivative of the Rankin-Selberg convolution of f with a certain weight one theta series attached to some ideal class of some imaginary quadratic field. Asymptotic formula for the first moments asociated to these Dirichlet series are proved and experimental results are carefully discussed.
Rotation evolution of late-type stars is dominated by magnetic braking and the underlying factors that control this angular momentum loss are important for the study of stellar spin-down. In this work, we study angular momentum loss as a function of two different aspects of magnetic activity using a calibrated Alfv\'en wave-driven magnetohydrodynamic wind model: the strengths of magnetic spots and their distribution in latitude. By driving the model using solar and modified solar surface magnetograms, we show that the topology of the field arising from the net interaction of both small-scale and large-scale field is important for spin-down rates and that angular momentum loss is not a simple function of large scale magnetic field strength. We find that changing the latitude of magnetic spots can modify mass and angular momentum loss rates by a factor of two. The general effect that causes these differences is the closing down of large-scale open field at mid- and high-latitudes by the addition of the small-scale field. These effects might give rise to modulation of mass and angular momentum loss through stellar cycles, and present a problem for ab initio attempts to predict stellar spin-down based on wind models. For all the magnetogram cases considered here, from dipoles to various spotted distributions, we find that angular momentum loss is dominated by the mass loss at mid-latitudes. The spin-down torque applied by magnetized winds therefore acts at specific latitudes and is not evenly distributed over the stellar surface, though this aspect is unlikely to be important for understanding spin-down and surface flows on stars.
We consider sensor array imaging for simultaneous noise blended sources. We study a migration imaging functional and we analyze its sensitivity to singular perturbations of the speed of propagation of the medium. We consider two kinds of random sources: randomly delayed pulses and stationary random processes, and three possible kinds of perturbations. Using high frequency analysis we prove the statistical stability (with respect to the realization of the noise blending) of the scheme and obtain quantitative results on the image contrast provided by the imaging functional, which strongly depends on the type of perturbations.
We report a computational study of the adsorption of zoledronic acid molecule on hydroxyapatite (001) surface within ab initio density functional theory. The systematic study has been performed, from hydroxyapatite bulk and surface, and zoledronic acid molecule to the adsorption of the molecule on the surface. The optimized bond lengths and bond angles were obtained and analyzed, giving an evidence of structural similarity between subjects under study. The formation energies of hydroxyapatite (001) surfaces with two kinds of terminations were computed as about 1.2 and 1.5 J/m^2 with detailed atomistic structural information. We determined the adsorption energies of zoledronic acid molecule on the surfaces, which are -260 kJ/mol at 0.25 ML and -400 kJ/mol at 0.5 ML. An atomistic insight of strong binding affinity of zoledronic acid to the hydroxyapatite surface was given and discussed.
Let $h$ be a positive integer and $A, B_1, B_2,\dots, B_h$ be finite sets in a commutative group. We bound $|A+B_1+...+B_h|$ from above in terms of $|A|, |A+B_1|,\dots,|A+B_h|$ and $h$. Extremal examples, which demonstrate that the bound is asymptotically sharp in all the parameters, are furthermore provided.
The physics of magnetic hot stars and how a large-scale magnetic field affects their interior properties is largely unknown. Few studies have combined high-quality observations and modelling of magnetic pulsating stars, known as magneto-asteroseismology, primarily because of the dearth of detected pulsations in stars with a confirmed and well-characterised large-scale magnetic field. We aim to characterise observational signatures of rotation and pulsation in chemically peculiar candidate magnetic stars using photometry from the K2 space mission. Thus, we identify the best candidate targets for ground-based, optical spectropolarimetric follow-up observations to confirm the presence of a large-scale magnetic field. We employed customised reduction and detrending tools to process the K2 photometry into optimised light curves for a variability analysis. We searched for the periodic photometric signatures of rotational modulation caused by surface abundance inhomogeneities in 56 chemically peculiar A and B stars. Furthermore, we searched for intrinsic variability caused by pulsations (coherent or otherwise) in the amplitude spectra of these stars. The rotation periods of 38 chemically peculiar stars are determined, 16 of which are the first determination of the rotation period in the literature. We confirm the discovery of high-overtone roAp pulsation modes in HD 177765 and find an additional 3 Ap and Bp stars that show evidence of high-overtone pressure modes found in roAp stars in the form of possible Nyquist alias frequencies in their amplitude spectra. Furthermore, we find 6 chemically peculiar stars that show evidence of intrinsic variability caused by gravity or pressure pulsation modes. The discovery of pulsations in a non-negligible fraction of chemically peculiar stars make these stars high-priority targets for spectropolarimetric campaigns.
We study the response function which describes the evolution of energy density induced by an initial disturbance for a Bjorken-expanding quark-gluon plasma (QGP). We compare the results from solving linearized Boltzmann equation under the relaxation time approximation with those from viscous hydrodynamics. While in long time limit the response becomes hydrodynamics, the non-hydrodynamic response is important at intermediate times when excitations of wavelength larger than the inverse of the relaxation time $1/\tau_{R}$ are not fully damped. Therefore observables sensitive to the jet-induced medium excitations might be employed to explore the properties of QGP at the "mesoscopic scale".
We consider an Ito stochastic differential equation with delay, driven by brownian motion, whose solution, by an appropriate reformulation, defines a Markov process $X$ with values in a space of continuous functions $\mathbf C$, with generator $\mathcal L$. We then consider a backward stochastic differential equation depending on $X$, with unknown processes $(Y,Z)$, and we study properties of the resulting system, in particular we identify the process $Z$ as a deterministic functional of $X$. We next prove that the forward-backward system provides a suitable solution to a class of parabolic partial differential equations on the space $\mathbf C$ driven by $\mathcal L$, and we apply this result to prove a characterization of the fair price and the hedging strategy for a financial market with memory effects. We also include applications to optimal stochastic control of differential equation with delay: in particular we characterize optimal controls as feedback laws in terms the process $X$.
Overionized recombining plasmas (RPs) have been discovered from a dozen of mixed- morphology (MM) supernova remnants (SNRs). However their formation process is still under debate. As pointed out by many previous studies, spatial variations of plasma temperature and ionization state provide clues to understand the physical origin of RPs. We report on a spatially resolved X-ray spectroscopy of W28, which is one of the largest MM SNRs found in our Galaxy. Two observations with Suzaku XIS cover the center of W28 to the northeastern rim where the shock is interacting with molecular clouds. The X-ray spectra in the inner regions are well reproduced by a combination of two-RP model with different temperatures and ionization states, whereas that in northeastern rim is explained with a single-RP model. Our discovery of the RP in the northeastern rim suggests an effect of thermal conduction between the cloud and hot plasma, which may be the production process of the RP. The X-ray spectrum of the north- eastern rim also shows an excess emission of the Fe I K{\alpha} line. The most probable process to explain the line would be inner shell ionization of Fe in the molecular cloud by cosmic-ray particles accelerated in W28.
We construct a scenario where the outburst of the young-stellar-object ASASSN-15qi is an intermediate luminosity optical transient (ILOT). In this scenario a sub-Jupiter young planet was tidally destructed on to a young main-sequence star. The system is young, therefore the radius of the planet is larger than its final value, and consequently its density is smaller. The lower density allows the tidal destruction of the young Saturn-like planet on to the main-sequence star of mass $\approx 2.4~\rm{M_\odot}$, resulting in a formation of a disc and a gravitationally-powered ILOT. Unlike the case of the more energetic ILOT V838~Mon, the mass of the destructed planet is too low to inflate a giant envelope, and hence the merger remnant stays hot. If our suggested model holds, this ILOT possesses two interesting properties: (1) its luminosity and total energy are below those of novae, and (2) it is not as red as other ILOTs. The unusual outburst of ASASSN-15qi, if indeed is an ILOT, further increases the diversity of the already heterogeneous group of ILOTs. We mark the region on the energy-time diagram occupied by such young ILOTs.
Saliency object detection estimates the objects that most stand out in an image. The available unsupervised saliency estimators rely on a pre-determined set of assumptions of how humans perceive saliency to create discriminating features. By fixing the pre-selected assumptions as an integral part of their models, these methods cannot be easily extended for specific settings and different image domains. We then propose a superpixel-based ITerative Saliency Estimation fLexible Framework (ITSELF) that allows any user-defined assumptions to be added to the model when required. Thanks to recent advancements in superpixel segmentation algorithms, saliency-maps can be used to improve superpixel delineation. By combining a saliency-based superpixel algorithm to a superpixel-based saliency estimator, we propose a novel saliency/superpixel self-improving loop to iteratively enhance saliency maps. We compare ITSELF to two state-of-the-art saliency estimators on five metrics and six datasets, four of which are composed of natural-images, and two of biomedical-images. Experiments show that our approach is more robust than the compared methods, presenting competitive results on natural-image datasets and outperforming them on biomedical-image datasets.
The antisymmetrization of the composite particles in cluster model calculations manifests itself in Pauli forbidden states (ghost states), if one restricts oneself on undeformed cluster in the low energy region. The resonating group method and the generating coordinate method rely on a property of the norm kernel, which introduces some of the ghost states. The norm kernel has been usually calculated under the assumption that the inner wavefunctions have a simple Gaussian form. It is the first time that this assumption is tested by the rigorous way. In the 4He+N system, we demonstrate a ghost state, which is calculated from a rigorous solution of Yakubovsky equations for the alpha particle. The ghost states calculated by rigorous and approximate methods turn out to have a very similar form. It is analytically proved that the trace of the norm kernel does not depend on the inner wavefunction we choose.
We study a dynamic optimal transport problem on a network. Despite the cost for transport along the edges, an additional cost, scaled with a parameter $\kappa$, has to be paid for interchanging mass between edges and vertices. We show existence f minimisers using duality and discuss the relationship of the model to other metrics such as Fisher-Rao and the classical Wasserstein metric. Finally, we examine the limiting behaviour of the model in terms of the parameter $\kappa$.
The Hodge-de Rham Laplacean is an extension to forms of the wave equation. A frame is a quartuple of 1-forms. The Hodge-de Rham Laplacean is modified to model it on the frame itself (not on the standard frame $dx$). This modified Laplacean is invariant. The basic equation is: The modified Laplacean operating on the frame is equal to a source term times the frame. Kaniel and Itin (Il Nuovo Cimento vol 113B,N3,1998) analyzed the equation for steady state and spherically symmetric frame (General Relativity). They computed a closed solution for which the derived metric is Rosen's. This closed solution is intrinsically different than Schwarzschild solution. Yet it passes the three classical experimental tests to the same accuracy. The same basic equation is,also, the alternative to Schroedinger equation, where the source term is the electromagnetic potential. The same quantization as in Schroedinger equation is attained. The suggested system is hyperbolic, in contrast to the time dependent Schroedinger equation which is parabolic. For time dependent frames the equation is quite complicated. Thus, the linearized equation is explicitly solved .
A statistically feasible data post-processing method for the conventional qubit state tomography is studied from an information geometrical point of view. It is shown that the space $(-1,1)^3$ of the Stokes parameters $(\xi_1, \xi_2,\xi_3)$ that specify qubit states should be regarded as a Riemannian manifold endowed with a metric $g_{ij}:=\delta_{ij}/(1-(\xi_i)^2)$, and that the data processing based on the maximum likelihood method is realized by the orthogonal projection from the empirical distribution onto the Bloch sphere with respect to the metric $g_{ij}$. An efficient algorithm for computing the maximum likelihood estimate is also proposed.
In the canonical picture of the evolution of the quark-gluon plasma during a high-energy heavy-ion collision, quarks are produced in two waves. The first is during the first fm/c of the collision, when gluons thermalize into the QGP. After a roughly isentropic expansion that roughly conserves the number of quarks, a second wave ensues at hadronization, 5-10 fm/c into the collision. Since each hadron contains at least two quarks, the majority of quark production occurs at this later time. For each quark produced in a heavy-ion collision, an anti-quark of the same flavor is created at the same point in space-time. Charge balance functions identify, on a statistical basis, the location of balancing charges for a given hadron, and given the picture above one expects the distribution in relative rapidity of balancing charges to be characterized by two scales. After first demonstrating how charge balance functions can be created using any pair of hadronic states, it will be shown how one can identify and study both processes of quark production. By considering balance functions of several hadronic species, and by performing illustrative calculations, this class of measurement appears to hold the prospect of providing the field's most stringent insight into the chemical evolution of the QGP.