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    Recent Developments in computing very specific helicity amplitudes in two loop QCD are presented. The techniques focus upon the singular structure of the amplitude rather than on a diagramatic and integration approach
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    The Bradley-Terry model assigns probabilities for the outcome of paired comparison experiments based on strength parameters associated with the objects being compared. We consider different proposed choices of prior parameter distributions for Bayesian inference of the strength parameters based on the paired comparison results. We evaluate them according to four desiderata motivated by the use of inferred Bradley-Terry parameters to rate teams on the basis of outcomes of a set of games: invariance under interchange of teams, invariance under interchange of winning and losing, normalizability and invariance under elimination of teams. We consider various proposals which fail to satisfy one or more of these desiderata, and illustrate two proposals which satisfy them. Both are one-parameter independent distributions for the logarithms of the team strengths: 1) Gaussian and 2) Type III generalized logistic.
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    Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL. It contains a primitive language construct Box phi intuitively expressing that 'after every public announcement of a formula, formula phi is true.' The logic APAL is undecidable and it has an infinitary axiomatization. Now consider restricting the APAL quantification to public announcements of boolean formulas only, such that Box phi intuitively expresses that 'after every public announcement of a boolean formula, formula phi is true.' This logic can therefore called boolean arbitrary public announcement logic, BAPAL. The logic BAPAL is the subject of this work. It is decidable and it has a finitary axiomatization. These results may be considered of interest, as for various applications quantification over booleans is sufficient in formal specifications.
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    LiSr was produced in a heat-pipe oven and its thermal emission spectrum around 9300 cm$^{-1}$ was recorded by a high resolution Fourier transform spectrometer. In addition, selected lines of the spectrum of deeply bound vibrational levels of the $1^2\Sigma^+$ and $2^2\Sigma^+$ states were studied using laser excitation to facilitate the assignment of the lines. The ground state could be described for $v^{\prime\prime} =$ 0 - 2, $N^{\prime\prime}$ up to 105 and the $2^2\Sigma^+$ state for $v^{\prime} = 0$ up to $N^\prime = 68$. For both states, Dunham coefficients, spin-rotation parameters and potential energy curves were evaluated. A coupling of the $2^2\Sigma^+$ state to the $1^2\Pi$ state was observed, allowing a local description with Dunham coefficients of the $1^2\Pi$ state and an approximate evaluation of the coupling strength.
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    Materials that exhibit a low work function and therefore easily emit electrons into vacuum form the basis of electronic devices used in applications ranging from satellite communications to thermionic energy conversion. W-Ba-O is the canonical materials system that functions as the thermionic electron emitter used commercially in a range of high power electron devices. However, the work functions, surface stability, and kinetic characteristics of a polycrystalline W emitter surface are still not well understood or characterized. In this study, we examined the work function and surface stability of the eight lowest index surfaces of the W-Ba-O system using Density Functional Theory methods. We found that under the typical thermionic cathode operating conditions of high temperature and low oxygen partial pressure, the most stable surface adsorbates are Ba-O species with compositions in the range of Ba0.125O to Ba0.25O per surface W atom, with O passivating all dangling W bonds and Ba creating work function-lowering surface dipoles. Wulff construction analysis reveals that the presence of O and Ba significantly alters the surface energetics and changes the proportions of surface facets present under equilibrium conditions. Analysis of previously published data on W sintering kinetics suggests that fine W particles in the size range of 100-500 nm may be at or near equilibrium during cathode synthesis, and thus may exhibit surface orientation fractions well-described by the calculated Wulff construction.
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    Vehicular networks are one of the cornerstone of an Intelligent Transportation System (ITS). They are expected to provide ubiquitous network connectivity to moving vehicles while supporting various ITS services, some with very stringent requirements in terms of latency and reliability. Two vehicular networking technologies are envisioned to jointly support the full range of ITS services : DSRC (Dedicated Short Range Communication) for direct vehicle to vehicle/Road Side Units (RSU) communications and cellular technologies. To the best of our knowledge, approaches from the literature usually divide ITS services on each of these networks according to their requirements and one single network is in charge of supporting the each service. Those that consider both network technologies to offer multi-path routing, load balancing or path splitting for a better quality of experience of ITS services assume obviously separately controlled networks. Under the umbrella of SDN (Software Defined Networking), we propose in this paper a hybrid network architecture that enables the joint control of the networks providing connectivity to multi-homed vehicles and, also, explore the opportunities brought by such an architecture. We show through some use cases, that in addition to the flexibility and fine-grained programmability brought by SDN, it opens the way towards the development of effective network control algorithms that are the key towards the successful support of ITS services and especially those with stringent QoS. We also show how these algorithms could also benefit from information related to the environment or context in which vehicles evolve (traffic density, planned trajectory, ..), which could be easily collected by data providers and made available via the cloud.
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    Using the results obtained by Staruszkiewicz in Acta Phys. Pol. B 23, 591 (1992) and in Acta Phys. Pol. B 23, 927 (1992) we show that the representations acting in the eigenspaces of the total charge operator corresponding to the eigenvalues $n_1, n_2$ whose absolute values are less than or equal $\sqrt{\pi/e^2}$ are inequivalent if $|n_1| \neq |n_2|$ and contain the supplementary series component acting as a discrete component. On the other hand the representations acting in the eigenspaces corresponding to eigenvalues whose absolute values are greater than $\sqrt{\pi/e^2}$ are all unitarily equivalent and do not contain any supplementary series component.
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    We study cross-correlations of the kinetic Sunyaev-Zel'dovich effect (kSZ) and 21 cm signals during the epoch of reionisation (EoR) to measure the effects of patchy reionisation. Since the kSZ effect is proportional to the line-of-sight velocity, the kSZ-21 cm cross correlation suffers from cancellation at small angular scales. We thus focus on the correlation between the kSZ-squared field (kSZ$^2$) and 21 cm signals. When the global ionisation fraction is low ($x_e\lesssim 0.7$), the kSZ$^2$ fluctuation is dominated by rare ionised bubbles which leads to an anti-correlation with the 21 cm signal. When $0.8\lesssim x_e<1$, the correlation is dominated by small pockets of neutral regions, leading to a positive correlation. However, at very high redshifts when $x_e<0.15$, the spin temperature fluctuations change the sign of the correlation from negative to positive, as weakly ionised regions can have strong 21 cm signals in this case. To extract this correlation, we find that Wiener filtering is effective in removing large signals from the primary CMB anisotropy. The expected signal-to-noise ratios for a $\sim$10-hour integration of upcoming Square Kilometer Array data cross-correlated with maps from the current generation of CMB observatories with 3.4~$\mu$K arcmin noise and 1.7~arcmin beam over 100~deg$^2$ are 51, 60, and 37 for $x_e=0.2$, 0.5, and 0.9, respectively.
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    The normal state of cuprate superconductors exhibit many exotic behaviors[1][2] qualitatively different from the Fermi liquid (FL), the foundation of condensed matter physics. Here we demonstrate that non-Fermi liquid behaviors emerge naturally from scattering against a two-orbital bosonic liquid of preformed pairs. Particularly, we find a finite zero-energy dissipation at low-temperature limit that grows linearly with respect to temperature, against the characteristics of Fermi liquid. In essence, unlike the diminishing low-energy phase space of FL, the peculiar feature of strong thermal fluctuation in a bosonic system with fixed particle number guarantees non-vanishing scattering channels even at low-temperature limit. Unexpectedly, our resulting quasiparticle dispersion also contains the experimentally observed "kink"[3-9], indicating that the widely investigated kink feature is in fact another manifestation of the non-FL scattering. Furthermore, the scattering rate also shows the observed puzzling correlation with the low-temperature superconducting gap[10]. Our findings provide a generic route for fermionic systems to generate non-Fermi liquid behavior, and suggest strongly that the cuprates be in this exotic regime in which doped holes develop bosonic features by forming tightly bound pairs, whose low-temperature condensation gives unconventional superconductivity.
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    This paper considers the integrated problem of quay crane assignment, quay crane scheduling, yard location assignment, and vehicle dispatching operations at a container terminal. The main objective is to minimize vessel turnover times and maximize the terminal throughput, which are key economic drivers in terminal operations. Due to their computational complexities, these problems are not optimized jointly in existing work. This paper revisits this limitation and proposes Mixed Integer Programming (MIP) and Constraint Programming (CP) models for the integrated problem, under some realistic assumptions. Experimental results show that the MIP formulation can only solve small instances, while the CP model finds optimal solutions in reasonable times for realistic instances derived from actual container terminal operations.
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    The energy released by Active Galactic Nuclei (AGN) in the form of radiation, winds, or radio plasma jets, is known to impact on the surrounding interstellar medium. The result of these processes, known as AGN (negative) feedback, is suggested to prevent gas, in and around galaxies, from cooling, and to remove, or at least redistribute, gas by driving massive and fast outflows, hence playing a key role in galaxy evolution. Given its importance, a large effort is devoted by the astronomical community to trace the effects of AGN on the surrounding gaseous medium and to quantify their impact for different types of AGN. This review briefly summarizes some of the recent observational results obtained in different wavebands, tracing different phases of the gas. I also summarize the new insights they have brought, and the constraints they provide to numerical simulations of galaxy formation and evolution. The recent addition of deep observations of cold gas and, in particular, of cold molecular gas, has brought some interesting surprises and has expanded our understanding of AGN and AGN feedback.
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    An expression for the dimensionless dissipation rate was derived from the Karman-Howarth equation by asymptotic expansion of the second- and third- order structure functions in powers of the inverse Reynolds number. The implications of the time-derivative term for the assumption of local stationarity (or local equilibrium) which underpins the derivation of the Kolmogorov `4/5' law for the third-order structure function were studied. It was concluded that neglect of the time-derivative cannot be justified by reason of restriction to certain scales (the inertial range) nor to large Reynolds numbers. In principle, therefore, the hypothesis cannot be correct, although it may be a good approximation. It follows, at least in principle, that the quantitative aspects of the hypothesis of local stationarity could be tested by a comparison of the asymptotic dimensionless dissipation rate for free decay with that for the stationary case. But in practice this is complicated by the absence of an agreed evolution time for making the measurements during the decay. However, we can assess the quantitative error involved in using the hypothesis by comparing the exact asymptotic value of the dimensionless dissipation in free decay calculated on the assumption of local stationarity to the experimentally determined value (e.g. by means of direct numerical simulation), as this relationship holds for all measuring times. Should the assumption of local stationarity lead to significant error, then the `4/5' law needs to be corrected. Despite this, scale invariance in wavenumber space appears to hold in the formal limit of infinite Reynolds numbers, which implies that the `-5/3' energy spectrum does not require correction in this limit.
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    Computing the extensions between Verma modules is in general a very difficult problem. Using Soergel bimodules, one can construct a graded version of the principal block of Category $\mathcal{O}$ for any finite coxeter group. In this setting, we compute the extensions between Verma modules for dihedral groups.
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    We define a data exchange format for numerical values of Wilson coefficients of local operators parameterising low-energy effects of physics beyond the Standard Model. The format facilitates interfacing model-specific Wilson coefficient calculators, renormalisation group (RG) runners, and observable calculators. It is designed to be unambiguous (defining a non-redundant set of operators with fixed normalisation in each basis), extensible (allowing the addition of new EFTs or bases by the user), and robust (being based on industry standard file formats with parsers implemented in many programming languages). We have implemented the format for the Standard Model EFT (SMEFT) and for the weak effective theory (WET) below the electroweak scale and have added interfaces to a number of public codes dealing with SMEFT or WET. We also provide command-line utilities and a Python module for convenient manipulation of WCxf files, including translation between different bases and matching from SMEFT to WET.
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    We present a novel reconstruction algorithm based on a general cone-beam CT forward model which is capable of incorporating the blur and noise correlations that are exhibited in flat-panel CBCT measurement data. Specifically, the proposed model may include scintillator blur, focal-spot blur, and noise correlations due to light spread in the scintillator. The proposed algorithm (GPL-BC) uses a Gaussian Penalized-Likelihood objective function which incorporates models of Blur and Correlated noise. In a simulation study, GPL-BC was able to achieve lower bias as compared to deblurring followed by FDK as well as a model-based reconstruction method without integration of measurement blur. In the same study, GPL-BC was able to achieve better line-pair reconstructions (in terms of segmented-image accuracy) as compared to deblurring followed by FDK, a model based method without blur, and a model based method with blur but not noise correlations. A prototype extremities quantitative cone-beam CT test bench was used to image a physical sample of human trabecular bone. These data were used to compare reconstructions using the proposed method and model based methods without blur and/or correlation to a registered \muCT image of the same bone sample. The GPL-BC reconstructions resulted in more accurate trabecular bone segmentation. Multiple trabecular bone metrics, including Trabecular Thickness (Tb.Th.) were computed for each reconstruction approach as well as the \muCT volume. The GPL-BC reconstruction provided the most accurate Tb.Th. measurement, 0.255 mm, as compared to the \muCT derived value of 0.193 mm, followed by the GPL-B reconstruction, the GPL-I reconstruction, and then the FDK reconstruction (0.271 mm, 0.309 mm, and 0.335 mm, respectively).
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    We introduce the hypothesis that diquarks and antidiquarks in tetraquarks are separated by a potential barrier. We show that this notion can answer satisfactorily long standing questions challenging the diquark-antidiquark model of exotic resonances. The tetraquark description of X and Z resonances is shown to be compatible with present limits on the non-observation of charged partners X^+-, of the X(3872) and the absence of a hyperfine splitting between two different neutral states. In the same picture, Z_c and Z_b particles are expected to form complete isospin triplets plus singlets. It is also explained why the decay rate into final states including quarkonia are suppressed with respect to those having open charm/beauty states.
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    This article constructs a smooth weak Fano threefold of Picard number two with small anti-canonical morphism that arises as a blowup of a smooth curve of genus 5 and degree 8 in $\mathbb{P}^3$. While the existence of this weak Fano was known as a numerical possibility in \citeCM13 and constructed in BL12, this paper removes the dependencies on the results in \citeJPR11 needed in the construction of BL12 and constructs the link in the style of ACM17.
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    We demonstrate that multipartite entanglement is able to characterize one-dimensional topological order, which is witnessed by the scaling behavior of the quantum Fisher information of the ground state with respect to the spin operators defined in the original and dual lattices. We investigate an exactly-solvable long-range extended spin-$\frac{1}{2}$ Ising model with nontrivial $\mathbf{Z}$-symmetry topological order identified equivalently by winding numbers and paired Majorana zero modes at each end. For topologically ordered phases with high winding numbers, we can define a $\mathbf{Z}$ topological invariant by the scaling coefficient of the dual quantum Fisher information density. Containing richer properties and more complex structures than bipartite entanglement, the dual multipartite entanglement of the topologically ordered state has promising applications in robust quantum computation and quantum metrology, and could be generalized to higher-dimensional systems.
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    We give a Stinespring representation of the Schur block product, say (*), on pairs of square matrices with entries in a C*-algebra as a completely bounded bilinear operator of the form: A:=(a_ij), B:= (b_ij): A (*) B := (a_ijb_ij) = V* pi(A) F pi(B) V, such that V is an isometry, pi is a *-representation and F is a self-adjoint unitary. This implies an inequality due to Livshits and an apparently new one on diagonals of matrices. ||A (*) B|| ≤||A||_r ||B||_c operator, row and column norm; - diag(A*A) ≤A* (*) A ≤diag(A*A).
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    We present a terahertz (THz) frequency-domain spectroscopic (FDS) ellipsometer design which suppresses formation of standing waves by use of stealth technology approaches. The strategy to suppress standing waves consists of three elements \textitgeometry, \textitcoating and \textitmodulation. The instrument is based on the rotating analyzer ellipsometer principle and can incorporate various sample compartments, such as a superconducting magnet, \textitin-situ gas cells or resonant sample cavities, for example. A backward wave oscillator and three detectors are employed, which permit operation in the spectral range of 0.1--1~THz (3.3--33~cm$^{-1}$ or 0.4--4~meV). The THz frequency-domain ellipsometer allows for standard and generalized ellipsometry at variable angles of incidence in both reflection and transmission configurations. The methods used to suppress standing waves and strategies for an accurate frequency calibration are presented. Experimental results from dielectric constant determination in anisotropic materials, and free charge carrier determination in optical Hall effect, resonant-cavity enhanced optical Hall effect and \textitin-situ optical Hall effect experiments are discussed. Examples include silicon and sapphire optical constants, free charge carrier properties of two dimensional electron gas in group-III nitride high electron mobility transistor structure, and ambient effects on free electron mobility and density in epitaxial graphene.
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    Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights from one part of the literature can be used in the other. We then show that the metric induced by a characteristic kernel cannot reliably distinguish between distributions that are far apart in the total variation norm as soon as the underlying space of measures is infinite dimensional. In addition, we provide a characterization of characteristic kernels in terms of eigenvalues and -functions and apply this characterization to the case of continuous kernels on (locally) compact spaces. In the compact case we further show that characteristic kernels exist if and only if the space is metrizable. As special cases of our general theory we investigate translation-invariant kernels on compact Abelian groups and isotropic kernels on spheres. The latter are of particular interest for forecast evaluation of probabilistic predictions on spherical domains as frequently encountered in meteorology and climatology.
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    We consider the symbolic controller synthesis approach to enforce safety specifications on perturbed, nonlinear control systems. In general, in each state of the system several control values might be applicable to enforce the safety requirement and in the implementation one has the burden of picking a particular control value out of possibly many. We present a class of implementation strategies to obtain a controller with certain performance guarantees. This class includes two existing implementation strategies from the literature, based on discounted payoff and mean-payoff games. We unify both approaches by using games characterized by a single discount factor determining the implementation. We evaluate different implementations from our class experimentally on two case studies. We show that the choice of the discount factor has a significant influence on the average long-term costs, and the best performance guarantee for the symbolic model does not result in the best implementation. Comparing the optimal choice of the discount factor here with the previously proposed values, the costs differ by a factor of up to 50. Our approach therefore yields a method to choose systematically a good implementation for safety controllers with quantitative objectives.
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    We provide general arguments regarding the connection between low-energy theories (gravity and quantum field theory) and a hypothetical fundamental theory of quantum gravity, under the assumptions of (i) validity of the holographic bound and (ii) preservation of unitary evolution at the level of the fundamental theory. In particular, the appeal to the holographic bound imposed on generic physical systems by the Bekenstein-Hawking entropy implies that both classical geometry and quantum fields propagating on it should be regarded as phenomena emergent from the dynamics of the fundamental theory. The reshuffling of the fundamental degrees of freedom during the unitary evolution then leads to an entanglement between geometry and quantum fields. The consequences of such scenario are considered in the context of black hole evaporation and the related information-loss issue: we provide a simplistic toy model in which an average loss of information is obtained as a consequence of the geometry-field entanglement.
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    In recent years, neural networks have been used to generate music pieces, especially symbolic melody. However, the long-term structure in the melody has posed great difficulty for designing a good model. In this paper, we present a hierarchical recurrent neural network for melody generation, which consists of three Long-Short-Term-Memory (LSTM) subnetworks working in a coarse-to-fine manner. Specifically, the three subnetworks generate bar profiles, beat profiles and notes in turn, and the output of the high-level subnetworks are fed into the low-level subnetworks, serving as guidance for generating the finer time-scale melody components. Two human behavior experiments demonstrate the advantage of this structure over the single-layer LSTM which attempts to learn all hidden structures in melodies. In the third human behavior experiment, subjects are asked to judge whether the generated melody is composed by human or computer. The results show that 33.69% of the generated melodies are wrongly classified as human composed.
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    This paper examines the dependence of performance measures on network size with a focus on large networks. We develop a framework where it is shown that poor performance can be attributed to dimension--dependent scaling of network energy. Drawing from previous work, we show that such scaling in undirected networks can be attributed to the proximity of network spectrum to unity, or distance to instability. However, such a simple characterization does not exist for the case of directed networks. In fact, we show that any arbitrary scaling can be achieved for a fixed distance to instability. The results here demonstrate that it is always favorable, in terms of performance scaling, to balance a large network. This justifies a popular observation that undirected networks generally perform better. We show the relationship between network energy and performance measures, such as output shortfall probability or centrality, that are used in economic or financial networks. The strong connection between them explains why a network topology behaves qualitatively similar under different performance measures. Our results suggest that there is a need to study performance degradation in large networks that focus on topological dependence and transcend application specific analyses.
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    We analysed the four-decades-long X-ray light curve of the low-luminosity active galactic nucleus (LLAGN) NGC 7213 and discovered a fast-rise-exponential-decay (FRED) pattern, i.e. the X-ray luminosity increased by a factor of $\approx 4$ within 200 days, and then decreased exponentially with an $e$-folding time $\approx 8116$ days ($\approx 22.2$ years). For the theoretical understanding of the observations, we examined three variability models proposed in the literature: the thermal-viscous disk instability model, the radiation pressure instability model and the tidal disruption event (TDE) model. We find that a delayed tidal disruption of a main sequence star is most favorable; either the thermal-viscous disk instability model or radiation pressure instability model fails to explain some key properties observed, thus we argue them unlikely.
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    The proper definition of subsystems in gauge theory and gravity requires an extension of the local phase space by including edge mode fields. Their role is on the one hand to restore gauge invariance with respect to gauge transformations supported on the boundary, and on the other hand to parametrize the largest set of boundary symmetries which can arise if both the gauge parameters and the dynamical fields are unconstrained at the boundary. In this work we construct the extended phase space for three-dimensional gravity in first order connection and triad variables. There, the edge mode fields consist of a choice of coordinate frame on the boundary and a choice of Lorentz frame on the bundle, which together constitute the Lorentz-diffeomorphism edge modes. After constructing the extended symplectic structure and proving its gauge invariance, we study the boundary symmetries and the integrability of their generators. We find that the infinite-dimensional algebra of boundary symmetries with first order variables is the same as that with metric variables, and explain how this can be traced back to the expressions for the diffeomorphism Noether charge in both formulations. This concludes the study of extended phase spaces and edge modes in three-dimensional gravity, which was done previously by the author in the BF and Chern-Simons formulations.
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    We present a genus 0 Belyi map for the sporadic Janko group J2 of degree 280. As a consequence we obtain a polynomial having Aut(J2) as a Galois group over K(t) where K is a number field of degree 10.
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    We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. First, the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter $\varepsilon$, and second, the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force $F$ applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition, and the mean position of the chain end in the case of the loop-stretch transition. Close to the transition points, both the static and the dynamic behavior of chains with different length $N$ are very well described by a scaling Ansatz with the scaling parameters $(\varepsilon - \varepsilon^*) N^\phi$ (adsorption transition) and $(F - F^*) N^\nu$ (loop-stretch transition), respectively, where $\phi$ is the crossover exponent of the adsorption transition, and $\nu$ the Flory exponent. We show that both the loop-stretch and the loop adsorption transitions provide an exceptional opportunity to construct explicit analytical expressions for the crossover functions which perfectly describe all simulation results on static properties in the finite-size scaling regime. Explicit crossover functions are based on the Ansatz for the analytical form of the order parameter distributions at the respective transition points. In contrast to the close similarity in equilibrium static behavior, the dynamic relaxation at the two transitions shows qualitative differences, especially in the strongly ordered regimes.
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    KTA (KTH's timing analyzer) is a research tool for performing timing analysis of program code. The currently available toolchain can perform two different kinds of analyses: i) exhaustive fine-grained timing analysis, where timing information can be provided between arbitrary timing program points within a function, and ii) abstract search-based timing analysis, where the tool can perform optimal worst-case execution time (WCET) analysis. The latter is based on a technique that combines divide-and-conquer search and abstract interpretation. The tool is under development and currently supports a subset of the MIPS instruction set architecture.
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    Feshbach resonances in ultra-cold atomic gases have led to some of the most important advances in atomic physics. They did not only enable ground breaking work in the BEC-BCS crossover regime [1], but are also widely used for the association of ultra-cold molecules [2], leading to the formation of molecular Bose-Einstein condensates [3,4] and ultra-cold dipolar molecular systems [5]. Here, we demonstrate the experimental realization of an optical Feshbach resonance using ultra-long range Rydberg molecules [6]. We show their practical use by tuning the revival time of a quantum many-body system quenched into a deep optical lattice. Our results open up many applications for Rydberg optical Feshbach resonances as ultra-long range Rydberg molecules have a plenitude of available resonances for nearly all atomic species. Among the most intriguing prospects is the engineering of genuine three- and four-body interactions via coupling to trimer and tetramer molecular states [7].
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    Motivated by the calculation of correlation functions in inhomogeneous one-dimensional (1d) quantum systems, the 2d Inhomogeneous Gaussian Free Field (IGFF) is studied and solved. The IGFF is defined in a domain $\Omega \subset \mathbb{R}^2$ equipped with a conformal class of metrics $[{\rm g}]$ and with a real positive coupling constant $K: \Omega \rightarrow \mathbb{R}_{>0}$ by the action $\mathcal{S}[h] = \frac{1}{8\pi } \int_\Omega \frac{\sqrt{{\rm g}} d^2 {\rm x}}{K({\rm x})} \, {\rm g}^{i j} (\partial_i h)(\partial_j h)$. All correlations functions of the IGFF are expressible in terms of the Green's functions of generalized Poisson operators that are familiar from 2d electrostatics in media with spatially varying dielectric constants. This formalism is then applied to the study of ground state correlations of the Lieb-Liniger gas trapped in an external potential $V(x)$. Relations with previous works on inhomogeneous Luttinger liquids are discussed. The main innovation here is in the identification of local observables $\hat{O} (x)$ in the microscopic model with their field theory counterparts $\partial_x h, e^{i h(x)}, e^{-i h(x)}$, etc., which involve non-universal coefficients that themselves depend on position --- a fact that, to the best of our knowledge, was overlooked in previous works on correlation functions of inhomogeneous Luttinger liquids ---, and that can be calculated thanks to Bethe Ansatz form factors formulae available for the homogeneous Lieb-Liniger model. Combining those position-dependent coefficients with the correlation functions of the IGFF, ground state correlation functions of the trapped gas are obtained. Numerical checks from DMRG are provided for density-density correlations and for the one-particle density matrix, showing excellent agreement.
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    Recently it was shown that mesoscopic superpositions of photonic states can be prepared based on a spin-gated chiral photon rotation in a Fock-state lattice of three cavities coupled to a spin (two-level atom). By exchanging the roles of the cavities and the spin, we have performed parallel operations on chiral spin states based on an antisymmetric spin exchange interaction (ASI) in a superconducting circuit. The ASI, which is also called Dzyaloshinskii-Moriya interaction, plays an important role in the formation of topological spin textures such as skyrmions. By periodically modulating the transition frequencies of three superconducting qubits interacting with a bus resonator, we synthesize a chiral ASI Hamiltonian with spin-gated chiral dynamics, which allow us to demonstrate a three-spin chiral logic gate and entangle up to five qubits in Greenberger-Horne-Zeilinger states. Our results pave the way for quantum simulation of magnetism with ASI and quantum computation with chiral spin states.
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    Kontsevich designed a scheme to generate infinitesimal symmetries $\dot{\mathcal{P}} = \mathcal{Q}(\mathcal{P})$ of Poisson brackets $\mathcal{P}$ on all affine manifolds $M^r$; every such deformation is encoded by oriented graphs on $n+2$ vertices and $2n$ edges. In particular, these symmetries can be obtained by orienting sums of non-oriented graphs $\gamma$ on $n$ vertices and $2n-2$ edges. The bi-vector flow $\dot{\mathcal{P}} = \text{Or}(\gamma)(\mathcal{P})$ preserves the space of Poisson structures if $\gamma$ is a cocycle with respect to the vertex-expanding differential in the graph complex. A class of such cocycles $\boldsymbol{\gamma}_{2\ell+1}$ is known to exist: marked by $\ell \in \mathbb{N}$, each of them contains a $(2\ell+1)$-gon wheel with a nonzero coefficient. At $\ell=1$ the tetrahedron $\boldsymbol{\gamma}_3$ itself is a cocycle; at $\ell=2$ the Kontsevich--Willwacher pentagon-wheel cocycle $\boldsymbol{\gamma}_5$ consists of two graphs. We reconstruct the symmetry $\mathcal{Q}_5(\mathcal{P}) = \text{Or}(\boldsymbol{\gamma}_5)(\mathcal{P})$ and verify that $\mathcal{Q}_5$ is a Poisson cocycle indeed: $[\![\mathcal{P},\mathcal{Q}_5(\mathcal{P})]\!]\doteq 0$ via $[\![\mathcal{P},\mathcal{P}]\!]=0$.
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    Let $n$ be a positive integer. In this paper we provide a general theory to produce full orbit sequences in the affine $n$-dimensional space over a finite field. For $n=1$ our construction covers the case of the Inversive Congruential Generators.
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    In this paper we solve a problem posed by H. Bommier-Hato, M. Engliš and E.H. Youssfi in [3] on the boundedness of the Bergman-type projections in generalized Fock spaces. It will be a consequence of two facts: a full description of the embeddings between generalized Fock-Sobolev spaces and a complete characterization of the boundedness of the above Bergman type projections between weighted $L^p$-spaces related to generalized Fock-Sobolev spaces.
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    The prospect of pileup induced backgrounds at the High Luminosity LHC (HL-LHC) has stimulated intense interest in developing technologies for charged particle detection with accurate timing at high rates. The required accuracy follows directly from the nominal interaction distribution within a bunch crossing ($\sigma_z\sim5$ cm, $\sigma_t\sim170$ ps). A time resolution of the order of 20-30 ps would lead to significant reduction of these backgrounds. With this goal, we present a new detection concept called PICOSEC, which is based on a "two-stage" Micromegas detector coupled to a Cherenkov radiator and equipped with a photocathode. First results obtained with this new detector yield a time resolution of 24 ps for 150 GeV muons, and 76 ps for single photoelectrons.
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    Large scale flows in the Sun play an important role in the dynamo process linked to the solar cycle. The important large scale flows are the differential rotation and the meridional circulation with an amplitude of km/s and few m/s , respectively. These flows also have a cycle related components, namely the torsional oscillations. Our attempt is to determine large-scale plasma flows on the solar surface by deriving horizontal flow velocities using the techniques of solar granule tracking, dopplergrams, and time distance helioseismology. Coherent structure tracking (CST) and time distance helioseismology were used to investigate the solar differential rotation and meridional circulation at the solar surface on a 30 day HMI SDO sequence. The influence of a large sunspot on these large scale flows with a specific 7 day HMI SDO sequence has been also studied. The large scale flows measured by the CST on the solar surface and the same flow determined from the same data with the helioseismology in the first 1 Mm below the surface are in good agreement in amplitude and direction. The torsional waves are also located at the same latitudes with amplitude of the same order. We are able to measure the meridional circulation correctly using the CST method with only three days of data and after averaging between + and -15 degrees in longitude. We conclude that the combination of CST and Doppler velocities allows us to detect properly the differential solar rotation and also smaller amplitude flows such as the meridional circulation and torsional waves. The results of our methods are in good agreement with helioseismic measurements.
  • PDF
    The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stocks that pay constant dividends when the payoff is a power function. Finally, lower bound of Asian options and some special cases are provided.
  • PDF
    We consider the question, asked by Friedl, Livingston and Zentner, of which sums of torus knots are concordant to alternating knots. After a brief analysis of the problem in its full generality, we focus on sums of two torus knots. We describe some effective obstructions based on Heegaard Floer homology.
  • PDF
    We use a sequential $R$-matrix model to describe the breakup of the Hoyle state into three $\alpha$ particles via the ground state of $^8\mathrm{Be}$. It is shown that even in a sequential picture, features resembling a direct breakup branch appear in the phase space distribution of the $\alpha$ particles. We construct a toy model to describe the Coulomb interaction in the three-body final state and its effects on the decay spectrum are investigated. The framework is also used to predict the phase space distribution of the $\alpha$ particles emitted in a direct breakup of the Hoyle state and the possibility of interference between a direct and sequential branch is discussed. Our numerical results are compared to the current upper limit on the direct decay branch determined in recent experiments.
  • PDF
    We consider Fock spaces $F^{p,\ell}_{\alpha}$ of entire functions on ${\mathbb C}$ associated to the weights $e^{-\alpha |z|^{2\ell}}$, where $\alpha>0$ and $\ell$ is a positive integer. We compute explicitly the corresponding Bergman kernel associated to $F^{2,\ell}_{\alpha}$ and, using an adequate factorization of this kernel, we characterize the boundedness and the compactness of the small Hankel operator $\mathfrak{h}^{\ell}_{b,\alpha}$ on $F^{p,\ell}_{\alpha}$. Moreover, we also determine when $\mathfrak{h}^{\ell}_{b,\alpha}$ is a Hilbert-Schmidt operator on $F^{2,\ell}_{\alpha}$.
  • PDF
    We explore the potential of a selected model of radiative neutrino masses to be implemented in a renormalizable SU(5) unification framework. The Zee-type model under consideration uncovers the SU(5) representations in which the new fields are embedded and which may contain also other light states leading to the unification of gauge couplings. We perform an exhaustive search which reveals specific patterns of new states and demonstrate that such patterns are consistent with a general choice of relevant scalar potential. It turns out that all of the specific scenarios which lead to successful unification include the colored scalars testable at the LHC.
  • PDF
    We consider a wireless network in which $K$ transmitters, each equipped with a single antenna, fully cooperate to serve $K$ single antenna receivers, each equipped with a cache memory. The transmitters have access to partial knowledge of the channel state information. For a symmetric setting, in terms of channel strength levels, partial channel knowledge levels and cache sizes, we characterize the generalized degrees of freedom (GDoF) up to a constant multiplicative factor. The achievability scheme exploits the interplay between spatial multiplexing gains and coded-multicasting gain. On the other hand, a cut-set argument in conjunction with a new application of the aligned image sets approach are used to derive the outer bound. We further show that the characterized order-optimal GDoF is also attained in a decentralized setting, where no coordination is required for content placement in the caches.
  • PDF
    We exploit the theoretical strength of (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the proper (anti-)BRST symmetry transformations for any arbitrary D-dimensional interacting non-Abelian gauge theory where there is an SU(N) gauge invariant coupling between the gauge field and Dirac fields. We derive the conserved and nilpotent (anti-)BRST charges and establish their nilpotency and absolute anticommutativity within the framework of ACSA to BRST formalism. The proof of absolute anticommutativity property of the (anti-)BRST charges is a novel result in view of the fact that we consider, in our present endeavor, only the (anti-)chiral super expansions of the superfields that are defined on the (D, 1)-dimensional super-submanifolds of the general (D, 2)-dimensional supermanifold on which our D-dimensional ordinary interacting non-Abelian 1-form gauge theory is generalized. The latter supermanifold is parameterized by the superspace coordinates Z^M = (x, \theta, \bar\theta) where x^\mu \;(\mu = 0, 1,...D-1) are the bosonic D-dimensional coordinates and Grassmannian variables (\theta, \bar\theta) of the superspace coordinates satisfy the standard (fermionic) relationships: \theta^2 = \bar\theta^2 = 0, \theta\bar\theta + \bar\theta\theta = 0.
  • PDF
    We consider stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of barotropic gaseous stars. The equation of states is supposed to be near to that of the polytropic gaseous stars of the adiabatic exponent $\gamma$ such that $6/5<\gamma <2$ at the vacuum, so that, besides the exact $\gamma$-laws of polytropic stars, as an example, the equation of states for white dwarfs can be treated. A generic condition of the existence of stationary solutions with differential rotation is given, and the existence of slowly rotating configurations near spherically symmetric equilibria is given. The problem is formulated as a nonlinear integral equation, and is solved by application of the infinite dimensional implicit function theorem. Properties of solutions such as physical vacuum boundary condition and oblateness of star surface are clarified.
  • PDF
    A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of the sequence. This approximation scheme is fast, requiring only one pass through the sequence, and produces small probability distribution distances for large sequences.
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    Purpose: Experimental measurements of bone mineral density distributions (BMDDs) enable a determination of secondary mineralisation kinetics in bone, but the maximum degree of mineralisation and how this maximum is approached remain uncertain. We thus test computationally different hypotheses on late stages of bone mineralisation by simulating BMDDs in low turnover conditions. Materials and Methods: An established computational model of the BMDD that accounts for mineralisation and remodelling processes was extended to limit mineralisation to various maximum calcium capacities of bone. Simulated BMDDs obtained by reducing turnover rate from the reference trabecular BMDD under different assumptions on late stage mineralisation kinetics were compared with experimental BMDDs of low-turnover bone. Results: Simulations show that an abrupt stopping of mineralisation near a maximum calcium capacity induces a pile-up of minerals in the BMDD statistics that is not observed experimentally. With a smooth decrease of mineralisation rate, imposing low maximum calcium capacities helps to match peak location and width of simulated low turnover BMDDs with peak location and width of experimental BMDDs, but results in a distinctive asymmetric peak shape. No tuning of turnover rate and maximum calcium capacity was able to explain the differences found in experimental BMDDs between trabecular bone (high turnover) and femoral cortical bone (low turnover). Conclusions: Secondary mineralisation in human bone does not stop abruptly, but continues slowly up to a calcium content greater than 30 wt% Ca. The similar mineral heterogeneity seen in trabecular and femoral cortical bones at different peak locations was unexplained by turnover differences tested.
  • PDF
    Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in stationary random Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and spatial disorder emerges also naturally. Two type of potential correlations are studied: exponentially-decaying (Ornstein-Uhlenbeck process in space) and algebraically-decaying with an infinite correlation length. It is shown that for a relatively small disorder strength in units of thermal energy (several $k_BT$) viscoelastic subdiffusion in the ensemble sense easily overcomes the potential disorder and asymptotically is not distinguishable from the free-space subdiffusion. However, such subdiffusion on the level of single-tajectory averages still exhibits transiently a characteristic scatter featuring weak ergodicity breaking. With an increase of disorder strength to $5\div 10\; k_BT$, a very long regime of logarithmic Sinai-like diffusion emerges. Long correlations in the potentials fluctuations make such a transient regime essentially longer, but faster in the absolute terms. This nominally ultraslow Sinai diffusion is, however, not dramatically slower than the free-space viscoelastic subdiffusion, in the absolute terms, on the ensemble level. It can transiently be even faster. The explanation of this paradoxical phenomenon is provided. On the level of single-trajectories, such disorder-obstructed persistent viscoelastic subdiffusion is always slower and exhibits a strong scatter in single-trajectory averages.
  • PDF
    We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We prove that an inverse system of groupoids with Haar system preserving bonding maps has a limit, and that we get a corresponding direct system of groupoid $C^*$-algebras. An explicit construction of an inverse system of groupoids is used to approximate a $\sigma$-compact groupoid $G$ by second countable groupoids; if $G$ is equipped with a Haar system and 2-cocycle then so are the approximation groupoids, and the maps in the inverse system are Haar system preserving. As an application of this construction, we show how to easily extend the Maximal Equivalence Theorem of Jean Renault to $\sigma$-compact groupoids.

Recent comments

Andrew W Simmons Dec 14 2017 11:40 UTC

Hi Māris, you might well be right! Stabiliser QM with more qubits, I think, is also a good candidate for further investigation to see if we can close the gap a bit more between the analytical upper bound and the example-based lower bound.

Planat Dec 14 2017 08:43 UTC

Interesting work. You don't require that the polar space has to be symplectic. In ordinary quantum mechanics the commutation of n-qudit observables is ruled by a symplectic polar space. For two qubits, it is the generalized quadrangle GQ(2,2). Incidently, in https://arxiv.org/abs/1601.04865 this pro

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Māris Ozols Dec 12 2017 19:41 UTC

$E_7$ also has some nice properties in this regard (in fact, it might be even better than $E_8$). See https://arxiv.org/abs/1009.1195.

Danial Dervovic Dec 10 2017 15:25 UTC

Thank you for the insightful observations, Simon.

In response to the first point, there is a very short comment in the Discussion section to this effect. I felt an explicit dependence on $T$ as opposed to the diameter would make the implications of the result more clear. Namely, lifting can mix

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Simon Apers Dec 09 2017 07:54 UTC

Thanks for the comment, Simone. A couple of observations:

- We noticed that Danial's result can in fact be proved more directly using the theorem that is used from ([arXiv:1705.08253][1]): by choosing the quantum walk Cesaro average as the goal distribution, it can be attained with a lifted Markov

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Simone Severini Dec 07 2017 02:51 UTC

Closely related to

Simon Apers, Alain Sarlette, Francesco Ticozzi, Simulation of Quantum Walks and Fast Mixing with Classical Processes, https://scirate.com/arxiv/1712.01609

In my opinion, lifting is a good opportunity to put on a rigorous footing the relationship between classical and quantu

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Mark Everitt Dec 05 2017 07:50 UTC

Thank you for the helpful feedback.

Yes these are 14 pairs of graphs [This is an edit - I previously mistakenly posted that it was 7 pairs] that share the same equal angle slice. We have only just started looking at the properties of these graphs. Thank you for the link - that is a really useful r

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Simone Severini Dec 05 2017 01:13 UTC

When looking at matrix spectra as graph invariants, it is easy to see that the spectrum of the adjacency matrix or the Laplacian fails for 4 vertices. Also, the spectrum of the adjacency matrix together with the spectrum of the adjacency matrix of the complement fail for 7 vertices. So, the algorith

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Mark Everitt Dec 04 2017 17:52 UTC

Thank you for this - its the sort of feedback we were after.

We have found 14 examples of 8 node graphs (of the possible 12,346) that break our conjecture.

We are looking into this now to get some understanding and see if we can overcome this issue. We will check to see if the failure of our algo

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Dave Bacon Dec 02 2017 00:08 UTC

A couple of comments:

1. To be a complete algorithm I think you need to specify how many of the equal angles you need to sample from (i.e. how many Euler angles)? And also maybe what "experimental accuracy means"? If those are exponential in order to work that's bad (but still very interesting

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