Modelling Time-varying Dark Energy with Constraints from Latest Observations

We introduce a set of two-parameter models for the dark energy equation of state (EOS) $w(z)$ to investigate time-varying dark energy. The models are classified into two types according to their boundary behaviors at the redshift $z=(0,\infty)$ and their local extremum properties. A joint analysis based on four observations (SNe + BAO + CMB + $H_0$) is carried out to constrain all the models. It is shown that all models get almost the same $\chi^2_{min}\simeq 469$ and the cosmological parameters $(\Omega_M, h, \Omega_bh^2)$ with the best-fit results $(0.28, 0.70, 2.24)$, although the constraint results on two parameters $(w_0, w_1)$ and the allowed regions for the EOS $w(z)$ are sensitive to different models and a given extra model parameter. For three of Type I models which have similar functional behaviors with the so-called CPL model, the constrained two parameters $w_0$ and $w_1$ have negative correlation and are compatible with the ones in CPL model, and the allowed regions of $w(z)$ get a narrow node at $z\sim 0.2$. The best-fit results from the most stringent constraints in Model Ia give $(w_0,w_1) = (-0.96^{+0.26}_{-0.21}, -0.12^{+0.61}_{-0.89})$ which may compare with the best-fit results $(w_0,w_1) = (-0.97^{+0.22}_{-0.18}, -0.15^{+0.85}_{-1.33})$ in the CPL model. For four of Type II models which have logarithmic function forms and an extremum point, the allowed regions of $w(z)$ are found to be sensitive to different models and a given extra parameter. It is interesting to obtain two models in which two parameters $w_0$ and $w_1$ are strongly correlative and appropriately reduced to one parameter by a linear relation $w_1 \propto (1+w_0)$.Comment: 30 pages, 7 figure

Primitive Cohomology of Hopf algebras

Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications are presented. Firstly we classify all non locally PI, pointed Hopf algebra domains of Gelfand-Kirillov dimension two; and secondly we classify all pointed Hopf algebras of rank one. The first classification extends some results of Brown, Goodearl and others in an ongoing project to understand all Hopf algebras of low Gelfand-Kirillov dimension. The second generalizes results of Krop-Radford and Wang-You-Chen which classified Hopf algebras of rank one under extra hypothesis. Properties and algebraic structures of the primitive cohomology are discussed

On cost-effective communication network designing

How to efficiently design a communication network is a paramount task for network designing and engineering. It is, however, not a single objective optimization process as perceived by most previous researches, i.e., to maximize its transmission capacity, but a multi-objective optimization process, with lowering its cost to be another important objective. These two objectives are often contradictive in that optimizing one objective may deteriorate the other. After a deep investigation of the impact that network topology, node capability scheme and routing algorithm as well as their interplays have on the two objectives, this letter presents a systematic approach to achieve a cost-effective design by carefully choosing the three designing aspects. Only when routing algorithm and node capability scheme are elegantly chosen can BA-like scale-free networks have the potential of achieving good tradeoff between the two objectives. Random networks, on the other hand, have the built-in character for a cost-effective design, especially when other aspects cannot be determined beforehand.Comment: 6 pages, 4 figure

Einstein's Theory of Gravity and the Problem of Missing Mass

The observed matter in the universe accounts for just 5 percent of the observed gravity. A possible explanation is that Newton's and Einstein's theories of gravity fail where gravity is either weak or enhanced. The modified theory of Newtonian dynamics (MOND) reproduces, without dark matter, spiral-galaxy orbital motions and the relation between luminosity and rotation in galaxies, although not in clusters. Recent extensions of Einstein's theory are theoretically more complete. They inevitably include dark fields that seed structure growth, and they may explain recent weak lensing data. However, the presence of dark fields reduces calculability and comes at the expense of the original MOND premise -- that the matter we see is the sole source of gravity. Observational tests of the relic radiation, weak lensing, and the growth of structure may distinguish modified gravity from dark matter.Comment: 11 pages, 3 figures. As published (with corrected typos in caption of Figure 1 and address of one author). Figures much better in published versio

Buried heterostructure vertical-cavity surface-emitting laser with semiconductor mirrors

We report a buried heterostructure vertical-cavity surface-emitting laser fabricated by epitaxial regrowth over an InGaAs quantum well gain medium. The regrowth technique enables microscale lateral confinement that preserves a high cavity quality factor (loaded $Q\approx$ 4000) and eliminates parasitic charging effects found in existing approaches. Under optimal spectral overlap between gain medium and cavity mode (achieved here at $T$ = 40 K) lasing was obtained with an incident optical power as low as $P_{\rm th}$ = 10 mW ($\lambda_{\rm p}$ = 808 nm). The laser linewidth was found to be $\approx$3 GHz at $P_{\rm p}\approx$ 5 $P_{\rm th}$

Interacting Individuals Leading to Zipf's Law

We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statisticsComment: 4 pages 2 figure

MgB2 tunnel junctions and 19 K low-noise dc superconducting quantum interference devices

Point contact junctions made from two pieces of MgB2 can be adjusted to exhibit either superconductor-insulator-superconductor (SIS) or superconductor-normal metal-superconductor (SNS) current-voltage characteristics. The SIS characteristics are in good agreement with the standard tunneling model for s-wave superconductors, and yield an energy gap of (2.02 +/- 0.08) meV. The SNS characteristics are in good agreement with the predictions of the resistively-shunted junction model. DC Superconducting QUantum Interference Devices made from two SNS junctions yield magnetic field noise as low as 35 fT/Hz^{1/2} at 19 K.Comment: 4 pages, 4 figure