Hardness of Exact Distance Queries in Sparse Graphs Through Hub Labeling

A distance labeling scheme is an assignment of bit-labels to the vertices of an undirected, unweighted graph such that the distance between any pair of vertices can be decoded solely from their labels. An important class of distance labeling schemes is that of hub labelings, where a node $v \in G$ stores its distance to the so-called hubs $S_v \subseteq V$, chosen so that for any $u,v \in V$ there is $w \in S_u \cap S_v$ belonging to some shortest $uv$ path. Notice that for most existing graph classes, the best distance labelling constructions existing use at some point a hub labeling scheme at least as a key building block. Our interest lies in hub labelings of sparse graphs, i.e., those with $|E(G)| = O(n)$, for which we show a lowerbound of $\frac{n}{2^{O(\sqrt{\log n})}}$ for the average size of the hubsets. Additionally, we show a hub-labeling construction for sparse graphs of average size $O(\frac{n}{RS(n)^{c}})$ for some $0 < c < 1$, where $RS(n)$ is the so-called Ruzsa-Szemer{\'e}di function, linked to structure of induced matchings in dense graphs. This implies that further improving the lower bound on hub labeling size to $\frac{n}{2^{(\log n)^{o(1)}}}$ would require a breakthrough in the study of lower bounds on $RS(n)$, which have resisted substantial improvement in the last 70 years. For general distance labeling of sparse graphs, we show a lowerbound of $\frac{1}{2^{O(\sqrt{\log n})}} SumIndex(n)$, where $SumIndex(n)$ is the communication complexity of the Sum-Index problem over $Z_n$. Our results suggest that the best achievable hub-label size and distance-label size in sparse graphs may be $\Theta(\frac{n}{2^{(\log n)^c}})$ for some $0<c < 1$

Is My Exercise Partner Similar Enough? Partner Characteristics as a Moderator of the Köhler Effect in Exergames

Objective: Recent research has shown the Köhler motivation gain effect (working at a task with a more capable partner where one's performance is indispensable to the group) leads to greater effort in partnered exercise videogame play. The purpose of this article was to examine potential moderators of the Köhler effect by exploring dissimilarities in one's partner's appearance, namely, having an older partner (compared with a same-age partner) and having a heavier-weight partner (compared with a same-weight partner). Subjects and Methods: One hundred fifty-three male and female college students completed a series of plank exercises using the “EyeToy: Kinetic™” for the PlayStation® 2 (Sony, Tokyo, Japan). Participants first completed the exercises individually and, after a rest, completed the same exercises with a virtually present partner. Exercise persistence, subjective effort, self-efficacy beliefs, enjoyment, and intentions to exercise were recorded and analyzed. Results: A significant Köhler motivation gain was observed in all partner conditions (compared with individual controls) such that participants with a partner held the plank exercises longer (P<0.001) and reported higher subjective effort (P<0.01). These results were unmoderated by partner's age and weight, with one exception: Males tended to persist longer when paired with an obese partner (P=0.08). Conclusions: These results suggest that differences in age and weight do not attenuate the Köhler effect in exergames and may even strengthen it

Electronic Structure and Lattice dynamics of NaFeAs

The similarity of the electronic structures of NaFeAs and other Fe pnictides has been demonstrated on the basis of first-principle calculations. The global double-degeneracy of electronic bands along X-M and R-A direction indicates the instability of Fe pnictides and is explained on the basis of a tight-binding model. The de Haas-van Alphen parameters for the Fermi surface (FS) of NaFeAs have been calculated. A $\mathbf{Q}_{M}=(1/2,1/2,0)$ spin density wave (SDW) instead of a charge density wave (CDW) ground state is predicted based on the calculated generalized susceptibility $\chi(\mathbf{q})$ and a criterion derived from a restricted Hatree-Fock model. The strongest electron-phonon (e-p) coupling has been found to involve only As, Na z-direction vibration with linear-response calculations. A possible enhancement mechanism for e-p coupling due to correlation is suggested

Chemical weathering and provenance evolution of Holocene–Recent sediments from the Western Indus Shelf, Northern Arabian Sea inferred from physical and mineralogical properties

We present a multi-proxy mineral record based on X-ray diffraction and diffuse reflectance spectrophotometry analysis for two cores from the western Indus Shelf in order to reconstruct changing weathering intensities, sediment transport, and provenance variations since 13 ka. Core Indus-10 is located northwest of the Indus Canyon and exhibits fluctuations in smectite/(illite + chlorite) ratios that correlate with monsoon intensity. Higher smectite/(illite + chlorite) and lower illite crystallinity, normally associated with stronger weathering, peaked during the Early–Mid Holocene, the period of maximum summer monsoon. Hematite/goethite and magnetic susceptibility do not show clear co-variation, although they both increase at Indus-10 after 10 ka, as the monsoon weakened. At Indus-23, located on a clinoform just west of the canyon, hematite/goethite increased during a period of monsoon strengthening from 10 to 8 ka, consistent with increased seasonality and/or reworking of sediment deposited prior to or during the glacial maximum. After 2 ka terrigenous sediment accumulation rates in both cores increased together with redness and hematite/goethite, which we attribute to widespread cultivation of the floodplain triggering reworking, especially after 200 years ago. Over Holocene timescales sediment composition and mineralogy in two localities on the high-energy shelf were controlled by varying degrees of reworking, as well as climatically modulated chemical weathering

Rapid changes in ice core gas records Part 2: Understanding the rapid rise in atmospheric CO2 at the onset of the Bølling/Allerød

During the last glacial/interglacial transition the Earth's climate underwent rapid changes around 14.6 kyr ago. Temperature proxies from ice cores revealed the onset of the Bølling/Allerød (B/A) warm period in the north and the start of the Antarctic Cold Reversal in the south. Furthermore, the B/A is accompanied by a rapid sea level rise of about 20 m during meltwater pulse (MWP) 1A, whose exact timing is matter of current debate. In situ measured CO₂ in the EPICA Dome C (EDC) ice core also revealed a remarkable jump of 10&plusmn;1 ppmv in 230 yr at the same time. Allowing for the age distribution of CO₂ in firn we here show, that atmospheric CO₂ rose by 20–35 ppmv in less than 200 yr, which is a factor of 2–3.5 larger than the CO₂ signal recorded in situ in EDC. Based on the estimated airborne fraction of 0.17 of CO₂ we infer that 125 Pg of carbon need to be released to the atmosphere to produce such a peak. Most of the carbon might have been activated as consequence of continental shelf flooding during MWP-1A. This impact of rapid sea level rise on atmospheric CO₂ distinguishes the B/A from other Dansgaard/Oeschger events of the last 60 kyr, potentially defining the point of no return during the last deglaciation

Full counting statistics of heteronuclear molecules from Feshbach-assisted photo association

We study the effects of quantum statistics on the counting statistics of ultracold heteronuclear molecules formed by Feshbach-assisted photoassociation [Phys. Rev. Lett. {\bf 93}, 140405 (2004)]. Exploiting the formal similarities with sum frequency generation and using quantum optics methods we consider the cases where the molecules are formed from atoms out of two Bose-Einstein condensates, out of a Bose-Einstein condensate and a gas of degenerate fermions, and out of two degenerate Fermi gases with and without superfluidity. Bosons are treated in a single mode approximation and fermions in a degenerate model. In these approximations we can numerically solve the master equations describing the system's dynamics and thus we find the full counting statistics of the molecular modes. The full quantum dynamics calculations are complemented by mean field calculations and short time perturbative expansions. While the molecule production rates are very similar in all three cases at this level of approximation, differences show up in the counting statistics of the molecular fields. The intermediate field of closed-channel molecules is for short times second-order coherent if the molecules are formed from two Bose-Einstein condensates or a Bose-Fermi mixture. They show counting statistics similar to a thermal field if formed from two normal Fermi gases. The coherence properties of molecule formation in two superfluid Fermi gases are intermediate between the two previous cases. In all cases the final field of deeply-bound molecules is found to be twice as noisy as that of the intermediate state. This is a consequence of its coupling to the lossy optical cavity in our model, which acts as an input port for quantum noise, much like the situation in an optical beam splitter.Comment: replacement of earlier manuscript cond-mat/0508080 ''Feshbach-assisted photoassociation of ultracold heteronuclear molecules'' with minor revision

The QSO evolution derived from the HBQS and other complete QSO surveys

An ESO Key programme dedicated to an Homogeneous Bright QSO Survey (HBQS) has been completed. 327 QSOs (Mb<-23, 0.3<z<2.2) have been selected over 555 deg^2 with 15<B<18.75. For B<16.4 the QSO surface density turns out to be a factor 2.2 higher than what measured by the PG survey, corresponding to a surface density of 0.013+/-.006 deg^{-2}. If the Edinburgh QSO Survey is included, an overdensity of a factor 2.5 is observed, corresponding to a density of 0.016+/-0.005 deg^{-2}. In order to derive the QSO optical luminosity function (LF) we used Monte Carlo simulations that take into account of the selection criteria, photometric errors and QSO spectral slope distribution. The LF can be represented with a Pure Luminosity Evolution (L(z)\propto(1+z)^k) of a two power law both for q_0=0.5 and q_0=0.1. For q_0=0.5 k=3.26, slower than the previous Boyle's (1992) estimations of k=3.45. A flatter slope beta=-3.72 of the bright part of the LF is also required. The observed overdensity of bright QSOs is concentrated at z<0.6. It results that in the range 0.3<z<0.6 the luminosity function is flatter than observed at higher redshifts. In this redshift range, for Mb<-25, 32 QSOs are observed instead of 19 expected from our best-fit PLE model. This feature requires a luminosity dependent luminosity evolution in order to satisfactorily represent the data in the whole 0.3<z<2.2 interval.Comment: Invited talk in "Wide Field Spectroscopy" (20-24 May 1996, Athens), eds. M. Kontizas et al. 6 pages and 3 eps figures, LaTex file, uses epfs.sty and crckapb.sty (included

Carbon Isotope Constraints on the Deglacial CO2 Rise from Ice Cores

The stable carbon isotope ratio of atmospheric CO2 (d13Catm) is a key parameter in deciphering past carbon cycle changes. Here we present d13Catm data for the past 24,000 years derived from three independent records from two Antarctic ice cores. We conclude that a pronounced 0.3 per mil decrease in d13Catm during the early deglaciation can be best explained by upwelling of old, carbon-enriched waters in the Southern Ocean. Later in the deglaciation, regrowth of the terrestrial biosphere, changes in sea surface temperature, and ocean circulation governed the d13Catm evolution. During the Last Glacial Maximum, d13Catm and atmospheric CO2 concentration were essentially constant, which suggests that the carbon cycle was in dynamic equilibrium and that the net transfer of carbon to the deep ocean had occurred before then

Diffusion-Limited One-Species Reactions in the Bethe Lattice

We study the kinetics of diffusion-limited coalescence, A+A-->A, and annihilation, A+A-->0, in the Bethe lattice of coordination number z. Correlations build up over time so that the probability to find a particle next to another varies from \rho^2 (\rho is the particle density), initially, when the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic limit. As a result, the particle density decays inversely proportional to time, \rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant value.Comment: To be published in JPCM, special issue on Kinetics of Chemical Reaction