Majority Dynamics and Aggregation of Information in Social Networks

Consider n individuals who, by popular vote, choose among q >= 2 alternatives, one of which is "better" than the others. Assume that each individual votes independently at random, and that the probability of voting for the better alternative is larger than the probability of voting for any other. It follows from the law of large numbers that a plurality vote among the n individuals would result in the correct outcome, with probability approaching one exponentially quickly as n tends to infinity. Our interest in this paper is in a variant of the process above where, after forming their initial opinions, the voters update their decisions based on some interaction with their neighbors in a social network. Our main example is "majority dynamics", in which each voter adopts the most popular opinion among its friends. The interaction repeats for some number of rounds and is then followed by a population-wide plurality vote. The question we tackle is that of "efficient aggregation of information": in which cases is the better alternative chosen with probability approaching one as n tends to infinity? Conversely, for which sequences of growing graphs does aggregation fail, so that the wrong alternative gets chosen with probability bounded away from zero? We construct a family of examples in which interaction prevents efficient aggregation of information, and give a condition on the social network which ensures that aggregation occurs. For the case of majority dynamics we also investigate the question of unanimity in the limit. In particular, if the voters' social network is an expander graph, we show that if the initial population is sufficiently biased towards a particular alternative then that alternative will eventually become the unanimous preference of the entire population.Comment: 22 page

Minimum Decision Cost for Quantum Ensembles

For a given ensemble of $N$ independent and identically prepared particles, we calculate the binary decision costs of different strategies for measurement of polarised spin 1/2 particles. The result proves that, for any given values of the prior probabilities and any number of constituent particles, the cost for a combined measurement is always less than or equal to that for any combination of separate measurements upon sub-ensembles. The Bayes cost, which is that associated with the optimal strategy (i.e., a combined measurement) is obtained in a simple closed form.Comment: 11 pages, uses RevTe

Channel kets, entangled states, and the location of quantum information

The well-known duality relating entangled states and noisy quantum channels is expressed in terms of a channel ket, a pure state on a suitable tripartite system, which functions as a pre-probability allowing the calculation of statistical correlations between, for example, the entrance and exit of a channel, once a framework has been chosen so as to allow a consistent set of probabilities. In each framework the standard notions of ordinary (classical) information theory apply, and it makes sense to ask whether information of a particular sort about one system is or is not present in another system. Quantum effects arise when a single pre-probability is used to compute statistical correlations in different incompatible frameworks, and various constraints on the presence and absence of different kinds of information are expressed in a set of all-or-nothing theorems which generalize or give a precise meaning to the concept of ``no-cloning.'' These theorems are used to discuss: the location of information in quantum channels modeled using a mixed-state environment; the $CQ$ (classical-quantum) channels introduced by Holevo; and the location of information in the physical carriers of a quantum code. It is proposed that both channel and entanglement problems be classified in terms of pure states (functioning as pre-probabilities) on systems of $p\geq 2$ parts, with mixed bipartite entanglement and simple noisy channels belonging to the category $p=3$, a five-qubit code to the category $p=6$, etc.; then by the dimensions of the Hilbert spaces of the component parts, along with other criteria yet to be determined.Comment: Latex 32 pages, 4 figures in text using PSTricks. Version 3: Minor typographical errors correcte

The cytoplasm of living cells: A functional mixture of thousands of components

Inside every living cell is the cytoplasm: a fluid mixture of thousands of different macromolecules, predominantly proteins. This mixture is where most of the biochemistry occurs that enables living cells to function, and it is perhaps the most complex liquid on earth. Here we take an inventory of what is actually in this mixture. Recent genome-sequencing work has given us for the first time at least some information on all of these thousands of components. Having done so we consider two physical phenomena in the cytoplasm: diffusion and possible phase separation. Diffusion is slower in the highly crowded cytoplasm than in dilute solution. Reasonable estimates of this slowdown can be obtained and their consequences explored, for example, monomer-dimer equilibria are established approximately twenty times slower than in a dilute solution. Phase separation in all except exceptional cells appears not to be a problem, despite the high density and so strong protein-protein interactions present. We suggest that this may be partially a byproduct of the evolution of other properties, and partially a result of the huge number of components present.Comment: 11 pages, 1 figure, 1 tabl

ALMA Observations of Gas-Rich Galaxies in z~1.6 Galaxy Clusters: Evidence for Higher Gas Fractions in High-Density Environments

We present ALMA CO (2-1) detections in 11 gas-rich cluster galaxies at z~1.6, constituting the largest sample of molecular gas measurements in z>1.5 clusters to date. The observations span three galaxy clusters, derived from the Spitzer Adaptation of the Red-sequence Cluster Survey. We augment the >5sigma detections of the CO (2-1) fluxes with multi-band photometry, yielding stellar masses and infrared-derived star formation rates, to place some of the first constraints on molecular gas properties in z~1.6 cluster environments. We measure sizable gas reservoirs of 0.5-2x10^11 solar masses in these objects, with high gas fractions and long depletion timescales, averaging 62% and 1.4 Gyr, respectively. We compare our cluster galaxies to the scaling relations of the coeval field, in the context of how gas fractions and depletion timescales vary with respect to the star-forming main sequence. We find that our cluster galaxies lie systematically off the field scaling relations at z=1.6 toward enhanced gas fractions, at a level of ~4sigma, but have consistent depletion timescales. Exploiting CO detections in lower-redshift clusters from the literature, we investigate the evolution of the gas fraction in cluster galaxies, finding it to mimic the strong rise with redshift in the field. We emphasize the utility of detecting abundant gas-rich galaxies in high-redshift clusters, deeming them as crucial laboratories for future statistical studies.Comment: 8 pages, 3 figures, published in ApJ Letters; updated to match published versio

Pair creation: back-reactions and damping

We solve the quantum Vlasov equation for fermions and bosons, incorporating spontaneous pair creation in the presence of back-reactions and collisions. Pair creation is initiated by an external impulse field and the source term is non-Markovian. A simultaneous solution of Maxwell's equation in the presence of feedback yields an internal current and electric field that exhibit plasma oscillations with a period tau_pl. Allowing for collisions, these oscillations are damped on a time-scale, tau_r, determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless tau_r >> tau_pl and tau_pl approx. 1/Lambda_QCD approx 1 fm/c.Comment: 16 pages, 6 figure, REVTEX, epsfig.st

Galaxy Merger Candidates in High-Redshift Cluster Environments

We compile a sample of spectroscopically- and photometrically-selected cluster galaxies from four high-redshift galaxy clusters ($1.59 < z < 1.71$) from the Spitzer Adaptation of the Red-Sequence Cluster Survey (SpARCS), and a comparison field sample selected from the UKIDSS Deep Survey. Using near-infrared imaging from the \textit{Hubble Space Telescope} we classify potential mergers involving massive ($M_* \geq 3\times 10^{10}\mathrm{M}_\odot$) cluster members by eye, based on morphological properties such as tidal distortions, double nuclei, and projected near neighbors within 20 kpc. With a catalogue of 23 spectroscopic and 32 photometric massive cluster members across the four clusters and 65 spectroscopic and 26 photometric comparable field galaxies, we find that after taking into account contamination from interlopers, $11.0 ^{+7.0}_{-5.6}\%$ of the cluster members are involved in potential mergers, compared to $24.7^{+5.3}_{-4.6}\%$ of the field galaxies. We see no evidence of merger enhancement in the central cluster environment with respect to the field, suggesting that galaxy-galaxy merging is not a stronger source of galaxy evolution in cluster environments compared to the field at these redshifts.Comment: Accepted by Ap

Classical Equations for Quantum Systems

The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We investigate the requirements for coarse grainings to yield decoherent sets of histories that are quasiclassical, i.e. such that the individual histories obey, with high probability, effective classical equations of motion interrupted continually by small fluctuations and occasionally by large ones. We discuss these requirements generally but study them specifically for coarse grainings of the type that follows a distinguished subset of a complete set of variables while ignoring the rest. More coarse graining is needed to achieve decoherence than would be suggested by naive arguments based on the uncertainty principle. Even coarser graining is required in the distinguished variables for them to have the necessary inertia to approach classical predictability in the presence of the noise consisting of the fluctuations that typical mechanisms of decoherence produce. We describe the derivation of phenomenological equations of motion explicitly for a particular class of models. Probabilities of the correlations in time that define equations of motion are explicitly considered. Fully non-linear cases are studied. Methods are exhibited for finding the form of the phenomenological equations of motion even when these are only distantly related to those of the fundamental action. The demonstration of the connection between quantum-mechanical causality and causalty in classical phenomenological equations of motion is generalized. The connections among decoherence, noise, dissipation, and the amount of coarse graining necessary to achieve classical predictability are investigated quantitatively.Comment: 100pages, 1 figur

Mean Field Calculations of Bose-Einstein Condensation of 7Li Atoms In a Harmonic Trap

A self-consistent mean-field theory for bosons for T>0 is used to reconcile predictions of collapse with recent observations of Bose-Einstein condensation of 7Li. Eigenfunctions of a (non-separable) Hamiltonian that includes the anisotropic external trap field and atom-atom interactions are obtained by an iteration process. A sum over the Bose distribution, and the ``alternating direction implicit'' algorithm are used. Near Tc, the ensemble exhibits a localized condensate composed of atoms in the few lowest states. For lower T, numerical instability indicates collapse to a more dense phase.Comment: 11 pages + 4 figure

Drag in paired electron-hole layers

We investigate transresistance effects in electron-hole double layer systems with an excitonic condensate. Our theory is based on the use of a minimum dissipation premise to fix the current carried by the condensate. We find that the drag resistance jumps discontinuously at the condensation temperature and diverges as the temperature approaches zero.Comment: 12 pages, 1 Figure, .eps file attache