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Continuing our earlier work (quant-ph/0401060), we give two alternative proofs of the result that a noiseless qubit channel has identification capacity 2: the first is direct by a "maximal code with random extension" argument, the second is by showing that 1 bit of entanglement (which can be generated by transmitting 1 qubit) and negligible (quantum) communication has identification capacity 2. This generalises a random hashing construction of Ahlswede and Dueck: that 1 shared random bit together with negligible communication has identification capacity 1. We then apply these results to prove capacity formulas for various quantum feedback channels: passive classical feedback for quantum-classical channels, a feedback model for classical-quantum channels, and "coherent feedback" for general channels.
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Identification via Quantum Channels in the Presence of Prior Correlation and Feedback
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We report measurements of the charmless semileptonic decays $B^0 \to \pi^- / \rho^- \ell^{+} \nu$ and $B^+ \to \pi^0 / \rho^0 \ell^{+} \nu$, based on a sample of $2.75 \times 10^8$ $B \bar{B}$ events collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+e^-$ asymmetric collider. In this analysis, the accompanying $B$ meson is reconstructed in the semileptonic mode $B \to D^{(*)} \ell \nu$, enabling detection of the signal modes with high purity. We measure the branching fractions ${\mathcal B}(B^0 \to \pi^- \ell^+ \nu) = (1.38\pm 0.19\pm 0.14\pm 0.03) \times 10^{-4}$, ${\mathcal B}(B^0 \to \rho^- \ell^+ \nu) = (2.17\pm 0.54\pm 0.31\pm 0.08) \times 10^{-4}$, ${\mathcal B}(B^+ \to \pi^0 \ell^+ \nu) = (0.77\pm 0.14\pm 0.08\pm 0.00) \times 10^{-4}$ and ${\mathcal B}(B^+ \to \rho^0 \ell^+ \nu) = (1.33\pm 0.23\pm 0.17\pm 0.05) \times 10^{-4}$, where the errors are statistical, experimental systematic, and systematic due to form-factor uncertainties, respectively. For each mode we also present the partial branching fractions in three $q^2$ intervals: $q^2 < 8$, $8 \leq q^2 < 16$, and $q^2 \geq 16$ GeV$^2/c^2$. From our partial branching fractions for $B \to \pi \ell \nu$ and recent results for the form factor from unquenched Lattice QCD calculations, we obtain values of the CKM matrix element $|V_{ub}|$.
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Measurements of branching fractions and $q^2$ distributions for $B \to \pi \ell \nu$ and $B \to \rho \ell \nu$ Decays with $B \to D^{(*)} \ell \nu$ Decay Tagging
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The short review of theoretical aspects of ultra high energy (UHE) neutrinos and superGZK neutrinos. The sources and diffuse fluxes of UHE neutrinos are discussed. Much attention is given to comparison of the cascade and cosmic ray upper bounds for diffuse neutrino fluxes. Cosmogenic neutrinos and neutrinos from the mirror mater are considered as superGZK neutrinos.
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Ultra High Energy Neutrino Astronomy
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Recently it has been suggested that the hard x-ray power-law tails exhibited in the ASCA spectra of several nearby giant elliptical galaxies are caused by low-radiative efficiency accretion flows (ADAFs) onto a massive black hole in the centers of the galaxies. The estimated fluxes from these central ADAFs as derived from the ASCA x-ray spectral analyses indicate that they may be visible as x-ray point sources. We analyze archival ROSAT HRI images of three such galaxies, NGCs 1399, 4636, and 4696, to determine whether point x-ray sources consistent with ASCA-derived fluxes are present in the centers of the galaxies. We find that the upper limit for the flux of a central point x-ray source in each of these galaxies as determined by the ROSAT HRI data is only marginally consistent with the predicted flux inferred from the ASCA spectra. We suggest that although a central point source, such as a ADAF associated with a massive black hole, cannot be completely ruled out, they can only account for a fraction of the flux of the observed hard x-ray power law components.
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Are There ADAFs in Nearby Giant Elliptical Galaxies?
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A multiobjective optimization problem is $C^r$ simplicial if the Pareto set and the Pareto front are $C^r$ diffeomorphic to a simplex and, under the $C^r$ diffeomorphisms, each face of the simplex corresponds to the Pareto set and the Pareto front of a subproblem, where $0\leq r\leq \infty$. In the paper titled "Topology of Pareto sets of strongly convex problems," it has been shown that a strongly convex $C^r$ problem is $C^{r-1}$ simplicial under a mild assumption on the ranks of the differentials of the mapping for $2\leq r \leq \infty$. On the other hand, in this paper, we show that a strongly convex $C^1$ problem is $C^0$ simplicial under the same assumption. Moreover, we establish a specialized transversality theorem on generic linear perturbations of a strongly convex $C^r$ mapping $(r\geq 2)$. By the transversality theorem, we also give an application of singularity theory to a strongly convex $C^r$ problem for $2\leq r \leq \infty$.
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Simpliciality of strongly convex problems
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This paper studies an auction design problem for a seller to sell a commodity in a social network, where each individual (the seller or a buyer) can only communicate with her neighbors. The challenge to the seller is to design a mechanism to incentivize the buyers, who are aware of the auction, to further propagate the information to their neighbors so that more buyers will participate in the auction and hence, the seller will be able to make a higher revenue. We propose a novel auction mechanism, called information diffusion mechanism (IDM), which incentivizes the buyers to not only truthfully report their valuations on the commodity to the seller, but also further propagate the auction information to all their neighbors. In comparison, the direct extension of the well-known Vickrey-Clarke-Groves (VCG) mechanism in social networks can also incentivize the information diffusion, but it will decrease the seller's revenue or even lead to a deficit sometimes. The formalization of the problem has not yet been addressed in the literature of mechanism design and our solution is very significant in the presence of large-scale online social networks.
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Mechanism Design in Social Networks
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We calculate the amplitudes of $b\to s$ transition in extension of the Standard Model with $Wtb$ anomalous couplings. We found that i) there exist the Ward identity violating terms in effective vertix of $b\to s\gamma$. The terms, which come from the tensor parts of $Wtb$ anomalies, and can be canceled exactly by introducing corresponding $Wtb\gamma$ interactions, ii) $Br(B_{s} \to \mu^{+}\mu^{-})$ provides unique information on $\delta v_L$ which is set to zero in top decay experiments, and stringent bounds on $v_R,\ g_L$ by $Br(B\to X_s\gamma)$ are obtained.
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Constraints on $Wtb$ anomalous coupling with $ B\to X_{s}\gamma $ and $B_{s}\to\mu^{+}\mu^{-}
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We made C18O (2-1) and CS (7-6) images of the protostellar envelope around B335 with a high spatial dynamic range from ~10000 to ~400 AU, by combining the Submillimeter Array and single-dish data. The C18O emission shows an extended (~10000 AU) structure as well as a compact (~1500 AU) component concentrated at the protostellar position. The CS emission shows a compact (~900 AU) component surrounding the protostar, plus a halo-like (~3000 AU) structure elongated along the east-west direction. At higher velocities (|dV| >~0.3 km s^-1), the CS emission is stronger and more extended than the C18O emission. Physical conditions of the envelope were examined through an LVG model. At |dV| >~0.3 km s^-1, the gas temperature is higher (>40 K) than that at |dV| <~0.3 km s^-1, whereas the gas density is lower (<10^6 cm^-3). We consider that the higher-temperature and lower-density gas at |dV| >~0.3 km s^-1 is related to the associated outflow, while the lower-temperature and higher-density gas at |dV| <~0.3 km s^-1 is the envelope component. From the inspection of the positional offsets in the velocity channel maps, the radial profile of the specific angular momentum of the envelope rotation in B335 was revealed at radii from ~10^4 down to ~10^2 AU. The specific angular momentum decreases down to the radius of ~370 AU, and then appears to be conserved within that radius. A possible scenario of the evolution of envelope rotation is discussed.
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Kinematics and Physical Conditions of the Innermost Envelope in B335
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This paper is the eighth in a sequence on the structure of sets of solutions to systems of equations in free and hyperbolic groups, projections of such sets (Diophantine sets), and the structure of definable sets over free and hyperbolic groups. In the eighth paper we use a modification of the sieve procedure, that was presented as part of the quantifier elimination process, to prove that free and torsion-free (Gromov) hyperbolic groups are stable.
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Diophantine Geometry over Groups VIII: Stability
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What we appreciate in dance is the ability of people to sponta- neously improvise new movements and choreographies, sur- rendering to the music rhythm, being inspired by the cur- rent perceptions and sensations and by previous experiences, deeply stored in their memory. Like other human abilities, this, of course, is challenging to reproduce in an artificial entity such as a robot. Recent generations of anthropomor- phic robots, the so-called humanoids, however, exhibit more and more sophisticated skills and raised the interest in robotic communities to design and experiment systems devoted to automatic dance generation. In this work, we highlight the importance to model a computational creativity behavior in dancing robots to avoid a mere execution of preprogrammed dances. In particular, we exploit a deep learning approach that allows a robot to generate in real time new dancing move- ments according to to the listened music.
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Creative Robot Dance with Variational Encoder
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Hidden-order phases that occur in a number of correlated f-electron systems are among the most elusive states of electronic matter. Their investigations are hindered by the insensitivity of standard physical probes, such as neutron diffraction, to the order parameter that is usually associated with higher-order multipoles of the f-orbitals. The heavy-fermion compound Ce3Pd20Si6 exhibits magnetically hidden order at subkelvin temperatures, known as phase II. Additionally, for magnetic field applied along the [001] cubic axis, another phase II' was detected, but the nature of the transition from phase II to phase II' remained unclear. Here we use inelastic neutron scattering to demonstrate that this transition is associated with a change in the propagation vector of the antiferroquadrupolar order from (111) to (100). Despite the absence of magnetic Bragg scattering in phase II', its ordering vector is revealed by the location of an intense magnetic soft mode at the (100) wave vector, orthogonal to the applied field. At the II-II' transition, this mode softens and transforms into quasielastic and nearly Q-independent incoherent scattering, which is likely related to the non-Fermi-liquid behavior recently observed at this transition. Our experiment also reveals sharp collective excitations in the field-polarized paramagnetic phase, after phase II' is suppressed in fields above 4 T.
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Evolution of the propagation vector of antiferroquadrupolar phases in Ce3Pd20Si6 with magnetic field
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This paper introduces a new encoder-decoder architecture that is trained to reconstruct images by disentangling the salient information of the image and the values of attributes directly in the latent space. As a result, after training, our model can generate different realistic versions of an input image by varying the attribute values. By using continuous attribute values, we can choose how much a specific attribute is perceivable in the generated image. This property could allow for applications where users can modify an image using sliding knobs, like faders on a mixing console, to change the facial expression of a portrait, or to update the color of some objects. Compared to the state-of-the-art which mostly relies on training adversarial networks in pixel space by altering attribute values at train time, our approach results in much simpler training schemes and nicely scales to multiple attributes. We present evidence that our model can significantly change the perceived value of the attributes while preserving the naturalness of images.
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Fader Networks: Manipulating Images by Sliding Attributes
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We consider a classical problem of Computer Algebra: symbolic solution of PDEs. We transform the famous Darboux theorems on differential transformations of hyperbolic operator into the space of invariants. We introduce a new idea -- $X$- and $Y$-invariants of such operator as solutions of some equations written in terms of the Laplace invariants of this operator. Explicit formula for the changes in the sets of the $X$- and $Y$-invariants under the Darboux transformations are obtained.
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$X$- and $Y$-invariants of Linear Partial Differential Operators in the plane (In Russian)
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By giving up the best constants, we will see that the original argument of Spielman and Srivastava for proving the Bourgain-Tzafriri Restricted Invertibility Theorem \cite{SS} still works - and is much simplier than the final version. We do not intend on publishing this since it is their argument with just a trivial modification, but we want to make it available to the mathematics community since several people have requested it already.
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The simplified version of the Spielman and Srivastava algorithm for proving the Bourgain-Tzafriri restricted invertiblity theorem
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The forces acting on bridge structural elements caused by live loads are computed by live load models defined in design codes. In most cases, such live load models are defined by studies performed on girder bridges, where extreme values of shear forces and bending moment are intended to be predicted. This paper shows that when code live load models are applied to truss bridges, the estimated forces in some structural elements may not be representative of those caused by actual traffic. Three WIM (weigh-in-motion) databases, which are recorded on roads in Mexico, are used as real traffic data. The results suggest that current code live load models are not entirely adequate to estimate forces in structural elements of truss bridges.
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Inconsistencies between the forces from code live load models and real traffic on truss bridges
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We investigate theoretically the interaction of dark solitons in materials with a spatially nonlocal nonlinearity. In particular we do this analytically and for arbitrary degree of nonlocality. We employ the variational technique to show that nonlocality induces an attractive force in the otherwise repulsive soliton interaction.
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Analytical theory for dark soliton interaction in nonlocal nonlinear materials with arbitrary degree of nonlocality
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Pairs of planets in a system may end up close to their host star on eccentric orbits as a consequence of planet planet scattering, Kozai or secular migration. In this scenario, general relativity and secular perturbations have comparable timescales and may interfere with each other with relevant effects on the eccentricity and pericenter evolution of the two planets. We explore, both analytically and via numerical integration, how the secular evolution is changed by general relativity for a wide range of different initial conditions. We find that when the faster secular frequency approaches the general relativity precession rate, which tipically occurs when the outer planet moves away from the inner one, it relaxes to it and a significant damping of the proper eccentricity of the inner planet occurs. The proper eccentricity of the outer planet is reduced as well due to the changes in the secular interaction of the bodies. The lowering of the peak eccentricities of the two planets during their secular evolution has important implications on their stability. A significant number of two planet systems, otherwise chaotic because of the mutual secular perturbations, are found stable when general relativity is included.
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Secular evolution of close in planets: the effects of general relativity
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This work concerns the global well-posedness problem for the 3D axisymmetric viscous Boussinesq system with critical rough initial data. More precisely, we aim to extending our recent result \cite{Hanachi-Houamed-Zerguine} to the case of initial data of measure type. To this end, we should first develop some notions of axisymmetric measures in a general context, then, in the spirit of \cite{Gallay-Sverak}, we prove the global wellposedness result provided that the atomic parts of the initial measures are small enough.
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Remarks on the global well-posedness of the axisymmetric Boussinesq system with rough initial data
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Semi-empirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semi-empirical model still in widespread use in chemistry is H\"uckel's $\pi$-electron molecular orbital theory. In this work, we implemented a H\"uckel program using differentiable programming with the JAX framework, based on limited modifications of a pre-existing NumPy version. The auto-differentiable H\"uckel code enabled efficient gradient-based optimization of model parameters tuned for excitation energies and molecular polarizabilities, respectively, based on as few as 100 data points from density functional theory simulations. In particular, the facile computation of the polarizability, a second-order derivative, via auto-differentiation shows the potential of differentiable programming to bypass the need for numeric differentiation or derivation of analytical expressions. Finally, we employ gradient-based optimization of atom identity for inverse design of organic electronic materials with targeted orbital energy gaps and polarizabilities. Optimized structures are obtained after as little as 15 iterations, using standard gradient-based optimization algorithms.
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Inverse molecular design and parameter optimization with H\"uckel theory using automatic differentiation
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We propose a new matrix model describing multi-baryon systems. We derive the action from open string theory on the wrapped baryon vertex D-branes embedded in the D4-D8 model of large N holographic QCD. The positions of k baryons are unified into k x k matrices, with spin/isospin of the baryons encoded in a set of k-vectors. Holographic baryons are known to be very small in the large 't Hooft coupling limit, and our model offers a better systematic approach to dynamics of such baryons at short distances. We compute energetics and spectra (k=1), and also short-distance nuclear force (k=2). In particular, we obtain a new size of the holographic baryon and find a precise form of the repulsive core of nucleons. This matrix model complements the instanton soliton picture of holographic baryons, whose small size turned out to be well below the natural length scale of the approximation involved there. Our results show that, nevertheless, the basic properties of holographic baryons obtained there are robust under stringy corrections within a few percents.
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A Matrix Model for Baryons and Nuclear Forces
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For a large class of two-loop selfenergy- and vertex-type diagrams with only one non-zero mass ($M$) and the vertices also with only one non-zero external momentum squared ($q^2$) the first few expansion coefficients are calculated by the large mass expansion. This allows to `guess' the general structure of these coefficients and to verify them in terms of certain classes of `basis elements', which are essentially harmonic sums. Since for this case with only one non-zero mass the large mass expansion and the Taylor series in terms of $q^2$ are identical, this approach yields analytic expressions of the Taylor coefficients, from which the diagram can be easily evaluated numerically in a large domain of the complex $q^2-$plane by well known methods. It is also possible to sum the Taylor series and present the results in terms of polylogarithms.
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Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
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We review the anomaly inflow mechanism on D-branes and O-planes. In particular, we compute the one-loop world-volume anomalies and derive the RR anomalous couplings required for their cancellation.
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Anomaly inflow and RR anomalous couplings
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We prove that, for any finite Blaschke product $w=B(z)$ in the unit disk, the corresponding Riemann surface over the $w$--plane contains a one-sheeted disk of the radius $0.5$. Moreover, it contains a unit one-sheeted disk with a radial slit. We apply this result to obtain a universal sharp lower estimate of the Bloch seminorm for finite Blaschke products.
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On Bloch seminorm of finite Blaschke products in the unit disk
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Computer modeling of the one-dimensional and three-dimensional nanoparticles with Van-der-Waals interaction was performed. The arrangement of atoms was defined on the grounds of an energy minimum. The calculations have shown that in the presence of vacancies in a nanoparticle and the account of a relaxation and oscillations the nanoparticle will pulse. This pulsation on distance between atoms of a nanoparticle is observed in both one-dimensional and a three-dimensional cases.
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Influence of Vacancies on the Nanoparticle Pulsation
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We construct and analyse the moduli space (collective coordinates) for a classical field theory in 1 + 1 dimensions that possesses complex stable multi-soliton solutions with real energies when PT-regularized. For the integrable Bullough-Dodd model we show, by comparing with the exact solutions, that a one-dimensional moduli space captures well the main feature of the centre of mass motion of the one and two-soliton solutions. We demonstrate that even the time-delay and spatial displacements occurring for the one-soliton constituents in a multi-soliton scattering process can be extracted from a moduli space analysis. We propose a two dimensional moduli space to describe the newly found triple bouncing scattering amongst the constituents of a dark two double peakon scattering.
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Moduli spaces for PT-regularized solitons
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In this paper, we have selected a sample of 64 teraelectronvolt blazars, with redshift, from those classified in the fourth Fermi Large Area Telescope source catalog\footnote{\url{https://fermi.gsfc.nasa.gov/ssc/data/access/lat/8yr_catalog/}}. We have obtained the values of the relevant physical parameters by performing a log-parabolic fitting of the average-state multiwavelength spectral energy distributions. We estimate the range of the radiation zone parameters, such as the Doppler factor (${D}$), the magnetic field strength ($B$), the radiative zone radius ($R$) and the peak Lorentz factor (${\gamma _{\rm p}}$) of nonthermal electrons. Here, we show that (1) there is a strong linear positive correlation between the intrinsic synchrotron peak frequency and the intrinsic inverse Compton scattering (ICs) peak frequency among different types of blazars; (2) if radio bands are excluded, the spectral index of each band is negatively correlated with the intrinsic peak frequency; (3) there is a strong linear negative correlation between the curvature at the peak and the intrinsic peak frequency of the synchrotron bump, and a weak positive correlation between the curvature at the peak and the intrinsic peak frequency of the ICs bump; (4) there is a strong linear positive correlation between the intrinsic ICs peak luminosity and intrinsic $\gamma$-ray luminosity and between the intrinsic ICs peak frequency and peak Lorentz factor; (5) there is a strong negative linear correlation between $\rm log{\;B}$ and $\rm log{\;\gamma_{p}}$; and (6) there is no correlation between $\rm log{\;R}$ and $\rm log{\;\gamma_{p}}$.
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The Intrinsic Properties of Multiwavelength Energy Spectra for Fermi Teraelectronvolt Blazars
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We present extensive radio observations of a Type Ic supernova, ASASSN-16fp. Our data represents the lowest frequency observations of the SN beyond 1000 days with a frequency range of $0.33-25$ GHz and a temporal range of $\sim$ 8 to 1136 days post-explosion. The observations are best represented by a model of synchrotron emission from a shocked circumstellar shell initially suppressed by synchrotron self-absorption. Assuming equipartition of energy between relativistic particles and magnetic fields, we estimate the velocity and radius of the blast wave to be $v \sim 0.15c$ and $r \sim 3.4$ $\times$ $10^{15}$ cm respectively at $t_{0}$ $\sim$ 8 days post-explosion. We infer the total internal energy of the radio-emitting material evolves as $E$ $\sim$ 0.37 $\times$ $10^{47}$ (t/t$_{0}$)$^{0.65}$ erg. We determine the mass-loss rate of the progenitor star to be $\dot{M}$ $\sim$ $(0.4-3.2) \times10^{-5}$ $M_{\odot}\rm yr^{-1}$ at various epochs post-explosion, consistent with the mass-loss rate of Galactic Wolf-Rayet stars. The radio light curves and spectra show a signature of density enhancement in the CSM at a radius of $\sim$ $1.10 \times 10^{16}$ cm from the explosion center.
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Radio view of a broad-line Type Ic supernova ASASSN-16fp
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This thesis by publication is devoted to the study of aspects of the early universe in the context of primordial black hole (PBH) physics. Firstly, we review the fundamentals of the early universe cosmology and we recap the basics of the PBHs physics. In particular, we propose a refinement in the determination of the PBH formation threshold, a fundamental quantity in PBH physics, in the context of a time-dependent equation-of-state parameter. Afterwards, we briefly present the theory of inflationary perturbations, which is the theoretical framework within which PBHs are studied in this thesis. Then, in the second part of the thesis, we review the core of the research conducted within my PhD, in which aspects of the early universe and the gravitational wave physics are combined with the physics of PBHs. Moreover, aspects of the PBH gravitational collapse process are studied in the presence of anisotropies. Specifically, we study PBHs produced from the preheating instability in the context of single-field inflation. Interestingly, we find that PBHs produced during preheating can potentially dominate the universe's content and drive reheating through their evaporation. Then, we focus on the scalar induced second-order stochastic gravitational wave background (SGWB) induced from Poisson energy density fluctuations of ultralight PBHs. By taking then into account gravitational wave backreaction effects we set model-independent constraints on the initial abundance of ultralight PBHs as a function of their mass. Afterwards, we study in a covariant way the anisotropic spherical gravitational collapse of PBHs during a radiation-dominated era in which one can compute the PBH formation threshold as a function of the anisotropy. Finally, we summarize our research results by discussing future prospects opened up as a result of the research work conducted within this thesis.
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Studying Aspects of the Early Universe with Primordial Black Holes
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K-means is one of the most widely used clustering models in practice. Due to the problem of data isolation and the requirement for high model performance, how to jointly build practical and secure K-means for multiple parties has become an important topic for many applications in the industry. Existing work on this is mainly of two types. The first type has efficiency advantages, but information leakage raises potential privacy risks. The second type is provable secure but is inefficient and even helpless for the large-scale data sparsity scenario. In this paper, we propose a new framework for efficient sparsity-aware K-means with three characteristics. First, our framework is divided into a data-independent offline phase and a much faster online phase, and the offline phase allows to pre-compute almost all cryptographic operations. Second, we take advantage of the vectorization techniques in both online and offline phases. Third, we adopt a sparse matrix multiplication for the data sparsity scenario to improve efficiency further. We conduct comprehensive experiments on three synthetic datasets and deploy our model in a real-world fraud detection task. Our experimental results show that, compared with the state-of-the-art solution, our model achieves competitive performance in terms of both running time and communication size, especially on sparse datasets.
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Scalable and Sparsity-Aware Privacy-Preserving K-means Clustering with Application to Fraud Detection
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We study irreducible odd mod $p$ Galois representations $\bar{\rho} \colon \mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_p)$, for $F$ a totally real number field and $G$ a general reductive group. For $p \gg_{G, F} 0$, we show that any $\bar{\rho}$ that lifts locally, and at places above $p$ to de Rham and Hodge-Tate regular representations, has a geometric $p$-adic lift. We also prove non-geometric lifting results without any oddness assumption.
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Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations
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Let $q$ be a prime power. We estimate the number of tuples of degree bounded monic polynomials $(Q_1,\ldots,Q_v) \in (\mathbb{F}_q[z])^v$ that satisfy given pairwise coprimality conditions. We show how this generalises from monic polynomials in finite fields to Dedekind domains with finite norms.
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Tuples of polynomials over finite fields with pairwise coprimality conditions
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According to the Omori-Utsu law, the rate of aftershocks after a mainshock decays as a power law with an exponent close to 1. This well-established law was intensively used in the past to study and model the statistical properties of earthquakes. Moreover, according to the so-called inverse Omori law, the rate of earthquakes should also increase prior to a mainshock -- this law has received much less attention due to its large uncertainty. Here, we mainly study the inverse Omori law based on a highly detailed Southern California earthquake catalog, which is complete for magnitudes larger than M>0.3. First, we develop a technique to identify mainshocks, foreshocks, and aftershocks. We then find, based on a statistical procedure we developed, that the rate of earthquakes is higher a few days prior to a mainshock. We find that this increase is much smaller for a catalog with a magnitude threshold of m over 2.5 and for the Epidemic-Type Aftershocks Sequence (ETAS) model catalogs, even when used with a small magnitude threshold. We also analyze the rate of aftershocks after mainshocks and find that the Omori-Utsu law does not hold for many individual mainshocks and that it may be valid only statistically when considering many mainshocks together. Yet, the analysis of the ETAS model based on the Omori-Utsu law exhibits similar behavior as that of the real catalogs, indicating the validity of this law.
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Increased earthquake rate prior to mainshocks
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Stellar evolution computations provide the foundation of several methods applied to study the evolutionary properties of stars and stellar populations, both Galactic and extragalactic. The accuracy of the results obtained with these techniques is linked to the accuracy of the stellar models, and in this context the correct treatment of the transport of chemical elements is crucial. Unfortunately, in many respects calculations of the evolution of the chemical abundance profiles in stars are still affected by sometime sizable uncertainties. Here, we review the various mechanisms of element transport included in the current generation of stellar evolution calculations, how they are implemented, the free parameters and uncertainties involved, the impact on the models, and the observational constraints.
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Chemical element transport in stellar evolution models
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The Panchromatic Hubble Andromeda Treasury (PHAT) survey is an on-going Hubble Space Telescope (HST) multi-cycle program to obtain high spatial resolution imaging of one-third of the M31 disk at ultraviolet through near-infrared wavelengths. In this paper, we present the first installment of the PHAT stellar cluster catalog. When completed, the PHAT cluster catalog will be among the largest and most comprehensive surveys of resolved star clusters in any galaxy. The exquisite spatial resolution achieved with HST has allowed us to identify hundreds of new clusters that were previously inaccessible with existing ground-based surveys. We identify 601 clusters in the Year 1 sample, representing more than a factor of four increase over previous catalogs within the current survey area (390 arcmin^2). This work presents results derived from the first \sim25% of the survey data; we estimate that the final sample will include \sim2500 clusters. For the Year 1 objects, we present a catalog with positions, radii, and six-band integrated photometry. Along with a general characterization of the cluster luminosities and colors, we discuss the cluster luminosity function, the cluster size distributions, and highlight a number of individually interesting clusters found in the Year 1 search.
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PHAT Stellar Cluster Survey I. Year 1 Catalog and Integrated Photometry
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In order to solve the hierarchy problem, several extra-dimensional models have received considerable attention. We have considered a process where a Higgs boson is produced in association with a KK-graviton ($G_{\rm KK}$) at the LHC. At the leading order, this process occurs through gluon fusion mechanism $gg \to h G_{\rm KK}$ via a quark loop. We compute the cross section and examine some features of this process in the ADD model. We find that the quark in the loop does not decouple in the large quark-mass limit just as in the case of $gg\to h$ process. We compute the cross section of this process for the case of the RS model also. We examine the feasibility of this process being observed at the LHC.
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Associated Production of a KK-Graviton with a Higgs Boson via Gluon Fusion at the LHC
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We have constructed empirical formulae for fusion and interaction barrier heights using experimental values available in the literature. Fusion excitation function measurements are used for the former and back angle quasi-elastic excitation function for the latter case. The fusion barriers so obtained have been compared with various model predictions such as Bass potential, Christenson and Winther, Broglia and Winther, Aage Winther, Siwek-Wilczynska and J.Wilczynski, Skyrme energy density function model, and the Sao Paulo optical potential along with experimental results. The comparison allows us to find the best model, which is found to be the Broglia and Winther model. Further, to examine its predictability, the Broglia and Winther model parameters are used to obtain total fusion cross sections showing good agreement with the experimental values for beam energies above the fusion barriers. Thus, this model can be useful for planning any experiments, especially ones aiming for super heavy elements. Similarly, current interaction barrier heights have also been compared with the Bass potential model predictions. It shows that the present model calculations are much lower than the Bass potential model predictions. We believe the current interaction barrier model prediction will be a good starting point for future quasi-elastic scattering experiments. Whereas both the Broglia and Winther model and our interaction barrier model will have practical implications in carrying out physics research near the Coulomb barrier energies.
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Exploring the accurate nuclear potential
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We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension $1 < d_f \le 3$ in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of Wolff cluster and are able to establish a new scaling relation. It enables us to introduce a new exponent associated to the surface energy of Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via an inequality.
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Scaling law of Wolff cluster surface energy
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Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases, location-based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest-neighbor queries in a probabilistic framework in which the location of each input point is specified as a probability distribution function. We present efficient algorithms for - computing all points that are nearest neighbors of a query point with nonzero probability; and - estimating the probability of a point being the nearest neighbor of a query point, either exactly or within a specified additive error.
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Nearest-Neighbor Searching Under Uncertainty II
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The Minimal Ancestral Deviation (MAD) method is a recently introduced procedure for estimating the root of a phylogenetic tree, based only on the shape and branch lengths of the tree. The method is loosely derived from the midpoint rooting method, but, unlike its predecessor, makes use of all pairs of OTUs when positioning the root. In this note we establish properties of this method and then describe a fast and memory efficient algorithm. As a proof of principle, we use our algorithm to determine the MAD roots for simulated phylogenies with up to 100,000 OTUs. The calculations take a few minutes on a standard laptop.
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MAD roots for large trees
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In this paper we study the effect of stochastic errors on two constrained incremental sub-gradient algorithms. We view the incremental sub-gradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a particular agent of a distributed network. We first study the standard cyclic incremental sub-gradient algorithm in which the agents form a ring structure and pass the iterate in a cycle. We consider the method with stochastic errors in the sub-gradient evaluations and provide sufficient conditions on the moments of the stochastic errors that guarantee almost sure convergence when a diminishing step-size is used. We also obtain almost sure bounds on the algorithm's performance when a constant step-size is used. We then consider \ram{the} Markov randomized incremental subgradient method, which is a non-cyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time non-homogeneous Markov chain. Such a model is appropriate for mobile networks, as the network topology changes across time in these networks. We establish the convergence results and error bounds for the Markov randomized method in the presence of stochastic errors for diminishing and constant step-sizes, respectively.
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Incremental Stochastic Subgradient Algorithms for Convex Optimization
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In this paper, we propose a graph neural network architecture to solve the AC power flow problem under realistic constraints. To ensure a safe and resilient operation of distribution grids, AC power flow calculations are the means of choice to determine grid operating limits or analyze grid asset utilization in planning procedures. In our approach, we demonstrate the development of a framework that uses graph neural networks to learn the physical constraints of the power flow. We present our model architecture on which we perform unsupervised training to learn a general solution of the AC power flow formulation independent of the specific topologies and supply tasks used for training. Finally, we demonstrate, validate and discuss our results on medium voltage benchmark grids. In our approach, we focus on the physical and topological properties of distribution grids to provide scalable solutions for real grid topologies. Therefore, we take a data-driven approach, using large and diverse data sets consisting of realistic grid topologies, for the unsupervised training of the AC power flow graph neural network architecture and compare the results to a prior neural architecture and the Newton-Raphson method. Our approach shows a high increase in computation time and good accuracy compared to state-of-the-art solvers. It also out-performs that neural solver for power flow in terms of accuracy.
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Solving AC Power Flow with Graph Neural Networks under Realistic Constraints
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In this paper we prove several theorems about abelian varieties over finite fields by studying the set of monic real polynomials of degree 2n all of whose roots lie on the unit circle. In particular, we consider a set V_n of vectors in R^n that give the coefficients of such polynomials. We calculate the volume of V_n and we find a large easily-described subset of V_n. Using these results, we find an asymptotic formula --- with explicit error terms --- for the number of isogeny classes of n-dimensional abelian varieties over F_q. We also show that if n>1, the set of group orders of n-dimensional abelian varieties over F_q contains every integer in an interval of length roughly q^{n-1/2} centered at q^n+1. Our calculation of the volume of V_n involves the evaluation of the integral over the simplex {(x_1,...,x_n) | 0 < x_1 < ... < x_n < 1} of the determinant of the n-by-n matrix whose (i,j)th entry is x_j^{e_i-1}, where the e_i are positive real numbers.
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Real polynomials with all roots on the unit circle and abelian varieties over finite fields
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We give a simple, multiplicative-weight update algorithm for learning undirected graphical models or Markov random fields (MRFs). The approach is new, and for the well-studied case of Ising models or Boltzmann machines, we obtain an algorithm that uses a nearly optimal number of samples and has quadratic running time (up to logarithmic factors), subsuming and improving on all prior work. Additionally, we give the first efficient algorithm for learning Ising models over general alphabets. Our main application is an algorithm for learning the structure of t-wise MRFs with nearly-optimal sample complexity (up to polynomial losses in necessary terms that depend on the weights) and running time that is $n^{O(t)}$. In addition, given $n^{O(t)}$ samples, we can also learn the parameters of the model and generate a hypothesis that is close in statistical distance to the true MRF. All prior work runs in time $n^{\Omega(d)}$ for graphs of bounded degree d and does not generate a hypothesis close in statistical distance even for t=3. We observe that our runtime has the correct dependence on n and t assuming the hardness of learning sparse parities with noise. Our algorithm--the Sparsitron-- is easy to implement (has only one parameter) and holds in the on-line setting. Its analysis applies a regret bound from Freund and Schapire's classic Hedge algorithm. It also gives the first solution to the problem of learning sparse Generalized Linear Models (GLMs).
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Learning Graphical Models Using Multiplicative Weights
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I report on a new component in the pre-main sequence multiple system V 773 Tauri. This second visual companion, V 773 Tau C, with a projected separation of about 0."2 has been detected using speckle interferometry in the near-infrared. Repeated observations from 1996 to 2002 show significant orbital motion and thus confirm the character of the new companion as a gravitationally bound star. Together with the two components of the spectroscopic binary V 773 Tau A and the previously known visual companion V 773 Tau B, the V 773 Tau system appears as a young "mini-cluster" of four T Tauri stars within a sphere of a radius less than 100 AU. V 773 Tau, A, B and C form a triple system that is not hierarchic, but is apparently stable despite of this. The brightness of V 773 Tau C has probably increased over the last years, which may explain its non-detection in previous binary surveys.
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A fourth component in the young multiple system V 773 Tau
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In the optically thin regime, the intensity ratio of the two Si IV resonance lines (1394 and 1403 \AA\ ) are theoretically the same as the ratio of their oscillator strengths, which is exactly 2. Here, we study the ratio of the integrated intensity of the Si IV lines ($R=\int I_{1394}(\lambda)\mathrm{d}\lambda/\int I_{1403}(\lambda)\mathrm{d}\lambda$) and the ratio of intensity at each wavelength point ($r(\Delta\lambda)=I_{1394}(\Delta\lambda)/I_{1403}(\Delta\lambda)$) in two solar flares observed by the Interface Region Imaging Spectrograph. We find that at flare ribbons, the ratio $R$ ranges from 1.8 to 2.3 and would generally decrease when the ribbons sweep across the slit position. Besides, the distribution of $r(\Delta\lambda)$ shows a descending trend from the blue wing to the red wing. In loop cases, the Si IV line presents a wide profile with a central reversal. The ratio $R$ deviates little from 2, but the ratio $r(\Delta\lambda)$ can vary from 1.3 near the line center to greater than 2 in the line wings. Hence we conclude that in flare conditions, the ratio $r(\Delta\lambda)$ varies across the line, due to the variation of the opacity at the line center and line wings. We notice that, although the ratio $r(\Delta\lambda)$ could present a value which deviates from 2 as a result of the opacity effect near the line center, the ratio $R$ is still close to 2. Therefore, caution should be taken when using the ratio of the integrated intensity of the Si IV lines to diagnose the opacity effect.
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Diagnosing the Optically Thick/Thin Features Using the Intensity Ratio of Si IV Resonance Lines in Solar Flares
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We use G\"odel's Dialectica interpretation to analyse Nash-Williams' elegant but non-constructive "minimal bad sequence" proof of Higman's Lemma. The result is a concise constructive proof of the lemma (for arbitrary decidable well-quasi-orders) in which Nash-Williams' combinatorial idea is clearly present, along with an explicit program for finding an embedded pair in sequences of words.
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Applying G\"odel's Dialectica Interpretation to Obtain a Constructive Proof of Higman's Lemma
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As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation. Near grazing-sliding bifurcations structurally stable dynamics are captured by piecewise-linear continuous maps. Recently it was shown that maps of this class can have infinitely many asymptotically stable periodic solutions of a simple type. Here this result is used to show that at a grazing-sliding bifurcation an asymptotically stable periodic orbit can bifurcate into infinitely many asymptotically stable periodic orbits. For an abstract ODE system the periodic orbits are continued numerically revealing subsequent bifurcations at which they are destroyed.
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Grazing-sliding bifurcations creating infinitely many attractors
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In this article, we give the exact interval of the cross section of the Multibrot sets generated by the polynomial $z^p+c$ where $z$ and $c$ are complex numbers and $p \geq 2$ is an even integer. Furthermore, we show that the same Multibrots defined on the hyperbolic numbers are always squares. Moreover, we give a generalized 3D version of the hyperbolic Multibrot set and prove that our generalization is an octahedron for a specific 3D slice of the tricomplex polynomial $\eta^p+c$ where $p \geq 2$ is an even integer.
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Tricomplex dynamical systems generated by polynomials of even degree
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In a low energy approximation of the massless Yukawa theory (Nelson model) we derive a Faddeev-Kulish type formula for the scattering matrix of $N$ electrons and reformulate it in LSZ terms. To this end, we perform a decomposition of the infrared finite Dollard modifier into clouds of real and virtual photons, whose infrared divergencies mutually cancel. We point out that in the original work of Faddeev and Kulish the clouds of real photons are omitted, and consequently their scattering matrix is ill-defined on the Fock space of free electrons. To support our observations, we compare our final LSZ expression for $N=1$ with a rigorous non-perturbative construction due to Pizzo. While our discussion contains some heuristic steps, they can be formulated as clear-cut mathematical conjectures.
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From Faddeev-Kulish to LSZ. Towards a non-perturbative description of colliding electrons
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We aim to study the standing fundamental kink mode of coronal loops in the nonlinear regime, investigating the changes in energy evolution in the cross-section and oscillation amplitude of the loop which are related to nonlinear effects, in particular to the development of the Kelvin-Helmholtz instability (KHI). We run idea, high-resolution three-dimensional (3D) magnetohydrodynamics (MHD) simulations, studying the influence of the initial velocity amplitude and the inhomogeneous layer thickness. We model the coronal loop as a straight, homogeneous magnetic flux tube with an outer inhomogeneous layer, embedded in a straight, homogeneous magnetic field. We find that, for low amplitudes which do not allow for the KHI to develop during the simulated time, the damping time agrees with the theory of resonant absorption. However, for higher amplitudes, the presence of KHI around the oscillating loop can alter the loop's evolution, resulting in a significantly faster damping than predicted by the linear theory in some cases. This questions the accuracy of seismological methods applied to observed damping profiles, based on linear theory.
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Damping of nonlinear standing kink oscillations: a numerical study
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The transverse mass spectra of light mesons produced in Au-Au collisions at 200 GeV/nucleon are analyzed in Tsallis statistics. In high energy collisions, it has been found that the spectra follow a generalized scaling law. We applied Tsallis statistics to the description of different particles using the scaling properties. The calculated results are in agreement with experimental data of PHENIX Collaboration. And, the temperature of emission sources is extracted consistently.
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Formulation of transverse mass distributions in Au-Au collisions at 200 GeV/nucleon
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The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.
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A representation of isometries on function spaces
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One of the most effective approaches to improving the performance of a machine learning model is to procure additional training data. A model owner seeking relevant training data from a data owner needs to appraise the data before acquiring it. However, without a formal agreement, the data owner does not want to share data. The resulting Catch-22 prevents efficient data markets from forming. This paper proposes adding a data appraisal stage that requires no data sharing between data owners and model owners. Specifically, we use multi-party computation to implement an appraisal function computed on private data. The appraised value serves as a guide to facilitate data selection and transaction. We propose an efficient data appraisal method based on forward influence functions that approximates data value through its first-order loss reduction on the current model. The method requires no additional hyper-parameters or re-training. We show that in private, forward influence functions provide an appealing trade-off between high quality appraisal and required computation, in spite of label noise, class imbalance, and missing data. Our work seeks to inspire an open market that incentivizes efficient, equitable exchange of domain-specific training data.
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Data Appraisal Without Data Sharing
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We present an experimental study demonstrating the manipulation of atom-number distributions of spinor gases after nonequilibrium quantum quenches across superfluid to Mott-insulator phase transitions in cubic optical lattices. Our data indicate that atom distributions in individual Mott lobes can be tuned by properly designing quantum quench sequences, which suggests methods of maximizing the fraction of atoms in Mott lobes of even occupation numbers and has applications in attaining different quantum magnetic phases including massively entangled states. Spatial distributions of gases in three-dimensional lattices are derived from the observed number distributions, which reveal complex spatial dynamics during the quantum quenches. Qualitative agreements are also found between our experimental data and numerical simulations based on time-dependent Gutzwiller approximations in two-dimensional systems.
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Manipulating atom-number distributions and detecting spatial distributions in lattice-confined spinor gases
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A cross-section calculation for the Standard Model reaction $e^+e^- \rightarrow (Z^0Z^0) \rightarrow f_1\bar{f_1}f_2\bar{f_2}$ including the effects of the finite $Z^0$~width and initial state radiative corrections is presented. The angular phase space integrations are performed analytically, leaving the invariant masses for numerical integration. Semi-analytical and numerical results in the energy range $\sqrt{s}=150\;GeV$ to $1\;TeV$ are reported.
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Complete Initial State Radiation to off-Shell $Z^0$~PAIR Production in $e^+e^-$~ANNIHILATION
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The weak gravitational lensing of high redshift type Ia supernovae has the potential of probing the structure of matter on galaxy halo scales. This is complementary to the weak lensing of galaxies which probes structure of larger scales. There are already several organized searches for these supernovae being carried out for the purposes of cosmological parameter estimation. A method is proposed for extracting from future supernovae data information on lensing and the structures responsible. This method utilizes the correlations between SN luminosities and foreground galaxies. Simulations of the lensing and uncertainties will be presented. It is found that with a hundred supernovae or more at $z\simgt 1$ or larger, significant measurements of the mass, shape and extent of dark matter halos could be made if they contain a significant proportion of the matter in the universe.
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The Detection of The Gravitational Lensing of Supernovae
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We apply a new highly efficient method of solving Faddeev-Merkuriev equations to multi-channel scattering calculations of the antihydrogen formation cross section for antiproton scattering off the ground and excited states of the positronium. Our results demonstrate good agreement with the known data on total and partial cross sections for all the reaction channels. Using moderate computational resources we have achieved a supreme energy resolution.
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Theoretical study of reactions in the three body $e^-e^+\bar{p}$ system and antihydrogen formation cross sections
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When a freely suspended liquid film ruptures, it retracts spontaneously under the action of surface tension. If the film is surrounded by air, the retraction velocity is known to approach the constant Taylor-Culick velocity. However, when surrounded by an external viscous medium, the dissipation within that medium dictates the magnitude of the retraction velocity. In the present work, we study the retraction of a liquid (water) film in a viscous oil ambient (\emph{two-phase} Taylor-Culick retractions), and that sandwiched between air and a viscous oil (\emph{three-phase} Taylor-Culick retractions). In the latter case, the experimentally-measured retraction velocity is observed to have a weaker dependence on the viscosity of the oil phase as compared to the configuration where the water film is surrounded completely by oil. Numerical simulations indicate that this weaker dependence arises from the localization of viscous dissipation near the three-phase contact line. The speed of retraction only depends on the viscosity of the surrounding medium and not on that of the film. From the experiments and the numerical simulations, we reveal unprecedented regimes for the scaling of the Weber number $We_f$ of the film (based on its retraction velocity) or the capillary number $Ca_s$ of the surroundings vs. the Ohnesorge number $Oh_s$ of the surroundings in the regime of large viscosity of the surroundings ($Oh_s \gg 1$), namely $We_f \sim Oh_s^{-2}$ and $Ca_s \sim Oh_s^{0}$ for the two-phase Taylor-Culick configuration, and $We_f \sim Oh_s^{-1}$ and $Ca_s \sim Oh_s^{1/2}$ for the three-phase Taylor-Culick configuration.
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Taylor-Culick retractions and the influence of the surroundings
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We start the study of reduced complex projective plane curves, whose Jacobian syzygy module has 3 generators. Among these curves one finds the nearly free curves introduced by the authors, and the plus-one generated line arrangements introduced by Takuro Abe. All the Thom-Sebastiani type plane curves, and more generally, any curve whose global Tjurina number is equal to a lower bound given by A. du Plessis and C.T.C. Wall, are 3-syzygy curves. Rational plane curves which are nearly cuspidal, i.e. which have only cusps except one singularity with two branches, are also related to this class of curves.
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Plane curves with three syzygies, minimal Tjurina curves curves, and nearly cuspidal curves
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With the development of information technology and the Internet, recommendation systems have become an important means to solve the problem of information overload. However, recommendation system is greatly fragile as it relies heavily on behavior data of users, which makes it very easy for a host of malicious merchants to inject shilling attacks in order to manipulate the recommendation results. Some papers on shilling attack have proposed the detection methods, whether based on false user profiles or abnormal items, but their detection rate, false alarm rate, universality, and time overhead need to be further improved. In this paper, we propose a new item anomaly detection method, through T-distribution technology based on Dynamic Time Intervals. First of all, based on the characteristics of shilling attack quickness (Attackers inject a large number of fake profiles in a short period in order to save costs), we use dynamic time interval method to divide the rating history of item into multiple time windows. Then, we use the T-distribution to detect the exception windows. By conducting extensive experiments on a dataset that accords with real-life situations and comparing it to currently outstanding methods, our proposed approach has a higher detection rate, lower false alarm rate and smaller time overhead to the different attack models and filler sizes.
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Detection of Shilling Attack Based on T-distribution on the Dynamic Time Intervals in Recommendation Systems
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We study the steady state properties of a genotype selection model in presence of correlated Gaussian white noise. The effect of the noise on the genotype selection model is discussed. It is found that correlated noise can break the balance of gene selection and induce the phase transition which can makes us select one type gene haploid from a gene group.
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Noise in Genotype Selection Model
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The excellent soft X-ray sensitivity of the PSPC detector onboard the ROSAT satellite provided the first chance to study precisely the spectral and timing properties of Narrow-Line Seyfert 1 galaxies. ROSAT observations of Narrow-Line Seyfert 1 galaxies have revealed (1) the existence of a giant soft X-ray excess, (2) a striking, clear correlation between the strength of the soft X-ray excess emission and the FWHM of the H-beta line, (3) the general absence of significant soft X-ray absorption by neutral hydrogen above the Galactic column, (4) short doubling time scales down to about 1000 seconds, (5) the existence of persistent giant (above a factor of 10), and rapid (less than 1 day) X-ray variability in extragalactic sources. The soft X-ray results on Narrow-Line Seyfert 1 galaxies indicate that their black hole regions are directly visible, further supporting the Seyfert 1 nature of these objects. The extreme X-ray properties of Narrow-Line Seyfert 1 galaxies make them ideal objects for understanding many of the problems raised generally by the Seyfert phenomenon.
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ROSAT Results on Narrow-Line Seyfert 1 Galaxies
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Social choice theory is a theoretical framework for analysis of combining individual preferences, interests, or welfare to reach a collective decision or social welfare in some sense. We introduce a new criterion for social choice protocols called social disappointment. Social disappointment happens when the outcome of a voting system occurs for those alternatives which are at the end of at least half of individual preference profiles. Here we introduce some protocols that prevent social disappointment and prove an impossibility theorem based on this key concept.
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Disappointment in Social Choice Protocols
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We study the role the the p-mode-like vertical oscillation on the photosphere in driving solar winds in the framework of Alfven-wave-driven winds. By performing one-dimensional magnetohydrodynamical numerical simulations from the photosphere to the interplanetary space, we discover that the mass-loss rate is raised up to 4 times as the amplitude of longitudinal perturbations at the photosphere increases. When the longitudinal fluctuation is added, transverse waves are generated by the mode conversion from longitudinal waves in the chromosphere, which increases Alfvenic Poynting flux in the corona. As a result, the coronal heating is enhanced to yield higher coronal density by the chromospheric evaporation, leading to the increase of the mass-loss rate. Our findings clearly show the importance of the p-mode oscillation in the photosphere and the mode conversion in the chromosphere in determining the basic properties of the wind from the sun and solar-type stars.
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Role of Longitudinal Waves in Alfven-wave-driven Solar/Stellar Wind
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The present work is devoted to study the high-energy $QCD$ events, such as the di-jet productions from proton-proton inelastic collisions at the $LHC$ in the forward-center and the forward-forward configurations, using the $unintegrated$ parton distribution functions ($UPDF$) in the $k_t$-factorization framework. The $UPDF$ of $Kimber$ et. al. ($KMR$) and $Martin$ et.al. ($MRW$) are generated in the leading order ($LO$) and next-to-leading order ($NLO$), using the $Harland-Lang$ et al. ($MMHT2014$) $PDF$ libraries. While working in the forward-center and the forward-forward rapidity sectors, one can probe the parton densities at very low longitudinal momentum fractions ($x$). Therefore, such a computation can provide a valuable test-field for these $UPDF$. We find very good agreement with the corresponding di-jet production data available from $LHC$ experiments. On the other hand, as we have also stated in our previous works, (i.e. the protons longitudinal and transverse structure function as well as hadron-hadron $LHC$ $W/Z$ production), the present calculations based on the $KMR$ prescriptions show a better agreement with the corresponding experimental data. This conclusion is achieved, due to the particular visualization of the angular ordering constraint ($AOC$), despite the fact that the $LO-MRW$ and the $NLO-MRW$ formalisms both employ better theoretical descriptions of the $Dokshitzer$-$Gribov$-$Lipatov$ -$Altarelli$-$Parisi$ ($DGLAP$) evolution equation, and hence are expected to produce better results. The form of the $AOC$ in the $KMR$ prescription automatically includes the re-summation of the higher-order $ln({1/x})$ type contributions, i.e. the $Balitski$-$Fadin$-$Kuraev$-$Lipatov$ ($BFKL$) logarithms, in the $LO$-$DGLAP$ evolution equation.
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LHC production of forward-center and forward-forward di-jets in the $k_t$-factorization $unintegrated$ parton distribution frameworks
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Delivering hands-on practice laboratories for introductory courses on operating systems is a difficult task. One of the main sources of the difficulty is the sheer size and complexity of the operating systems software. Consequently, some of the solutions adopted in the literature to teach operating systems laboratory consider smaller and simpler systems, generally referred to as instructional operating systems. This work continues in the same direction and is threefold. First, it considers a simpler hardware platform. Second, it argues that a minimal operating system is a viable option for delivering laboratories. Third, it presents a laboratory teaching platform, whereby students build a minimal operating system for an embedded hardware platform. The proposed platform is called MiniOS. An important aspect of MiniOS is that it is sufficiently supported with additional technical and pedagogic material. Finally, the effectiveness of the proposed approach to teach operating systems laboratories is illustrated through the experience of using it to deliver laboratory projects in the Operating Systems course at the University of Northern British Columbia. Finally, we discuss experimental research in computing education and considered the qualitative results of this work as part of a larger research endeavour.
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MiniOS: an instructional platform for teaching operating systems labs
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The optimum distance profiles of linear block codes were studied for increasing or decreasing message length while keeping the minimum distances as large as possible, especially for Golay codes and the second-order Reed-Muller codes, etc. Cyclic codes have more efficient encoding and decoding algorithms. In this paper, we investigate the optimum distance profiles with respect to the cyclic subcode chains (ODPCs) of the punctured generalized second-order Reed-Muller codes $\mathcal{GRM}(2,m)^*$ which were applied in Power Control in OFDM Modulations in channels with synchronization, and so on. For this, two standards are considered in the inverse dictionary order, i.e., for increasing message length. Four lower bounds and upper bounds on ODPC are presented, where the lower bounds almost achieve the corresponding upper bounds in some sense. The discussions are over nonbinary prime field.
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On the bounds and achievability about the ODPC of $\mathcal{GRM}(2,m)^*$ over prime field for increasing message length
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Let $f : X \longrightarrow Y$ be a proper and local complete intersection morphism of schemes. We prove that $\mathbb{R}f_{*}$ preserves perfect complexes, without any projectivity or noetherian assumptions. This provides a different proof of a theorem by Neeman and Lipman based on techniques from derived algebraic geometry to proceed a reduction to the noetherian case.
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Proper local complete intersection morphisms preserve perfect complexes
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Social metaverse is a shared digital space combining a series of interconnected virtual worlds for users to play, shop, work, and socialize. In parallel with the advances of artificial intelligence (AI) and growing awareness of data privacy concerns, federated learning (FL) is promoted as a paradigm shift towards privacy-preserving AI-empowered social metaverse. However, challenges including privacy-utility tradeoff, learning reliability, and AI model thefts hinder the deployment of FL in real metaverse applications. In this paper, we exploit the pervasive social ties among users/avatars to advance a social-aware hierarchical FL framework, i.e., SocialFL for a better privacy-utility tradeoff in the social metaverse. Then, an aggregator-free robust FL mechanism based on blockchain is devised with a new block structure and an improved consensus protocol featured with on/off-chain collaboration. Furthermore, based on smart contracts and digital watermarks, an automatic federated AI (FedAI) model ownership provenance mechanism is designed to prevent AI model thefts and collusive avatars in social metaverse. Experimental findings validate the feasibility and effectiveness of proposed framework. Finally, we envision promising future research directions in this emerging area.
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Social Metaverse: Challenges and Solutions
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We re-derive, compactly, a TMG decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We can then generalize it to include matter, which is necessarily null.
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Circular Symmetry in Topologically Massive Gravity
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Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.
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Cyber-Physical Systems as General Distributed Parameter Systems: Three Types of Fractional Order Models and Emerging Research Opportunities
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In this work, we present a new class of genuine multipartite Bell inequalities, that is particularly designed for multipartite device-independent (DI) quantum key distribution (QKD), also called DI conference key agreement. We prove the classical bounds of this inequality, discuss how to maximally violate it and show its usefulness by calculating achievable conference key rates via the violation of this Bell inequality. To this end, semidefinite programming techniques based on [Nat. Commun. 2, 238 (2011)] are employed and extended to the multipartite scenario. Our Bell inequality represents a nontrivial multipartite generalization of the Clauser-Horne-Shimony-Holt inequality and is motivated by the extension of the bipartite Bell state to the n-partite Greenberger-Horne-Zeilinger state. For DIQKD, we suggest an honest implementation for any number of parties and study the effect of noise on achievable asymptotic conference key rates.
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A Genuine Multipartite Bell Inequality for Device-independent Conference Key Agreement
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We propose a novel algorithm for greedy forward feature selection for regularized least-squares (RLS) regression and classification, also known as the least-squares support vector machine or ridge regression. The algorithm, which we call greedy RLS, starts from the empty feature set, and on each iteration adds the feature whose addition provides the best leave-one-out cross-validation performance. Our method is considerably faster than the previously proposed ones, since its time complexity is linear in the number of training examples, the number of features in the original data set, and the desired size of the set of selected features. Therefore, as a side effect we obtain a new training algorithm for learning sparse linear RLS predictors which can be used for large scale learning. This speed is possible due to matrix calculus based short-cuts for leave-one-out and feature addition. We experimentally demonstrate the scalability of our algorithm and its ability to find good quality feature sets.
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Linear Time Feature Selection for Regularized Least-Squares
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The Lagrangian action for the D4-D5-E6 model of hep-th/9306011 has 8-dim spacetime V8 of the vector representation of Spin(0,8); 8-dim fermion fields S8+ = S8- of the half-spinor reps of Spin(0,8); and 28 gauge boson fields of the bivector adjoint rep of Spin(0,8). In this paper, the structure of the positive definite Clifford algebra Cl(0,8) of Spin(0,8), and the triality automorphism V8 = S8+ = S8-, are used to reduce the spacetime to 4 dimensions and thereby change the gauge group from Spin(0,8) to the realistic SU(3)xSU(2)xU(1), Higgs, and Gravity. The effect of dimensional reduction on fermions, to introduce 3 generations, has been described in hep-ph/9301210. The global geometry of manifolds V8 = S8+ = S8- = RP1xS7, the effects of dimensional reduction on them, and the calculation of force strength constants, has been described in hep-th/9302030.
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SU(3)xSU(2)xU(1), Higgs, and Gravity from Spin(0,8) Clifford Algebra Cl(0,8)
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Applying reinforcement learning (RL) to traffic signal control (TSC) has become a promising solution. However, most RL-based methods focus solely on optimization within simulators and give little thought to deployment issues in the real world. Online RL-based methods, which require interaction with the environment, are limited in their interactions with the real-world environment. Additionally, acquiring an offline dataset for offline RL is challenging in the real world. Moreover, most real-world intersections prefer a cyclical phase structure. To address these challenges, we propose: (1) a cyclical offline dataset (COD), designed based on common real-world scenarios to facilitate easy collection; (2) an offline RL model called DataLight, capable of learning satisfactory control strategies from the COD; and (3) a method called Arbitrary To Cyclical (ATC), which can transform most RL-based methods into cyclical signal control. Extensive experiments using real-world datasets on simulators demonstrate that: (1) DataLight outperforms most existing methods and achieves comparable results with the best-performing method; (2) introducing ATC into some recent RL-based methods achieves satisfactory performance; and (3) COD is reliable, with DataLight remaining robust even with a small amount of data. These results suggest that the cyclical offline dataset might be enough for offline RL for TSC. Our proposed methods make significant contributions to the TSC field and successfully bridge the gap between simulation experiments and real-world applications. Our code is released on Github.
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Data Might be Enough: Bridge Real-World Traffic Signal Control Using Offline Reinforcement Learning
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In a previous paper we examined the role of a conscious observer in a typical quantum mechanical measurement. Four rules were given that were found to govern the stochastic choice and state reduction in several cases of continuous and intermittent observation. It was shown that consciousness always accompanies a state reduction leading to observation, but its presence is not sufficient to 'cause' a reduction. The distinction is clarified and codified by the rules that are repeated below. In this paper, these rules are successfully applied to two different versions of the Schrodinger cat experiment. Key Words: Brain states, boundary conditions, cat paradox, consciousness, conscious observer, environment, decoherence, macroscopic superposition, measurement, state reduction, state collapse, von Neumann.
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Schrodinger's cat: The rules of engagement
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We report on the pion-pion scattering length in the I=2 channel using the parametrized fixed point action. Pion masses of 320 MeV were reached in this quenched calculation of the scattering length.
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I=2 pion scattering length with the parametrized fixed point action
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Three dimensional relative free energy calculations are used to directly calculate the dependence of the preferred sidechain rotamers for valine and leucine on the conformation of the backbone. Specifically, umbrella restrained molecular dynamics calculations are used to sample all of Ramachandran space for chi values surrounding the common rotameric states of leucine and valine. Relative free enegy slices were calculated from the biased trajectories using the weighted histogram analysis method (WHAM). The slices were connected together by another set of slices perpendicular to Ramachandran space to determine the favored rotamer for a given backbone conformation. The calculated preferences are quite similar to those seen in the backbone-dependent rotamer library of Dunbrack and Karplus, despite the fact that the current calculations neglect the effects of neighboring residues. It appears likely that these calculations could be extended to calculate the optimal sidechain conformation for a peptide with known backbone conformation in the context of structure refinement and prediction
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Dependence of Sidechain Rotamer Preference on Backbone Conformation: Relative Free Energy Calculations for Valine and Leucine
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By exploring a phase space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the Fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle, observable in experiments in an one dimensional free Fermi gas or Tonk's gas (Bose gas with infinite repulsion).
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Quantum quench and thermalization of one-dimensional Fermi gas via phase space hydrodynamics
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The Hermitian Cartesian quantum momentum operator $\mathbf{p}$ for an embedded surface $M$ in $R^{3}$ is proved to be a constant factor $-i\hbar $ times the mean curvature vector field $H\mathbf{n}$ added to the usual differential term. With use of this form of momentum operators, the operator-ordering ambiguity exists in the construction of the correct kinetic energy operator and three different operator-orderings lead to the same result. PACS: 03.65.-w Quantum mechanics, 04.60.Ds Canonical quantization
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Constraint-induced mean curvature dependence of Cartesian momentum operators
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In this paper, we investigate a multi-node multi-antenna wireless-powered sensor networks (WPSN) comprised of one power beacon and multiple sensor nodes. We have implemented a real-life multi-node multi-antenna WPSN testbed that operates in real time. We propose a beam-splitting beamforming technique that enables a power beacon to split microwave energy beams towards multiple nodes for simultaneous charging. We experimentally demonstrate that the beam-splitting beamforming technique achieves the Pareto optimality. For a perpetual operation of the sensor nodes, we adopt an energy neutral control algorithm that keeps a sensor node alive by balancing the harvested and the consumed power. The joint beam-splitting and energy neutral control algorithm is designed by means of the Lyapunov optimization technique. By experiments, we have shown that the proposed algorithm can successfully keep all sensor nodes alive by optimally splitting energy beams towards multiple sensor nodes.
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Theory and Experiment for Wireless-Powered Sensor Networks: How to Keep Sensors Alive
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We report the results of the pressure-dependent measurements of the static magnetization and of the ferromagnetic resonance (FMR) of Cr$_2$Ge$_2$Te$_6$ to address the properties of the ferromagnetic phase of this quasi-two-dimensional van der Waals magnet. The static magnetic data at hydrostatic pressures up to 3.4 GPa reveal a gradual suppression of ferromagnetism in terms of a reduction of the critical transition temperature, a broadening of the transition width and an increase of the field necessary to fully saturate the magnetization $M_{\rm s}$. The value of $M_{\rm s} \simeq 3\mu_{\rm B}$/Cr remains constant within the error bars up to a pressure of 2.8 GPa. The anisotropy of the FMR signal continuously diminishes in the studied hydrostatic pressure range up to 2.39 GPa suggesting a reduction of the easy-axis type magnetocrystalline anisotropy energy (MAE). A quantitative analysis of the FMR data gives evidence that up to this pressure the MAE constant $K_{\rm U}$, although getting significantly smaller, still remains finite and positive, i.e. of the easy-axis type. Therefore, a recently discussed possibility of switching the sign of the magnetocrystalline anisotropy in Cr$_2$Ge$_2$Te$_6$ could only be expected at still higher pressures, if possible at all due to the observed weakening of the ferromagnetism under pressure. This circumstance may be of relevance for the design of strain-engineered functional heterostructures containing layers of Cr$_2$Ge$_2$Te$_6$.
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Pressure control of the magnetic anisotropy of the quasi-two-dimensional van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$
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We present measurements of $Z^0$ to heavy-quark coupling electroweak parameters, $R_b$, $R_c$, and parity-violation parameter $A_c$, from SLD. The measurements are based on approximately 550k hadronic $Z^0$ events collected in 1993-98. Obtained preliminary results of $R_b$ and $R_c$ measurements are $R_b = 0.2159 \pm 0.0014 \pm 0.0014$ and $R_c = 0.1685 \pm 0.0047 \pm 0.0043$. In the $A_c$ measurement, we use four methods to determine the initial-quark charge: combined Kaon charge and Vertex charge, lepton, exclusively reconstructed D*, D-mesons, and a new method using inclusive soft-pion from D*. The preliminary results of these four methods were combined to give $A_c = 0.634 \pm 0.027$.
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Measurements of $Z^0$ to Heavy-quark couplings at SLD
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We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions ($\mathrm{PPD}$)which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the $\mathrm{PPD}$s. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from $\mathrm{PPD}$s are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained in the case of Fitzhugh-Nagumo model neurons, the theory can be readily applied to systems of Hodgkin-Huxley type model neurons of arbitrary dimension.
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Mean field analysis of large-scale interacting populations of stochastic conductance-based spiking neurons using the Klimontovich method
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Deep networks thrive when trained on large scale data collections. This has given ImageNet a central role in the development of deep architectures for visual object classification. However, ImageNet was created during a specific period in time, and as such it is prone to aging, as well as dataset bias issues. Moving beyond fixed training datasets will lead to more robust visual systems, especially when deployed on robots in new environments which must train on the objects they encounter there. To make this possible, it is important to break free from the need for manual annotators. Recent work has begun to investigate how to use the massive amount of images available on the Web in place of manual image annotations. We contribute to this research thread with two findings: (1) a study correlating a given level of noisily labels to the expected drop in accuracy, for two deep architectures, on two different types of noise, that clearly identifies GoogLeNet as a suitable architecture for learning from Web data; (2) a recipe for the creation of Web datasets with minimal noise and maximum visual variability, based on a visual and natural language processing concept expansion strategy. By combining these two results, we obtain a method for learning powerful deep object models automatically from the Web. We confirm the effectiveness of our approach through object categorization experiments using our Web-derived version of ImageNet on a popular robot vision benchmark database, and on a lifelong object discovery task on a mobile robot.
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Learning Deep Visual Object Models From Noisy Web Data: How to Make it Work
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We study the influence of unitarity corrections on the Drell-Yan transverse momentum distribution within the color dipole approach. These unitarity corrections are implemented through the multiple scattering Glauber-Mueller approach, which is contrasted with a phenomenological saturation model. The process is analyzed for the center of mass energies of the Relativistic Heavy Ion Collider (RHIC, $\sqrt{s}=500$ GeV) and of the Large Hadron Collider (LHC, $\sqrt{s}=14$ TeV). In addition, the results are extrapolated down to current energies of proton-proton collisions, where non-asymptotic corrections to the dipole approach are needed. It is also shown that in the absence of saturation, the dipole approach can be related to the QCD Compton process.
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Investigating the Drell-Yan transverse momentum distribution in the color dipole approach
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Part mobility analysis is a significant aspect required to achieve a functional understanding of 3D objects. It would be natural to obtain part mobility from the continuous part motion of 3D objects. In this study, we introduce a self-supervised method for segmenting motion parts and predicting their motion attributes from a point cloud sequence representing a dynamic object. To sufficiently utilize spatiotemporal information from the point cloud sequence, we generate trajectories by using correlations among successive frames of the sequence instead of directly processing the point clouds. We propose a novel neural network architecture called PointRNN to learn feature representations of trajectories along with their part rigid motions. We evaluate our method on various tasks including motion part segmentation, motion axis prediction and motion range estimation. The results demonstrate that our method outperforms previous techniques on both synthetic and real datasets. Moreover, our method has the ability to generalize to new and unseen objects. It is important to emphasize that it is not required to know any prior shape structure, prior shape category information, or shape orientation. To the best of our knowledge, this is the first study on deep learning to extract part mobility from point cloud sequence of a dynamic object.
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Self-Supervised Learning of Part Mobility from Point Cloud Sequence
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This review is devoted to the large-scale rheology of suspensions of rigid particles in Stokes fluid. After describing recent results on the definition of the effective viscosity of such systems in the framework of homogenization theory, we turn to our new results on the asymptotic expansion of the effective viscosity in the dilute regime. This includes an optimal proof of Einstein's viscosity formula for the first-order expansion, as well as the continuation of this expansion to higher orders. The essential difficulty originates in the long-range nature of hydrodynamic interactions: suitable renormalizations are needed and are captured by means of diagrammatic expansions.
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Effective viscosity of semi-dilute suspensions
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We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector bundle $(\mathcal{S},D,\omega)$ defined over the scalar manifold $\mathcal{M}$. The construction uses a taming of $(\mathcal{S}, \omega)$, which encodes globally the inverse gauge couplings and theta angles of the "twisted" Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give classical locally geometric U-folds. We also describe the groups of duality transformations and scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of $\mathcal{M}$ to a particular class of flat automorphisms of the bundle $\mathcal{S}$ and hence differ from expectations based on local analysis. The appropriate version of the Dirac quantization condition involves a discrete local system defined over $\mathcal{M}$ and gives rise to a smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows that a generalization of part of the mathematical structure familiar from $\mathcal{N}=2$ supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetry.
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Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds
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We study the effects of gravity waves, or g-modes, on hot extrasolar planets. These planets are expected to possess stably-stratified atmospheres, which support gravity waves. In this paper, we review the derivation of the equation that governs the linear dynamics of gravity waves and describe its application to a hot extrasolar planet, using HD209458 b as a generic example. We find that gravity waves can exhibit a wide range of behaviors, even for a single atmospheric profile. The waves can significantly accelerate or decelerate the background mean flow, depending on the difference between the wave phase and mean flow speeds. In addition, the waves can provide significant heating (~100 to ~1000 K per planetary rotation), especially to the region of the atmosphere above about 10 scale heights from the excitation region. Furthermore, by propagating horizontally, gravity waves provide a mechanism for transporting momentum and heat from the dayside of a tidally locked planet to its nightside. We discuss work that needs to be undertaken to incorporate these effects in current atmosphere models of extrasolar planets.
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Gravity Waves on Hot Extrasolar Planets: I. Propagation and Interaction with the Background
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Despite recent progress in generative image modeling, successfully generating high-resolution, diverse samples from complex datasets such as ImageNet remains an elusive goal. To this end, we train Generative Adversarial Networks at the largest scale yet attempted, and study the instabilities specific to such scale. We find that applying orthogonal regularization to the generator renders it amenable to a simple "truncation trick," allowing fine control over the trade-off between sample fidelity and variety by reducing the variance of the Generator's input. Our modifications lead to models which set the new state of the art in class-conditional image synthesis. When trained on ImageNet at 128x128 resolution, our models (BigGANs) achieve an Inception Score (IS) of 166.5 and Frechet Inception Distance (FID) of 7.4, improving over the previous best IS of 52.52 and FID of 18.6.
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Large Scale GAN Training for High Fidelity Natural Image Synthesis
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We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1 embeds canonically into the centers of the stated skein algebras whose deforming parameter is an odd root unity. We also construct an isomorphism between the stated skein algebra at +1 and the algebra of regular function of a generalization of the SL2-character variety of the surface. As a result, we associate to each isomorphism class of irreducible or local representations of the stated skein algebra, an invariant which is a point in the character variety.
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Classical shadows of stated skein representations at roots of unity
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Touch data, and in particular text-entry data, has been mostly collected in the laboratory, under controlled conditions. While touch and text-entry data have consistently shown its potential for monitoring and detecting a variety of conditions and impairments, its deployment in-the-wild remains a challenge. In this paper, we present WildKey, an Android keyboard toolkit that allows for the usable deployment of in-the-wild user studies. WildKey is able to analyze text-entry behaviors through implicit and explicit text-entry data collection while ensuring user privacy. We detail each of the WildKey's components and features, all of the metrics collected, and discuss the steps taken to ensure user privacy and promote compliance.
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WildKey: A Privacy-Aware Keyboard Toolkit for Data Collection In-The-Wild
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Deep reinforcement learning (RL) has enabled training action-selection policies, end-to-end, by learning a function which maps image pixels to action outputs. However, it's application to visuomotor robotic policy training has been limited because of the challenge of large-scale data collection when working with physical hardware. A suitable visuomotor policy should perform well not just for the task-setup it has been trained for, but also for all varieties of the task, including novel objects at different viewpoints surrounded by task-irrelevant objects. However, it is impractical for a robotic setup to sufficiently collect interactive samples in a RL framework to generalize well to novel aspects of a task. In this work, we demonstrate that by using adversarial training for domain transfer, it is possible to train visuomotor policies based on RL frameworks, and then transfer the acquired policy to other novel task domains. We propose to leverage the deep RL capabilities to learn complex visuomotor skills for uncomplicated task setups, and then exploit transfer learning to generalize to new task domains provided only still images of the task in the target domain. We evaluate our method on two real robotic tasks, picking and pouring, and compare it to a number of prior works, demonstrating its superiority.
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Adversarial Feature Training for Generalizable Robotic Visuomotor Control
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We compute logarithmic corrections to the twisted index $B^g_6$ in four-dimensional $\mathcal{N}=4$ and $\mathcal{N}=8$ string theories using the framework of the Quantum Entropy Function. We find that these vanish, matching perfectly with the large--charge expansion of the corresponding microscopic expressions.
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Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
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We investigate how loop-level propagators arise from tree level via a forward-limit procedure in two modern approaches to scattering amplitudes, namely the BCFW recursion relations and the scattering equations formalism. In the first part of the paper, we revisit the BCFW construction of one-loop integrands in momentum space, using a convenient parametrisation of the D-dimensional loop momentum. We work out explicit examples with and without supersymmetry, and discuss the non-planar case in both gauge theory and gravity. In the second part of the paper, we study an alternative approach to one-loop integrands, where these are written as worldsheet formulas based on new one-loop scattering equations. These equations, which are inspired by BCFW, lead to standard Feynman-type propagators, instead of the `linear'-type loop-level propagators that first arose from the formalism of ambitwistor strings. We exploit the analogies between the two approaches, and present a proof of an all-multiplicity worldsheet formula using the BCFW recursion.
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Propagators, BCFW Recursion and New Scattering Equations at One Loop
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We examine the determinization of monitors for HML with recursion. We demonstrate that every monitor is equivalent to a deterministic one, which is at most doubly exponential in size with respect to the original monitor. When monitors are described as CCS-like processes, this doubly exponential bound is optimal. When (deterministic) monitors are described as finite automata (as their LTS), then they can be exponentially more succinct than their CCS process form.
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Determinizing Monitors for HML with Recursion
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Complete flavour decompositions of the scalar, axial and tensor charges of the proton, deuteron, diproton and $^3$He at SU(3)-symmetric values of the quark masses corresponding to a pion mass $m_\pi\sim806$ MeV are determined using lattice QCD. At the physical quark masses, the scalar charges constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor charges of nuclei constrain their spin content, integrated transversity and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. Significant nuclear modifications are found, with particularly large, O(10%), effects in the scalar charges. Typically, these nuclear effects reduce the effective charge of the nucleon (quenching), although in some cases an enhancement is not excluded. Given the size of the nuclear modifications of the scalar charges resolved here, contributions from correlated multi-nucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.
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Nuclear modification of scalar, axial and tensor charges from lattice QCD
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The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a degree-constrained subgraph instance, can we transform one solution into the other by adding and removing individual edges, such that each intermediate subgraph satisfies the degree constraints and contains at least a certain minimum number of edges? This problem is a generalization of the matching reconfiguration problem, which is known to be in P. We show that even in the more general setting the reconfiguration problem is in P.
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Degree-constrained Subgraph Reconfiguration is in P
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The Galactic center has some of the highest stellar densities in the Galaxy and a range of interstellar scattering properties that may aid in the detection of new radio-selected transient events. Here we describe a search for radio transients in the Galactic center using over 200 hours of archival data from the Very Large Array (VLA) at 5 and 8.4 GHz. Every observation of SgrA* from 1985$-$2005 has been searched using an automated processing and detection pipeline sensitive to transients with timescales between 30 seconds and five minutes with a typical detection threshold of $\sim$100 mJy. Eight possible candidates pass tests to filter false-positives from radio-frequency interference, calibration errors, and imaging artifacts. Two events are identified as promising candidates based on the smoothness of their light curves. Despite the high quality of their light curves, these detections remain suspect due to evidence of incomplete subtraction of the complex structure in the Galactic center, and apparent contingency of one detection on reduction routines. Events of this intensity ($\sim$100 mJy) and duration ($\sim$100 s) are not obviously associated with known astrophysical sources, and no counterparts are found in data at other wavelengths. We consider potential sources, including Galactic center pulsars, dwarf stars, sources like GCRT J1745-3009, and bursts from X-ray binaries. None can fully explain the observed transients, suggesting either a new astrophysical source or a subtle imaging artifact. More sensitive multiwavelength studies are necessary to characterize these events which, if real, occur with a rate of $14^{+32}_{-12}~{\rm hr}^{-1}\,{\rm deg}^{-2}$ in the Galactic center.
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Transient Events in Archival Very Large Array Observations of the Galactic Center
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