Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (M\"obius) strip graphs composed of $p$-sided polygons. Our results suggest a general rule concerning the maximal region in the complex $q$ plane to which one can analytically continue from the physical interval where $S_0 > 0$. The chromatic zeros and their accumulation set ${\cal B}$ exhibit the rather unusual property of including support for $Re(q) < 0$ and provide further evidence for a relevant conjecture.Comment: 7 pages, Latex, 4 figs., J. Phys. A Lett., in pres

Cultural complexity and complexity evolution

We review issues stemming from current models regarding the drivers of cultural complexity and cultural evolution. We disagree with the implication of the treadmill model, based on dual-inheritance theory, that population size is the driver of cultural complexity. The treadmill model reduces the evolution of artifact complexity, measured by the number of parts, to the statistical fact that individuals with high skills are more likely to be found in a larger population than in a smaller population. However, for the treadmill model to operate as claimed, implausibly high skill levels must be assumed. Contrary to the treadmill model, the risk hypothesis for the complexity of artifacts relates the number of parts to increased functional efficiency of implements. Empirically, all data on hunter-gatherer artifact complexity support the risk hypothesis and reject the treadmill model. Still, there are conditions under which increased technological complexity relates to increased population size, but the dependency does not occur in the manner expressed in the treadmill model. Instead, it relates to population size when the support system for the technology requires a large population size. If anything, anthropology and ecology suggest that cultural complexity generates high population density rather than the other way around

The missing metals problem. III How many metals are expelled from galaxies?

[Abridged] We revisit the metal budget at z~2. In the first two papers of this series, we already showed that ~30% (to <60% if extrapolating the LF) of the metals are observed in all z~2.5 galaxies detected in current surveys. Here, we extend our analysis to the metals outside galaxies, i.e. in intergalactic medium (IGM), using observational data and analytical calculations. Our results for the two are strikingly similar: (1) Observationally, we find that, besides the small (5%) contribution of DLAs, the forest and sub-DLAs contribute subtantially to make <30--45% of the metal budget, but neither of these appear to be sufficient to close the metal budget. The forest accounts for 15--30% depending on the UV background, and sub-DLAs for >2% to <17% depending on the ionization fraction. Together, the `missing metals' problem is substantially eased. (2) We perform analytical calculations based on the effective yield--mass relation. At z=2, we find that the method predicts that 2$--50% of the metals have been ejected from galaxies into the IGM, consistent with the observations. The metal ejection is predominantly by L<1/3L_B^*(z=2) galaxies, which are responsible for 90% the metal enrichment, while the 50 percentile is at L~1/10L^*_B(z=2). As a consequence, if indeed 50% of the metals have been ejected from galaxies, 3--5 bursts of star formation are required per galaxy prior to z=2. The ratio between the mass of metals outside galaxies to those in stars has changed from z=2 to z=0: it was 2:1 or 1:1 and is now 1:8 or 1:9. This evolution implies that a significant fraction of the IGM metals will cool and fall back into galaxies.Comment: 18pages, MNRAS, in press; small changes to match proofs; extended version with summary tabl

Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

We present exact calculations of chromatic polynomials for families of cyclic graphs consisting of linked polygons, where the polygons may be adjacent or separated by a given number of bonds. From these we calculate the (exponential of the) ground state entropy, $W$, for the q-state Potts model on these graphs in the limit of infinitely many vertices. A number of properties are proved concerning the continuous locus, ${\cal B}$, of nonanalyticities in $W$. Our results provide further evidence for a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where $S_0 > 0$.Comment: 27 pages, Latex, 17 figs. J. Phys. A, in pres

Spin-Peierls states of quantum antiferromagnets on the CaV4O9Ca V_4 O_9 lattice

We discuss the quantum paramagnetic phases of Heisenberg antiferromagnets on the 1/5-depleted square lattice found in $Ca V_4 O_9$. The possible phases of the quantum dimer model on this lattice are obtained by a mapping to a quantum-mechanical height model. In addition to the ``decoupled'' phases found earlier, we find a possible intermediate spin-Peierls phase with spontaneously-broken lattice symmetry. Experimental signatures of the different quantum paramagnetic phases are discussed.Comment: 9 pages; 2 eps figure

Fourteen candidate RR Lyrae star streams in the inner Galaxy

We apply the GC3 stream-finding method to RR Lyrae stars (RRLSs) in the Catalina survey. We find 2 RRLS stream candidates at >4σ confidence and another 12 at >3.5σ confidence over the Galactocentric distance range 4 < D/kpc < 26. Of these, only two are associated with known globular clusters (NGC 1261 and Arp2). The remainder are candidate ‘orphan’ streams, consistent with the idea that globular cluster streams are most visible close to dissolution. Our detections are likely a lower bound on the total number of dissolving globulars in the inner galaxy, since many globulars have few RRLSs, while only the brightest streams are visible over the Galactic RRLS background, particularly given the current lack of kinematical information. We make all of our candidate streams publicly available and provide a new galstreamsPYTHON library for the footprints of all known streams and overdensities in the Milky Way

Effects of soccer match-play on unilateral jumping and Inter-limb asymmetry: a repeated measures design

The aims of the present study were twofold: 1) determine the effects of repeated soccer match-play on unilateral jump performance and inter-limb asymmetries and, 2) examine associations between asymmetry and commonly reported external load variables collected during competition. Single leg countermovement jumps (SLCMJ) and drop jumps (SLDJ) were collected pre and immediately post five soccer matches in elite academy soccer players. GPS data was also collected each match as part of the routine match-day procedures. SLCMJ height and concentric impulse showed significant reductions post-matches (p 0.05; ES: -0.05 to -0.13). SLDJ height and reactive strength also showed significant reductions post-matches (p < 0.01; ES: -0.39 to -0.58). No meaningful reductions in asymmetry were present at the group level, but individual responses were highly variable. Significant associations between post-match reactive strength asymmetry and explosive distance (r = 0.29; p < 0.05), relative explosive distance (r = 0.34; p < 0.05), high speed running (r = 0.35; p < 0.05) and relative high speed running (r = 0.44; p < 0.01). These findings show that unilateral jump tests are more appropriate than asymmetry to detect real change post soccer competition and practitioners should be cautious about using asymmetry to inform decision-making during the temporal recovery period

Stochastic polarization formation in exciton-polariton Bose-Einstein condensates

We demonstrate theoretically the spontaneous formation of a stochastic polarization in exciton-polariton Bose-Einstein condensates in planar microcavities under pulsed excitation. Below the threshold pumping intensity (dependent on the polariton life-time) the average polarization degree is close to zero, whilst above threshold the condensate acquires a polarization described by a (pseudospin) vector with random orientation, in general. We establish the link between second order coherence of the polariton condensate and the distribution function of its polarization. We examine also the mechanisms of polarization dephasing and relaxation.Comment: 4 pages, 3 figure

The value of nothing : asymmetric attention to opportunity costs drives intertemporal decision making

This paper proposes a novel account of why intertemporal decisions tend to display impatience: People pay more attention to the opportunity costs of choosing larger, later rewards than to the opportunity costs of choosing smaller, sooner ones. Eight studies show that when the opportunity costs of choosing smaller, sooner rewards are subtly highlighted, people become more patient, whereas highlighting the opportunity costs of choosing larger, later rewards has no effect. This pattern is robust to variations in the choice task, to the participant population, and is observed for both incentivized and hypothetical choices. We argue that people are naturally aware of the opportunity costs associated with delayed rewards, but pay less attention to those associated with taking smaller, sooner ones. We conclude by discussing implications for theory and policy