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We observe 84 candidate young high-mass sources in the rare isotopologues C17O and C18O to investigate whether there is evidence for depletion (freeze-out) towards these objects. Observations of the J=2-1 transitions of C18O and C17O are used to derive the column densities of gas towards the sources and these are compared with those derived from submillimetre continuum observations. The derived fractional abundance suggests that the CO species show a range of degrees of depletion towards the objects. We then use the radiative transfer code RATRAN to model a selection of the sources to confirm that the spread of abundances is not a result of assumptions made when calculating the column densities. We find a range of abundances of C17O that cannot be accounted for by global variations in either the temperature or dust properties and so must reflect source to source variations. The most likely explanation is that different sources show different degrees of depletion of the CO. Comparison of the C17O linewidths of our sources with those of CS presented by other authors reveal a division of the sources into two groups. Sources with a CS linewidth >3 km/s have low abundances of C17O while sources with narrower CS lines have typically higher C17O abundances. We suggest that this represents an evolutionary trend. Depletion towards these objects shows that the gas remains cold and dense for long enough for the trace species to deplete. The range of depletion measured suggests that these objects have lifetimes of 2-4x10^5 years.
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arxiv:0712.1512
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This article is the written version of the closing talk presented at the conference `A Century of Cosmology' held at San Servolo, Italy, in August 2007. I focus on the prospects of constraining fundamental physics from cosmological observations, using the search for gravitational waves from inflation and constraints on the equation of state of dark energy as topical examples. I argue that it is important to strike a balance between the importance of a scientific discovery against the likelihood of making the discovery in the first place. Astronomers should be wary of embarking on large observational projects with narrow and speculative scientific goals. We should maintain a diverse range of research programmes as we move into a second century of cosmology. If we do so, discoveries that will reshape fundamental physics will surely come.
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arxiv:0712.1513
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This survey starts with the historical landmarks leading to the study of principal configurations on surfaces, their structural stability and further generalizations. Here it is pointed out that in the work of Monge, 1796, are found elements of the qualitative theory of differential equations (QTDE), founded by Poincar\'e in 1881. Here are also outlined a number of recent results developed after the assimilation into the subject of concepts and problems from the QTDE and Dynamical Systems, such as Structural Stability, Bifurcations and Genericity, among others, as well as extensions to higher dimensions. References to original works are given and open problems are proposed at the end of some sections.
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arxiv:0712.1585
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We present new results on the evolution of the mass function of the globular cluster system of the Milky Way, taking the effect of residual gas expulsion into account. We assume that gas embedded star clusters start with a power-law mass function with slope \beta=2. The dissolution of the clusters is then studied under the combined influence of residual gas expulsion driven by energy feedback from massive stars, stellar mass-loss, two-body relaxation and an external tidal field. The influence of residual gas expulsion is studied by applying results from a large grid of N-body simulations computed by Baumgardt & Kroupa (2007). In our model, star clusters with masses less than 10^5 M_sun lose their residual gas on timescales much shorter than their crossing time and residual gas expulsion is the main dissolution mechanism for star clusters, destroying about 95% of all clusters within a few 10s of Myr. We find that in this case the final mass function of globular clusters is established mainly by the gas expulsion and therefore nearly independent of the strength of the external tidal field, and that a power-law mass function for the gas embedded star clusters is turned into a present-day log-normal one. Another consequence of residual gas expulsion and the associated strong infant mortality of star clusters is that the Galactic halo stars come from dissolved star clusters. Since field halo stars would come mainly from low-mass, short-lived clusters, our model provides an explanation for the observed abundance variations of light elements among globular cluster stars and the absence of such variations among the halo field stars.
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arxiv:0712.1591
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We have studied the density of states of the normal state of the electron-doped superconductor Pr$_{2-x}$Ce$_x$CuO$_4$ at low temperatures and in magnetic fields up to 31 Tesla using point contact spectroscopy on single crystals. Our data clearly reveal an anomalous gap in the normal state density of states. This normal state gap survives even in the highest applied field of 31 T. Our results cast doubt over whether this gap found in electron-doped cuprates is the analog of the pseudogap in hole-doped cuprates. We have suggested an alternate origin of the normal state gap, which involves the effect of disorder and electron correlations at the surface of cuprates.
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arxiv:0712.1614
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We present a solution of the problem of the optimal unambiguous comparison of two ensembles of unknown quantum states (psi_1)^k and (psi_2)^l. We consider two cases: 1) The two unknown states psi_1 and psi_2 are arbitrary states of qudits. 2) Alternatively, they are coherent states of a harmonic oscillator. For the case of coherent states we propose a simple experimental realization of the optimal "comparison" machine composed of a finite number of beam-splitters and a single photodetector.
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arxiv:0712.1616
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The structure of transition amplitudes in field theory in a three-dimensional space whose spatial coordinates are noncommutative and satisfy the SU(2) Lie algebra commutation relations is examined. In particular, the basic notions for constructing the observables of the theory as well as subtleties related to the proper treatment of $\delta$ distributions (corresponding to conservation laws) are introduced. Explicit examples are given for scalar field theory amplitudes in the lowest order of perturbation.
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arxiv:0712.1670
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The notion of double coset for semisimple finite dimensional Hopf algebras is introduced. This is done by considering an equivalence relation on the set of irreducible characters of the dual Hopf algebra. As an application formulae for the restriction of the irreducible characters to normal Hopf subalgebras are given.
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arxiv:0712.1719
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We have investigated the stability limits of small spin-polarized clusters consisting of up to ten spin-polarized tritium T$\downarrow$ atoms and the mixtures of T$\downarrow$ with spin-polarized deuterium D$\downarrow$ and hydrogen H$\downarrow$ atoms. All of our calculations have been performed using the variational and diffusion Monte Carlo methods. For clusters with D$\downarrow$ atoms, the released node procedure is used in cases where the wave function has nodes. In addition to the energy, we have also calculated the structure of small clusters using unbiased estimators. Results obtained for pure T$\downarrow$ clusters are in good accordance with previous calculations, confirming that the trimer is the smallest spin-polarized tritium cluster. Our results show that mixed T$\downarrow$-H$\downarrow$ clusters having up to ten atoms are unstable and that it takes at least three tritium atoms to bind one, two or three D$\downarrow$ atoms. Among all the considered clusters, we have found no other Borromean states except the ground state of the T$\downarrow$ trimer.
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arxiv:0712.1730
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The nature of fast magnetoacoustic and Alfv\'en waves is investigated in a zero $\beta$ plasma. This gives an indication of wave propagation in the low $\beta$ solar corona. It is found that for a two-dimensional null point, the fast wave is attracted to that point and the front of the wave slows down as it approaches the null point, causing the current density to accumulate there and rise rapidly. Ohmic dissipation will extract the energy in the wave at this point. This illustrates that null points play an important role in the rapid dissipation of fast magnetoacoustic waves and suggests the location where wave heating will occur in the corona. The Alfv\'en wave behaves in a different manner in that the wave energy is dissipated along the separatrices. For Alfv\'en waves that are decoupled from fast waves, the value of the plasma $\beta$ is unimportant. However, the phenomenon of dissipating the majority of the wave energy at a specific place is a feature of both wave types.
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arxiv:0712.1792
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The superfluid-insulator transition of bosons is strongly modified by the presence of Fermions. Through an imaginary-time path integral approach, we derive the self-consistent mean-field transition line, and account for both the static and the dynamic screening effects of the fermions. We find that an effect akin to the fermionic orthogonality catastrophe, arising from the fermionic screening fluctuations, suppresses superfluidity. We analyze this effect for various mixture parameters and temperatures, and consider possible signatures of the orthogonality catastrophe effect in other measurables of the mixture.
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arxiv:0712.1828
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Stability of dark solitons generated by a supersonic flow of Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to decay of disturbances of solitons at fixed distance from the obstacle and formation of effectively stable dark solitons. This phenomenon explains surprising stability of the flow picture that has been observed in numerical simulations.
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arxiv:0712.1891
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We observe a large number of functions differing from each other only by a translation parameter. While the main pattern is unknown, we propose to estimate the shift parameters using $M$-estimators. Fourier transform enables to transform this statistical problem into a semi-parametric framework. We study the convergence of the estimator and provide its asymptotic behavior. Moreover, we use the method in the applied case of velocity curve forecasting.
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arxiv:0712.1936
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The Dirac and Pauli form factors of the proton and neutron are obtained in the framework of the generalized parton distributions (GPDs) with some simple momentum transfer dependence. It is shown that both sets of the existing experimental data of the form factors, obtained by the Rosenbluth and polarization transfer, can be described by changing only the slope of the GPDs $E$. The description of neutron form factors is substantially better when the proton data obtained by the studies of polarization transfer are used.
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arxiv:0712.1947
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The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.
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arxiv:0712.1978
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It is well known that a spherically symmetric compact star whose energy density decreases monotonically possesses an upper bound on its mass-to-radius ratio, $2M/R\leq 8/9$. However, field configurations typically will not be compact. Here we investigate non-compact static configurations whose matter fields have a slow global spatial decay, bounded by a power law behavior. These matter distributions have no sharp boundaries. We derive an upper bound on the fundamental ratio max_r{2m(r)/r} which is valid throughout the bulk. In its simplest form, the bound implies that in any region of spacetime in which the radial pressure increases, or alternatively decreases not faster than some power law $r^{-(c+4)}$, one has $2m(r)/r \leq (2+2c)/(3+2c)$. [For $c \leq 0$ the bound degenerates to $2m(r)/r \leq 2/3$.] In its general version, the bound is expressed in terms of two physical parameters: the spatial decaying rate of the matter fields, and the highest occurring ratio of the trace of the pressure tensor to the local energy density.
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arxiv:0712.1988
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After the concept of industry cluster was tangibly applied in many countries, SMEs trended to link to each other to maintain their competitiveness in the market. The major key success factors of the cluster are knowledge sharing and collaboration between partners. This knowledge is collected in form of tacit and explicit knowledge from experts and institutions within the cluster. The objective of this study is about enhancing the industry cluster with knowledge management by using knowledge engineering which is one of the most important method for managing knowledge. This work analyzed three well known knowledge engineering methods, i.e. MOKA, SPEDE and CommonKADS, and compares the capability to be implemented in the cluster context. Then, we selected one method and proposed the adapted methodology. At the end of this paper, we validated and demonstrated the proposed methodology with some primary result by using case study of handicraft cluster in Thailand.
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arxiv:0712.1994
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This letter presents a remarkably simple approach to the first-principles determination of the ergodic-non-ergodic transition in monodisperse colloidal suspensions. It consists of an equation for the long-time asymptotic value $\gamma$ of the mean squared displacement of the colloidal particles, whose finite real solutions signal the non-ergodic state, and determines the non-ergodic parameter $f(k)$. We illustrate its concrete application to three simple model colloidal systems, namely, hard-spheres, hard-spheres plus repulsive (screened Coulomb) Yukawa interaction, and hard-sphere plus attractive Yukawa tail. The results indicate that this is quite a competitive theory, similar in spirit to, but conceptually independent from, the well-known mode coupling theory.
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arxiv:0712.2071
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A mixture of spin-1/2 fermionic atoms and molecules of paired fermionic atoms is studied in an optical lattice. The molecules are formed by an attractive nearest-neighbor interaction. A functional integral is constructed for this many-body system and analyzed in terms of a mean-field approximation and Gaussian fluctuations. This provides a phase diagram with the two merging Mott insulators and an intermediate superfluid. The Gaussian fluctuations give rise to an induced repulsive dimer-dimer interaction mediated by the unpaired fermions. The effect of an unbalanced distribution of spin-up and spin-down fermions is also discussed.
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arxiv:0712.2128
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We present a general information theoretic approach for identifying functional subgraphs in complex networks where the dynamics of each node are observable. We show that the uncertainty in the state of each node can be expressed as a sum of information quantities involving a growing number of correlated variables at other nodes. We demonstrate that each term in this sum is generated by successively conditioning mutual informations on new measured variables, in a way analogous to a discrete differential calculus. The analogy to a Taylor series suggests efficient search algorithms for determining the state of a target variable in terms of functional groups of other degrees of freedom. We apply this methodology to electrophysiological recordings of networks of cortical neurons grown it in vitro. Despite strong stochasticity, we show that each cell's patterns of firing are generally explained by the activity of a small number of other neurons. We identify these neuronal subgraphs in terms of their mutually redundant or synergetic character and reconstruct neuronal circuits that account for the state of each target cell.
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arxiv:0712.2218
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The rich-get-richer mechanism (agents increase their ``wealth'' randomly at a rate proportional to their holdings) is often invoked to explain the Pareto power-law distribution observed in many physical situations, such as the degree distribution of growing scale free nets. We use two different analytical approaches, as well as numerical simulations, to study the case where the number of agents is fixed and finite (but large), and the rich-get-richer mechanism is invoked a fraction r of the time (the remainder of the time wealth is disbursed by a homogeneous process). At short times, we recover the Pareto law observed for an unbounded number of agents. In later times, the (moving) distribution can be scaled to reveal a phase transition with a Gaussian asymptotic form for r < 1/2 and a Pareto-like tail (on the positive side) and a novel stretched exponential decay (on the negative side) for r > 1/2.
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arxiv:0712.2220
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We report on the detection of variable stars in the Canes Venatici II (CVn II) dwarf spheroidal galaxy, a new satellite of the Milky Way recently discovered by the Sloan Digital Sky Survey. We also present a V, B-V color-magnitude diagram that reaches V = 25.5 mag, showing the galaxy's main sequence turn off at V = 24.5 mag and revealing several candidate blue straggler stars. Two RR Lyrae stars have been identified within the half-light radius of CVn II,a fundamental-mode variable (RRab) with period P_ab = 0.743 days, and a first-overtone (RRc) RR Lyrae star with P_c = 0.358 days. The rather long periods of these variables along with their position on the period-amplitude diagram support an Oosterhoff type II classification for CVn II. The average apparent magnitude of the RR Lyrae stars, <V> = 21.48 +/- 0.02 mag, is used to obtain a precision distance modulus of mu_0 = 21.02 +/- 0.06 mag and a corresponding distance of 160(+4,-5} kpc, for an adopted reddening E(B-V) = 0.015 mag.
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arxiv:0712.2241
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The elementary excitations in antiferromagnets are magnons, quasiparticles with integer spin and Bose statistics. In an experiment their density is controlled efficiently by an applied magnetic field and can be made finite to cause the formation of a Bose-Einstein condensate (BEC). Studies of magnon condensation in a growing number of magnetic materials provide a unique window into an exciting world of quantum phase transitions (QPT) and exotic quantum states.
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arxiv:0712.2250
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We describe a general framework for studying duality between different phase spaces which share the same symmetry group $\mathrm{H}$. Solutions corresponding to collective dynamics become dual in the sense that they are generated by the same curve in $\mathrm{H}$. Explicit examples of phase spaces which are dual with respect to a common non trivial coadjoint orbit $\mathcal{O}_{c,0}(\mathbf{\alpha},1) \subset\mathfrak{h}^{\ast}$ are constructed on the cotangent bundles of the factors of a double Lie group $\mathrm{H}=\mathrm{N}\Join\mathrm{N}^{\ast}$. In the case $\mathrm{H}=LD$, the loop group of a Drinfeld double Lie group $D$, a hamiltonian description of Poisson-Lie T-duality for non trivial monodromies and its relation with non trivial coadjoint orbits is obtained.
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arxiv:0712.2259
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We prove a special case of a dynamical analogue of the classical Mordell-Lang conjecture. In particular, let $\phi$ be a rational function with no superattracting periodic points other than exceptional points. If the coefficients of $\phi$ are algebraic, we show that the orbit of a point outside the union of proper preperiodic subvarieties of $(\bP^1)^g$ has only finite intersection with any curve contained in $(\bP^1)^g$. We also show that our result holds for indecomposable polynomials $\phi$ with coefficients in $\bC$. Our proof uses results from $p$-adic dynamics together with an integrality argument. The extension to polynomials defined over $\bC$ uses the method of specializations coupled with some new results of Medvedev and Scanlon for describing the periodic plane curves under the action of $(\phi,\phi)$ on $\bA^2$.
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arxiv:0712.2344
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We give positivity conditions on the embedding of a smooth variety which guarantee the normality of the secant variety, generalizing earlier results of the author and others. We also give classes of secant varieties satisfying the Hodge conjecture as well as a result on the singular locus of degenerate secant varieties.
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arxiv:0712.2364
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It is shown that the known notion of selective coideal can be extended to a family $\mathcal{H}$ of subsets of $\mathcal{R}$, where $(\mathcal{R},\leq,r)$ is a topological Ramsey space in the sense of Todorcevic (see \cite{todo}). Then it is proven that, if $\mathcal{H}$ selective, the $\mathcal{H}$-Ramsey and $\mathcal{H}$-Baire subsets of $\mathcal{R}$ are equivalent. This extends the results of Farah in \cite{farah} for semiselective coideals of $\mathbb{N}$. Also, it is proven that the family of ${\cal H}$--Ramsey subsets of ${\cal R}$ is closed under the Souslin operation.
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arxiv:0712.2393
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We present multi-epoch high-angular resolution observations of 22 GHz H2O masers toward the silicate carbon star EU And to probe the spatio-kinematic distribution of oxygen-rich material. EU And was observed at three epochs (maximum time interval of 14 months) with the Very Long Baseline Array (VLBA). Our VLBA observations of the 22 GHz H2O masers have revealed that the maser spots are distributed along a straight line across ~20 mas, with a slight hint of an S-shaped structure. The observed spectra show three prominent velocity components at V_LSR = -42, -38, and -34 km s^-1, with the masers in SW redshifted and those in NE blueshifted. The maser spots located in the middle of the overall distribution correspond to the component at V_LSR = -38 km s^-1, which approximately coincides with the systemic velocity. These observations can be interpreted as either an emerging helical jet or a disk viewed almost edge-on (a circumbinary or circum-companion disk). However, the outward motion measured in the VLBA images taken 14 months apart is much smaller than that expected from the jet scenario. Furthermore, the mid-infrared spectrum obtained with the Spitzer Space Telescope indicates that the 10 micron silicate emission is optically thin and the silicate grains are of sub-micron size. This lends support to the presence of a circum-companion disk, because an optically thin circumbinary disk consisting of such small grains would be blown away by the intense radiation pressure of the primary (carbon-rich) star. If we assume Keplerian rotation for the circum-companion disk, the mass of the companion is estimated to be 0.5--0.8 M_sun. We also identify CO2 emission features at 13--16 micron in the Spitzer spectrum of EU And--the first unambiguous detection of CO2 in silicate carbon stars.
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arxiv:0712.2395
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Parity nonconserving two-pion exchange in elastic pp scattering is investigated in the presence of phenomenological strong distortions in various models. Parity violation is included in the nucleon-pion vertex considering NN and N Delta(1232) intermediate states in box and crossed box diagrams. Using the derived parity nonconserving two-pion exchange potential we calculate the longitudinal analyzing power A_L in elastic $pp$ scattering. The predicted effect is of the same order as vector meson exchanges.
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arxiv:0712.2399
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At this time there does not exist a robust set of rules connecting low and high $\beta$ waves across the $\beta \approx 1$ layer. The work here contributes specifically to what happens when a low $\beta$ fast wave crosses the $\beta \approx 1$ layer and transforms into high $\beta$ fast and slow waves. The nature of fast and slow magnetoacoustic waves is investigated in a finite $\beta$ plasma in the neighbourhood of a two-dimensional null point. The linearised equations are solved in both polar and cartesian forms with a two-step Lax-Wendroff numerical scheme. Analytical work (e.g. small $\beta$ expansion and WKB approximation) also complement the work. It is found that when a finite gas pressure is included in magnetic equilibrium containing an X-type null point, a fast wave is attracted towards the null by a refraction effect and that a slow wave is generated as the wave crosses the $\beta \approx 1$ layer. Current accumulation occurs close to the null and along nearby separatrices. The fast wave can now \emph{pass through the origin} due to the non-zero sound speed, an effect not previously seen in related papers but clear seen for larger values of $\beta$. Some of the energy can now leave the region of the null point and there is again generation of a slow wave component (we find that the fraction of the incident wave converted to a slow wave is proportional to $\beta$). We conclude that there are two competing phenomena; the refraction effect (due to the variable Alfv\'en speed) and the contribution from the non-zero sound speed. These experiments illustrate the importance of the magnetic topology and of the location of the $\beta \approx 1$ layer in the system.
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arxiv:0712.2402
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We propose a new approximation scheme within equation of motion approach (EOM) to spin polarized transport through a quantum dot coupled to ferromagnetic leads. It has some advantages over a widely used in the literature standard EOM technique, in particular when we are interested in spin polarized quantities. Namely, it gives the values of the dot spin polarization which are closer to the ones obtained within numerical renormalization group (NRG), than the standard EOM approach. While restoring the Kondo effect, the spin polarization vanishes and the transport becomes unpolarized, in agreement with NRG and a real time diagrammatic calculations. The standard EOM procedure gives nonzero values of the spin polarization, and the transport is still spin polarized. Both approximations give the same correct splitting of the Kondo peaks due to ferromagnetism in the electrodes.
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arxiv:0712.2414
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We consider folded spinning strings in AdS_5xS^5 (with one spin component S in AdS_5 and J in S^5) corresponding to the Tr(D^S Z^J) operators in the sl(2) sector of the N=4 SYM theory in the special scaling limit in which both the string mass M ~ \sqrt \lambda \ln S and J are sent to infinity with their ratio fixed. Expanding in the parameter \el= J/M we compute the 2-loop string sigma model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena in arxiv:0708.0672. We suggest that a resummation of the logarithmic \el^2 \ln^n \el terms is necessary in order to establish an interpolation to the weakly coupled gauge theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multi-spin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite ``renormalization'' of the relation between the parameters of the classical solution and the fixed spins, i.e. the charges of the SO(2,4) x SO(6) symmetry.
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arxiv:0712.2479
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We show that the moduli space M(r,c) of semistable sheaves on n-dimensional projective space with support of dimension one, with multiplicity r and with Euler characteristic c is isomorphic to M(r,-c).
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arxiv:0712.2498
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Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been used to produce difference triangle sets whose scopes are the best currently known.
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arxiv:0712.2553
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Motion of a continuous fluid can be decomposed into an "incompressible" rearrangement, which preserves the volume of each infinitesimal fluid element, and a gradient map that transfers fluid elements in a way unaffected by any pressure or elasticity (the polar decomposition of Y. Brenier). The Euler equation describes a system whose kinematics is dominated by the incompressible rearrangement. The opposite limit, in which the incompressible component is negligible, corresponds to the Zel'dovich approximation, a model of motion of self-gravitating fluid in cosmology. We present a method of approximate reconstruction of the large-scale proper motions of matter in the Universe from the present-day mass density field. The method is based on recovering the corresponding gradient transfer map. We discuss its algorithmics, tests of the method against mock cosmological catalogues, and its application to observational data, which result in tight constraints on the mean mass density Omega_m and age of the Universe.
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arxiv:0712.2561
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Current experimental data allow the zero value for one neutrino mass, either m_1 =0 or m_3 =0. This observation implies that a realistic neutrino mass texture can be established by starting from the limit (a) m_1 = m_2 =0 and m_3 \neq 0 or (b) m_1 = m_2 \neq 0 and m_3 =0. In both cases, we may introduce a particular perturbation which ensures the resultant neutrino mixing matrix to be the tri-bimaximal mixing pattern or its viable variations. We find that it is natural to incorporate this kind of neutrino mass matrix in the minimal Type-II seesaw model with only one heavy right-handed Majorana neutrino N. We show that it is possible to account for the cosmological baryon number asymmetry in the m_3 =0 case via thermal leptogenesis, in which the CP-violating asymmetry of N decays is attributed to the electron flavor.
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arxiv:0712.2610
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In a recent note (arXiv:0711.4930[hep-th]) Ito and Seiler claim that there is a 'missing link' in the derivation in arXiv:0707.2179[hep-th] by the present author; namely, that no proof of a certain inequality used there is given at weak coupling. Here it is pointed out that in fact no such missing link is present. The argument in 0707.2179 is, among other things, specifically constructed so that the inequality in question is invoked {\it only} at strong coupling, where it is easily proven. Underlying the mangling of the argument in 0707.2179 by Ito and Seiler are their incorrect statements concerning the dependence of the potential-moving decimation procedures used in 0707.2179 on space-time dimensionality and other decimation parameters.
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arxiv:0712.2620
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Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes of compact subsets of Euclidean space $\R^d$. However, the complexities of these methods scale up exponentially with d, which makes them impractical in medium or high dimensions, even for handling low-dimensional submanifolds. In this paper, we introduce a novel approach that stands in-between classical reconstruction and topological estimation, and whose complexity scales up with the intrinsic dimension of the data. Specifically, when the data points are sufficiently densely sampled from a smooth $m$-submanifold of $\R^d$, our method retrieves the homology of the submanifold in time at most $c(m)n^5$, where $n$ is the size of the input and $c(m)$ is a constant depending solely on $m$. It can also provably well handle a wide range of compact subsets of $\R^d$, though with worse complexities. Along the way to proving the correctness of our algorithm, we obtain new results on \v{C}ech, Rips, and witness complex filtrations in Euclidean spaces.
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arxiv:0712.2638
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We apply a PDE-based method to deduce the critical time and the size of the giant component of the ``triangle percolation'' on the Erd\H{o}s-R\'enyi random graph process investigated by Palla, Der\'enyi and Vicsek
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arxiv:0712.2646
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We study the layer of electrons on bare strange star surfaces, taking the Dirac exchange-energy into account. Because electrons are fermions, the electron wave function must be of exchange-antisymmetry. The Dirac exchange-energy originates, consequently, from the exchange-antisymmetry of electron wave functions. This consideration may result in changing the electron distribution and the electric field on the surface of bare strange star. The strong magnetic field effect on the structures of the electrospheres is also discussed.
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arxiv:0712.2650
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In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (\textit{ANS}). In order to do so, we first introduce the scaling invariant Besov-Sobolev type spaces, $B^{-1+\frac{2}{p},{1/2}}_{p}$ and $B^{-1+\frac{2}{p},{1/2}}_{p}(T)$, $p\geq2$. Then, we prove the global wellposedness for (\textit{ANS}) provided the initial data are sufficient small compared to the horizontal viscosity in some suitable sense, which is stronger than $B^{-1+\frac{2}{p},{1/2}}_{p}$ norm. In particular, our results imply the global wellposedness of (\textit{ANS}) with high oscillatory initial data.
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arxiv:0712.2652
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Neutron matter at low density is studied within the hole-line expansion. Calculations are performed in the range of Fermi momentum $k_F$ between 0.4 and 0.8 fm$^{-1}$. It is found that the Equation of State is determined by the $^1S_0$ channel only, the three-body forces contribution is quite small, the effect of the single particle potential is negligible and the three hole-line contribution is below 5% of the total energy and indeed vanishing small at the lowest densities. Despite the unitary limit is actually never reached, the total energy stays very close to one half of the free gas value throughout the considered density range. A rank one separable representation of the bare NN interaction, which reproduces the physical scattering length and effective range, gives results almost indistinguishable from the full Brueckner G-matrix calculations with a realistic force. The extension of the calculations below $k_F = 0.4$ fm$^{-1}$ does not indicate any pathological behavior of the neutron Equation of State.
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arxiv:0712.2662
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Generalized quantum measurements (POVMs or POMs) are important for optimally extracting information for quantum communication and computation. The standard realization via the Neumark extension requires extensive resources in the form of operations in an extended Hilbert space. For an arbitrary measurement, we show how to construct a binary search tree with a depth logarithmic in the number of possible outcomes. This could be implemented experimentally by coupling the measured quantum system to a probe qubit which is measured, and then iterating.
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arxiv:0712.2665
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We discuss the relic abundance of massive long lived colored particles with mass of the order of 1 TeV. We first examine the case where the massive colored particles have the standard color only. Next we consider the "Quirk Model" suggested by M. Luty, in which the colored particles transform under an additional non-abelian gauge group with a scale much smaller than the particles' mass. In both cases, the relic abundance is reduced via a "late" hadronic annihilation stage. In the second case the relic Quirks bind to ordinary quarks forming fractional charged objects and also anomalous heavy isotopes, and the bounds on the relic abundance become extremely severe. The force between Quirks, however, has a new confining part that manifests via macroscopic strings and the resulting efficient "very late" annihilations reduce the relic abundance to acceptable levels. The prospects of creating and detecting such particles at LHC and the fate of the particles created are discussed.
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arxiv:0712.2681
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We show that temporal two-photon interference effects involving the signal and idler photons created by parametric down-conversion can be fully characterized in terms of the variations of two length parameters--called the biphoton path-length difference and the biphoton path-asymmetry- length difference--which we construct using the six different length parameters that a general two-photon interference experiment involves. We perform an experiment in which the effects of the variations of these two parameters can be independently controlled and studied. In our experimental setup, which does not involve mixing of signal and idler photons at a beam splitter, we further report observations of Hong-Ou-Mandel- (HOM-)like effects both in coincidence and in one-photon count rates. As an important consequence, we argue that the HOM and the HOM-like effects are best described as observations of how two-photon coherence changes as a function of the biphoton path- asymmetry-length difference.
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arxiv:0712.2735
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Data from LEP2 on hadron production in gamma gamma interactions at high pT exceed the predictions of QCD by about an order of magnitude. The amplitude for the process is asymptotically proportional to the sum of the squares of the charges of quarks. The data are suggestive of models where quarks have unit charges, or larger. Unequivocal tests could be made with the ILC or CLIC, but a plasma wakefield e-e- collider might provide the most affordable option.
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arxiv:0712.2744
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We investigate the interplay of the electronic and structural transition in La$_{0.2}$Sr$_{0.8}$MnO$_{3}$. The transport and specific heat measurements exhibit unusual evolutions and signature of a first order phase transition around 265 K. Mn K-edge extended $x$-ray absorption fine structure results reveal distortion in the MnO$_6$ octahedra even in the cubic phase and a remarkable evolution of the distortion across the phase transition. These results manifest the importance of fluctuations in Mn 3$d$ orbital occupancy and disorder in their electronic properties, which may help in understanding the orbital and spin ordering proposed in these systems.
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arxiv:0712.2746
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The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. The ``no-go'' result is extended to the investigation of point transformations (admissible transformations, equivalence transformations, Lie symmetries) and Lie reductions of the determining equations for the nonclassical symmetries. Transformations linearizing the determining equations are obtained in the general case and under different additional constraints. A nontrivial example illustrating applications of reduction operators to finding exact solutions of equations from the class under consideration is presented. An observed connection between reduction operators and Darboux transformations is discussed.
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arxiv:0712.2764
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Let G be the product of an abelian variety and a torus defined over a number field K. Let R be a K-rational point on G of infinite order. Call n_R the number of connected components of the smallest algebraic K-subgroup of G to which R belongs. We prove that n_R is the greatest positive integer which divides the order of (R mod p) for all but finitely many primes p of K. Furthermore, let m>0 be a multiple of n_R and let S be a finite set of rational primes. Then there exists a positive Dirichlet density of primes p of K such that for every l in S the l-adic valuation of the order of (R mod p) equals v_l(m).
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arxiv:0712.2812
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We use the Gutzwiller method to investigate the importance of the on-site Coulomb interaction in graphene. We apply it to Hubbard Hamiltonian to study the renormalization of the kinetic energy in graphene due to the on-site Coulomb interaction. We find that a reasonable strength of the interaction has a very weak effect in reducing the kinetic energy. Hence we predict that the Brinkmann-Rice metal-insulator transition in graphene is not possible. The effect is understood in terms of the high kinetic energy in graphene.
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arxiv:0712.2836
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Any complete theory of physical reality must allow for the ubiquitous phenomenon of subjective experience at some level, or risk being conceptually incoherent. However, as long as the ontological status of subjectivity itself remains unresolved, the topic will be seen as more within the purview of philosophy than of physics. Towards a resolution of this issue within empirically motivated physical theory, this article introduces an operational definition that ultilizes the general consensus that subjective mental states, whatever else is controversial about them, at least correlate in some way to physical states. It is shown here that implementing this underappreciated assumption within the framework of a physical theory in fact leads to wide-ranging consequences. In particular, a correlation requires there exist a well-defined mapping from a space of subjective mental states onto a space of information-bearing elements of some physical theory. Given the peculiar nature of subjective states as inherently private appearances, any empirical identification of states must be performed by the experiencing subject. It is argued that such an operationally defined 'self-measuring' act leads unavoidably to an 'uncertainty principle' that is analogous in some intriguing ways to Heisenberg's principle for quantum mechanics. A model is then introduced for subjective states as algorithmically incomputable numbers. Additionaally, an inequality similar to Bell's theorem may be derived, indicating an analogy with the violations of local reality and the ontology of observables within quantum mechanics.
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arxiv:0712.2873
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We provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for an SOS polynomial that proves simultaneous contractibility of a finite set of matrices. We provide a bound on the quality of the approximation that unifies several earlier results and is independent of the number of matrices. Additionally, we present a comparison between our approximation scheme and earlier techniques, including the use of common quadratic Lyapunov functions and a method based on matrix liftings. Theoretical results and numerical investigations show that our approach yields tighter approximations.
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arxiv:0712.2887
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In 2007 Mark I. Gorenstein celebrated his 60th birthday. This report is dedicated to Mark and it sketches the results obtained during the past ten years of our collaboration and friendship. They concern search for and study of the onset of deconfinement in high energy nucleus-nucleus collisions.
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arxiv:0712.3001
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We prove that, for any g greater or equal than 3, a matrix g x 5 with tropical rank 3 has Kapranov rank 3.
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arxiv:0712.3007
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QMA (Quantum Merlin-Arthur) is the quantum analogue of the class NP. There are a few QMA-complete problems, most notably the ``Local Hamiltonian'' problem introduced by Kitaev. In this dissertation we show some new QMA-complete problems. The first one is ``Consistency of Local Density Matrices'': given several density matrices describing different (constant-size) subsets of an n-qubit system, decide whether these are consistent with a single global state. This problem was first suggested by Aharonov. We show that it is QMA-complete, via an oracle reduction from Local Hamiltonian. This uses algorithms for convex optimization with a membership oracle, due to Yudin and Nemirovskii. Next we show that two problems from quantum chemistry, ``Fermionic Local Hamiltonian'' and ``N-representability,'' are QMA-complete. These problems arise in calculating the ground state energies of molecular systems. N-representability is a key component in recently developed numerical methods using the contracted Schrodinger equation. Although these problems have been studied since the 1960's, it is only recently that the theory of quantum computation has allowed us to properly characterize their complexity. Finally, we study some special cases of the Consistency problem, pertaining to 1-dimensional and ``stoquastic'' systems. We also give an alternative proof of a result due to Jaynes: whenever local density matrices are consistent, they are consistent with a Gibbs state.
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arxiv:0712.3041
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Let M and \bar M be n-dimensional manifolds equipped with suitable Borel probability measures \rho and \bar\rho. Ma, Trudinger & Wang gave sufficient conditions on a transportation cost c \in C^4(M \times \bar M) to guarantee smoothness of the optimal map pushing \rho forward to \bar\rho; the necessity of these conditions was deduced by Loeper. The present manuscript shows the form of these conditions to be largely dictated by the covariance of the question; it expresses them via non-negativity of the sectional curvature of certain null-planes in a novel but natural pseudo-Riemannian geometry which the cost c induces on the product space M \times \bar M. H\"older continuity of optimal maps was established for rougher mass distributions by Loeper, still relying on a key result of Trudinger & Wang which required certain structure on the domains and the cost. We go on to develop this theory for mass distributions on differentiable manifolds -- recovering Loeper's Riemannian examples such as the round sphere as particular cases -- give a direct proof of the key result mentioned above, and revise Loeper's H\"older continuity argument to make it logically independent of all earlier works, while extending it to less restricted geometries and cost functions even for subdomains M and \bar M of R^n. We also give new examples of geometries satisfying the hypotheses -- obtained using submersions and tensor products -- and some connections to spacelike Lagrangian submanifolds in symplectic geometry.
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arxiv:0712.3077
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We present the properties of active galactic nuclei (AGN) selected by optical variability in the Subaru/XMM-Newton Deep Field (SXDF). Based on the locations of variable components and light curves, 211 optically variable AGN were reliably selected. We made three AGN samples; X-ray detected optically non-variable AGN (XA), X-ray detected optically variable AGN (XVA), and X-ray undetected optically variable AGN (VA). In the VA sample, we found a bimodal distribution of the ratio between the variable component flux and the host flux. One of these two components in the distribution, a class of AGN with a faint variable component $i'_{\rm{vari}}\sim25$ mag in bright host galaxies $i'\sim21$ mag, is not seen in the XVA sample. These AGN are expected to have low Eddington ratios if we naively consider a correlation between bulge luminosity and black hole mass. These galaxies have photometric redshifts $z_{\rm{photo}}\sim0.5$ and we infer that they are low-luminosity AGN with radiatively inefficient accretion flows (RIAFs). The properties of the XVA and VA objects and the differences from those of the XA objects can be explained within the unified scheme for AGN. Optical variability selection for AGN is an independent method and could provide a complementary AGN sample which even deep X-ray surveys have not found.
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arxiv:0712.3106
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We study the stellar and star formation (SF) properties of the host galaxies of 58 X-ray selected AGN in the GOODS portion of the Chandra Deep Field South (CDF-S) region at z~0.5-1.4. The AGN are selected such that their rest-frame UV to near-IR SEDs are dominated by stellar emission, i.e., they show a prominent 1.6micron bump, thus minimizing the AGN emission 'contamination'. This AGN population comprises approximately 50% of the X-ray selected AGN at these redshifts. Using models of stellar and dust emission we model their SEDs to derive stellar masses (M*) and total (UV+IR) star formation rates (SFR). AGN reside in the most massive galaxies at the redshifts probed here. Their characteristic stellar masses (M*~7.8x10^10 Msun and M*~1.2x10^11 Msun at median z of 0.67 and 1.07, respectively) appear to be representative of the X-ray selected AGN population at these redshifts, and are intermediate between those of local type 2 AGN and high redshift (z~2) AGN. The inferred black hole masses (MBH~ 2x10^8 Msun) of typical AGN are similar to those of optically identified quasars at similar redshifts. Since the AGN in our sample are much less luminous (L(2-10keV)<10^44 erg/s) than quasars, typical AGN have low Eddington ratios (eta~0.01-0.001). This suggests that, at least at intermediate z, the cosmic AGN 'downsizing' is due to both a decrease in the characteristic stellar mass of typical host galaxies, and less efficient accretion. Finally there is no strong evidence in AGN host galaxies for either highly suppressed SF (expected if AGN played a role in quenching SF) or elevated SF when compared to mass selected (i.e., IRAC-selected) galaxies of similar stellar masses and redshifts. This may be explained by the fact that galaxies with M*~5x 10^10 - 5x10^11 Msun are still being assembled at the redshifts probed here.
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arxiv:0712.3121
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Let $G$ be a finitely generated group and $X$ its Cayley graph with respect to a finite, symmetric generating set $S$. Furthermore, let $H$ be a finite group and $H \wr G$ the lamplighter group (wreath product) over $G$ with group of "lamps" $H$. We show that the spectral measure (Plancherel measure) of any symmetric "switch--walk--switch" random walk on $H \wr G$ coincides with the expected spectral measure (integrated density of states) of the random walk with absorbing boundary on the cluster of the group identity for Bernoulli site percolation on $X$ with parameter $p = 1/|H|$. The return probabilities of the lamplighter random walk coincide with the expected (annealed) return probabilites on the percolation cluster. In particular, if the clusters of percolation with parameter $p$ are almost surely finite then the spectrum of the lamplighter group is pure point. This generalizes results of Grigorchuk and Zuk, resp. Dicks and Schick regarding the case when $G$ is infinite cyclic. Analogous results relate bond percolation with another lamplighter random walk. In general, the integrated density of states of site (or bond) percolation with arbitrary parameter $p$ is always related with the Plancherel measure of a convolution operator by a signed measure on $H \wr G$, where $H = Z$ or another suitable group.
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arxiv:0712.3135
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Employing the Monte-Carlo method and the exact diagonalization, we have investigated the temperature dependence of the thermoelectric power (TEP) for the double exchange model in the dilute carrier concentration limit. We have found that the TEP follows the Heikes formula in the high temperature regime, whereas, in the intermediate temperature regime, the TEP is suppressed by the exchange coupling between itinerant electrons and local spins. In the low temperature regime, the TEP exhibits an anomalous peak and dip feature near the magnetic transition temperature $T_C$ which can be understood based on the magnetic polaron state. We have also found that the TEP, in the presence of the magnetic field, shows the positive magnetothermoelectric power near $T_C$.
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arxiv:0712.3161
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In an earlier paper, we studied solutions g to convolution equations of the form a_d*g^{*d}+a_{d-1}*g^{*(d-1)}+...+a_1*g+a_0=0, where a_0, ..., a_d are given arithmetic functions associated with Dirichlet series which converge on some right half plane, and also g is required to be such a function. In this article, we extend our previous results to multidimensional general Dirichlet series of the form \sum_{x\in X} f(x) e^{-sx} (s in C^k), where X is an additive subsemigroup of [0,\infty)^k. If X is discrete and a certain solvability criterion is satisfied, we determine solutions by an elementary recursive approach, adapting an idea of Feckan. The solution of the general case leads us to a more comprehensive question: Let X be an additive subsemigroup of a pointed, closed convex cone C in R^k. Can we find a complex Radon measure on X whose Laplace transform satisfies a given polynomial equation whose coefficients are Laplace transforms of such measures?
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arxiv:0712.3172
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Based on the amplitude behavior of quantum Rabi oscillation driven by a coherent field we show that there exists an upper bound to the number of logical operation performed on any single qubit within one error-correction period of a quantum computation. We introduce a parameter to depict the maximum of this number and estimate its decoherence limit. The analysis shows that a generally accepted error-rate threshold of quantum logic gates limits the parameter to so small a number that even a double of fault-tolerant Toffoli gates can hardly be implemented reliably within one error-correction period. This result suggests that the design of feasible fault-tolerant quantum circuits is still an arduous task.
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arxiv:0712.3197
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We present the first observation of planet-induced stellar X-ray activity, identified for the HD 179949 system, using Chandra / ACIS-S. The HD 179949 system consists of a close-in giant planet orbiting an F9V star. Previous ground-based observations already showed enhancements in Ca II K in phase with the planetary orbit. We find an ~30% increase in the X-ray flux over quiescent levels coincident with the phase of the Ca II enhancements. There is also a trend for the emission to be hotter at increased fluxes, confirmed by modeling, showing the enhancement at ~1 keV compared to ~0.4 keV for the background star.
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arxiv:0712.3270
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We study thermodynamics of the Schwarzschild-de Sitter black hole in five dimensions by introducing two temperatures based on the standard and Bousso-Hawking normalizations. We use the first-law of thermodynamics to derive thermodynamic quantities. The two temperatures indicate that the Nariai black hole is thermodynamically unstable. However, it seems that black hole thermodynamics favors the standard normalization, and does not favor the Bousso-Hawking normalization.
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arxiv:0712.3315
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A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.
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arxiv:0712.3329
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A compressed full-text self-index represents a text in a compressed form and still answers queries efficiently. This technology represents a breakthrough over the text indexing techniques of the previous decade, whose indexes required several times the size of the text. Although it is relatively new, this technology has matured up to a point where theoretical research is giving way to practical developments. Nonetheless this requires significant programming skills, a deep engineering effort, and a strong algorithmic background to dig into the research results. To date only isolated implementations and focused comparisons of compressed indexes have been reported, and they missed a common API, which prevented their re-use or deployment within other applications. The goal of this paper is to fill this gap. First, we present the existing implementations of compressed indexes from a practitioner's point of view. Second, we introduce the Pizza&Chili site, which offers tuned implementations and a standardized API for the most successful compressed full-text self-indexes, together with effective testbeds and scripts for their automatic validation and test. Third, we show the results of our extensive experiments on these codes with the aim of demonstrating the practical relevance of this novel and exciting technology.
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arxiv:0712.3360
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RZBENCH is a benchmark suite that was specifically developed to reflect the requirements of scientific supercomputer users at the University of Erlangen-Nuremberg (FAU). It comprises a number of application and low-level codes under a common build infrastructure that fosters maintainability and expandability. This paper reviews the structure of the suite and briefly introduces the most relevant benchmarks. In addition, some widely known standard benchmark codes are reviewed in order to emphasize the need for a critical review of often-cited performance results. Benchmark data is presented for the HLRB-II at LRZ Munich and a local InfiniBand Woodcrest cluster as well as two uncommon system architectures: A bandwidth-optimized InfiniBand cluster based on single socket nodes ("Port Townsend") and an early version of Sun's highly threaded T2 architecture ("Niagara 2").
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arxiv:0712.3389
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A particular form for the quantum indeterminacy of relative spacetime position of events is derived from the limits of measurement possible with Planck wavelength radiation. The indeterminacy predicts fluctuations from a classically defined geometry in the form of ``holographic noise'' whose spatial character, absolute normalization, and spectrum are predicted with no parameters. The noise has a distinctive transverse spatial shear signature, and a flat power spectral density given by the Planck time. An interferometer signal displays noise due to the uncertainty of relative positions of reflection events. The noise corresponds to an accumulation of phase offset with time that mimics a random walk of those optical elements that change the orientation of a wavefront. It only appears in measurements that compare transverse positions, and does not appear at all in purely radial position measurements. A lower bound on holographic noise follows from a covariant upper bound on gravitational entropy. The predicted holographic noise spectrum is estimated to be comparable to measured noise in the currently operating interferometer GEO600. Because of its transverse character, holographic noise is reduced relative to gravitational wave effects in other interferometer designs, such as LIGO, where beam power is much less in the beamsplitter than in the arms.
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arxiv:0712.3419
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We propose a description of the vortex dynamics in YBCO films from the critical to the normal states. This description supposes that the vortex motion is thermally activated along the twin boundaries of the films. The discontinuity observed in the current-voltage curves at the transition to the normal state is explained by the sudden increase in the dissipated power rate due to vortex depinning. However, near the critical temperature, this phenomenon does not occur because the vortex activation energy is near zero. We also show how the current at the transition to the normal state can be computed from the current-voltage curves measured at low currents. The predictions of this description are compared to the data published by Gonzalez et al. [Phys.Rev.B68,054514 (2003)].
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arxiv:0712.3446
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The spin chain formulation of the operator spectrum of the N=4 super Yang-Mills theory is haunted by the problem of ``wrapping'', i.e. the inapplicability of the formalism for short spin chain length at high loop-order. The first instance of wrapping concerns the fourth anomalous dimension of the Konishi operator. While we do not obtain this number yet, we lay out an operational scheme for its calculation. The approach passes through a five- and six-loop sector. We show that all but one of the Feynman integrals from this sector are related to five master graphs which ought to be calculable by the method of partial integration. The remaining supergraph is argued to be vanishing or finite; a numerical treatment should be possible. The number of numerator terms remains small even if a further four-loop sector is included. There is no need for infrared rearrangements.
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arxiv:0712.3513
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Using the light-cone gauge approach to relativistic field dynamics, we study arbitrary spin fermionic and bosonic fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for totally symmetric and mixed-symmetry massive and massless fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives. These restrictions provide a complete classification of parity invariant cubic interaction vertices for totally symmetric fermionic and bosonic fields. As an example of application of the light-cone formalism, we obtain simple expressions for the Yang-Mills and gravitational interactions of massive arbitrary spin fermionic fields. For some particular cases, using our light-cone cubic vertices, we discuss the corresponding manifestly Lorentz invariant and on-shell gauge invariant cubic vertices.
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arxiv:0712.3526
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We study the diluted Ising ferromagnet on the Bethe lattice as a case study for the application of the cavity method to problems with Griffiths-McCoy singularities. Specifically, we are able to make much progress at infinite coupling where we compute, from the cavity method, the density of Lee-Yang zeroes in the paramagnetic Griffiths region as well as the properties of the phase transition to the ferromagnet. This phase transition is itself of a Griffiths-McCoy character albeit with a power law distribution of cluster sizes.
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arxiv:0712.3540
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Gauss-Bonnet gravity provides one of the most promising frameworks to study curvature corrections to the Einstein action in supersymmetric string theories, while avoiding ghosts and keeping second order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for long, the Kerr-Gauss-Bonnet metric is missing. In this paper, a five dimensional Gauss-Bonnet approximation is analytically derived for spinning black holes and the related thermodynamical properties are briefly outlined.
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arxiv:0712.3546
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In this note we compute exact boundary spectra for D-instantons in sigma-models on the supergroup PSL(2|2). Our results are obtained through an explicit summation of the perturbative expansion for conformal dimensions to all orders in the curvature radius. The analysis exploits several remarkable properties of the perturbation series that arises from rescalings of the metric on PSL(2|2) relative to a fixed Wess-Zumino term. According to Berkovits, Vafa and Witten, the models are relevant in the context of string theory on AdS3 with non-vanishing RR-flux. The note concludes with a number of comments on various possible generalizations to other supergroups and higher dimensional supercoset theories.
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arxiv:0712.3549
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This paper proposes an axiomatic for Cyclic Foam Topological Field theories. That is Topological Field theories, corresponding to String theories, where particles are arbitrary graphs. World surfaces in this case are two-manifolds with one-dimensional singularities. We proved that Cyclic Foam Topological Field theories one-to-one correspond to graph-Cardy-Frobenius algebras, that are families $(A,B_\star,\phi)$, where $A=\{A^s|s\in S\}$ are families of commutative associative Frobenius algebras, $B_\star = \bigoplus_{\sigma\in\Sigma} B_\sigma$ is an graduated by graphes, associative algebras of Frobenius type and $\phi=\{\phi_\sigma^s: A^s\to (B_\sigma)|s\in S,\sigma\in \Sigma\}$ is a family of special representations. There are constructed examples of Cyclic Foam Topological Field theories and its graph-Cardy-Frobenius algebras
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arxiv:0712.3557
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The random sequential adsorption (RSA) model is modified to describe damage and crack accumulation. The exclusion for object deposition (for damaged region formation) is not for the whole object, as in the standard RSA, but only for the initial point (or higher-dimensional defect) from which the damaged region or crack initiates. The one-dimensional variant of the model is solved exactly.
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arxiv:0712.3567
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We propose a simple model to analyze the traffic of droplets in microfluidic ``dual networks''. Such functional networks which consist of two types of channels, namely those accessible or forbidden to droplets, often display a complex behavior characteristic of dynamical systems. By focusing on three recently proposed configurations, we offer an explanation for their remarkable behavior. Additionally, the model allows us to predict the behavior in different parameter regimes. A verification will clarify fundamental issues, such as the network symmetry, the role of the driving conditions, and of the occurrence of reversible behavior. The model lends itself to a fast numerical implementation, thus can help designing devices, identifying parameter windows where the behavior is sufficiently robust for a devices to be practically useful, and exploring new functionalities.
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arxiv:0712.3591
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Using full-disk observations obtained with the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) spacecraft, we present variations of the solar acoustic mode frequencies caused by the solar activity cycle. High-degree (100 < l < 900) solar acoustic modes were analyzed using global helioseismology analysis techniques over most of solar cycle 23. We followed the methodology described in details in Korzennik, Rabello-Soares and Schou (2004) to infer unbiased estimates of high-degree mode parameters (see also Rabello-Soares, Korzennik and Schou, 2006). We have removed most of the known instrumental and observational effects that affect specifically high-degree modes. We show that the high-degree changes are in good agreement with the medium-degree results, except for years when the instrument was highly defocused. We analyzed and discuss the effect of defocusing on high degree estimation. Our results for high-degree modes confirm that the frequency shift scaled by the relative mode inertia is a function of frequency and it is independent of degree.
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arxiv:0712.3608
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We determine the equation of state of stoichiometric FeO employing the diffusion Monte Carlo method. The fermionic nodes are fixed to those of a wave function having the form of a single Slater determinant. The calculated ambient pressure properties (lattice constant, bulk modulus and cohesive energy) agree very well with available experimental data. At approximately 65 GPa, the lattice structure is found to change from rocksalt type (B1) to NiAs based (inverse B8).
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arxiv:0712.3610
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The hysteretic ac loss of a current-carrying conductor in which multiple superconducting strips are polygonally arranged around a cylindrical former is theoretically investigated as a model of superconducting cables. Using the critical state model, we analytically derive the ac loss $Q_n$ of a total of $n$ strips. The normalized loss $Q_n/Q_1$ is determined by the number of strips $n$ and the ratio of the strip width $2w$ to the diameter $2R$ of the cylindrical former. When $n>> 1$ and $w/R<< 1$, the behavior of $Q_n$ is similar to that of an infinite array of coplanar strips.
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arxiv:0712.3612
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Shannon's Capacity Theorem is the main concept behind the Theory of Communication. It says that if the amount of information contained in a signal is smaller than the channel capacity of a physical media of communication, it can be transmitted with arbitrarily small probability of error. This theorem is usually applicable to ideal channels of communication in which the information to be transmitted does not alter the passive characteristics of the channel that basically tries to reproduce the source of information. For an {\it active channel}, a network formed by elements that are dynamical systems (such as neurons, chaotic or periodic oscillators), it is unclear if such theorem is applicable, once an active channel can adapt to the input of a signal, altering its capacity. To shed light into this matter, we show, among other results, how to calculate the information capacity of an active channel of communication. Then, we show that the {\it channel capacity} depends on whether the active channel is self-excitable or not and that, contrary to a current belief, desynchronization can provide an environment in which large amounts of information can be transmitted in a channel that is self-excitable. An interesting case of a self-excitable active channel is a network of electrically connected Hindmarsh-Rose chaotic neurons.
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arxiv:0712.3770
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Recently a covariant entropy conjecture has been proposed for dynamical horizons. We apply this conjecture to concordance cosmological models, namely, those cosmological models filled with perfect fluids, in the presence of a positive cosmological constant. As a result, we find this conjecture has a severe constraint power. Not only does this conjecture rule out those cosmological models disfavored by the anthropic principle, but also it imposes an upper bound $10^{-60}$ on the cosmological constant for our own universe, which thus provides an alternative macroscopic perspective for understanding the long-standing cosmological constant problem.
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arxiv:0712.3821
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The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.
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arxiv:0712.3856
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The interaction of electron-hole pairs with lattice vibrations exhibits a wealth of intriguing physical phenomena. The Kohn anomaly is a renowned example where electron-phonon coupling leads to non-analytic phonon dispersion at specific momentum nesting the Fermi surface. Here we report evidence of another type of phonon anomaly discovered by low temperature Raman spectroscopy in bilayer graphene where the charge density is modulated by the electric field effect. This anomaly, arising from charge-tunable modulations of particle-hole pairs that are resonantly coupled to lattice vibrations, is predicted to exhibit a logarithmic divergence in the long-wavelength optical-phonon energy. In a non-uniform bilayer of graphene, the logarithmic divergence is abated by charge density inhomogeneity leaving as a vestige an anomalous phonon softening. The observed softening marks the first confirmation of the phonon anomaly as a key signature of the resonant deformation-potential electron-phonon coupling. The high sensitivity of the phonon softening to charge density non-uniformity creates significant venues to explore the interplay between fundamental interactions and disorder in the atomic layers.
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arxiv:0712.3879
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We propose and demonstrate experimentally the concept of the annular interdigital transducer that focuses acoustic waves on the surface of a piezoelectric material to a single, diffraction-limited, spot. The shape of the transducing fingers follows the wave surface. Experiments conducted on lithium niobate substrates evidence that the generated surface waves converge to the center of the transducer, producing a spot that shows a large concentration of acoustic energy. This concept is of practical significance to design new intense microacoustic sources, for instance for enhanced acouto-optical interactions.
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arxiv:0712.3899
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The effects of edge irregularity and mixed edge shapes on the characteristics of graphene nanoribbon transistors are examined by self-consistent atomistic simulations based on the non-equilibrium Green's function formalism. The minimal leakage current increases due to the localized states induced in the band gap, and the on-current decreases due to smaller quantum transmission and the self-consistent electrostatic effect in general. Although the ratio between the on-current and minimal leakage current decreases, the transistor still switches even in the presence of edge roughness. The variation between devices, however, can be large, especially for a short channel length.
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arxiv:0712.3928
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We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm. These relations suffice, as we shall demonstrate with a few examples, to write down enough relations in Bloch's integral higher Chow group CH^2(F,3) for certain number fields F to detect torsion cycles. Using the regulator map to Deligne cohomology, one can check the non-triviality of the torsion cycles thus obtained. Using this combination of methods, we obtain explicit higher Chow cycles generating the integral motivic cohomology groups of some number fields.
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arxiv:0712.3987
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We consider functions $f:B\to\Rset$ that obey tropical analogs of classical Pl\"ucker relations on minors of a matrix. The most general set $B$ that we deal with in this paper is of the form $\{x\in \Zset^n\colon 0\le x\le a, m\le x_1+...+x_n\le m'\}$ (a rectangular integer box ``truncated from below and above''). We construct a basis for the set $\Tscr$ of tropical Pl\"ucker functions on $B$, a subset $\Bscr\subseteq B$ such that the restriction map $\Tscr\to\Rset^\Bscr$ is bijective. Also we characterize, in terms of the restriction to the basis, the classes of submodular, so-called skew-submodular, and discrete concave functions in $\Tscr$, discuss a tropical analogue of the Laurentness property, and present other results.
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arxiv:0712.3996
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We calculate the mean free path of protons and neutrons in symmetric and asymmetric nuclear matter, based on microscopic in-medium nucleon-nucleon cross sections. Those are obtained from calculations of the G-matrix including relativistic "Dirac" effects. The dependence of the mean free path on energy and isospin asymmetry is discussed. We conclude by suggesting possible ways our microscopic predictions may be helpful in conjunction with studies of rare isotopes.
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arxiv:0712.4028
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We study self-consistent cosmological solutions for an Einstein universe in a graph-based induced gravity model. Especially, we demonstrate specific results for cycle graphs.
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arxiv:0712.4055
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Sums of the form add((-1)^n q^(n(n-1)/2) x^n, n>=0) are called partial theta functions. In his lost notebook, Ramanujan recorded many identities for those functions. In 2003, Warnaar found an elegant formula for a sum of two partial theta functions. Subsequently, Andrews and Warnaar established a similar result for the product of two partial theta functions. In this note, I discuss the relation between the Andrews-Warnaar identity and the (1986) product formula due to Gasper and Rahman. I employ nonterminating extension of Sears-Carlitz transformation for 3\phi_2 to provide a new elegant proof for a companion identity for the difference of two partial theta series. This difference formula first appeared in the work of Schilling-Warnaar (2002). Finally, I show that Schilling-Warnnar (2002) and Warnaar (2003) formulas are, in fact, equivalent.
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arxiv:0712.4087
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The impact of extreme events across the globe is extraordinary which continues to handicap the advancement of the struggling developing societies and threatens most of the industrialized countries in the globe. Various fields of Information and Communication Technology have widely been used for efficient disaster management; but only to a limited extent though, there is a tremendous potential for increasing efficiency and effectiveness in coping with disasters with the utilization of emerging wireless network technologies. Early warning, response to the particular situation and proper recovery are among the main focuses of an efficient disaster management system today. Considering these aspects, in this paper we propose a framework for developing an efficient Disaster Management Communications and Information System (DMCIS) which is basically benefited by the exploitation of the emerging wireless network technologies combined with other networking and data processing technologies.
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arxiv:0712.4172
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In this paper, knotted objects (RS vortices) in the theory of topological phase singularity in electromagnetic field have been investigated in details. By using the $\phi$-mapping topological current theory proposed by Prof. Duan, we rewrite the topological current form of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum of the linking and self-linking numbers of the knotted RS vortices. Furthermore, the conservation of the Hopf invariant in the splitting, the mergence and the intersection processes of knotted RS vortices is also discussed.
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arxiv:0712.4198
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Scalar top studies at the ILC are reviewed from initial sensitivity studies to a new precision mass determination method.
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arxiv:0712.4207
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In an earlier work, the statistical physics associated with finite--temperature decoding of code ensembles, along with the relation to their random coding error exponents, were explored in a framework that is analogous to Derrida's random energy model (REM) of spin glasses, according to which the energy levels of the various spin configurations are independent random variables. The generalized REM (GREM) extends the REM in that it introduces correlations between energy levels in an hierarchical structure. In this paper, we explore some analogies between the behavior of the GREM and that of code ensembles which have parallel hierarchical structures. In particular, in analogy to the fact that the GREM may have different types of phase transition effects, depending on the parameters of the model, then the above--mentioned hierarchical code ensembles behave substantially differently in the various domains of the design parameters of these codes. We make an attempt to explore the insights that can be imported from the statistical mechanics of the GREM and be harnessed to serve for code design considerations and guidelines.
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arxiv:0712.4209
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We survey the definition of the radial Julia set of a meromorphic function (in fact, more generally, any "Ahlfors islands map"), and give a simple proof that the Hausdorff dimension of the reduced Julia set always coincides with the hyperbolic dimension.
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arxiv:0712.4267
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Integrability of the string worldsheet theory in AdS(5) x S(5) is related to the existence of a flat connection depending on the spectral parameter. The transfer matrix is the open-ended Wilson line of this flat connection. We study the product of transfer matrices in the near-flat space expansion of the AdS(5) x S(5) string theory in the pure spinor formalism. The natural operations on Wilson lines with insertions are described in terms of r- and s-matrices satisfying a generalized classical Yang-Baxter equation. The formalism is especially transparent for infinite or closed Wilson lines with simple gauge invariant insertions.
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arxiv:0712.4278
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Work published in Sky and Telescope in 2004 discusses Galileo's observations of the star Mizar. These observations raise questions regarding Galileo's assumptions about the universe and the conclusions he drew from his observations. Galileo would have expected Mizar to reveal annual parallax and thus provide evidence of Earth's motion, but Mizar shows no such parallax.
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arxiv:0712.4281
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In this paper we will show how to construct holomorphic L^{p}-functions on unbranched coverings of strongly pseudoconvex manifolds. Also, we prove some extension and approximation theorems for such functions.
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arxiv:0712.4302
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Numerical model of the peripheral circulation and dynamical model of the large vessels and the heart are discussed in this paper. They combined together into the global model of blood circulation. Some results of numerical simulations concerning matter transport through the human organism and heart diseases are represented in the end.
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arxiv:0712.4342
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