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In this paper we obtain several model structures on {\bf DblCat}, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in {\bf Cat} and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, {\bf DblCat} inherits a model structure as a category of algebras over a 2-monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofibrant objects. As part of this program we give explicit descriptions and discuss properties of free double categories, quotient double categories, colimits of double categories, several nerves, and horizontal categorification.
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arxiv:0711.0473
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We revise the notion of the quasi-sectorial contractions. Our main theorem establishes a relation between semigroups of quasi-sectorial contractions and a class of m-sectorial generators. We discuss a relevance of this kind of contractions to the theory of operator-norm approximations of strongly continuous semigroups.
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arxiv:0711.0478
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The main purpose of this paper is calculation of differential invariants which arise from prolonged actions of two Lie groups SL(2) and SL(3) on the $n$th jet space of $R^2$. It is necessary to calculate $n$th prolonged infenitesimal generators of the action.
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arxiv:0711.0511
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We report new results obtained from multi-frequency observations of PSR B0826-34 with the Giant Metrewave Radio Telescope (GMRT). (1) We find no evidence of weak emission during the typical long null state of this pulsar, simultaneously at 303 and 610 MHz, as well as individually at 157, 325, 610 and 1060 MHz at separate epochs. Our limit of non-detection is at ~ 1% or better of the peak of the active state profile, and corresponds to ~ 2 mJy at 610 MHz. (2) Significant correlation in the total intensity of the individual pulses between 303 and 610 MHz is reported from the simultaneous dual frequency observations, which is indicative of the broadband nature of the emission. We also report correlation between total energy in the main pulse and inter-pulse region from the high sensitivity single frequency observations at 610 and 1060 MHz. (3) Though we find the drift pattern to be very similar in the simultaneous 303 and 610 MHz data, we observe that the drift band separation (P2) evolves significantly between these two frequencies, and in a manner opposite to the average profile evolution. In addition, we confirm the dependence of P2 on pulse longitude at 303 MHz and find indications for the same at 610 MHz. We also present results for subpulse width at different frequencies, and as well as a function of pulse longitude. (4) As a natural out-come of the simultaneous dual frequency observations, we obtain an accurate DM value, equal to 52.2(6) pc/cc, for this pulsar.
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arxiv:0711.0526
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Phonons change remarkable the interatomic bond length in solids and this work suggest a novel method how this behavior can be displayed and analyzed. The bond-length spectrum is plotted for each of the different atomic bonding types. When comparing the bond-length to an un-deformed crystal by the so-called difference bond length spectrum, the effect of phonons is clearly visible. The Perovskite lattice of SrTiO3 is used as an example and several lattice vibration modes are applied in a frozen phonon calculation in a 2x2x2 supercell. Ab-initio DFT simulations using the Vasp software were performed to calculate the density of states. The results show the important finding reported here first, that certain phonon interactions with shorter Ti-O bonds decrease the band gap, while changes in the Sr-Ti bond length enlarge the band gap.
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arxiv:0711.0567
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The covariogram g_K of a convex body K in E^d is the function which associates to each x in E^d the volume of the intersection of K with K+x. In 1986 G. Matheron conjectured that for d=2 the covariogram g_K determines K within the class of all planar convex bodies, up to translations and reflections in a point. This problem is equivalent to some problems in stochastic geometry and probability as well as to a particular case of the phase retrieval problem in Fourier analysis. It is also relevant for the inverse problem of determining the atomic structure of a quasicrystal from its X-ray diffraction image. In this paper we confirm Matheron's conjecture completely.
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arxiv:0711.0572
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In agile software development, test code can considerably contribute to the overall source code size. Being a valuable asset both in terms of verification and documentation, the composition of a test suite needs to be well understood in order to identify opportunities as well as weaknesses for further evolution. In this paper, we argue that the visualization of structural characteristics is a viable means to support the exploration of test suites. Thanks to general agreement on a limited set of key test design principles, such visualizations are relatively easy to interpret. In particular, we present visualizations that support testers in (i) locating test cases; (ii) examining the relation between test code and production code; and (iii) studying the composition of and dependencies within test cases. By means of two case studies, we demonstrate how visual patterns help to identify key test suite characteristics. This approach forms the first step in assisting a developer to build up understanding about test suites beyond code reading.
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arxiv:0711.0607
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Given a closed, bounded convex set $\mathcal{W}\subset{\mathbb {R}}^d$ with nonempty interior, we consider a control problem in which the state process $W$ and the control process $U$ satisfy \[W_t= w_0+\int_0^t\vartheta(W_s) ds+\int_0^t\sigma(W_s) dZ_s+GU_t\in \mathcal{W},\qquad t\ge0,\] where $Z$ is a standard, multi-dimensional Brownian motion, $\vartheta,\sigma\in C^{0,1}(\mathcal{W})$, $G$ is a fixed matrix, and $w_0\in\mathcal{W}$. The process $U$ is locally of bounded variation and has increments in a given closed convex cone $\mathcal{U}\subset{\mathbb{R}}^p$. Given $g\in C(\mathcal{W})$, $\kappa\in{\mathbb{R}}^p$, and $\alpha>0$, consider the objective that is to minimize the cost \[J(w_0,U)\doteq\mathbb{E}\biggl[\int_0^{\infty}e^{-\alpha s}g(W_s) ds+\int_{[0,\infty)}e^{-\alpha s} d(\kappa\cdot U_s)\biggr]\] over the admissible controls $U$. Both $g$ and $\kappa\cdot u$ ($u\in\mathcal{U}$) may take positive and negative values. This paper studies the corresponding dynamic programming equation (DPE), a second-order degenerate elliptic partial differential equation of HJB-type with a state constraint boundary condition. Under the controllability condition $G\mathcal{U}={\mathbb{R}}^d$ and the finiteness of $\mathcal{H}(q)=\sup_{u\in\mathcal{U}_1}\{-Gu\cdot q-\kappa\cdot u\}$, $q\in {\mathbb{R}}^d$, where $\mathcal{U}_1=\{u\in\mathcal{U}:|Gu|=1\}$, we show that the cost, that involves an improper integral, is well defined. We establish the following: (i) the value function for the control problem satisfies the DPE (in the viscosity sense), and (ii) the condition $\inf_{q\in{\mathbb{R}}^d}\mathcal{H}(q)<0$ is necessary and sufficient for uniqueness of solutions to the DPE. The existence and uniqueness of solutions are shown to be connected to an intuitive ``no arbitrage'' condition. Our results apply to Brownian control problems that represent formal diffusion approximations to control problems associated with stochastic processing networks.
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arxiv:0711.0641
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We say that Wiener's property holds for the exponent $p>0$ if we have that whenever a positive definite function $f$ belongs to $L^p(-\epsilon,\epsilon)$ for some $\epsilon>0$, then $f$ necessarily belongs to $L^p(\TT)$, too. This holds true for $p\in 2\NN$ by a classical result of Wiener. Recently various concentration results were proved for idempotents and positive definite functions on measurable sets on the torus. These new results enable us to prove a sharp version of the failure of Wiener's property for $p\notin 2\NN$. Thus we obtain strong extensions of results of Wainger and Shapiro, who proved the negative answer to Wiener's problem for $p\notin 2\NN$.
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arxiv:0711.0676
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We discuss the sensitivity of nucleon properties (mass, magnetic moments and electromagnetic form factors) on the variation of the pseudoscalar meson masses in the context of the perturbative chiral quark model. The obtained results are compared to data and other theoretical predictions.
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arxiv:0711.0691
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Some examples and basic properties of ultrametric spaces are briefly discussed.
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arxiv:0711.0709
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Assuming that a stochastic process $X=(X_t)_{t\geq 0}$ is a sum of a compound Poisson process $Y=(Y_t)_{t\geq 0}$ with known intensity $\lambda$ and unknown jump size density $f,$ and an independent Brownian motion $Z=(Z_t)_{t\geq 0},$ we consider the problem of nonparametric estimation of $f$ from low frequency observations from $X.$ The estimator of $f$ is constructed via Fourier inversion and kernel smoothing. Our main result deals with asymptotic normality of the proposed estimator at a fixed point.
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arxiv:0711.0719
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We present Suzaku X-ray observations of the recurrent nova T CrB in quiescence. T CrB is the first recurrent nova to be detected in the hard-X-ray band (E ~ 40.0 keV) during quiescence. The X-ray spectrum is consistent with cooling-flow emission emanating from an optically thin region in the boundary layer of an accretion disk around the white dwarf. The detection of strong stochastic flux variations in the light curve supports the interpretation of the hard X-ray emission as emanating from a boundary layer.
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arxiv:0711.0725
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We present our finding that an especially simple scaling expression describes the formation of a new state of quantum matter, the Kondo Fermi liquid (KL) in heavy electron materials. Emerging at $T^*$ as a result of the collective coherent hybridization of localized f electrons and conduction electrons, the KL possesses a non-Landau density of states varying as $(1-T/T^*)^{3/2}[1+\ln(T^*/T)]$. We show that four independent experimental probes verify this scaling behavior and that for CeIrIn$_5$ the KL state density is in excellent agreement with the recent microscopic calculations of hybridization in this material by Shim, Haule, and Kotliar.
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arxiv:0711.0789
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The effects of absence of inversion symmetry on superconducting states are investigated theoretically. In particular we focus on the noncentrosymmetric compounds which have the cubic symmetry $O$ like Li$_2$Pt$_3$B. An appropriate and isotropic spin-orbital interaction is added in the Hamiltonian and it acts like a magnetic monopole in the momentum space. The consequent pairing wavefunction has an additional triplet component in the pseudospin space, and a Zeeman magnetic field $\bf{B}$ can induce a collinear supercurrent $\bf{J}$ with a coefficient $\kappa(T)$. The effects of anisotropy embedded in the cubic symmetry and the nodal superconducting gap function on $\kappa(T)$ are also considered. From the macroscopic perspectives, the pair of mutually induced $\bf{J}$ and magnetization ${\bf{M}}$ can affect the distribution of magnetic field in such noncentrosymmetric superconductors, which is studied through solving the Maxwell equation in the Meissner geometry as well as the case of a single vortex line. In both cases, magnetic fields perpendicular to the external ones emerge as a signature of the broken symmetry.
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arxiv:0711.0800
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The aim of this work is to construct a monomial and explicit basis for the space $M_{\mu}$ relative to the $n!$ conjecture. We succeed completely for hook-shaped partitions, i.e. $\mu=(K+1,1^L)$. We are indeed able to exhibit a basis and to verify that its cardinality is $n!$, that it is linearly independent and that it spans $M_{\mu}$. We deduce from this study an explicit and simple basis for $I_{\mu}$, the annulator ideal of $\Delta_{\mu}$. This method is also successful for giving directly a basis for the homogeneous subspace of $M_{\mu}$ consisting of elements of 0 $x$-degree.
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arxiv:0711.0899
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We determine the abstract commensurator com(F) of Thompson's group F and describe it in terms of piecewise linear homeomorphisms of the real line and in terms of tree pair diagrams. We show com (F) is not finitely generated and determine which subgroups of finite index in F are isomorphic to F. We show that the natural map from the commensurator group to the quasi-isometry group of F is injective.
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arxiv:0711.0919
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The elliptic flow $v_2$ and the ratio of the shear viscosity over the entropy density, $\eta/s$, of gluon matter are calculated from the perturbative QCD (pQCD) based parton cascade Boltzmann approach of multiparton scatterings. For Au+Au collisions at $\sqrt{s}=200$A GeV the gluon plasma generates large $v_2$ values measured at the BNL Relativistic Heavy Ion Collider. Standard pQCD yields $\eta/s\approx 0.08-0.15$ as small as the lower bound found from the anti-de Sitter/conformal field theory conjecture.
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arxiv:0711.0961
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We examine structural relaxation in a supercooled glass-forming liquid simulated by NVE molecular dynamics. Time correlations of the total kinetic energy fluctuations are used as a comprehensive measure of the system's approach to the ergodic equilibrium. We find that, under cooling, the total structural relaxation becomes delayed as compared with the decay of the component of the intermediate scattering function corresponding to the main peak of the structure factor. This observation can be explained by collective movements of particles preserving many-body structural correlations within compact 3D cooperatively rearranging regions.
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arxiv:0711.1061
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We consider the factorization properties of on-shell QCD amplitudes with massive partons in the limit when all kinematical invariants are large compared to the parton mass and discuss the structure of their infrared singularities. The dimensionally regulated soft poles and the large collinear logarithms of the parton masses exponentiate to all orders. Based on this factorization a simple relation between massless and massive scattering amplitudes in gauge theories can be established. We present recent applications of this relation for the calculation of the two-loop virtual QCD corrections to the hadro-production of heavy quarks.
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arxiv:0711.1121
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We present very long baseline interferometry polarization images of an X-ray selected sample of BL Lacertae objects belonging to the first High Energy Astronomy Observatory (HEAO-1) and the ROSAT-Green Bank (RGB) surveys. These are primarily high-energy-peaked BL Lacs (HBLs) and exhibit core-jet radio morphologies on pc-scales. They show moderately polarized jet components, similar to those of low-energy-peaked BL Lacs (LBLs). The fractional polarization in the unresolved cores of the HBLs is, on average, lower than in the LBLs, while the fractional polarizations in the pc-scale jets of HBLs and LBLs are comparable. However a difference is observed in the orientation of the inferred jet magnetic fields -- while LBL jets are well-known to preferentially exhibit transverse magnetic fields, the HBL jets tend to display longitudinal magnetic fields. Although a `spine-sheath' jet velocity structure, along with larger viewing angles for HBLs could produce the observed magnetic field configuration, differences in other properties of LBLs and HBLs, such as their total radio power, cannot be fully reconciled with the different-angle scenario alone. Instead it appears that LBLs and HBLs differ intrinsically, perhaps in the spin rates of their central black holes.
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arxiv:0711.1158
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We provide formulas for the entropy of free-string states depending on their mass, charges and size, both in bosonic and superstring theory (IIA or IIB). We properly define these quantities in full-fledged string theory. We then investigate the corrections to the entropy due to self-interactions of the string for states with fixed mass, charge and size, both for BPS and non-BPS configurations. Again, the analysis is performed using string theory techniques.
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arxiv:0711.1159
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The X-ray burster GS 1826-24 shows extremely regular Type I X-ray bursts whose energetics and recurrence times agree well with thermonuclear ignition models. We present calculations of sequences of burst lightcurves using multizone models which follow the rp-process nucleosynthesis with an extensive nuclear reaction network. The theoretical and observed burst lightcurves show remarkable agreement. The models naturally explain the slow ~5s rise and long ~100s tails of these bursts, as well as their dependence on mass accretion rate. This comparison provides further evidence for solar metallicity in the accreted material in this source, and constrains the distance to the source. The main difference is that the observed lightcurves do not show the distinct two-stage rise of the models. This may reflect the time for burning to spread over the stellar surface, or may indicate that our treatment of heat transport or nuclear physics needs to be revised. The trends in burst properties with accretion rate are well-reproduced by our spherically symmetric models which include chemical and thermal inertia from the ashes of previous bursts. Changes in the covering fraction of the accreted fuel are not required.
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arxiv:0711.1195
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We hypothesize possible new types of forces that would be the result of new types of interactions, static and a slow transient, between objects with related information contents (pattern). Such mechanism could make material composition dependence claimed by Fishbach, et al in Eotvos type experiments plausible. We carried out experiments by using a high-resolution scale with the following memories: USB-2 flash drives (1-16GB), DVD and CD disks to determine if such an interaction exist/detectable with a scale resolution of 10 microgram with these test objects. We applied zero information, white noise and 1/f noise type data. Writing or deleting the information in any of these devices causes peculiar negative weight transients, up to milligrams (mass fraction around 10^-5), which is followed by various types of relaxation processes. These relaxations have significantly different dynamics compared to transients observed during cooling after stationary external heating. Interestingly, a USB-1 MP3 player has also developed comparable transient mass loss during playing music. A classical interpretation of the negative weight transients could be absorbed water in hygroscopic components however comparison of relaxation time constants with air humidity data does not support an obvious explanation. Another classical interpretation with certain contribution is the lifting Bernoulli force caused by the circulation due to convection of the warm air. However, in this case all observed time constants with a device should have been the same unless some hidden parameter causes the observed variations. Further studies are warranted to clarify if there is indeed a new force, which is showing up as negative mass at weight measurement when high-density structural information is changed or read out (measured).
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arxiv:0711.1197
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We study the intrinsic spin Hall conductivity (SHC) in various $5d$-transition metals (Ta, W, Re, Os, Ir, Pt, and Au) and 4d-transition metals (Nb, Mo, Tc, Ru, Rh, Pd, and Ag) based on the Naval Research Laboratory tight-binding model, which enables us to perform quantitatively reliable analysis. In each metal, the obtained intrinsic SHC is independent of resistivity in the low resistive regime ($\rho < 50 \mu\Omega\text{cm}$) whereas it decreases in proportion to $\rho^{-2}$ in the high resistive regime. In the low resistive regime, the SHC takes a large positive value in Pt and Pd, both of which have approximately nine $d$-electrons per ion ($n_d=9$). On the other hand, the SHC takes a large negative value in Ta, Nb, W, and Mo where $n_d<5$. In transition metals, a conduction electron acquires the trajectory-dependent phase factor that originates from the atomic wavefunction. This phase factor, which is reminiscent of the Aharonov-Bohm phase, is the origin of the SHC in paramagnetic metals and that of the anomalous Hall conductivity in ferromagnetic metals. Furthermore, each transition metal shows huge and positive $d$-orbital Hall conductivity (OHC), independently of the strength of the spin-orbit interaction (SOI). Since the OHC is much larger than the SHC, it will be possible to realize a {\it orbitronics device} made of transition metals.
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arxiv:0711.1263
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This text presents the cognitive-ergonomics approach to design, in both its individual and collective form. It focuses on collective design with respect to individual design. The theoretical framework adopted is that of information processing, specified for design problems. The cognitive characteristics of design problems are presented: the effects of their ill-defined character and of the different types of representation implemented in solving these problems, amongst others the more or less "satisficing" character of the different possible solutions. The text first describes the cognitive activities implemented in both individual and collective design: different types of control activities and of the executive activities of solution development and evaluation. Specific collective-design characteristics are then presented: co-design and distributed-design activities, temporo-operative and cognitive synchronisation, and different types of argumentation, of co-designers' intervention modes in the design process, of solution-proposals evaluation. The paper concludes by a confrontation between the two types of design, individual and collective.
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arxiv:0711.1290
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We report measurements of the spin susceptibility in dilute (rs up to 10) AlAs two-dimensional (2D) electrons occupying a single conduction-band valley with an anisotropic in-plane Fermi contour, characterized by longitudinal and transverse effective masses, ml and mt. As the density is decreased, the spin susceptibility is significantly enhanced over its band value, reflecting the role of interaction. Yet the enhancement is suppressed compared to the results of quantum Monte Carlo based calculations that take the finite thickness of the electron layer into account but assume an isotropic effective mass equal to sqrt(ml.mt). Proper treatment of an interacting 2D system with an anisotropic effective mass therefore remains a theoretical challenge.
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arxiv:0711.1294
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Over the finite field with two elements, we present a method for obtaining explicit expressions for the number of rank i matrices of the form A above B, where A is persymmetric (A matrix [a(i,j)] is persymmetric if a(i,j) = a(r,s) for i+j = r+s).
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arxiv:0711.1306
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We test Bohr's complementary relation, which captures the most counterintuitive difference of a classical and a quantum world, for single and bipartite neutral kaons. They present a system that is naturally interfering, oscillating and decaying. Moreover, kaons break the CP symmetry (C...charge conjugation, P...parity). In detail we discuss the effect of the CP violation on Bohr's relation, i.e. the effect on the "particle-like" information and the "wave-like" information. Further we show that the quantity that complements the single partite information for bipartite kaons is indeed concurrence, a measure of entanglement, strengthening our concept of entanglement. We find that the defined entanglement measure is independent of CP violation while it has been shown that nonlocality is sensitive to CP violation.
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arxiv:0711.1368
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We confirm rigorously the conjecture, based on numerical and asymptotic evidence, that all the eigenvalues of a certain non-self-adjoint operator are real.
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arxiv:0711.1371
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Let L be an exact Lagrangian submanifold inside the cotangent bundle of a closed manifold N. We prove that if N satisfies a mild homotopy assumption then the image of \pi_2(L) in \pi_2(N) has finite index. We make no assumption on the Maslov class of L, and we make no orientability assumptions. The homotopy assumption is either that N is simply connected, or more generally that \pi_m(N) is finitely generated for each m \geq 2. The result is proved by constructing the Novikov homology theory for symplectic cohomology and generalizing Viterbo's construction of a transfer map between the homologies of the free loopspaces of N and L.
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arxiv:0711.1396
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The asymptotic mean number of distinct sites visited by a subdiffusive continuous time random walker in two dimensions seems not to have been explicitly calculated anywhere in the literature. This number has been calculated for other dimensions for only one specific asymptotic behavior of the waiting time distribution between steps. We present an explicit derivation for two cases in all integer dimensions so as to formally complete a tableaux of results. In this tableaux we include the dominant as well as subdominant contributions in all integer dimensions. Other quantities that can be calculated from the mean number of distinct sites visited are also discussed.
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arxiv:0711.1422
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The phase diagram of the classical \jj model on the \kag lattice is investigated using extensive \mc simulations. In a realistic range of parameters, this model has a low-temperature chiral-ordered phase without long-range spin order. We show that the critical transition marking the destruction of chiral order is preempted by the first order proliferation of \Zdeux point defects. The core energy of these vortices appears to vanish when approaching the T=0 phase boundary, where both \Zdeux defects and gapless magnons contribute to disordering the system at very low temperature. This situation might be typical of a large class of frustrated magnets. Possible relevance for real materials is also discussed.
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arxiv:0711.1497
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This course aims to introduce the student to random matrix models for decoherence and fidelity decay. They present a very powerful alternate approach, that emphasizes the disordered character of many environments and uncontrollable perturbations/couplings. The inherent integrability of such models makes analytic studies possible. We limit our considerations to linear response treatment, as high fidelity and small decoherence are the backbone of quantum information processes. For fidelity decay, where experimental results are available, a comparison with experiments shows excellent agreement with random matrix theory predictions.
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arxiv:0711.1503
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The MAGIC telescope has observed very-high energy gamma-ray emission from the BL Lac object PG 1553+113 in 2005 and 2006 at an overall significance is 8.8 sigma. The light curve shows no significant flux variations on a daily timescale. The flux level during 2005 was, however, significantly higher as compared to 2006. The differential energy spectrum between approx. 90 GeV and 500 GeV is well described by a power law with a spectral index of -4.2+-0.3. The photon energy spectrum and spectral modeling allow to pose upper limits of z=0.74 and z=0.56, respectively, on the yet undetermined redshift of PG 1553+113. Recent VLT observations of this blazar show featureless spectra in the near-IR, thus no direct redshift could be determined from these measurements.
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arxiv:0711.1586
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We report on a comprehensive study of the electronic and magnetic structure of the striped nickelate La5/3Sr1/3NiO4. The investigation is carried out using band structure calculations based on density functional theory. A magnetic structure compatible with experiment is obtained from spin-polarized calculations within the generalized gradient approximation (GGA), whereas inclusion of a local Coulomb interaction in the LDA+U framework results in a different ground state. The influence of the various interaction parameters is discussed in detail.
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arxiv:0711.1599
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LLR and GPB geodetic precessions have tested flatness for Einsten-Infeld-Hoffmann dynamics of distributed relativistic matter
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arxiv:0711.1620
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We analytically derive the effective layer elastic energy of smectic-A and smectic-C liquid crystals by adiabatic elimination of the orientational degree of freedom from the generalized Chen-Lubensky model. In the smectic-A phase, the effective layer bending elastic modulus is calculated as a function of the wavelength of the layer undulation mode. It turns out that an unlocking of the layer normal and the director reduces the layer bending rigidity for wavelengths smaller than the director penetration length. In the achiral smectic-C phase, an anisotropic bending elasticity appears due to the coupling between the layer displacement and director. The effective layer bending rigidity is calculated as a function of the angle $\vartheta$ between the layer undulation wave-vector and the director field. We compute the free energy minimizer $\vartheta=\theta$. It turns out that $\theta$ varies from $0\deg$ to $90\deg$ depending on the tilt angle, undulation wave-length and other elastic constants. We also discover a new important characteristic length and the discontinuous change of $\theta$. Using the elastic constants of Chen-Lubensky model, we determine the parameters of the more macroscopic model [Y. Hatwalne and T. C. Lubensky, Phys. Rev. E {\bf 52}, 6240 (1995)]. We then discuss the hydrodynamics, and demonstrate the alignment of director and the propagation of the anisotropic layer displacement wave in the presence of an oscillatory wall and a vibrating cylindrical source respectively.
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arxiv:0711.1659
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It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence. Gibbsian theory is extended on the fundamental level to statistically dependent subsystems introducing an `ordering parameter' $\kappa$. Particular forms for the entropy and partition functions are derived with super-additive (non-extensive) entropy, and a redefinition of temperature in such systems is given.
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arxiv:0711.1676
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We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of random matrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two bounded derivatives.
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arxiv:0711.1718
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We present an explicit set of matrices giving the action of the Hecke operators $T(p)$, $T_j(p^2)$ on Siegel modular forms.
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arxiv:0711.1747
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We summarize a novel approach which has been recently proposed for direct detection of low energy neutrino backgrounds such as the cosmological relic neutrinos, exploiting neutrino/antineutrino capture on nuclei that spontaneously undergo beta decay.
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arxiv:0711.1762
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The aim of this paper is to bring into the picture a new phenomenon in the theory of orthogonal matrix polynomials satisfying second order differential equations. The last few years have witnessed some examples of a (fixed) family of orthogonal matrix polynomials whose elements are common eigenfunctions of several linearly independent second order differential operators. We show that the dual situation is also possible: there are examples of different families of matrix polynomials, each family orthogonal with respect to a different weight matrix, whose elements are eigenfunctions of a common second order differential operator. These examples are constructed by adding a discrete mass at certain point to a weight matrix: $\widetilde{W}=W+\delta_{t_0}M(t_0)$. Our method consists in showing how to choose the discrete mass $M(t_0)$, the point $t_0$ where the mass lives and the weight matrix $W$ so that the new weight matrix $\widetilde{W}$ inherits some of the symmetric second order differential operators associated with $W$. It is well known that this situation is not possible for the classical scalar families of Hermite, Laguerre and Jacobi.
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arxiv:0711.1763
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We investigated the nucleation process at the molecular level. Controlled sticking of individual atoms onto mass selected clusters over a wide mass range has been carried out for the first time. We measured the absolute unimolecular nucleation cross sections of cationic sodium clusters Na_{n}^{+} in the range n=25-200 at several collision energies. The widely used hard sphere approximation clearly fails for small sizes: not only should vapor-to-liquid nucleation theories be modified, but also, through the microreversibility principle, cluster decay rate statistical models.
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arxiv:0711.1797
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We study general properties of the restriction of the representations of the finite complex reflection groups $G(de,e,r+1)$ to their maximal parabolic subgroups of type $G(de,e,r)$, and focus notably on the multiplicity of components. In combinatorial terms, this amounts to the following question : which symmetries arise or disappear when one changes (exactly) one pearl in a combinatorial necklace ?
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arxiv:0711.1845
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We report the results of our HST snapshot survey with the ACS HRC PR200L prism, designed to measure the near-UV emission in a sample of nearby M dwarfs. 33 stars were observed, spanning the mass range from 0.1 - 0.6 solar masses (T_eff ~ 2200K - 4000K) where the UV energy distributions vary widely between active and inactive stars. These observations provide much-needed constraints on models of the habitability zone and the atmospheres of possible terrestrial planets orbiting M dwarf hosts, and will be useful in refining the target selection for future space missions such as TPF. We compare our data with a new generation of M dwarf atmospheric models and discuss their implication for the chromospheric energy budget. These NUV data will also be valuable in conjunction with existing optical, FUV and X-ray data to explore unanswered questions regarding the dynamo generation and magnetic heating in low-mass stars.
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arxiv:0711.1861
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Dynamic micromagnetic simulation studies have been completed to observe the motion of a domain wall in a magnetic nanowire in an effort to increase the field-driven domain wall speed. Previous studies have shown that the wire dimensions place a cap on the maximum speed attainable by a domain wall when driven by a magnetic field placed along the direction of the nanowire. Here we present data showing a significant increase in the maximum speed of a domain wall due to the addition of a magnetic field placed perpendicular to the longitudinal driving field. The results are expressed in terms of the relative alignment of the transverse field direction with respect to the direction of the magnetic moments within the domain wall. In particular, when the transverse field is parallel to the magnetic moments within the domain wall, the velocity of the wall varies linearly with the strength of the transverse field increasing by up to 20%. Further examination of the domain wall structure shows that the length of the domain wall also depends linearly on the strength of the transverse field. We present a simple model to correlate the effects.
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arxiv:0711.1864
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We discuss the relation between the highest energy cosmic rays (UHECR) and UHE neutrinos. The neutrinos produced in the sources of optically thin astrophysical sources have been linked to the UHECR emissivity of the Universe. The fluxes of cosmogenic neutrinos, generated in propagation by UHECR, also reflect the acceleration of these particles, the maximum acceleration energy, and the cosmological evolution of their sources.
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arxiv:0711.1872
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The differential cross section of the process gamma gamma -> pi^0 pi^0 has been measured in the kinematical range 0.6 GeV < W < 4.0 GeV and |cos theta*|<0.8 in energy and pion scattering angle, respectively, in the gamma gamma center-of-mass system. We find at least four resonant structures including a peak from f_0(980). In addition, there is evidence for chi_{c0} production. We also make a preliminary discussion of the angular dependence and cross section ratio to gamma gamma -> pi^+ pi^-.
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arxiv:0711.1926
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This article concerns the application of bootstrap methodology to construct a likelihood-based confidence region for operating conditions associated with the maximum of a response surface constrained to a specified region. Unlike classical methods based on the stationary point, proper interpretation of this confidence region does not depend on unknown model parameters. In addition, the methodology does not require the assumption of normally distributed errors. The approach is demonstrated for concave-down and saddle system cases in two dimensions. Simulation studies were performed to assess the coverage probability of these regions.
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arxiv:0711.1930
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Two simple mathematical models of electric neuro-stimulation are derived and discussed. It is found that the common injected-charge model is less realistic than a model, in which a latency period, which follows after a short electric pulse, plays a role as important as the electric pulse. A stimulation signal is proposed that takes advantage of these findings and calls for experimental testing.
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arxiv:0711.1938
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We study non-topological solitons, so called Q-balls, which carry a non-vanishing Noether charge and arise as lump solutions of self-interacting complex scalar field models. Explicit examples of new axially symmetric non-spinning Q-ball solutions that have not been studied so far are constructed numerically. These solutions can be interpreted as angular excitations of the fundamental $Q$-balls and are related to the spherical harmonics. Correspondingly, they have higher energy and their energy densities possess two local maxima on the positive z-axis. We also study two Q-balls interacting via a potential term in (3+1) dimensions and construct examples of stationary, solitonic-like objects in (3+1)-dimensional flat space-time that consist of two interacting global scalar fields. We concentrate on configurations composed of one spinning and one non-spinning Q-ball and study the parameter-dependence of the energy and charges of the configuration. In addition, we present numerical evidence that for fixed values of the coupling constants two different types of 2-Q-ball solutions exist: solutions with defined parity, but also solutions which are asymmetric with respect to reflexion through the x-y-plane.
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arxiv:0711.1969
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In this article we focus on the problem of channel decoding in presence of a-priori information. In particular, assuming that the a-priori information reliability is not perfectly estimated at the receiver, we derive a novel analytical framework for evaluating the decoder's performance. It is derived the important result that a "good code", i.e., a code which allows to fully exploit the potential benefit of a-priori information, must associate information sequences with high Hamming weights to codewords with low Hamming weights. Basing on the proposed analysis, we analyze the performance of convolutional codes, random codes, and turbo codes. Moreover, we consider the transmission of correlated binary sources from independent nodes, a problem which has several practical applications, e.g. in the case of sensor networks. In this context, we propose a very simple joint source-channel turbo decoding scheme where each decoder works by exploiting a-priori information given by the other decoder. In the case of block fading channels, it is shown that the inherent correlation between information signals provide a form of non-cooperative diversity, thus allowing joint source-channel decoding to outperform separation-based schemes.
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arxiv:0711.1986
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A spectacular, transient mass-loss event in the hydrogen-deficient central star of the planetary nebula Longmore 4 was discovered in 1992 by Werner et al. During that event, the star temporarily changed from its normal PG 1159 spectrum to that of an emission-line [WCE] star. I have been monitoring the spectrum of Lo 4 since 2003. Out of 31 spectra, two of them reveal mass-loss outbursts similar to the one seen in 1992, showing that the phenomenon recurs. I speculate on possible mechanisms for these unique outbursts, but emphasize that we still have no fully convincing explanation.
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arxiv:0711.2056
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It is shown that strongly correlated electrons on frustrated lattices like pyrochlore, checkerboard or kagome lattice can lead to the appearance of closed and open strings. They are resulting from nonlocal subsidiary conditions which propagating strongly correlated electrons require. The dynamics of the strings is discussed and a number of their properties are pointed out. Some of them are reminiscent of particle physics.
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arxiv:0711.2129
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The observation of high-energy neutrinos from astrophysical sources would substantially improve our knowledge and understanding of the non-thermal processes in these sources, and would in particular pinpoint the accelerators of cosmic rays. The sensitivity of different design options for a future cubic-kilometre scale neutrino telescope in the Mediterranean Sea is investigated for generic point sources and in particular for some of the galactic objects from which TeV gamma emmission has recently been observed by the H.E.S.S. atmospheric Cherenkov telescope. The effect of atmospheric background on the source detection probabilities has been taken into account through full simulation. The estimated event rates are compared to previous results and limits from present neutrino telescopes.
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arxiv:0711.2145
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The biharmonic supercritical equation $\Delta^2u=|u|^{p-1}u$, where $n>4$ and $p>(n+4)/(n-4)$, is studied in the whole space $\mathbb{R}^n$ as well as in a modified form with $\lambda(1+u)^p$ as right-hand-side with an additional eigenvalue parameter $\lambda>0$ in the unit ball, in the latter case together with Dirichlet boundary conditions. As for entire regular radial solutions we prove oscillatory behaviour around the explicitly known radial {\it singular} solution, provided $p\in((n+4)/(n-4),p_c)$, where $p_c\in ((n+4)/(n-4),\infty]$ is a further critical exponent, which was introduced in a recent work by Gazzola and the second author. The third author proved already that these oscillations do not occur in the complementing case, where $p\ge p_c$. Concerning the Dirichlet problem we prove existence of at least one singular solution with corresponding eigenvalue parameter. Moreover, for the extremal solution in the bifurcation diagram for this nonlinear biharmonic eigenvalue problem, we prove smoothness as long as $p\in((n+4)/(n-4),p_c)$.
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arxiv:0711.2202
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We provide a comprehensive overview of the current theoretical understanding of the dynamic structure factor of stiff polymers in semidilute solution based on the wormlike chain (WLC) model. We extend previous work by computing exact numerical coefficients and an expression for the dynamic mean square displacement (MSD) of a free polymer and compare various common approximations for the hydrodynamic interactions, which need to be treated accurately if one wants to extract quantitative estimates for model parameters from experimental data. A recent controversy about the initial slope of the dynamic structure factor is thereby resolved. To account for the interactions of the polymer with a surrounding (sticky) polymer solution, we analyze an extension of the WLC model, the glassy wormlike chain (GWLC), which predicts near power-law and logarithmic long-time tails in the dynamic structure factor.
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arxiv:0711.2427
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We characterize and study variable importance (VIMP) and pairwise variable associations in binary regression trees. A key component involves the node mean squared error for a quantity we refer to as a maximal subtree. The theory naturally extends from single trees to ensembles of trees and applies to methods like random forests. This is useful because while importance values from random forests are used to screen variables, for example they are used to filter high throughput genomic data in Bioinformatics, very little theory exists about their properties.
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arxiv:0711.2434
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The article `Global regularity for the 3D Navier-Stokes and the 3D Euler equations'(arXiv:0711.2453) is withdrawn due to a serious error in the proof.
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arxiv:0711.2453
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In this paper we deal with the problem of axiomatizing the preference relations modelled through Choquet integral with respect to a $k$-additive capacity, i.e. whose M\"obius transform vanishes for subsets of more than $k$ elements. Thus, $k$-additive capacities range from probability measures ($k=1$) to general capacities ($k=n$). The axiomatization is done in several steps, starting from symmetric 2-additive capacities, a case related to the Gini index, and finishing with general $k$-additive capacities. We put an emphasis on 2-additive capacities. Our axiomatization is done in the framework of social welfare, and complete previous results of Weymark, Gilboa and Ben Porath, and Gajdos.
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arxiv:0711.2489
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A quark model is applied to the spectrum of baryons containing heavy quarks. The model gives masses for the known heavy baryons that are in agreement with experiment, but for the doubly-charmed baryon Cascade_{cc}, the model prediction is too heavy. Mixing between the Cascade_Q and Cascade_Q^\prime states is examined and is found to be small for the lowest lying states. In contrast with this, mixing between the Cascade_{bc} and Cascade_{bc}^\prime states is found to be large, and the implication of this mixing for properties of these states is briefly discussed. We also examine heavy-quark spin-symmetry multiplets, and find that many states in the model can be placed in such multiplets. We compare our predictions with those of a number of other authors.
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arxiv:0711.2492
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We prove that inflation is forbidden in the most well understood class of semi-realistic type IIA string compactifications: Calabi-Yau compactifications with only standard NS-NS 3-form flux, R-R fluxes, D6-branes and O6-planes at large volume and small string coupling. With these ingredients, the first slow-roll parameter satisfies epsilon >= 27/13 whenever V > 0, ruling out both inflation (including brane/anti-brane inflation) and de Sitter vacua in this limit. Our proof is based on the dependence of the 4-dimensional potential on the volume and dilaton moduli in the presence of fluxes and branes. We also describe broader classes of IIA models which may include cosmologies with inflation and/or de Sitter vacua. The inclusion of extra ingredients, such as NS 5-branes and geometric or non-geometric NS-NS fluxes, evades the assumptions used in deriving the no-go theorem. We focus on NS 5-branes and outline how such ingredients may prove fruitful for cosmology, but we do not provide an explicit model. We contrast the results of our IIA analysis with the rather different situation in IIB.
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arxiv:0711.2512
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In this manuscript we present a comprehensive study on the multifractal properties of high-frequency price fluctuations and instantaneous volatility of the equities that compose Dow Jones Industrial Average. The analysis consists about quantification of dependence and non-Gaussianity on the multifractal character of financial quantities. Our results point out an equivalent influence of dependence and non-Gaussianity on the multifractality of time series. Moreover, we analyse l-diagrams of price fluctuations. In the latter case, we show that the fractal dimension of these maps is basically independent of the lag between price fluctuations that we assume.
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arxiv:0711.2550
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Higgs boson production by the gluon fusion and its decay into two photons at the LHC are investigated in the context of the gauge-Higgs unification scenario. The qualitative behaviors for these processes in the gauge-Higgs unification are quite distinguishable from those of the Standard Model and the universal extra dimension scenario because of the overall sign difference for the effective couplings induced by one-loop corrections through Kaluza-Klein (KK) modes. For the KK mode mass smaller than 1 TeV, the Higgs productions cross section and its branching ratio into two photons are sizably deviated from those in the Standard Model. Associated with the discovery of Higgs boson, this deviation may be measured at the LHC.
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arxiv:0711.2589
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Although known for almost a century, the photophoretic force has only recently been considered in astrophysical context for the first time. In our work, we have examined the effect of photophoresis, acting together with stellar gravity, radiation pressure, and gas drag, on the evolution of solids in transitional circumstellar disks. We have applied our calculations to four different systems: the disks of HR 4796A and HD 141569A, which are several Myr old AB-type stars, and two hypothetical systems that correspond to the solar nebula after disk dispersal has progressed sufficiently for the disk to become optically thin. Our results suggest that solid objects migrate inward or outward, until they reach a certain size-dependent stability distance from the star. The larger the bodies, the closer to the star they tend to accumulate. Photophoresis increases the stability radii, moving objects to larger distances. What is more, photophoresis may cause formation of a belt of objects, but only in a certain range of sizes and only around low-luminosity stars. The effects of photophoresis are noticeable in the size range from several micrometers to several centimeters (for older transitional disks) or even several meters (for younger, more gaseous, ones). We argue that due to gas damping, rotation does not substantially inhibit photophoresis.
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arxiv:0711.2595
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We study the band gap in some semi-conducting polymers with two models: H\"uckel molecular orbital theory and the so-called free electron model. The two models are directly related to spectral theory on combinatorial and metric graphs.
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arxiv:0711.2621
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Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite dimensional quantum systems. Moreover, we show that any quasi-probability representation satisfying two reasonable properties is equivalent to a frame representation and then prove that any such representation of quantum mechanics must exhibit either negativity or a deformed probability calculus.
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arxiv:0711.2658
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We give two proofs that the 3-torus is not weakly d-congruent to the connected sum of three S^1xS^2's, if d>2. We study how cohomology ring structure relates to weak congruence. We give an example of three 3--manifolds which are weakly 5-congruent but are not 5-congruent.
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arxiv:0711.2673
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We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels and quantum key distribution protocols. The test of quantum behavior can be phrased as the verification of effective entanglement. Necessary separability criteria are formulated in terms of a matrix of expectation values in conjunction with the partial transposition map. Our method is designed to reduce the resources for entanglement verification. A particular protocol based on coherent states and homodyne detection is used to illustrate the method. A possible test for the quantum nature of memories using two non-orthogonal signal states arises naturally. Furthermore, closer inspection of the measurement process in terms of the Stokes operators reveals a security threat for quantum key distribution involving phase reference beams.
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arxiv:0711.2709
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This paper proposes a relaying strategy for the multiple-relay network in which each relay decodes a selection of transmitted messages by other transmitting terminals, and forwards parities of the decoded codewords. This protocol improves the previously known achievable rate of the decode-and-forward (DF) strategy for multirelay networks by allowing relays to decode only a selection of messages from relays with strong links to it. Hence, each relay may have several choices as to which messages to decode, and for a given network many different parity forwarding protocols may exist. A tree structure is devised to characterize a class of parity forwarding protocols for an arbitrary multirelay network. Based on this tree structure, closed-form expressions for the achievable rates of these DF schemes are derived. It is shown that parity forwarding is capacity achieving for new forms of degraded relay networks.
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arxiv:0711.2712
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To a considerable extent, the continuing importance and popularity of complex networks as models of real-world structures has been motivated by scale free degree distributions as well as the respectively implied hubs. Being related to sequential connections of edges in networks, paths represent another important, dual pattern of connectivity (or motif) in complex networks (e.g., paths are related to important concepts such as betweeness centrality). The present work proposes a new supercategory of complex networks which are organized and/or constructed in terms of paths. Two specific network classes are proposed and characterized: (i) PA networks, obtained by star-path transforming Barabasi-Albert networks; and (ii) PN networks, built by performing progressive paths involving all nodes without repetition. Such new networks are important not only from their potential to provide theoretical insights, but also as putative models of real-world structures. The connectivity structure of these two models is investigated comparatively to four traditional complex networks models (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz and a geographical model). A series of interesting results are described, including the corroboration of the distinct nature of the two proposed models and the importance of considering a comprehensive set of measurements and multivariated statistical methods for the characterization of complex networks.
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arxiv:0711.2736
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We revisit Weyl geometry in the context of recent higher-dimensional theories of spacetime. After introducing the Weyl theory in a modern geometrical language we present some results that represent extensions of Riemannian theorems. We consider the theory of local embeddings and submanifolds in the context of Weyl geometries and show how a Riemannian spacetime may be locally and isometrically embedded in a Weyl bulk. We discuss the problem of classical confinement and the stability of motion of particles and photons in the neighbourhood of branes for the case when the Weyl bulk has the geometry of a warped product space. We show how the confinement and stability properties of geodesics near the brane may be affected by the Weyl field. We construct a classical analogue of quantum confinement inspired in theoretical-field models by considering a Weyl scalar field which depends only on the extra coordinate.
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arxiv:0711.2754
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We present a universal Holevo-like upper bound on the locally accessible information for arbitrary multipartite ensembles. This bound allows us to analyze the indistinguishability of a set of orthogonal states under LOCC. We also derive the upper bound for the capacity of distributed dense coding with multipartite senders and multipartite receivers.
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arxiv:0711.2787
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A 6-parametric family of 6--dimensional quasi-K\"ahler manifolds with Norden metric is constructed on a Lie group. This family is characterized geometrically.
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arxiv:0711.2796
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The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY L\'{e}vy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral process for which we infer the first passage times of stock prices to 30% of the price level at contract initiation. These distributions are then used in pricing 50% recovery rate equity default swap (EDS) contracts and the resulting prices are compared with the prices of credit default swaps (CDS). An illustrative analysis is presented for these contracts on Ford and GM.
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arxiv:0711.2807
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We present a quantum secure direct communication(QSDC) scheme as an extension for a proposed supervised secure entanglement sharing protocol. Starting with a quick review on the supervised entanglement sharing protocol -- the "Wuhan" protocol [Y. Li and Y. Liu, arXiv:0709.1449v2], we primarily focus on its further extend using for a QSDC task, in which the communication attendant Alice encodes the secret message directly onto a sequence of 2-level particles which then can be faithfully teleported to Bob using the shared maximal entanglement states obtained by the previous "Wuhan" protocol. We also evaluate the security of the QSDC scheme, where an individual self-attack performed by Alice and Bob -- the out of control attack(OCA) is introduced and the robustness of our scheme on the OCA is documented.
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arxiv:0711.2827
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This paper has been withdrawn by the authors, due the copyright policy of the journal it has been submited to.
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arxiv:0711.2893
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Hara, Takemura and Yoshida discuss toric ideals arising from two way subtable sum problems and shows that these toric ideals are generated by quadratic binomials if and only if the subtables are either diagonal or triangular. In the present paper, we show that if the subtables are either diagonal or triangular, then their toric ideals possess quadratic Groebner bases.
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arxiv:0711.2938
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This paper presents the first convergence result for random search algorithms to a subset of the Pareto set of given maximum size k with bounds on the approximation quality. The core of the algorithm is a new selection criterion based on a hypothetical multilevel grid on the objective space. It is shown that, when using this criterion for accepting new search points, the sequence of solution archives converges with probability one to a subset of the Pareto set that epsilon-dominates the entire Pareto set. The obtained approximation quality epsilon is equal to the size of the grid cells on the finest level of resolution that allows an approximation with at most k points within the family of grids considered. While the convergence result is of general theoretical interest, the archiving algorithm might be of high practical value for any type iterative multiobjective optimization method, such as evolutionary algorithms or other metaheuristics, which all rely on the usage of a finite on-line memory to store the best solutions found so far as the current approximation of the Pareto set.
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arxiv:0711.2949
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After a brief introduction to the statistical description of data, these lecture notes focus on quantum field theories as they emerge from lattice models in the critical limit. For the simulation of these lattice models, Markov chain Monte-Carlo methods are widely used. We discuss the heat bath and, more modern, cluster algorithms. The Ising model is used as a concrete illustration of important concepts such as correspondence between a theory of branes and quantum field theory or the duality map between strong and weak couplings. The notes then discuss the inclusion of gauge symmetries in lattice models and, in particular, the continuum limit in which quantum Yang-Mills theories arise.
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arxiv:0711.3004
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Experiments with cold Fermi atoms can be tuned to probe strongly interacting fluids that are very similar to the low-density neutron matter found in the crusts of neutron stars. In contrast to traditional superfluids and superconductors, matter in this regime is very strongly paired, with gaps of the order of the Fermi energy. We compute the T=0 equation of state and pairing gap for cold atoms and low-density neutron matter as a function of the Fermi momentum times the scattering length. Results of quantum Monte Carlo calculations show that the equations of state are very similar. The neutron matter pairing gap at low densities is found to be very large but, except at the smallest densities, significantly suppressed relative to cold atoms because of the finite effective range in the neutron-neutron interaction.
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arxiv:0711.3006
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A module is called absolutely indecomposable if it is directly indecomposable in every generic extension of the universe. We want to show the existence of large abelian groups that are absolutely indecomposable. This will follow from a more general result about R-modules over a large class of commutative rings R with endomorphism ring R which remains the same when passing to a generic extension of the universe. It turns out that `large' in this context has the precise meaning, namely being smaller then the first omega-Erdos cardinal defined below. We will first apply result on large rigid trees with a similar property established by Shelah in 1982, and will prove the existence of related ` R_omega-modules' (R-modules with countably many distinguished submodules) and finally pass to R-modules. The passage through R_omega-modules has the great advantage that the proofs become very transparent essentially using a few `linear algebra' arguments accessible also for graduate students. The result gives a new construction of indecomposable modules in general using a counting argument.
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arxiv:0711.3011
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We investigate an extension of ideas of Atiyah-Patodi-Singer (APS) to a noncommutative geometry setting framed in terms of Kasparov modules. We use a mapping cone construction to relate odd index pairings to even index pairings with APS boundary conditions in the setting of KK-theory, generalising the commutative theory. We find that Cuntz-Kreiger systems provide a natural class of examples for our construction and the index pairings coming from APS boundary conditions yield complete K-theoretic information about certain graph C*-algebras.
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arxiv:0711.3028
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In the color glass condensate framework the saturation scale measured in deep inelastic scattering of high energy hadrons and nuclei can be determined from the correlator of Wilson lines in the hadron wavefunction. These same Wilson lines give the initial condition of the classical field computation of the initial gluon multiplicity and energy density in a heavy ion collision. In this paper the Wilson line correlator in both adjoint and fundamental representations is computed using exactly the same numerical procedure that has been used to calculate gluon production in a heavy ion collision. In particular the discretization of the longitudinal coordinate has a large numerical effect on the relation between the color charge density parameter g^2 mu and the saturation scale Qs. Our result for this relation is Qs = 0.6 g^2 mu, which results in the classical Yang-Mills value for the "gluon liberation coefficient" c = 1.1.
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arxiv:0711.3039
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When fragile molecules such as glycine, polyglicine, alkanes, and alkanethiols are embedded in liquid helium nanodroplets, electron-impact ionization of the beam leads to fragmentation which is as extensive as that of isolated gas-phase molecules. However, it turns out that if a few molecules of water are co-embedded with the peptide and alkane chains, their fragmentation is drastically reduced or completely eliminated. On the other hand, the fragmentation of alkanethiols remains unaffected. On the basis of these observations, it is proposed that the fragmentation "buffering" effect may correlate with the magnitude of the impurity's electric dipole moment, which steers the migration of the ionizing He^+ hole in the droplet.
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arxiv:0711.3052
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The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution towards the limiting Hartree dynamics. More precisely, we prove bounds on the difference between the one-particle density associated with the solution of the N-body Schroedinger equation and the orthogonal projection onto the solution of the Hartree equation.
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arxiv:0711.3087
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In nuclear power generation, fissile materials are mainly used. For example, $U^{235}$ is fissile and therefore quite essential for use of nuclear energy. However, the material $U^{235}$ has very small natural abundance less than 1 %. We should seek possibility of utilizing fissionable materials such as $U^{238}$ because natural abundance of such fissionable materials is generally much larger than fissile ones. In this paper, we show that thermal neutrons with vanishing kinetic energy can induce nuclear fission when high voltage is applied to fissionable materials. To obtain this result, we use the liquid-drop model for nuclei. Finally, we propose how fissionable materials can be utilized.
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arxiv:0711.3153
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We explore the relationship among three coronal mass ejections (CMEs), observed on 28 October 2003, 7 November 2004, and 20 January 2005, the type II burst-associated shock waves in the corona and solar wind, as well as the arrival of their related shock waves and magnetic clouds at 1 AU. Using six different coronal/interplanetary density models, we calculate the speeds of shocks from the frequency drifts observed in metric and decametric radio wave data. We compare these speeds with the velocity of the CMEs as observed in the plane-of-the-sky white-light observations and calculated with a cone model for the 7 November 2004 event. We then follow the propagation of the ejecta using Interplanetary Scintillation (IPS) measurements, which were available for the 7 November 2004 and 20 January 2005 events. Finally, we calculate the travel time of the interplanetary (IP) shocks between the Sun and Earth and discuss the velocities obtained from the different data. This study highlights the difficulties in making velocity estimates that cover the full CME propagation time.
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arxiv:0711.3168
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In quantum gravity, one seeks to combine quantum mechanics and general relativity. In attempting to do so, one comes across the `problem of time' impasse: the notion of time is conceptually different in each of these theories. In this seminar, I consider the timeless records approach toward resolving this. Records are localized, information-containing subconfigurations of a single instant. Records theory is the study of these and of how science (or history) is to be abstracted from correlations between them. I explain how to motivate this approach, provide a ground-level structure for it and discuss what kind of further tools are needed. For a more comprehensive account with many more references, see [1].
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arxiv:0711.3174
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The nuclear K-shell electron-capture (EC)and positron (beta+) decay constants, lambda_(EC) and lambda_(beta^+) of H-like 140Pr58+ and He-like 140Pr57+ ions, measured recently in the ESR ion storage ring at GSI, were calculated using standard weak interaction theory. The calculated ratios R = lambda_(EC)/lambda_(beta^+) of the decay constants agree with the experimental values within an accuracy better than 3 %.
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arxiv:0711.3184
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This paper considers the problem of selecting a subset of nodes in a two-hop wireless network to act as relays in aiding the communication between the source-destination pair. Optimal relay subset selection with the objective of maximizing the overall throughput is a difficult problem that depends on multiple factors including node locations, queue lengths and power consumption. A partial decode-and-forward strategy is applied in this paper to improve the tractability of the relay selection problem and performance of the overall network. Note that the number of relays selected ultimately determines the performance of the network. This paper benchmarks this performance by determining the net diversity achieved using the relays selected and the partial decode-and-forward strategy. This framework is subsequently used to further transform relay selection into a simpler relay placement problem, and two proximity-based approximation algorithms are developed to determine the appropriate set of relays to be selected in the network. Other selection strategies such as random relay selection and a greedy algorithm that relies on channel state information are also presented. This paper concludes by showing that the proposed proximity-based relay selection strategies yield near-optimal expected rates for a small number of selected relays.
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arxiv:0711.3205
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We study inelastic processes for ultracold three-body systems in which only one interaction is resonant. We have found that the decay rates for weakly bound molecules due to collisions with other atoms can be suppressed not only without fermionic statistics but also when bosonic statistics applies. In addition, we show that at ultracold temperatures three-body recombination involving a single resonant pair of atoms leads mainly to formation of weakly bound molecules which, in turn, are stable against decay. These results indicate that recombination in three-component atomic gases can be used as an efficient mechanism for molecular formation, allowing the achievement of high molecular densities.
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arxiv:0711.3238
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In this paper the feasibility study of an IR sensor card is presented. The methodology and the results of a quasi real-time thermal characterization tool and method for the temperature mapping of circuits and boards based on sensing the infrared radiation is introduced. With the proposed method the IR radiation-distribution of boards from the close proximity of the sensor card is monitored in quasi real-time. The proposed method is enabling in situ IR measurement among operating cards of a system e.g. in a rack.
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arxiv:0711.3324
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For any finite poset P, there is a natural operator $X$ acting on the antichains of P. We discuss conjectural properties of this operator for some graded posets associated with irreducible root systems. In particular, if $\Delta^+$ is the set of positive roots and $\Pi$ is the set of simple roots in $\Delta^+$, then we consider the cases $P=\Delta^+$ and $\Delta^+\setminus \Pi$. For the root system of type $A_n$, we consider an $X$-invariant integer-valued function on the set of antichains of $\Delta^+$ and establish some properties of it.
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arxiv:0711.3353
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Conformally compact asymptotically hyperbolic metrics have been intensively studied. The goal of this note is to understand what intrinsic conditions on a complete Riemannian manifold (M,g) will ensure that g is asymptotically hyperbolic in this sense. We use the geodesic compactification by asymptotic geodesic rays to compactify M and appropriate curvature decay conditions to study the regularity of the conformal compactification. We also present an interesting example that shows our conclusion is nearly optimal for our assumptions.
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arxiv:0711.3371
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Fermions play an essential role in many areas of quantum physics and it is desirable to understand the nature of entanglement within systems that consists of fermions. Whereas the issue of separability for bipartite fermions has extensively been studied in the present literature, this paper is concerned with maximally entangled fermions. A complete characterization of maximally entangled quasifree (gaussian) fermion states is given in terms of the covariance matrix. This result can be seen as a step towards distillation protocols for maximally entangled fermions.
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arxiv:0711.3394
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We study the propagation of bubbles of new vacuum in a radially inhomogeneous Lemaitre-Tolman-Bondi background that includes a cosmological constant. This exemplifies the classical evolution of a tunneling bubble through a metastable state with curvature inhomogeneities, and will be relevant in the context of the Landscape. We demand that the matter profile in the LTB background satisfy the weak energy condition. For sample profiles that satisfy this restriction, we find that the evolution of the bubble (in terms of the physically relevant coordinates intrinsic to the shell) is largely unaffected by the prsence of local inhomogeneities. Our setup should also be a useful toy model for capturing the effects of ambient inhomogeneities on an inflating region.
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arxiv:0711.3417
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High resolution magnetoresistance data in highly oriented pyrolytic graphite thin samples manifest non-homogenous superconductivity with critical temperature $T_c \sim 25 $K. These data exhibit: i) hysteretic loops of resistance versus magnetic field similar to Josephson-coupled grains, ii) quantum Andreev's resonances and iii) absence of the Schubnikov-de Haas oscillations. The results indicate that graphite is a system with non-percolative superconducting domains immersed in a semiconducting-like matrix. As possible origin of the superconductivity in graphite we discuss interior-gap superconductivity when two very different electronic masses are present.
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arxiv:0711.3542
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We prove local in time Strichartz estimates without loss for the restriction of the solution of the Schroedinger equation, outside a large compact set, on a class of asymptotically hyperbolic manifolds.
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arxiv:0711.3587
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