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    Athermal disordered systems can exhibit a remarkable response to an applied oscillatory shear: after a relatively few shearing cycles, the system falls into a configuration that had already been visited in a previous cycle. After this point the system repeats its dynamics periodically despite undergoing many particle rearrangements during each cycle. We study the behavior of orbits as we approach the jamming point in simulations of jammed particles subject to oscillatory shear at fixed pressure and zero temperature. As the pressure is lowered, we find that it becomes more common for the system to find periodic states where it takes multiple cycles before returning to a previously visited state. Thus, there is a proliferation of longer periods as the jamming point is approached.
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    The abundance of metals in galaxies is a key parameter which permits to distinguish between different galaxy formation and evolution models. Most of the metallicity determinations are based on optical line ratios. However, the optical spectral range is subject to dust extinction and, for high-z objects (z > 3), some of the lines used in optical metallicity diagnostics are shifted to wavelengths not accessible to ground based observatories. For this reason, we explore metallicity diagnostics using far-infrared (IR) line ratios which can provide a suitable alternative in such situations. To investigate these far-IR line ratios, we modeled the emission of a starburst with the photoionization code CLOUDY. The most sensitive far-IR ratios to measure metallicities are the [OIII]52$\mu$m and 88$\mu$m to [NIII]57$\mu$m ratios. We show that this ratio produces robust metallicities in the presence of an AGN and is insensitive to changes in the age of the ionizing stellar. Another metallicity sensitive ratio is the [OIII]88$\mu$m/[NII]122$\mu$m ratio, although it depends on the ionization parameter. We propose various mid- and far-IR line ratios to break this dependency. Finally, we apply these far-IR diagnostics to a sample of 19 local ultraluminous IR galaxies (ULIRGs) observed with Herschel and Spitzer. We find that the gas-phase metallicity in these local ULIRGs is in the range 0.7 < Z_gas/Z_sun < 1.5, which corresponds to 8.5 < 12 + log (O/H) < 8.9. The inferred metallicities agree well with previous estimates for local ULIRGs and this confirms that they lie below the local mass-metallicity relation.
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    We consider compact Kählerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic holomorphic Poisson structure $\Pi$ which is sufficiently general, in a precise linear sense, with respect to its (normal-crossing) degeneracy divisor $D(\Pi)$. We prove that $(X, \Pi)$ has unobsrtuced deformations, that the tangent space to its deformation space can be identified in terms of the mixed Hodge structure on $H^2$ of the open symplectic manifold $X\setminus D(\Pi)$, and in fact coincides with this $H^2$ provided the Hodge number $h^{2,0}_X=0$, and finally that the degeneracy locus $D(\Pi)$ deforms locally trivially under deformations of $(X, \Pi)$. \
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    We provide a short proof of a conjecture of Davila and Kenter concerning a lower bound on the zero forcing number $Z(G)$ of a graph $G$. More specifically, we show that $Z(G)\geq (g-2)(\delta-2)+2$ for every graph $G$ of girth $g$ at least $3$ and minimum degree $\delta$ at least $2$.
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    In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen \citeLM. We also extend the result to rough homogeneous singular integral operators.
  • May 24 2017 math.NT arXiv:1705.08363v1
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    The existence and construction of vector-valued modular forms (vvmf) for any arbitrary Fuchsian group $\rG$, for any representation $\rho:\rG \longrightarrow \mr{GL}_{d}(\C)$ of finite image can be established by lifting scalar-valued modular forms of the finite index subgroup $\ker(\rho)$ of $\rG$. In this article vvmf are explicitly constructed for any admissible multiplier (representation) $\rho$, see section~\refaf for the definition of admissible multiplier. In other words, the following question has been partially answered\,: \emph For which representations $\rho$ of a given $\rG$, is there a vvmf with at least one nonzero component ?
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    We develop a coalgebraic generalization of the classical Paige-Tarjan algorithm for efficient bisimilarity checking. Coalgebraic generality implies that our algorithm applies to systems beyond the standard relational setup, in particular various flavours of weighted systems. The specific requirements of the algorithm force rather strong assumptions on the coalgebraic type functors, but by using modularity principles in multi-sorted coalgebra and generalizing our methods beyond the category of sets, we nevertheless arrive at covering not just the known examples (transition systems and Markov chains) but also systems with mixed transition types, such as Segala-style probabilistic automata.
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    We propose a fast method with statistical guarantees for learning an exponential family density model where the natural parameter is in a reproducing kernel Hilbert space, and may be infinite dimensional. The model is learned by fitting the derivative of the log density, the score, thus avoiding the need to compute a normalization constant. We improved the computational efficiency of an earlier solution with a low-rank, Nyström-like solution. The new solution remains consistent, and is shown to converge in Fisher distance at the same rate as a full-rank solution, with guarantees on the degree of cost and storage reduction. We compare to a popular score learning approach using a denoising autoencoder, in experiments on density estimation and in the construction of an adaptive Hamiltonian Monte Carlo sampler. Apart from the lack of statistical guarantees for the autoencoder, our estimator is more data-efficient when estimating the score, runs faster, and has fewer parameters (which can be tuned in a principled and interpretable way).
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    We report the serendipitous discovery of the first gravitationally lensed quasar candidate from Pan-STARRS. The grizy images reveal four point-like images with magnitudes between 14.9 mag and 18.1 mag. The colors of the point sources are similar, and they are more consistent with quasars than stars or galaxies. The lensing galaxy is detected in the izy bands, with an inferred photometric redshift of ~0.6, lower than that of the point sources. We successfully model the system with a singular isothermal ellipsoid with shear, using the relative positions of the five objects as constraints. While the brightness ranking of the point sources is consistent with that of the model, we find discrepancies between the model-predicted and observed fluxes, likely due to microlensing by stars and millilensing due to dark matter substructure. In order to fully confirm the gravitational lens nature of this system, and add it to the small but growing number of the powerful probes of cosmology and astrophysics represented by quadruply lensed quasars, we further require spectroscopy and high-resolution imaging.
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    We study spin mixing dynamics in a chromium dipolar Bose-Einstein Condensate, after tilting the atomic spins by an angle $\theta$ with respect to the magnetic field. Spin mixing is triggered by dipolar coupling, but, once dynamics has started, it is mostly driven by contact interactions. For the particular case $\theta=\pi/2$, an external spin-orbit coupling term induced by a magnetic gradient is required to enable the dynamics. Then the initial ferromagnetic character of the gas is locally preserved, an unexpected feature that we attribute to large spin-dependent contact interactions.
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    Based on the third allotropic form of carbon (Fullerenes) through theoretical study have been predicted structures described as non-classical fullerenes. We have studied novel allotropic carbon structures with a closed cage configuration that have been predicted for the first time, by using DFT at the B3LYP level. Such carbon Cn-q structures (where, n=20, 42, 48 and 60), combine states of hybridization sp1 and sp2, for the formation of bonds. A comparative analysis of quasi-fullerenes with respect to their isomers of greater stability was also performed. Chemical stability was evaluated with the criteria of aromaticity through the different rings that build the systems. The results show new isomerism of carbon nanostructures with interesting chemical properties such as hardness, chemical potential and HOMO-LUMO gaps. We also studied thermal stability with Lagrangian molecular dynamics method using Atom- Center Density propagation (ADMP) method.
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    The Rafita asteroid family is an S-type group located in the middle main belt, on the right side of the 3J:-1A mean-motion resonance. The proximity of this resonance to the family left side in semi-major axis caused many former family members to be lost. As a consequence, the family shape in the $(a,1/D)$ domain is quite asymmetrical, with a preponderance of objects on the right side of the distribution. The Rafita family is also characterized by a leptokurtic distribution in inclination, which allows the use of methods of family age estimation recently introduced for other leptokurtic families such as Astrid, Hansa, Gallia, and Barcelona. In this work we propose a new method based on the behavior of an asymmetry coefficient function of the distribution in the $(a,1/D)$ plane to date incomplete asteroid families such as Rafita. By monitoring the time behavior of this coefficient for asteroids simulating the initial conditions at the time of the family formation, we were able to estimate that the Rafita family should have an age of $490\pm200$ Myr, in good agreement with results from independent methods such as Monte Carlo simulations of Yarkovsky and Yorp dynamical induced evolution and the time behaviour of the kurtosis of the $\sin{(i)}$ distribution. Asteroids from the Rafita family can reach orbits similar to 8\% of the currently known near Earth objects. $\simeq$1\% of the simulated objects are present in NEO-space during the final 10 Myr of the simulation, and thus would be comparable to objects in the present-day NEO population.
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    We establish several surjectivity theorems regarding the Galois groups of small iterates of $\phi_c(x)=x^2+c$ for $c\in\mathbb{Q}$. To do this, we use explicit techniques from the theory of rational points on curves, including the method of Chabauty-Coleman and the Mordell-Weil sieve. For example, we succeed in finding all rational points on a hyperelliptic curve of genus $7$, with rank $5$ Jacobian, whose points parametrize quadratic polynomials with a "newly small" Galois group at the fifth stage of iteration.
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    We study the affine quasi-Einstein equation, a second order linear homogeneous equation, which is invariantly defined on any affine manifold. We prove that the space of solutions is finite-dimensional, and its dimension is a strongly projective invariant. Moreover the maximal dimension is shown to be achieved if and only if the manifold is strongly projectively flat.
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    Quasi--local scalar variables approach is applied to a spherically symmetric inhomogeneous Lemaı̂ tre--Tolman--Bondi metric containing a mixture of non-relativistic cold dark matter and coupled dark energy with constant equation of state. The quasi--local coupling term considered is proportional to the quasi--local cold dark matter energy density and a quasi--local Hubble factor-like scalar via a coupling constant $\alpha$. The autonomous numerical system obtained from the evolution equations is classified for different choices of the free parameters: the adiabatic constant of the dark energy $w$ and $\alpha$. The presence of a past attractor in a non-physical region of the energy densities phase-space of the system makes the coupling term non physical when the energy flows from the matter to the dark energy in order to avoid negative values of the dark energy density in the past. On the other hand, if the energy flux goes from dark energy to dark matter, the past attractor lays in a physical region. The system is also numerically solved for some interesting initial profiles leading to different configurations: an ever expanding mixture, a scenario where the dark energy is completely consumed by the non-relativistic matter by means of the coupling term, a scenario where the dark energy disappears in the inner layers while the outer layers expand as a mixture of both sources, and, finally, a structure formation toy model scenario, where the inner shells containing the mixture collapse while the outer shells expand.
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    We analyze the caching overhead incurred by a class of multithreaded algorithms when scheduled by an arbitrary scheduler. We obtain bounds that match or improve upon the well-known $O(Q+S \cdot (M/B))$ caching cost for the randomized work stealing (RWS) scheduler, where $S$ is the number of steals, $Q$ is the sequential caching cost, and $M$ and $B$ are the cache size and block (or cache line) size respectively.
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    The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic parametrized partial differential equation that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges immersed in an ionic solution. Efficient numerical computation of the PBE yields a high number of degrees of freedom in the resultant algebraic system of equations, ranging from several hundred thousands to millions. Coupled with the fact that in most cases the PBE requires to be solved multiple times for a large number of system configurations, this poses great computational challenges to conventional numerical techniques. To accelerate such computations, we here present the reduced basis method (RBM) which greatly reduces this computational complexity by constructing a reduced order model of typically low dimension. We discretize the linearized PBE (LPBE) with a centered finite difference scheme and solve the resultant linear system by the preconditioned conjugate gradient (PCG) method with an algebraic multigrid (AMG) V-cycle as preconditioner at different samples of ionic strength on a three-dimensional Cartesian grid. We then apply the RBM to the high-fidelity full order model (FOM). The discrete empirical interpolation method (DEIM) is applied to the Dirichlet boundary conditions which are nonaffine in one parameter (the ionic strength) to reduce the complexity of the reduced order model (ROM). From the numerical results, we notice that the RBM reduces the model order from $\mathcal{N} = 2\times 10^{6}$ to $N = 6$ at an accuracy of $10^{-10}$ and reduces computational time by a factor of approximately $8,000$. DEIM, on the other hand, provides a speed-up of $20$ in the online phase at a single iteration of the greedy algorithm.
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    A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As a result, we study several super-critical semilinear Elliptic problems.
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    The yardstick of new first-principles approaches to key points on reaction paths at metal surfaces is chemical accuracy compared to reliable experiment. By this we mean that such values as the activation barrier are required to within 1 kcal/mol. Quantum Monte Carlo (QMC) is a promising (albeit lengthy) first-principles method for this and we are now beyond the dawn of QMC benchmarks for these systems, since hydrogen dissociation on Cu(111) has been studied with quite adequate accuracy in two improving QMC studies Hoggan ArXiv 2015, K. Doblhoff-Deir et al JCTC (2017). Pt and Cu require the use of pseudo-potentials in these calculations and we show that those of Pt are less problematic than those for Cu, particularly for QMC work. In this letter, we determine the activation barrier to hydrogen dissociation on Pt(111) using the bridging geometry. This is found to agree to better than chemical accuracy with recent Specific Reaction Parameter (SRP-DFT) work, which is itself within chemical accuracy of measurement (Kroes et al Cplett 2017). The results suggest the dissociation barrier for hydrogen on Pt(111) is close to 5.4 (QMC) and 6.2 (SRP-DFT) kcal/mol with a QMC standard error of 1.08 kcal/mol. This is encouraging for establishing less well-known benchmark values of industrial reaction barriers on Pt(111).
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    We show how Majoron models may be tested/limited in gravitational waves experiments. In particular, the Majoron self-interaction potential may induce a first order phase transition, producing gravitational waves from bubble collisions. We dubbed such a new scenario \it violent Majoron model, because it would be associated to a violent phase transition in the early Universe. Sphaleron constraints can be avoided if the global $U(1)_{B-L}$ is broken at scales lower than the electroweak scale, provided that the B-L spontaneously breaking scale is lower than $10\, {\rm TeV}$ in order to satisfy the cosmological mass density bound. The possibility of a sub-electroweak phase transition is practically unconstrained by cosmological bounds and it may be detected within the sensitivity of next generation of gravitational waves experiments: eLISA, DECIGO and BBO. We also comment on the possible detection in CEPC collider, where Majorons's production can be observed from Higgs' portals in missing transverse energy channels.
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    We report on the observation of the motional Stark effect of highly excited $^{87}$Rb Rydberg atoms moving in the presence of a weak homogeneous magnetic field in a vapor cell. Employing electromagnetically induced transparency for spectroscopy of an atomic vapor, we observe the velocity, quantum state and magnetic field dependent transition frequencies between the ground and Rydberg excited states. For atoms with the principal quantum number $n=100$ moving at velocities around 400m/s and a magnetic field of $B=100\mathrm{G}$, we measure a motional Stark shift of $\sim10\mathrm{MHz}$. Our experimental results are supported by numerical calculations based on a diagonalization of the effective Hamiltonian governing the valence electron of $^{87}$Rb in the presence of crossed electric and magnetic fields.
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    This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence $(S(n))_{n\ge 0}$ counting the number of positive entries on each row. By introducing a convenient tree structure, we provide a recurrence relation for $(S(n))_{n\ge 0}$. This leads to a connection with the $2$-regular Stern-Brocot sequence and the sequence of denominators occurring in the Farey tree. Then we extend our construction to the Zeckendorf numeration system based on the Fibonacci sequence. Again our tree structure permits us to obtain recurrence relations for and the F-regularity of the corresponding sequence.
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    In this paper, we propose an efficient numerical scheme for the approximate solution of the time fractional diffusion-wave equation with reaction term based on cubic trigonometric basis functions. The time fractional derivative is approximated by the usual finite difference formulation and the derivative in space is discretized using cubic trigonometric B-spline functions. A stability analysis of the scheme is conducted to confirm that the scheme does not amplify errors. Computational experiments are also performed to further establish the accuracy and validity of the proposed scheme. The results obtained are compared with a finite difference schemes based on the Hermite formula and radial basis functions. It is found that our numerical approach performs superior to the existing methods due to its simple implementation, straight forward interpolation and very less computational cost.
  • May 24 2017 math.CO arXiv:1705.08340v1
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    The stable roommates problem does not necessarily have a solution, i.e. a stable matching. We had found that, for the uniformly random instance, the expected number of solutions converges to $e^{1/2}$ as $n$, the number of members, grows, and with Rob Irving we proved that the limiting probability of solvability is $e^{1/2}/2$, at most. Stephan Mertens's extensive numerics compelled him to conjecture that this probability is of order $n^{-1/4}$. Jimmy Tan introduced a notion of a stable cyclic partition, and proved existence of such a partition for every system of members' preferences, discovering that presence of odd cycles in a stable partition is equivalent to absence of a stable matching. In this paper we show that the expected number of stable partitions with odd cycles grows as $n^{1/4}$. However the standard deviation of that number is of order $n^{3/8}\gg n^{1/4}$, too large to conclude that the odd cycles exist with high probability (whp). Still, as a byproduct, we show that whp the fraction of members with more than one stable "predecessor" is of order $n^{-1/4}$. Furthermore, whp the average rank of a predecessor in every stable partition is of order $n^{1/2}$. The likely size of the largest stable matching is $n/2-O(n^{1/4+o(1)})$, and the likely number of pairs of unmatched members blocking the optimal complete matching is $O(n^{3/4+o(1)})$.
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    This paper deals with the problem of beamforming design in a multibeam satellite, which is shared by different groups of terminals -clusters-, each served by an Earth station or gateway. Each gateway precodes the symbols addressed to its respective users; the design follows an MMSE criterion, and a regularization factor judiciously chosen allows to account for the presence of mutually interfering clusters, extending more classical results applicable to one centralized station. More importantly, channel statistics can be used instead of instantaneous channel state information, avoiding the exchange of information among gateways through backhaul links. The on-board satellite beamforming weights are designed to exploit the degrees of freedom of the satellite antennas to minimize the noise impact and the interference to some specific users. On-ground beamforming results are provided as a reference to compare the joint performance of MMSE precoders and on-board beamforming network. A non-adaptive design complements the results and makes them more amenable to practical use by designing a coarse beamforming network.
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    Smart cities must integrate a number of interdependent cyber-physical systems that operate in a coordinated manner to improve the well-being of the city's residents. A cyber-physical system (CPS) is a system of computational elements controlling physical entities. Large-scale CPSs are more vulnerable to attacks due to the cyber-physical interdependencies that can lead to cascading failures which can have a significant detrimental effect on a city. In this paper, a novel approach is proposed for analyzing the problem of allocating security resources, such as firewalls and anti-malware, over the various cyber components of an interdependent CPS to protect the system against imminent attacks. The problem is formulated as a Colonel Blotto game in which the attacker seeks to allocate its resources to compromise the CPS, while the defender chooses how to distribute its resources to defend against potential attacks. To evaluate the effects of defense and attack, various CPS factors are considered including human-CPS interactions as well as physical and topological characteristics of a CPS such as flow and capacity of interconnections and minimum path algorithms. Results show that, for the case in which the attacker is not aware of the CPS interdependencies, the defender can have a higher payoff, compared to the case in which the attacker has complete information. The results also show that, in the case of more symmetric nodes, due to interdependencies, the defender achieves its highest payoff at the equilibrium compared to the case with independent, asymmetric nodes.
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    The abundance of accelerators and the ambient conditions make Cygnus X a natural laboratory for studying the life cycle of cosmic-rays (CRs). This naturally makes the Cygnus X complex a highly interesting source in neutrino astronomy, in particular concerning a possible detection with the IceCube Neutrino Observatory, which has a good view of the northern hemisphere. In this paper, we model the multiwavelength spectrum of the Cygnus, for the first time using a broad data set from radio, MeV (COMPTEL), GeV (Fermi), TeV (Argo) and 10s of TeV (Milagro) energies. The modeling is performed assuming a leptohadronic model. We solve the steady-state transport equation for leptons and hadrons injected homogeneously in the region and test the role of diffusive transport and energy loss by radiation and interaction. The result shows that diffusion loss plays a significant role in Cygnus X and always exceeds the advection loss as well as almost all other loss processes. The best-fit parameters we find are a magnetic field of $B=8.9\times10^{-6}$ G, a target density of $N_t=19.4$ cm$^{-3}$, a cosmic ray spectral index of $\alpha=2.37$ and neutral gas distribution over a depth of 116 pc. We find that the fit describes the data up to TeV energies well, while the Milagro data are underestimated. This transport model with a broad multiwavelength fit provides a neutrino flux which approaches the sensitivity of IceCube at very high energies ($>$ 50 TeV). In the future, the flux sensitivity of IceCube will be improved. With this rather pessimistic model, leaving out the influence of possible strong, high-energy point sources, we already expect the flux in the Cygnus X region to suffice for IceCube to measure a significant neutrino flux in the next decade.
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    We report development and application of a fluid-structure interaction (FSI) solver for compressible flows with large-scale flow-induced deformation of the structure. The FSI solver utilizes partitioned approach to strongly couple a sharp-interface immersed boundary method based flow solver with an open-source finite-element structure dynamics solver. The flow solver is based on a higher-order finite-difference method on Cartesian grid and employs ghost-cell methodology to impose boundary conditions on the immersed boundary. A higher-order accuracy near the immersed boundary is achieved by combining the ghost-cell approach with a weighted least-square error method based on a higher-order approximate polynomial. The second order spatial accuracy of the flow solver is established by performing a grid refinement study. The structure solver is validated with a canonical elastostatics problem. The FSI solver is validated with published measurements and simulations for the large-scale deformation of a thin elastic steel panel subjected to blast loading in a shock tube. The solver correctly predicts oscillating behavior of the tip of the panel with reasonable fidelity and computed shock wave propagation is qualitatively consistent with the published results. In order to demonstrate the fidelity of the solver and to investigate coupled physics of the shock-structure interaction for a thin elastic plate, we employ the solver for simulating 6.4 kg TNT blast loading on the thin elastic plate. The initial conditions of the blast are taken from field tests reported in the literature. Using numerical schlieren, the shock front propagation, Mach reflection and vortex shedding at the tip of the plate are visualized during the shock wave impact on the plate. We discuss coupling between the non-linear dynamics of the plate and blast loading.
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    We show how DG categories arise naturally in noncommutative differential geometry and use them to derive noncommutative analogues of the Bianchi identities for the curvature of a connection. We also give a derivation of formulae for characteristic classes in noncommutative geometry following Chern's original derivation, rather than using cyclic cohomology. We show that a related DG category for extendable bimodule connections is a monoidal tensor category and in the metric compatible case give an analogue of a classical antisymmetry of the Riemann tensor. The monoidal structure implies the existence of a cup product on noncommutative sheaf cohomology. Another application is to prove that the curvature of a line module reduces to a 2-form on the base algebra. We illustrate the theory on the q-sphere, the permutation group S_3 and the bicrossproduct model quantum spacetime with algebra [r,t]=\lambda r
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    Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined morphologies. This is the case in numerous medical conditions where normally soluble proteins aggregate into fibers. Beyond the diversity of molecular mechanisms involved, we propose that fibers generically arise from the aggregation of irregular particles with short-range interactions. Using a minimal model of ill-fitting, sticky particles, we demonstrate robust fiber formation for a variety of particle shapes and aggregation conditions. Geometrical frustration plays a crucial role in this process, and accounts for the range of parameters in which fibers form as well as for their metastable character.
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    In this note we discuss uniform integrability of random variables. In a probability space, we introduce two new notions on uniform integrability of random variables, and prove that they are equivalent to the classic one. In a sublinear expectation space, we give de La Vallée Poussin criterion for the uniform integrability of random variables and do some other discussions.
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    We generalize the recently introduced TRILEX approach (TRiply Irreducible Local EXpansion) to superconducting phases. The method treats simultaneously Mott and spin-fluctuation physics using an Eliashberg theory supplemented by local vertex corrections determined by a self-consistent quantum impurity model. We show that, in the two-dimensional Hubbard model, at strong coupling, TRILEX yields a $d$-wave superconducting dome as a function of doping. Contrary to the standard cluster dynamical mean field theory (DMFT) approaches, TRILEX can capture $d$-wave pairing using only a single-site effective impurity model. We also systematically explore the dependence of the superconducting temperature on the bare dispersion at weak coupling, which shows a clear link between strong antiferromagnetic (AF) correlations and the onset of superconductivity. We identify a combination of hopping amplitudes particularly favorable to superconductivity at intermediate doping. Finally, we study within $GW$+EDMFT the low-temperature $d$-wave superconducting phase at strong coupling in a region of parameter space with reduced AF fluctuations.
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    We propose an adaptive confidence interval procedure (CIP) for the coefficients in the normal linear regression model. This procedure has a frequentist coverage rate that is constant as a function of the model parameters, yet provides smaller intervals than the usual interval procedure, on average across regression coefficients. The proposed procedure is obtained by defining a class of CIPs that all have exact $1-\alpha$ frequentist coverage, and then selecting from this class the procedure that minimizes a prior expected interval width. Such a procedure may be described as "frequentist, assisted by Bayes" or FAB. We describe an adaptive approach for estimating the prior distribution from the data so that exact non-asymptotic $1-\alpha$ coverage is maintained. Additionally, in a "$p$ growing with $n$" asymptotic scenario, this adaptive FAB procedure is asymptotically Bayes-optimal among $1-\alpha$ frequentist CIPs.
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    Glass corrosion is a crucial problem in keeping and conservation of beadworks in museums. All kinds of glass beads undergo deterioration but blue-green lead-potassium glass beads of the 19th century are subjected to the destruction to the greatest extent. Blue-green lead-potassium glass beads of the 19th century obtained from exhibits kept in Russian museums were studied with the purpose to determine the causes of the observed phenomenon. For the comparison, yellow lead beads of the 19th century were also explored. Both kinds of beads contain Sb but yellow ones are stable. Using scanning electron microscopy, energy dispersive X-ray microspectrometry, electron backscatter diffraction, transmission electron microscopy and X-ray powder analysis, we have registered the presence of crystallites of orthorhombic KSbOSiO$_4$ and cubic Pb$_2$Sb$_{1.5}$Fe$_{0.5}$O$_{6.5}$ in glass matrix of blue-green and yellow beads, respectively. Both compounds form at rather high temperatures obviously during glass melting and/or melt cooling. We suppose that the crystallites generate internal tensile strain in glass during its cooling which causes formation of multiple microcracks in inner domains of blue-green beads. We suggest that the deterioration degree depends on quantity of the precipitates, their sizes and their temperature coefficients of linear expansion. In blue-green beads, the crystallites are distributed in their sizes from $\sim\,$200 nm to several tens of $\mu$m and tend to gather in large colonies. The sizes of crystallites in yellow beads are several hundreds of nm and their clusters contain few crystallites. This explains the difference in corrosion of these kinds of beads containing crystals of Sb compounds.
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    Various estimates of the even-odd effect of the mass shell of atomic nuclei are considered. Based on the experimental mass values of the Ca, Sn, and Pb isotopes, the dependence of the energy gap on the neutrons number is traced and the relationship of this characteristic to the properties of external neutron subshells is shown. In nuclei with closed proton shells, effects directly related to neutron pairing and effects of nucleon shells are discussed.
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    We have revisited the mean-field treatment for the Blume-Capel model under the presence of a discrete random magnetic field as introduced by Kaufman and Kanner. The magnetic field ($H$) versus temperature ($T$) phase diagrams for given values of the crystal field $D$ were recovered in accordance to Kaufman and Kanner original work. However, our main goal in the present work was to investigate the distinct structures of the crystal field versus temperature phase diagrams as the random magnetic field is varied because similar models have presented reentrant phenomenon due to randomness. Following previous works we have classified the distinct phase diagrams according to five different topologies. The topological structure of the phase diagrams is maintained for both $H-T$ and $D-T$ cases. Althoug the phase diagrams exhibit a richness of multicritical phenomena we did not found any reentrant effect as have been seen in similar models.
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    We show that the deformation theory of Fréchet algebras for actions of Kählerian Lie groups developed by two of us, leads in a natural way to examples of non-compact locally compact quantum groups. This is achieved by constructing a manageable multiplicative unitary out of the Fréchet deformation of $C_0(G)$ for the action $\lambda\otimes \rho$ of $G\times G$ and the undeformed coproduct. We also prove that these quantum groups are isomorphic to those constructed out of the unitary dual $2$-cocycle discovered by Neshveyev and Tuset and associated with Bieliavsky's covariant $\star$-product, via the De Commer's results.
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    We give two new proofs of Perelman's theorem that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons, using the fact that the singularity models of type I solutions are shrinking gradient Ricci solitons and the fact that non-collapsed type I ancient solutions have rescaled limits being shrinking gradient Ricci solitons.
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    Many digital functions studied in the literature, e.g., the summatory function of the base-$k$ sum-of-digits function, have a behavior showing some periodic fluctuation. Such functions are usually studied using techniques from analytic number theory or linear algebra. In this paper we develop a method based on exotic numeration systems and we apply it on two examples motivated by the study of generalized Pascal triangles and binomial coefficients of words.
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    The Ryu-Takayanagi prescription reduces the problem of calculating entanglement entropy in CFTs to the determination of minimal surfaces in a dual anti-de Sitter geometry. For 3D gravity theories and BTZ black holes, we identify the minimal surfaces as special Lagrangian cycles calibrated by the real part of the holomorphic form of a spacelike hypersurface. We show that generalised calibrations provide a unified way to determine holographic entanglement entropy that is also valid for warped AdS$_3$ geometries. We briefly discuss generalisations to higher dimensions.
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    A deterministic application $\theta\,:\,\mathbb{R}^2\rightarrow\mathbb{R}^2$ deforms bijectively and regularly the plane and allows to build a deformed random field $X\circ\theta\,:\,\mathbb{R}^2\rightarrow\mathbb{R}$ from a regular, stationary and isotropic random field $X\,:\,\mathbb{R}^2\rightarrow\mathbb{R}$. The deformed field $X\circ\theta$ is in general not isotropic, however we give an explicit characterization of the deformations $\theta$ that preserve the isotropy. Further assuming that $X$ is Gaussian, we introduce a weak form of isotropy of the field $X\circ\theta$, defined by an invariance property of the mean Euler characteristic of some of its excursion sets. Deformed fields satisfying this property are proved to be strictly isotropic. Besides, assuming that the mean Euler characteristic of excursions sets of $X\circ\theta$ over some basic domains is known, we are able to identify $\theta$.
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  • PDF
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    Quantile regression, the prediction of conditional quantiles, finds applications in various fields. Often, some or all of the variables are discrete. The authors propose two new quantile regression approaches to handle such mixed discrete-continuous data. Both of them generalize the continuous D-vine quantile regression, where the dependence between the response and the covariates is modeled by a parametric D-vine. D-vine quantile regression provides very flexible models, that enable accurate and fast predictions. Moreover, it automatically takes care of major issues of classical quantile regression, such as quantile crossing and interactions between the covariates. The first approach keeps the parametric estimation of the D-vines, but modifies the formulas to account for the discreteness. The second approach estimates the D-vine using continuous convolution to make the discrete variables continuous and then estimates the D-vine nonparametrically. A simulation study is presented examining for which scenarios the discrete-continuous D-vine quantile regression can provide superior prediction abilities. Lastly, the functionality of the two introduced methods is demonstrated by a real-world example predicting the number of bike rentals.
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Recent comments

Noon van der Silk May 23 2017 11:15 UTC

I think this thread has reached it's end.

I've locked further comments, and I hope that the quantum computing community can thoughtfully find an approach to language that is inclusive to all and recognises the diverse background of all researchers, current and future.

I direct your attention t

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Varun Narasimhachar May 23 2017 02:14 UTC

While I would never want to antagonize my peers or to allow myself to assume they were acting irrationally, I do share your concerns to an extent. I worry about the association of social justice and inclusivity with linguistic engineering, virtual lynching, censorship, etc. (the latter phenomena sta

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Aram Harrow May 23 2017 01:30 UTC

I think you are just complaining about issues that arise from living with other people in the same society. If you disagree with their values, well, then some of them might have a negative opinion about you. If you express yourself in an aggressive way, and use words like "lynch" to mean having pe

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Steve Flammia May 23 2017 01:04 UTC

I agree with Noon that the discussion is becoming largely off topic for SciRate, but that it might still be of interest to the community to discuss this. I invite people to post thoughtful and respectful comments over at [my earlier Quantum Pontiff post][1]. Further comments here on SciRate will be

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Noon van der Silk May 23 2017 00:59 UTC

I've moderated a few comments on this post because I believe it has gone past useful discussion, and I'll continue to remove comments that I believe don't add anything of substantial value.

Thanks.

Aram Harrow May 22 2017 23:13 UTC

The problem with your argument is that no one is forcing anyone to say anything, or banning anything.

If the terms really were offensive or exclusionary or had other bad side effects, then it's reasonable to discuss as a community whether to keep them, and possibly decide to stop using them. Ther

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stan May 22 2017 22:53 UTC

Fair enough. At the end of the day I think most of us are concerned with the strength of the result not the particular language used to describe it.

VeteranVandal May 22 2017 22:41 UTC

But how obvious is ancilla? To me it is not even remotely obvious (nor clear as a term, but as the literature used it so much, I see such word in much the same way as I see auxiliary, in fact - now if you want to take offense with auxiliary, what can I say? I won't invent words just to please you).

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VeteranVandal May 22 2017 22:21 UTC

I don't think science can or should avoid the perpetuation of existing "historical unequal social order" by changing the language, as to me it seems that, if you try hard enough you can find problem with anything you want to be offended at - rationalizations are tricky things you can often get carri

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Fernando Brandao May 22 2017 21:37 UTC

I am not sure if the ArXiv is the best venue for this kind of paper/rant. Also, I’m concerned that so much energy is being put into the discussion. As a non-native speaker, I might not get all nuances of the language, but I have a hard time understanding why we should drop a scientific jargon like “

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