ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present an entanglement purification protocol for a mixture of a pure entangled state and a pure product state, which are orthogonal to each other. The protocol is combination of bisection method and one-way hashing protocol. We give recursive formula for the rate of the protocol for different states, i.e. the number of maximally entangled two-qubit pairs obtained with the protocol per a single copy of the initial state. We also calculate numerically the rate for some states.
We compute the statistical entropy of the three charge (D1-D5-p) five dimensional black hole to sub-leading order in a large charge expansion. We find an agreement with the macroscopic calculation of the Wald entropy in R^2 corrected supergravity theory. The two calculations have a overlapping regime of validity which is not the Cardy regime. We use this result to clarify the 4d-5d lift for black holes on Taub-NUT space. In particular, we compute sub-leading corrections to the formula S^{4d} = S^{5d}. In the microscopic analysis, this correction arises from excitations bound to the Taub-NUT space. In the macroscopic picture, the difference is accounted by a mechanism present in a higher derivative theory wherein the geometry of the Taub-NUT space absorbes some of the electric charge.
A kinetic approach to the notion of information is proposed, based on Liouville kinetic theory. The general kinetic equation for the evolution of the N-particle information $\mathcal{I}_N$ in a Hamiltonian system of large particle number $N\gg 1$ is obtained. It is shown that the $N$-particle information is strictly conserved. Defining reduced particle number information densities in phase space should be possible to obtain a kinetic equation for the ordinary one-particle information $\mathcal{I}_1\equiv \mathcal{I}$ following the Bogoliubov prescription. The kinetic equation for $\mathcal{I}$ is a kind of generalized Boltzmann equation with interaction term depending on the hierarchy of reduced informations. This term in its general form is the most general expression for the Kolmogorov entropy rate of evolution of the information.
We achieved for the first time a direct measurement of the thermal fluctuation of a pendulum in an off-resonant region using a laser interferometric gravitational wave detector. These measurements have been well identified for over one decade by an agreement with a theoretical prediction, which was derived by a fluctuation-dissipation theorem. Thermal fluctuation is dominated by the contribution of resistances in coil-magnet actuator circuits. When we tuned these resistances, the noise spectrum also changed according to a theoretical prediction. The measured thermal noise level corresponds to a high quality factor on the order of 10^5 of the pendulum.
In the previous submission of this paper we claimed to have solved the problem of constructing a consistent non-abelian Born Infeld action which is $\kappa$--supersymmetric to all orders. Our method was based on an extension of target superspace to $\mathrm{N} \times \mathrm{N}$ matrix--valued objects for all the items appearing in the geometric construction. Then we applied the \textit{double first order formalism} introduced by us in the previous construction of abelian brane actions to the non--abelian case and we claimed that the Bosonic action given by the prescription of the \textit{symmetrized trace} could be promoted to a fully kappa supersymmetric one. Unfortunately there is an internal inconsistency, relative to U(N) gauge invariance in the matricisation of target superspace geometry and there is a subtle inconsistency in the variation of the symmetric trace action due to the loss of associativity of the underlying symmetrized product. Because of that the entire construction previously submitted does not stand on its feet. Consequently the present resubmission is done in order to disclaim our previously claimed result and also to express our sincere gratitude to our friends Paul Howe and Ulf Lindstrom who, with their constructive criticism and private correspondence, have helped us to understand where the bugs in our construction were.
We prove that the maximum degree $\Delta_n$ of a random series-parallel graph with $n$ vertices satisfies $\Delta_n/\log n \to c$ in probability, and $\mathbb{E}\, \Delta_n \sim c \log n$ for a computable constant $c>0$. The same result holds for outerplanar graphs.
We investigate Douglis--Nirenberg uniformly elliptic systems in $\mathbb{R}^{n}$ on a class of H\"ormander inner product spaces. They are parametrized with a radial function parameter which is RO-varying at $+\infty$, considered as a function of $(1+|\xi|^{2})^{1/2}$ with $\xi\in\mathbb{R}^{n}$. An a'priori estimate for solutions is proved, and their interior regularity is studied. A sufficient condition for the systems to have the Fredholm property is given.
We present a new method to localize a camera within a previously unseen environment perceived from an egocentric point of view. Although this is, in general, an ill-posed problem, humans can effortlessly and efficiently determine their relative location and orientation and navigate into a previously unseen environments, e.g., finding a specific item in a new grocery store. To enable such a capability, we design a new egocentric representation, which we call ECO (Egocentric COgnitive map). ECO is biologically inspired, by the cognitive map that allows human navigation, and it encodes the surrounding visual semantics with respect to both distance and orientation. ECO possesses three main properties: (1) reconfigurability: complex semantics and geometry is captured via the synthesis of atomic visual representations (e.g., image patch); (2) robustness: the visual semantics are registered in a geometrically consistent way (e.g., aligning with respect to the gravity vector, frontalizing, and rescaling to canonical depth), thus enabling us to learn meaningful atomic representations; (3) adaptability: a domain adaptation framework is designed to generalize the learned representation without manual calibration. As a proof-of-concept, we use ECO to localize a camera within real-world scenes---various grocery stores---and demonstrate performance improvements when compared to existing semantic localization approaches.
We consider the 1D nonlinear Schr\"odinger equation with focusing point nonlinearity. "Point" means that the pure-power nonlinearity has an inhomogeneous potential and the potential is the delta function supported at the origin. This equation is used to model a Kerr-type medium with a narrow strip in the optic fibre. There are several mathematical studies on this equation and the local/global existence of solution, blow-up occurrence and blow-up profile have been investigated. In this paper we focus on the asymptotic behavior of the global solution, i.e, we show that the global solution scatters as t tends to minus/plus infinity in the $L^2$ supercritical case. The main argument we use is due to Kenig-Merle, but it is required to make use of an appropriate function space (not Strichartz space) according to the smoothing properties of the associated integral equation.
The nature of the unconventional ordered phase occurring in CeRu2Al10 below T0 = 27 K was investigated by neutron scattering. Powder diffraction patterns show clear superstructure peaks corresponding to forbidden (h + k)-odd reflections of the Cmcm space group. Inelastic neutron scattering experiments further reveal a pronounced magnetic excitation developing in the ordered phase at an energy of 8 meV.
A method based on the consistent use of the Green function formalism has been developed to calculate the distribution of the single-particle strength in odd nuclei with pairing. The method takes into account the quasiparticle-phonon interaction, ground state correlations and a "refinement" of phenomenological single-particle energies and pairing gap values from the quasiparticle-phonon interaction under consideration. The calculations for 121Sn and 119Sn that were performed in the quasiparticle$\otimes$phonon approximation, have shown a reasonable agreement with experiment. The ground state correlations play a noticeable role and mostly improve the agreement with experiment or shift the results to the right direction.
We perform an exploratory study of the allowed parameter range for the CKM-like mixing of hypothetical quarks of a fourth generation. As experimental constraints we use the tree-level determinations of the 3 $\times$ 3 CKM elements and FCNC processes ($K$-, $D$-, $B_d$-, $B_s$-mixing and the decay $b \to s \gamma$) under the assumption that the 4 $\times$ 4 CKM matrix is unitary. For the FCNCs we use some simplifying assumptions concerning the QCD corrections. Typically small mixing with the fourth family is favoured, but contrary to expectation we find that also a quite large mixing with the 4th family is not yet excluded.
In this paper we study the problem of classifying pencils of curves of degree $d$ in $\mathbb{P}^2$ using geometric invariant theory. We consider the action of $SL(3)$ and we relate the stability of a pencil to the stability of its generators, to the log canonical threshold of its members, and to the multiplicities of its base points, thus obtaining explicit stability criteria.
Using the difference between the gauge symmetric and standard pi-N-delta couplings, a contact pi-pi-N-N term, quadratic in the pi-N-delta coupling, is explicitly constructed. Besides, a contribution from the delta excitation mechanism to the photon spectrum for the radiative muon capture in hydrogen is derived from the gauge symmetric pi-N-delta and gamma-N-delta couplings. It is shown for the photon spectrum, studied recently experimentally, that the new spectrum is for the photon momentums k > 60 MeV by 4-10 % smaller than the one obtained from standardly used couplings with the on-shell deltas.
POET (Polarimeters for Energetic Transients) is a Small Explorer mission concept proposed to NASA in January 2008. The principal scientific goal of POET is to measure GRB polarization between 2 and 500 keV. The payload consists of two wide FoV instruments: a Low Energy Polarimeter (LEP) capable of polarization measurements in the energy range from 2-15 keV and a high energy polarimeter (Gamma-Ray Polarimeter Experiment -- GRAPE) that will measure polarization in the 60-500 keV energy range. Spectra will be measured from 2 keV up to 1 MeV. The POET spacecraft provides a zenith-pointed platform for maximizing the exposure to deep space. Spacecraft rotation will provide a means of effectively dealing with systematics in the polarization response. POET will provide sufficient sensitivity and sky coverage to measure statistically significant polarization for up to 100 GRBs in a two-year mission. Polarization data will also be obtained for solar flares, pulsars and other sources of astronomical interest.
We calculated the polarization of \psi' due to gg \to Q\bar{Q}[^3P_J^(8)]g \to \psi^\lambda color-octet quarkonia production. We find that at low transverse momenta the \psi' is unpolarized due to the contributions proportional to the L=S=0 and L=S=1 color-octet matrix elements. As p_\perp increases, the \psi' mesons become 100% polarized, as predicted by fragmentation calculations. Polarization due to lowest order color-singlet production is also considered, which qualitatively has a similar shape to the color-octet production.
A new repeated-slab calculation method is developed to simulate the electronic structures of charged surfaces by arranging density-variable charged sheets in vacuum regions to realize a constant potential on the charged sheets and maintain the charge neutrality condition. The charged sheets are fabricated so as to screen an electric field from charged slabs; consequently, they act like a counter electrode composed of flat perfect conductors, modeling a tip of a scanning tunneling microscope or a reference electrode in an electrochemical cell. This method has the advantages of ease of implementation into existing repeated-slab programs and low computational costs.
We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove that an arbitrary, positive-definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451. This result is analogous to Bhargava and Hanke's celebrated 290-theorem. In addition, we prove that these three remaining ternaries represent all positive odd integers, assuming the generalized Riemann hypothesis.   This result is made possible by a new analytic method for bounding the cusp constants of integer-valued quaternary quadratic forms $Q$ with fundamental discriminant. This method is based on the analytic properties of Rankin-Selberg $L$-functions, and we use it to prove that if $Q$ is a quaternary form with fundamental discriminant, the largest locally represented integer $n$ for which $Q(\vec{x}) = n$ has no integer solutions is $O(D^{2 + \epsilon})$.
We investigate the nitrogen substitutional impurity in semiconducting zigzag and metallic armchair single-wall carbon nanotubes using ab initio density functional theory. At low concentrations (less than 1 atomic %), the defect state in a semiconducting tube becomes spatially localized and develops a flat energy level in the band gap. Such a localized state makes the impurity site chemically and electronically active. We find that if two neighboring tubes have their impurities facing one another, an intertube covalent bond forms. This finding opens an intriguing possibility for tunnel junctions, as well as the functionalization of suitably doped carbon nanotubes by selectively forming chemical bonds with ligands at the impurity site. If the intertube bond density is high enough, a highly packed bundle of interlinked single-wall nanotubes can form.
This paper examines the outflows associated with the interaction of a stellar magnetosphere with an accretion disk. In particular, we investigate the magnetospheric ejections (MEs) due to the expansion and reconnection of the field lines connecting the star with the disk. Our aim is to study the dynamical properties of the outflows and evaluate their impact on the angular momentum evolution of young protostars. Our models are based on axisymmetric time-dependent magneto-hydrodynamic simulations of the interaction of the dipolar magnetosphere of a rotating protostar with a viscous and resistive disk, using alpha prescriptions for the transport coefficients. Our simulations are designed in order to model: the accretion process and the formation of accretion funnels; the periodic inflation/reconnection of the magnetosphere and the associated MEs; the stellar wind. Similarly to a magnetic slingshot, MEs can be powered by the rotation of both the disk and the star so that they can efficiently remove angular momentum from both. Depending on the accretion rate, MEs can extract a relevant fraction of the accretion torque and, together with a weak but non-negligible stellar wind torque, can balance the spin-up due to accretion. When the disk truncation approaches the corotation radius, the system enters a "propeller" regime, where the torques exerted by the disk and the MEs can even balance the spin-up due to the stellar contraction. The MEs spin-down efficiency can be compared to other scenarios, such as the Ghosh & Lamb, X-wind or stellar wind models. Nevertheless, for all scenarios, an efficient spin-down torque requires a rather strong dipolar component, which has been seldom observed in classical T Tauri stars. A better analysis of the torques acting on the protostar must take into account non-axisymmetric and multipolar magnetic components consistent with observations.
We consider quantum modifications to phantom cosmology in a Friedmann-Robertson-Walker spacetime. The cosmological evolution equations improved by the renormalization group are obtained. For exponential potential, we find two types of cosmological fixed point; the renormalization group scale either freezes in, or continues to evolve with scale factor. We discuss the implications of each of these points, and investigate especially whether the big rip can be avoided. If the fixed point of renormalization group flow coincides with the cosmological fixed point, the universe will be dominated by dark matter and will be free from the big rip.
We consider elastic antineutrino-electron scattering taking into account possible effects of neutrino masses and mixing and of neutrino magnetic moments and electric dipole moments. Having in mind antineutrinos produced in a nuclear reactor we compute, in particular, the weak-electromagnetic interference terms which are linear in the magnetic (electric dipole) moments and also in the neutrino masses. We show that these terms are, however, suppressed compared to the pure weak and electromagnetic cross section. We also comment upon the possibility of using the electromagnetic cross section to investigate neutrino oscillations.
Laser light is widely used for communication and sensing applications, so the optimal discrimination of coherent states--the quantum states of light emitted by a laser--has immense practical importance. However, quantum mechanics imposes a fundamental limit on how well different coher- ent states can be distinguished, even with perfect detectors, and limits such discrimination to have a finite minimum probability of error. While conventional optical receivers lead to error rates well above this fundamental limit, Dolinar found an explicit receiver design involving optical feedback and photon counting that can achieve the minimum probability of error for discriminating any two given coherent states. The generalization of this construction to larger sets of coherent states has proven to be challenging, evidencing that there may be a limitation inherent to a linear-optics-based adaptive measurement strategy. In this Letter, we show how to achieve optimal discrimination of any set of coherent states using a resource-efficient quantum computer. Our construction leverages a recent result on discriminating multi-copy quantum hypotheses (arXiv:1201.6625) and properties of coherent states. Furthermore, our construction is reusable, composable, and applicable to designing quantum-limited processing of coherent-state signals to optimize any metric of choice. As illustrative examples, we analyze the performance of discriminating a ternary alphabet, and show how the quantum circuit of a receiver designed to discriminate a binary alphabet can be reused in discriminating multimode hypotheses. Finally, we show our result can be used to achieve the quantum limit on the rate of classical information transmission on a lossy optical channel, which is known to exceed the Shannon rate of all conventional optical receivers.
In the theory of digraphs, the study of cycles is a subject of great importance and has given birth to a number of deep questions such as the Behzad-Chartrand-Wall conjecture (1970) and its generalization, the Caccetta-H\"{a}ggkvist conjecture (1978). Despite a lot of interest and efforts, the progress on these remains slow and mostly restricted to the solution of some special cases. In this note, we prove these conjectures for digraphs with girth is at least as large as their minimum out-degree and without short even cycles. More generally, we prove that if a digraph has sufficiently large girth and does not contain closed walks of certain lengths, then the conjectures hold. The proof makes use of some of the known results on the Caccetta-H\"{a}ggkvist conjecture, properties of direct products of digraphs and a construction that multiplies the girth of a digraph.
For every nonconstant monic polynomial $g \in \mathbb{Z}[X]$, let $\mathfrak{M}(g)$ be the set of positive integers $m$ for which there exist an integer linear recurrence $(s_n)_{n \geq 0}$ having characteristic polynomial $g$ and a positive integer $M$ such that $(s_n)_{n \geq 0}$ has exactly $m$ distinct residues modulo $M$. Dubickas and Novikas proved that $\mathfrak{M}(X^2 - X - 1) = \mathbb{N}$. We study $\mathfrak{M}(g)$ in the case in which $g$ is divisible by a monic quadratic polynomial $f \in \mathbb{Z}[X]$ with roots $\alpha,\beta$ such that $\alpha\beta = \pm 1$ and $\alpha / \beta$ is not a root of unity. We show that this problem is related to the existence of special primitive divisors of certain Lehmer sequences, and we deduce some consequences on $\mathfrak{M}(g)$. In particular, for $\alpha\beta = -1$, we prove that $m \in \mathfrak{M}(g)$ for every integer $m \geq 7$ with $m \neq 10$ and $4 \nmid m$.
We describe all the elliptic models with section on the Shioda supersingular K3 surface X of Artin invariant 1 over an algebraically closed field of characteristic 3. In particular, we compute elliptic parameters and Weierstrass equations for the fifty two different fibrations, and analyze the reducible fibers and Mordell-Weil lattices.
In order to study isovector dipole response of neutron-rich nuclei, we have applied a time-dependent method of antisymmetrized molecular dynamics. The dipole resonances in Be, B and C isotopes have been investigated. In $^{10}$Be, $^{15}$B, $^{16}$C, collective modes of the vibration between a core and valence neutrons cause soft resonances at the excitation energy $E_x=10-15$ MeV below the giant dipole resonance(GDR). In $^{16}$C, we found that a remarkable peak at $E_x=14$ MeV corresponds to coherent motion of four valence neutrons against a $^{12}$C core, while the GDR arises from the core vibration in the $E_x >20$ MeV region. In $^{17}$B and $^{18}$C, the dipole strengths in the low energy region decline compared with those in $^{15}$B and $^{16}$C. We also discuss the energy weighted sum rule for the $E1$ transitions.
Continuous sign language recognition (SLR) deals with unaligned video-text pair and uses the word error rate (WER), i.e., edit distance, as the main evaluation metric. Since it is not differentiable, we usually instead optimize the learning model with the connectionist temporal classification (CTC) objective loss, which maximizes the posterior probability over the sequential alignment. Due to the optimization gap, the predicted sentence with the highest decoding probability may not be the best choice under the WER metric. To tackle this issue, we propose a novel architecture with cross modality augmentation. Specifically, we first augment cross-modal data by simulating the calculation procedure of WER, i.e., substitution, deletion and insertion on both text label and its corresponding video. With these real and generated pseudo video-text pairs, we propose multiple loss terms to minimize the cross modality distance between the video and ground truth label, and make the network distinguish the difference between real and pseudo modalities. The proposed framework can be easily extended to other existing CTC based continuous SLR architectures. Extensive experiments on two continuous SLR benchmarks, i.e., RWTH-PHOENIX-Weather and CSL, validate the effectiveness of our proposed method.
In this work we present an analysis of the one-loop Slavnov-Taylor identities in noncommutative QED$_4$. The vectorial fermion-photon and the triple photon vertex functions were studied, with the conclusion that no anomalies arise.
Let {\nu} be a normal function on a complex manifold X. The infinitesimal invariant of {\nu} has a well-defined zero locus inside the tangent bundle TX. When X is quasi-projective, and {\nu} is admissible, we show that this zero locus is constructible in the Zariski topology.