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  • PDF
    The novel measurements of the $\gamma^\ast N \to \Delta(1232)$ Coulomb quadrupole form factor in the range $Q^2=0.04$--0.13 GeV$^2$ changed the trend of the previous data. With the new data the electric and Coulomb form factors are both in remarkable agreement with estimates of the pion cloud contributions to the quadrupole form factors at low $Q^2$. The pion cloud contributions to the electric and Coulomb form factors can be parametrized by the relations $G_E \propto G_{En}/\left(1 + \frac{Q^2}{2M_\Delta(M_\Delta-M)}\right)$ and $G_C \propto G_{En}$, where $G_{En}$ is the neutron electric form factor, and $M$, $M_\Delta$ are the nucleon and $\Delta$ masses, respectively. Those parametrizations are in full agreement with Siegert's theorem, which states that $G_E= \frac{M_\Delta-M}{2M_\Delta} G_C$ at the pseudothreshold, when $Q^2=-(M_\Delta -M)^2$, and improve previous parametrizations. For this agreement contributes also a small valence quark effects component estimated by a covariant quark model. The combination of the new data with the new parametrization for $G_E$ culminates an intense period of studying the $\gamma^\ast N \to \Delta(1232)$ quadrupole form factors at low $Q^2$, with the agreement between theory and data.
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    The first observation of top quark production in proton-nucleus collisions is reported using proton-lead data collected by the CMS experiment at the CERN LHC at a nucleon-nucleon center-of-mass energy of $\sqrt{s_\mathrm{NN}} =$ 8.16 TeV. The measurement is performed using events with exactly one isolated electron or muon and at least four jets. The data sample corresponds to an integrated luminosity of 174 nb$^{-1}$. The significance of the $\mathrm{t}\overline{\mathrm{t}}$ signal against the background-only hypothesis is above five standard deviations. The measured cross section is $\sigma_{\mathrm{t}\overline{\mathrm{t}}} =$ 45$\pm$8 nb, consistent with predictions from perturbative quantum chromodynamics.
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    We consider dark matter annihilation into a general set of final states of Standard Model particles, including two-body and four-body final states that result from the decay of intermediate states. For dark matter masses ~10-10^5 GeV, we use updated data from Planck and from high gamma-ray experiments such as Fermi-LAT, MAGIC, and VERITAS to constrain the annihilation cross section for each final state. The Planck constraints are the most stringent over the entire mass range for annihilation into light leptons, and the Fermi-LAT constraints are the most stringent for four-body final states up to masses ~10^4 GeV. We consider these constraints in light of the recent AMS antiproton results, and show that for light mediators it is possible to explain the AMS data with dark matter, and remain consistent with Fermi-LAT Inner Galaxy measurements, for m_\chi ~ 60-100 GeV mass dark matter and mediator masses m_\phi / m_\chi ~< 1.
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    We consider the Fermi polaron problem at zero temperature, where a single impurity interacts with non-interacting host fermions. We approach the problem starting with a Frohlich-like Hamiltonian where the impurity is described with canonical position and momentum operators. We apply the Lee-Low-Pine (LLP) transformation to change the fermionic Frohlich Hamiltonian into the fermionic LLP Hamiltonian which describes a many-body system containing host fermions only. We adapt the self-consistent Hartree-Fock (HF) approach, first proposed by Edwards, to the fermionic LLP Hamiltonian in which a pair of host fermions with momenta $\mathbf{k}$ and $\mathbf{k}'$ interact with a potential proportional to $\mathbf{k}\cdot\mathbf{k}'$. We apply the HF theory, which has the advantage of not restricting the number of particle-hole pairs, to repulsive Fermi polarons in one dimension. When the impurity and host fermion masses are equal our variational ansatz, where HF orbitals are expanded in terms of free-particle states, produces results in excellent agreement with McGuire's exact analytical results based on the Bethe ansatz. This work raises the prospect of using the HF ansatz and its time-dependent generalization as building blocks for developing all-coupling theories for both equilibrium and nonequilibrium Fermi polarons in higher dimensions
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    We prove sharp bounds for the growth rate of eigenfunctions of the Ornstein-Uhlenbeck operator and its natural generalizations. The bounds are sharp even up to lower order terms and have important applications to geometric flows.
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    For $L \hookrightarrow X$ a Lagrangian embedding associated with a real homogeneous space, we construct the moduli space of stable holomorphic discs mapping to $(X,L)$ as an orbifold with corners equipped with a group action. Some essential constructions involving orbifolds with corners are also discussed, including the existence of fibered products and pushforward and pullback of differential forms with values in a local system.
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    We study a unique network dataset including periodic surveys and electronic logs of dyadic contacts via smartphones. The participants were a sample of freshmen entering university in the Fall 2011. Their opinions on a variety of political and social issues and lists of activities on campus were regularly recorded at the beginning and end of each semester for the first three years of study. We identify a behavioral network defined by call and text data, and a cognitive network based on friendship nominations in ego-network surveys. Both networks are limited to study participants. Since a wide range of attributes on each node were collected in self-reports, we refer to these networks as attribute-rich networks. We study whether student preferences for certain attributes of friends can predict formation and dissolution of edges in both networks. We introduce a method for computing student preferences for different attributes which we use to predict link formation and dissolution. We then rank these attributes according to their importance for making predictions. We find that personal preferences, in particular political views, and preferences for common activities help predict link formation and dissolution in both the behavioral and cognitive networks.
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    Recent attacks on power grids demonstrated the vulnerability of the grids to cyber and physical attacks. To analyze this vulnerability, we study cyber-physical attacks that affect both the power grid physical infrastructure and its underlying Supervisory Control And Data Acquisition (SCADA) system. We assume that an adversary attacks an area by: (i) disconnecting some lines within that area, and (ii) obstructing the information (e.g., status of the lines and voltage measurements) from within the area to reach the control center. We leverage the algebraic properties of the AC power flows to introduce the efficient EXPOSE Algorithm for detecting line failures and recovering voltages inside that attacked area after such an attack. The EXPOSE Algorithm outperforms the state-of-the-art algorithm for detecting line failures using partial information under the AC power flow model in terms of scalability and accuracy. The main advantages of the EXPOSE Algorithm are that its running time is independent of the size of the grid and number of line failures, and that it provides accurate information recovery under some conditions on the attacked area. Moreover, it approximately recovers the information and provides the confidence of the solution when these conditions do not hold.
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    In this paper, we show that the $\Delta$-genus $\Delta(X,\mathcal{L})\ge 0$ for any connected polarized demi-normal scheme $(X,\mathcal{L})$. As a direct corollary, we obtain $\Delta(X,K_X+\Lambda)\ge 0$ for any Gorenstein stable log scheme $(X,\Lambda)$, which is an inequality of Noether's type.
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    In the domain of Fermi energy, it is extremely complex to isolate experimentally fragments and particles issued from the cooling of a hot nucleus produced during a heavy ion collision. This paper presents a new method to characterize more precisely hot Quasi-Projectiles. It tries to take into account as accurately as possible the distortions generated by all the other potential participants in the nuclear reaction. It is quantitatively shown that this method is a major improvement respect to classic calorimetries used with a 4$\pi$ detector array. By detailing and deconvolving the different steps of the reconstitution of the hot nucleus, this study shows also the respective role played by the experimental device and the event selection criteria on the quality of the determination of QP characteristics.
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    We show that the anti-de Sitter(AdS) space naturally emerges from the conformal field theory(CFT). The behavior of the leading divergent term in the entanglement entropy implies the underlying AdS geometry. The coefficient of the leading divergent term is related to the radius of the AdS space. All these are confirmed fully for the two dimensional CFTs. We also give comments for the higher dimensional CFTs.
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    We propose a new splitting scheme for general reaction-taxis-diffusion systems in one spatial dimension capable to deal with simultaneous concentrated and diffusive regions as well as travelling waves and merging phenomena. The splitting scheme is based on a mass transport strategy for the cell density coupled with classical finite element approximations for the rest of the system. The built-in mass adaption of the scheme allows for an excellent performance even with respect to dedicated mesh-adapted AMR schemes in original variables.
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    In this paper we explore the intermediate line region (ILR) by using the photoionisation simulations of the gas clouds present at different radial distances from the center, corresponding to the locations from BLR out to NLR in four types of AGNs. We let for the presence of dust whenever conditions allow for dust existence. All spectral shapes are taken from the recent multi-wavelength campaigns. The cloud density decreases with distance as a power law. We found that the slope of the power law density profile does not affect the line emissivity radial profiles of major emission lines: H${\beta}$, He~II, Mg~II, C~III] ~and [O~III]. When the density of the cloud at the sublimation radius is as high as 10$^{11.5}$ cm$^{-3}$, the ILR should clearly be seen in the observations independently of the shape of the illuminating radiation. Moreover, our result is valid for low ionization nuclear emission regions of active galaxies.
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    We derive a closed formula for the generating function of genus two Gromov-Witten invariants of quintic 3-folds and verify the corresponding mirror symmetry conjecture of Bershadsky, Cecotti, Ooguri and Vafa.
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    Calculation of the rotation-vibration spectrum of H3+, as well as of its deuterated isotopologues, with near-spectroscopic accuracy requires the development of sophisticated theoretical models, methods, and codes. The present paper reviews the state-of-the-art in these fields. Computation of rovibrational states on a given potential energy surface (PES) has now become standard for triatomic molecules, at least up to intermediate energies, due to developments achieved by the present authors and others. However, highly accurate Born--Oppenheimer energies leading to highly accurate PESs are not accessible even for this two-electron system using conventional electronic structure procedures e.g., configuration-interaction or coupled-cluster techniques with extrapolation to the complete basis set limit). For this purpose highly specialized techniques must be used, e.g., those employing explicitly correlated Gaussians and nonlinear parameter optimizations. It has also become evident that a very dense grid of \ai points is required to obtain reliable representations of the computed points extending from the minimum to the asymptotic limits. Furthermore, adiabatic, relativistic, and QED correction terms need to be considered to achieve near-spectroscopic accuracy during calculation of the rotation-vibration spectrum of H3+. The remaining and most intractable problem is then the treatment of the effects of non-adiabatic coupling on the rovibrational energies, which, in the worst cases, may lead to corrections on the order of several \cm. A promising way of handling this difficulty is the further development of effective, motion- or even coordinate-dependent, masses and mass surfaces. Finally, the unresolved challenge of how to describe and elucidate the experimental pre-dissociation spectra of H$_3^+$ and its isotopologues is discussed.
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    In this paper we set up a bivariate representation of partial theta functions which not only unifies some famous identities for partial theta functions due to Andrews and Warnaar, et al. but also unveils a new characteristic of such identities. As further applications, we establish a general form of Warnaar's identity and a general $q$--series transformation associated with Bailey pairs via the use of the power series expansion of partial theta functions.
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    We have compiled from the available literature a large set of radio measurements of black hole binaries in the hard X-ray state for which measurements of the gigahertz frequency radio spectral index are possible. We separate the sample into `radio loud' and `radio quiet' subsets based upon their distribution in the radio -- X-ray plane, and investigate the distribution of radio spectral indices within each subset. The distribution of spectral indices of the `radio loud' subset is well described by a Gaussian distribution with mean spectral index $\alpha = +0.2$ and standard deviation $0.2$ (here spectral index is defined such that a positive spectral index means more flux at higher frequencies). The sparser sample for the `radio quiet' subset can be approximated, less well, by a Gaussian with mean $\alpha = -0.2$ and standard deviation $0.3$; alternatively the simple mean of the distribution of the radio quiet subset is $-0.3$. The two spectral index distributions are different at high statistical significance. Confirming previous work in the literature, we test to see if the differences in observed spectra could result from different distributions of jet viewing angles, but find no evidence for this. We conclude therefore that the jets in the two groups are physically different in some way, and briefly discuss possible origins and further possible diagnostics. Finally we note that extrapolating to lower frequencies the two subsets move closer together in the radio -- X-ray plane, and approximately merge into a single distribution at around 400 MHz.
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    Context. The Evershed effect, a nearly horizontal outflow of material seen in the penumbrae of sunspots in the photospheric layers, is a common characteristic of well-developed penumbrae, but is still not well understood. Even less is known about photospheric horizontal inflows in the penumbra, also known as counter Evershed flows. Aims. Here we present a rare feature observed in the penumbra of the main sunspot of AR NOAA 10930. This spot displays the normal Evershed outflow in most of the penumbra, but harbors a fast photospheric inflow of material over a large sector of the disk-center penumbra. We investigate the driving forces of both, the normal and the counter Evershed flows. Methods. We invert the spectropolarimetric data from Hinode SOT/SP using the spatially coupled version of the SPINOR inversion code, which allows us to derive height-dependent maps of the relevant physical parameters in the sunspot. These maps show considerable fine structure. Similarities and differences between the normal Evershed outflow and the counter Evershed flow are investigated. Results. In both the normal and the counter Evershed flows, the material flows from regions with field strengths of the order of 1.5-2 kG to regions with stronger fields. The sources and sinks of both penumbral flows display opposite field polarities, with the sinks (tails of filaments) harboring local enhancements in temperature, which are nonetheless colder than their sources (heads of filaments). Conclusions. The anti-correlation of the gradients in the temperature and magnetic pressure between the endpoints of the filaments from the two distinct penumbral regions is compatible with both the convective driver and the siphon flow scenarios. A geometrical scale of the parameters is necessary to determine which is the dominant force driving the flows.
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    Transmission spectroscopy provides a window to study exoplanetary atmospheres, but that window is fogged by clouds and hazes. Clouds and haze introduce a degeneracy between the strength of gaseous absorption features and planetary physical parameters such as abundances. One way to break that degeneracy is via statistical studies. We collect all published HST/WFC3 transit spectra for 1.1-1.65 $\mu$m water vapor absorption, and perform a statistical study on potential correlations between the water absorption feature and planetary parameters. We fit the observed spectra with a template calculated for each planet using the Exo-Transmit code. We express the magnitude of the water absorption in scale heights, thereby removing the known dependence on temperature, surface gravity, and mean molecular weight. We find that the absorption in scale heights has a positive baseline correlation with planetary equilibrium temperature; our hypothesis is that decreasing cloud condensation with increasing temperature is responsible for this baseline slope. However, the observed sample is also intrinsically degenerate in the sense that equilibrium temperature correlates with planetary mass. We compile the distribution of absorption in scale heights, and we find that this distribution is closer to log-normal than Gaussian. However, we also find that the distribution of equilibrium temperatures for the observed planets is similarly log-normal. This indicates that the absorption values are affected by observational bias, whereby observers have not yet targeted a sufficient sample of the hottest planets.
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    The analysis of the momentum difference between charged hadrons in high-energy proton-proton collisions is performed in order to study coherent particle production. The observed correlation pattern agrees with a model of a helical QCD string fragmenting into a chain of ground-state hadrons. A threshold momentum difference in the production of adjacent pairs of charged hadrons is observed, in agreement with model predictions. The presence of low-mass hadron chains also explains the emergence of charge-combination-dependent two-particle correlations commonly attributed to Bose-Einstein interference. The data sample consists of 190 inverse microbarns of minimum bias events collected with proton-proton collisions at a center-of-mass energy of 7 TeV in the early low-luminosity data taking with the ATLAS detector at the LHC.
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    Extended gaps in the debris disks of both Vega and Fomalhaut have been observed. These structures have been attributed to tidal perturbations by multiple super-Jupiter gas giant planets. Within the current observational limits, however, no such massive planets have been detected. Here we propose a less stringent `lone-planet' scenario to account for the observed structure with a single eccentric gas giant and suggest that clearing of these wide gaps is induced by its sweeping secular resonance. During the depletion of the disk gas, the planet's secular resonance propagates inward and clears a wide gap over an extended region of the disk. Although some residual intermediate-size planetesimals may remain in the gap, their surface density is too low to either produce super-Earths or lead to sufficiently frequent disruptive collisions to generate any observable dusty signatures. The main advantage of this lone-planet sweeping-secular-resonance model over the previous multiple gas giant tidal truncation scenario is the relaxed requirement on the number of gas giants. The observationally inferred upper mass limit can also be satisfied provided the hypothetical planet has a significant eccentricity. A significant fraction of solar or more massive stars bear gas giant planets with significant eccentricities. If these planets acquired their present-day kinematic properties prior to the depletion of their natal disks, their sweeping secular resonance would effectively impede the retention of neighboring planets and planetesimals over a wide range of orbital semi-major axes.
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    This paper proposes a probabilistic framework for the sequential estimation of the likelihood of a driver or passenger(s) returning to the vehicle and time of arrival, from the available partial track of the user location. The latter can be provided by a smartphone navigational service and/or other dedicated (e.g. RF based) user-to-vehicle positioning solution. The introduced novel approach treats the tackled problem as an intent prediction task within a Bayesian formulation, leading to an efficient implementation of the inference routine with notably low training requirements. It effectively captures the long term dependencies in the trajectory followed by the driver/passenger to the vehicle, as dictated by intent, via a bridging distribution. Two examples are shown to demonstrate the efficacy of this flexible low-complexity technique.
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    We study the phase transition between conducting and insulating states taking place in disordered multi-channel Luttinger liquids with inter-channel interactions. We derive renormalisation group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii--Kosterlitz--Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interaction results in a variety of phases, expected to be observable at intermediate temperatures where the interaction and disorder are relevant but weak hybridization and the charge-density wave interaction may be ignored.
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    Submodular set-functions are extensively used in large-scale combinatorial optimization problems arising in complex networks and machine learning. While there has been significant interest in distributed formulations of convex optimization, distributed minimization of submodular functions has not received significant attention. Thus, our main contribution is a framework for minimizing submodular functions in a distributed manner. The proposed framework is based on the ideas of Lovász extension of submodular functions and distributed optimization of convex functions. The framework exploits a fundamental property of submodularity that the convex relaxation of a submodular function can be computed efficiently. Since a minimizer of the convex relaxation of a discrete function is also a minimizer of that function over the associated discrete state space, submodular functions can be minimized in polynomial time. In the proposed framework, we employ a consensus based distributed optimization algorithm to minimize set-valued submodular functions as well as general submodular functions defined over set products. We also identify distributed motion coordination in multiagent systems as a new application domain for submodular function minimization. For demonstrating key ideas of the proposed framework, we select a complex setup of the capture the flag game, which offers a variety of challenges relevant to multiagent system. We formulate the problem as a submodular minimization problem and verify through extensive simulations that the proposed framework results in feasible policies for the agents.
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    We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a sideband cooling blockade, stopping the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We compare the linear and nonlinear cases of these models in the ultrastrong and deep strong coupling regimes. Moreover, we propose a scheme that simulates the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red and blue sideband interactions, yielding applications as a dynamical quantum filter.
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    Classification of imbalanced datasets is a challenging task for standard algorithms. Although many methods exist to address this problem in different ways, generating artificial data for the minority class is a more general approach compared to algorithmic modifications. SMOTE algorithm and its variations generate synthetic samples along a line segment that joins minority class instances. In this paper we propose Geometric SMOTE (G-SMOTE) as a generalization of the SMOTE data generation mechanism. G-SMOTE generates synthetic samples in a geometric region of the input space, around each selected minority instance. While in the basic configuration this region is a hyper-sphere, G-SMOTE allows its deformation to a hyper-spheroid and finally to a line segment, emulating, in the last case, the SMOTE mechanism. The performance of G-SMOTE is compared against multiple standard oversampling algorithms. We present empirical results that show a significant improvement in the quality of the generated data when G-SMOTE is used as an oversampling algorithm.
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    A detailed analysis is presented about the precise values of the Tsallis parameters obtained in $p-p$ collisions for identified particles, pions, kaons and protons at the LHC at three beam energies $\sqrt{s} = 0.9, 2.72$ and $7$ TeV. Interpolated data at $\sqrt{s} = $ 5.02 TeV have also been included. It is shown that the Tsallis formula provides very good fits to the $p_T$ distributions in $p-p$ collisions at the LHC using three parameters $dN/dy$, $T$ and $q$. However, the parameters $T$ and $q$ depend on the particle species and are different for pions, kaons and protons. As a consequence there is no $m_T$ scaling and also no universality of the parameters for different particle species.
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    In this paper we prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth \begineqnarray* -∆u-\lambda c(x)u-\kappa\alpha(∆(|u|^2\alpha))|u|^2\alpha-2u = |u|^q-2u+|u|^2^*-2u,\quad u∈D^1,2(\mathbbR^N), \endeqnarray* via variational methods, where $\lambda\geq0$, $0<\alpha<1/2$, $2<q<2^*$. It is interesting that we do not need to add a weight function to control $|u|^{q-2}u$.
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    A semi-inclusive measurement of charged hadron multiplicities in deep inelastic muon scattering off an isoscalar target was performed using data collected by the COMPASS Collaboration at CERN. The following kinematic domain is covered by the data: photon virtuality $Q^{2}>1$ (GeV/$c$)$^2$, invariant mass of the hadronic system $W > 5$ GeV/$c^2$, Bjorken scaling variable in the range $0.003 < x < 0.4$, fraction of the virtual photon energy carried by the hadron in the range $0.2 < z < 0.8$, square of the hadron transverse momentum with respect to the virtual photon direction in the range 0.02 (GeV/$c)^2 < P_{\rm{hT}}^{2} < 3$ (GeV/$c$)$^2$. The multiplicities are presented as a function of $P_{\rm{hT}}^{2}$ in three-dimensional bins of $x$, $Q^2$, $z$ and compared to previous semi-inclusive measurements. We explore the small-$P_{\rm{hT}}^{2}$ region, i.e. $P_{\rm{hT}}^{2} < 1$ (GeV/$c$)$^2$, where hadron transverse momenta are expected to arise from non-perturbative effects, and also the domain of larger $P_{\rm{hT}}^{2}$, where contributions from higher-order perturbative QCD are expected to dominate. The multiplicities are fitted using a single-exponential function at small $P_{\rm{hT}}^{2}$ to study the dependence of the average transverse momentum $\langle P_{\rm{hT}}^{2}\rangle$ on $x$, $Q^2$ and $z$. The power-law behaviour of the multiplicities at large $P_{\rm{hT}}^{2}$ is investigated using various functional forms. The fits describe the data reasonably well over the full measured range.
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    We establish what semi-discrete linear Weingarten surfaces with Weierstrass-type representations in $3$-dimensional Riemannian and Lorentzian spaceforms are, confirming their required properties regarding curvatures and parallel surfaces, and then classify them. We then define and analyze their singularities. In particular, we discuss singularities of (1) semi-discrete surfaces with non-zero constant Gaussian curvature, (2) parallel surfaces of semi-discrete minimal and maximal surfaces, and (3) semi-discrete constant mean curvature $1$ surfaces in de Sitter $3$-space. We include comparisons with different previously known definitions of such singularities.
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    Understanding the wave transport and localisation is a major goal in the study of lattices of different nature. In general, inhibiting the energy transport on a perfectly periodic and disorder-free system is challenging, however, some specific lattice geometries allow localisation due to the presence of dispersionless (flat) bands in the energy spectrum. Here, we report on the experimental realisation of a quasi-one-dimensional photonic graphene ribbon supporting four flat-bands. We study the dynamics of fundamental and dipolar modes, which are analogous to the s and p orbitals, respectively. In the experiment, both modes (orbitals) are effectively decoupled from each other, implying two sets of six bands, where two of them are completely flat. Using an image generator setup, we excite the s and p flat band modes and demonstrate their non-diffracting propagation for the first time. Our results open an exciting route towards photonic emulation of higher orbital dynamics.
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    We study L-systems with sectorial main operator and connections of their impedance functions with sectorial Stieltjes and inverse Stieltjes functions. Conditions when the main and state space operators (the main and associated state space operators) of a given L-system have the same or not angle of sectoriality are presented in terms of their impedance functions with discussion provided. Detailed analysis of L-systems with one-dimensional sectorial Shroödinger operator on half-line is given as well as connections with the Kato problem on sectorial extensions of sectorial forms. Examples that illustrate the obtained results are presented.
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    Dynamic density functionals (DDFs) are popular tools for studying the dynamical evolution of inhomogeneous polymer systems. Here, we present a systematic evaluation of a set of diffusive DDF theories by comparing their predictions with data from particle-based Brownian dynamics (BD) simulations for two selected problems: Interface broadening in compressible A/B homopolymer blends after a sudden change of the incompatibility parameter, and microphase separation in compressible A:B diblock copolymer melts. Specifically, we examine (i) a local dynamics model, where monomers are taken to move independently from each other, (ii) a nonlocal "chain dynamics" model, where monomers move jointly with correlation matrix given by the local chain correlator, and (iii,iv) two popular approximations to (ii), namely (iii) the Debye dynamics model, where the chain correlator is approximated by its value in a homogeneous system, and (iv) the computationally efficient "external potential dynamics" (EPD) model. With the exception of EPD, the value of the compressibility parameter has little influence on the results. In the interface broadening problem, the chain dynamics model reproduces the BD data best. However, the closely related EPD model produces large spurious artefacts. These artefacts disappear when the blend system becomes incompressible. In the microphase separation problem, the predictions of the nonlocal models (ii-iv) agree with each other and significantly overestimate the ordering time, whereas the local model (i) underestimates it. We attribute this to the multiscale character of the ordering process, which involves both local and global chain rearrangements. To account for this, we propose a mixed local/nonlocal DDF scheme which quantitatively reproduces all BD simulation data considered here.
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    Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N=1 Supersymmetric Yang-Mills (SYM) theory and Minimal Walking Technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N=1 SYM, Minimal Walking Technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to compute the running coupling in the MiniMom scheme. We analyze several different ensembles of lattice Monte Carlo simulations for the SU(2) adjoint QCD with Nf=1/2, 1, 3/2, and 2 Dirac fermions. We show how the running of the coupling changes as the number of interacting fermions is increased towards the conformal window.
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    We study the joint probability generating function for $k$ occupancy numbers on disjoint intervals in the Bessel point process. This generating function can be expressed as a Fredholm determinant. We obtain an expression for it in terms of a system of coupled Painlevé V equations, which are derived from a Lax pair of a Riemann-Hilbert problem. This generalizes a result of Tracy and Widom [23], which corresponds to the case $k = 1$. We also provide some examples and applications. In particular, several relevant quantities can be expressed in terms of the generating function, like the gap probability on a union of disjoint bounded intervals, the gap between the two smallest particles, and large $n$ asymptotics for $n\times n$ Hankel determinants with a Laguerre weight possessing several jumps discontinuities near the hard edge.
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    In this article, the theory of sheaves is studied from a categorical point of view. This perspective vastly generalizes the usual theory of sheaves of sets to a more abstract setting which allows us to investigate the theory of sheaves with values in an arbitrary category.
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    Convective perturbations arising from nuclear shell burning can play an important role in propelling neutrino-driven core-collapse supernova explosions. In this work, we analyze the impact of vorticity waves on the shock dynamics and the post-shock flow using the solution of the linear hydrodynamics equations. We show that the entropy perturbations generated by the interaction of the shock with vorticity waves may play a dominant role in generating buoyancy-driven turbulence in the gain region. We estimate that the resulting reduction in the critical luminosity is 17-24%, which approximately agrees with the results of three-dimensional neutrino-hydrodynamics simulations.
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    Let $(W_n(\theta))_{n \in \mathbb{N}_0}$ be Biggins' martingale associated with a supercritical branching random walk, and let $W(\theta)$ be its almost sure limit. Under a natural condition for the offspring point process in the branching random walk, we show that if the law of $W_1(\theta)$ belongs to the domain of normal attraction of an $\alpha$-stable distribution for some $\alpha \in (1,2)$, then, as $n\to\infty$, there is weak convergence of the tail process $(W(\theta) - W_{n-k}(\theta))_{k \in \mathbb{N}_0}$, properly normalized, to a random scale multiple of a stationary autoregressive process of order one with $\alpha$-stable marginals.
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    We report the fabrication and electrical characterization of depletion-mode quantum dots in a two-dimensional hole gas (2DHG) in intrinsic silicon. We use fixed charge in a SiO$_2$/Al$_2$O$_3$ dielectric stack to induce a 2DHG at the Si/SiO$_2$ interface. Fabrication of the gate structures is accomplished with a single layer metallization process. Transport spectroscopy reveals regular Coulomb oscillations with charging energies of 10-15 meV and 3-5 meV for the few- and many-hole regimes, respectively. This depletion-mode design avoids complex multilayer architectures requiring precision alignment, and allows to adopt directly best practices already developed for depletion dots in other material systems. We also demonstrate a method to deactivate fixed charge in the SiO$_2$/Al$_2$O$_3$ dielectric stack using deep ultraviolet light, which may become an important procedure to avoid unwanted 2DHG build-up in Si MOS quantum bits.
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    A strict analytical solution of the problem of spin-noise signal formation in a volume medium with randomly moving spin carriers is presented. The treatment is performed in the model of light scattering in a medium with fluctuating inhomogeneity. Along with conventional single-beam, geometry, we consider the two-beam arrangement, with the scattering field of the auxiliary ("tilted") beam heterodyned on the photodetector illuminated by the main beam. It is shown that the spin noise signal detected in the two-beam arrangement is highly sensitive to motion (diffusion) of the spin carriers within the illuminated volume and thus can provide additional information about spin dynamics and spatial correlations of spin polarization in volume media. Our quantitative estimates show that, under real experimental conditions, spin diffusion may strongly suppress the spin-noise signal in the two-beam geometry. Mechanism of this suppression is similar to that of the time-of-flight broadening with the critical distance determined by the period of spatial interference of the two beams rather than by the beam diameter.
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    Suzuki and Niida (Ann. Pure. Appl. Logic, 2015) showed the following results on independent distributions (IDs) on an AND-OR tree, where they took only depth-first algorithms into consideration. (1) Among IDs such that probability of the root having value 0 is fixed as a given r such that 0 < r < 1, if d is a maximizer of cost of the best algorithm then d is an independent and identical distribution (IID). (2) Among all IDs, if d is a maximizer of cost of the best algorithm then d is an IID. In the case where non-depth-first algorithms are taken into consideration, the counter parts of (1) and (2) are left open in the above work. Peng et al. (Inform. Process. Lett., 2017) extended (1) and (2) to multi-branching trees, where in (2) they put an additional hypothesis on IDs that probability of the root having value 0 is neither 0 nor 1. We give positive answers for the two questions of Suzuki-Niida. A key to the proof is that if ID d achieves the equilibrium among IDs then we can chose an algorithm of the best cost against d from depth-first algorithms. In addition, we extend the result of Peng et al. to the case where non-depth-first algorithms are taken into consideration.
  • PDF
    The Rindler horizon in Minkowski spacetime can be implanted with supertranslation hair by a matter shock wave without planar symmetry, and the hair is observable as a supertranslation memory on the Rindler family of uniformly linearly accelerated observers. We show that this classical memory is accompanied by a supertranslation quantum memory that modulates the entanglement between the opposing Rindler wedges in quantum field theory. A corresponding phenomenon across a black hole horizon may play a role in Hawking, Perry and Strominger's proposal for supertranslations to provide a solution to the black hole information paradox.
  • PDF
    We present a new measurement of the Ly\alpha forest power spectrum at $1.8 < z < 3.4$ using 74 Keck/HIRES and VLT/UVES high-resolution, high-S/N quasar spectra. We developed a custom pipeline to measure the power spectrum and its uncertainty, which fully accounts for finite resolution and noise, and corrects for the bias induced by masking missing data, DLAs, and metal absorption lines. Our measurement results in unprecedented precision on the small-scale modes $k > 0.02\,\mathrm{s\,km^{-1}}$, unaccessible to previous SDSS/BOSS analyses. It is well known that these high-$k$ modes are highly sensitive to the thermal state of the intergalactic medium, however contamination by narrow metal lines is a significant concern. We quantify the effect of metals on the small-scale power, and find a modest effect on modes with $k < 0.1\,\mathrm{s\,km^{-1}} $. As a result, by masking metals and restricting to $k < 0.1\,\mathrm{s\,km^{-1}}$ their impact is completely mitigated. We present an end-to-end Bayesian forward modeling framework whereby mock spectra with the same noise, resolution, and masking as our data are generated from Ly\alpha forest simulations. These mocks are used to build a custom emulator, enabling us to interpolate between a sparse grid of models and perform MCMC fits. Our results agree well with BOSS on scales $k < 0.02\,\mathrm{s\,km^{-1}}$ where the measurements overlap. The combination of BOSS' percent level low-$k$ precision with our $5-15\%$ high-$k$ measurements, results in a powerful new dataset for precisely constraining the thermal history of the intergalactic medium, cosmological parameters, and the nature of dark matter. The power spectra and their covariance matrices are provided as electronic tables.
  • PDF
    We show that the geometry of Hrushovski's ab initio construction for a single $n$-ary relation not-permitting dependent sets of size less than $n$, can be itself constructed as a Hrushovski construction. This shows that the geometry of the ab initio construction is $\omega$-stable as a first order structure.
  • PDF
    Many equations have been introduced and derived by the author indicated in the title in relation to multi-electron densities between the Hohenberg-Kohn theorems and variational principle, conversion of the non-relativistic electronic Schrodinger equation to scaling correct moment functional of ground state one-electron density to estimate ground state electronic energy, participation of electron-electron repulsion energy operator in the non-relativistic electronic Schrodinger equation via the coupling strength parameter along with generalizing the Hund rule, the emblematic theorems virial-, Moller-Plesset-, Hohenberg-Kohn-, Koopmans-, Brillouin theorem and configuration interactions formalism, and with analytic evaluation of Coulomb integrals for one, two and three-electron operators, as well as focusing on ground state electronic energy, correlation energy and zero point energy of stationer molecular systems.
  • PDF
    We realise bistability in the spinor of polariton condensates under non-resonant optical excitation and in the absence of biasing external fields. Numerical modelling of the system using the Ginzburg-Landau equation with an internal Josephson coupling between the two spin components of the condensate qualitatively describes the experimental observations. We demonstrate that polariton spin bistability persists for sweep times in the range of $[10 \mu sec,1 sec]$ offering a promising route to spin switches and spin memory elements.
  • PDF
    We formulate a numerical method for predicting the tensorial linear response of a rigid, asymmetrically charged body to an applied electric field. This prediction requires calculating the response of the fluid to the Stokes drag forces on the moving body and on the countercharges near its surface. To determine the fluid's motion, we represent both the body and the countercharges using many point sources of drag known as stokeslets. Finding the correct flow field amounts to finding the set of drag forces on the stokeslets that is consistent with the relative velocities experienced by each stokeslet. The method rigorously satisfies the condition that the object moves with no transfer of momentum to the fluid. We demonstrate that a sphere represented by 1999 well-separated stokeslets on its surface produces flow and drag force like a solid sphere to one-percent accuracy. We show that a uniformly-charged sphere with 3998 body and countercharge stokeslets obeys the Smoluchowski prediction \citeMorrison for electrophoretic mobility when the countercharges lie close to the sphere. Spheres with dipolar and quadrupolar charge distributions rotate and translate as predicted analytically to four percent accuracy or better. We describe how the method can treat general asymmetric shapes and charge distributions. This method offers promise as a way to characterize and manipulate asymmetrically charged colloid-scale objects from biology (e.g. viruses) and technology (e.g. self-assembled clusters).
  • PDF
    The search for new materials, based on computational screening, relies on methods that accurately predict, in an automatic manner, total energy, atomic-scale geometries, and other fundamental characteristics of materials. Many technologically important material properties directly stem from the electronic structure of a material, but the usual workhorse for total energies, namely density-functional theory, is plagued by fundamental shortcomings and errors from approximate exchange-correlation functionals in its prediction of the electronic structure. At variance, the $GW$ method is currently the state-of-the-art \em ab initio approach for accurate electronic structure. It is mostly used to perturbatively correct density-functional theory results, but is however computationally demanding and also requires expert knowledge to give accurate results. Accordingly, it is not presently used in high-throughput screening: fully automatized algorithms for setting up the calculations and determining convergence are lacking. In this work we develop such a method and, as a first application, use it to validate the accuracy of $G_0W_0$ using the PBE starting point, and the Godby-Needs plasmon pole model ($G_0W_0^\textrm{GN}$@PBE), on a set of about 80 solids. The results of the automatic convergence study utilized provides valuable insights. Indeed, we find correlations between computational parameters that can be used to further improve the automatization of $GW$ calculations. Moreover, we find that $G_0W_0^\textrm{GN}$@PBE shows a correlation between the PBE and the $G_0W_0^\textrm{GN}$@PBE gaps that is much stronger than that between $GW$ and experimental gaps. However, the $G_0W_0^\textrm{GN}$@PBE gaps still describe the experimental gaps more accurately than a linear model based on the PBE gaps.
  • PDF
    Surfaces of homoepitaxially grown TiO2-terminated SrTiO3(001) were studied in situ with scanning tunneling microscopy and spectroscopy. By controlling the Ti/Sr ratio, two-dimensional domains of highly ordered linear nanostructures, so-called "nanolines", are found to form on the surface. To further study how the surface structure affects the band structure, spectroscopic studies of these surfaces were performed. Our results reveal significantly more band bending for surfaces with the nanolines, indicative of an acceptor state associated with these features. Additionally, an in-gap state is observed on nanoline surfaces grown under high oxygen deficient conditions. This state appears to be the same as that observed previously, arising from the (++/+) transition level of surface oxygen vacancies.
  • PDF
    Including an extra reactant in the Gray-Scott reaction-diffusion model, the dynamical competition between different chemical species during the Turing pattern formation can lead to species territory invasion phenomenon among different patterns of respective species. We report a peculiar oscillatory change on respective mass of a 2D pattern under competition condition by numerical simulation. The invaded Turing spot pattern can turn from a steady fading mode into a spontaneous resonant oscillation mode, the firefly lighting mode, which occurs synchronously among nearest neighboring spots, until the largest spot is annihilated finally. Such resonant oscillation behavior for annihilation can continue but in a more chaotic way towards final dying of the pattern by invasion of another pattern. The resonant frequency is found to be intrinsic character of the invaded pattern, depending on its control parameters.

Recent comments

James Wootton Sep 21 2017 05:41 UTC

What does this imply for https://scirate.com/arxiv/1608.00263? I'm guessing they still regard it as valid (it is ref [14]), but just too hard to implement for now.

Ben Criger Sep 08 2017 08:09 UTC

Oh look, there's another technique for decoding surface codes subject to X/Z correlated errors: https://scirate.com/arxiv/1709.02154

Aram Harrow Sep 06 2017 07:54 UTC

The paper only applies to conformal field theories, and such a result cannot hold for more general 1-D systems by 0705.4077 and other papers (assuming standard complexity theory conjectures).

Felix Leditzky Sep 05 2017 21:27 UTC

Thanks for the clarification, Philippe!

Philippe Faist Sep 05 2017 21:09 UTC

Hi Felix, thanks for the good question.

We've found it more convenient to consider trace-nonincreasing and $\Gamma$-sub-preserving maps (and this is justified by the fact that they can be dilated to fully trace-preserving and $\Gamma$-preserving maps on a larger system). The issue arises because

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Felix Leditzky Sep 05 2017 19:02 UTC

What is the reason/motivation to consider trace-non-increasing maps instead of trace-preserving maps in your framework and the definition of the coherent relative entropy?

Steve Flammia Aug 30 2017 22:30 UTC

Thanks for the reference Ashley. If I understand your paper, you are still measuring stabilizers of X- and Z-type at the top layer of the code. So it might be that we can improve on the factor of 2 that you found if we tailor the stabilizers to the noise bias at the base level.

Ashley Aug 30 2017 22:09 UTC

We followed Aliferis and Preskill's approach in [https://arxiv.org/abs/1308.4776][1] and found that the fault-tolerant threshold for the surface code was increased by approximately a factor of two, from around 0.75 per cent to 1.5 per cent for a bias of 10 to 100.

[1]: https://arxiv.org/abs/1308.

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Stephen Bartlett Aug 30 2017 21:55 UTC

Following on from Steve's comments, it's possible to use the bias-preserving gate set in Aliferis and Preskill directly to do the syndrome extraction, as you build up a CNOT gadget, but such a direct application of your methods would be very complicated and involve a lot of gate teleportation. If y

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Steve Flammia Aug 30 2017 21:38 UTC

We agree that finding good syndrome extraction circuits if an important question. At the moment we do not have such circuits, though we have started to think about them. We are optimistic that this can be done in principle, but it remains to be seen if the circuits can be made sufficiently simple to

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