Transition from fractal to non-fractal scalings in growing scale-free networks

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameter $q$. Interestingly, we show that by adjusting $q$, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from `large' to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.Comment: 7 pages, 3 figures, definitive version accepted for publication in EPJ

Role of fractal dimension in random walks on scale-free networks

Fractal dimension is central to understanding dynamical processes occurring on networks; however, the relation between fractal dimension and random walks on fractal scale-free networks has been rarely addressed, despite the fact that such networks are ubiquitous in real-life world. In this paper, we study the trapping problem on two families of networks. The first is deterministic, often called $(x,y)$-flowers; the other is random, which is a combination of $(1,3)$-flower and $(2,4)$-flower and thus called hybrid networks. The two network families display rich behavior as observed in various real systems, as well as some unique topological properties not shared by other networks. We derive analytically the average trapping time for random walks on both the $(x,y)$-flowers and the hybrid networks with an immobile trap positioned at an initial node, i.e., a hub node with the highest degree in the networks. Based on these analytical formulae, we show how the average trapping time scales with the network size. Comparing the obtained results, we further uncover that fractal dimension plays a decisive role in the behavior of average trapping time on fractal scale-free networks, i.e., the average trapping time decreases with an increasing fractal dimension.Comment: Definitive version published in European Physical Journal

Effects of dimensionality and anisotropy on the Holstein polaron

We apply weak-coupling perturbation theory and strong-coupling perturbation theory to the Holstein molecular crystal model in order to elucidate the effects of anisotropy on polaron properties in D dimensions. The ground state energy is considered as a primary criterion through which to study the effects of anisotropy on the self-trapping transition, the self-trapping line associated with this transition, and the adiabatic critical point. The effects of dimensionality and anisotropy on electron-phonon correlations and polaronic mass enhancement are studied, with particular attention given to the polaron radius and the characteristics of quasi-1D and quasi-2D structures. Perturbative results are confirmed by selected comparisons with variational calculations and quantum Monte Carlo data

The K\"ahler-Ricci flow with positive bisectional curvature

We show that the K\"ahler-Ricci flow on a manifold with positive first Chern class converges to a K\"ahler-Einstein metric assuming positive bisectional curvature and certain stability conditions.Comment: 15 page

Polaron Effective Mass, Band Distortion, and Self-Trapping in the Holstein Molecular Crystal Model

We present polaron effective masses and selected polaron band structures of the Holstein molecular crystal model in 1-D as computed by the Global-Local variational method over a wide range of parameters. These results are augmented and supported by leading orders of both weak- and strong-coupling perturbation theory. The description of the polaron effective mass and polaron band distortion that emerges from this work is comprehensive, spanning weak, intermediate, and strong electron-phonon coupling, and non-adiabatic, weakly adiabatic, and strongly adiabatic regimes. Using the effective mass as the primary criterion, the self-trapping transition is precisely defined and located. Using related band-shape criteria at the Brillouin zone edge, the onset of band narrowing is also precisely defined and located. These two lines divide the polaron parameter space into three regimes of distinct polaron structure, essentially constituting a polaron phase diagram. Though the self-trapping transition is thusly shown to be a broad and smooth phenomenon at finite parameter values, consistency with notion of self-trapping as a critical phenomenon in the adiabatic limit is demonstrated. Generalizations to higher dimensions are considered, and resolutions of apparent conflicts with well-known expectations of adiabatic theory are suggested.Comment: 28 pages, 15 figure

Shapes, contact angles, and line tensions of droplets on cylinders

Using an interface displacement model we calculate the shapes of nanometer-size liquid droplets on homogeneous cylindrical surfaces. We determine effective contact angles and line tensions, the latter defined as excess free energies per unit length associated with the two contact lines at the ends of the droplet. The dependences of these quantities on the cylinder radius and on the volume of the droplets are analyzed.Comment: 26 pages, RevTeX, 10 Figure

Analysis of the intraspinal calcium dynamics and its implications on the plasticity of spiking neurons

The influx of calcium ions into the dendritic spines through the N-metyl-D-aspartate (NMDA) channels is believed to be the primary trigger for various forms of synaptic plasticity. In this paper, the authors calculate analytically the mean values of the calcium transients elicited by a spiking neuron undergoing a simple model of ionic currents and back-propagating action potentials. The relative variability of these transients, due to the stochastic nature of synaptic transmission, is further considered using a simple Markov model of NMDA receptos. One finds that both the mean value and the variability depend on the timing between pre- and postsynaptic action-potentials. These results could have implications on the expected form of synaptic-plasticity curve and can form a basis for a unified theory of spike time-dependent, and rate based plasticity.Comment: 14 pages, 10 figures. A few changes in section IV and addition of a new figur

Sensitive detection of colorectal cancer in peripheral blood by septin 9 DNA methylation assay

BACKGROUND: Colorectal cancer (CRC) is the second leading cause of cancer deaths despite the fact that detection of this cancer in early stages results in over 90% survival rate. Currently less than 45% of at-risk individuals in the US are screened regularly, exposing a need for better screening tests. We performed two case-control studies to validate a blood-based test that identifies methylated DNA in plasma from all stages of CRC. METHODOLOGY/PRINCIPAL FINDINGS: Using a PCR assay for analysis of Septin 9 (SEPT9) hypermethylation in DNA extracted from plasma, clinical performance was optimized on 354 samples (252 CRC, 102 controls) and validated in a blinded, independent study of 309 samples (126 CRC, 183 controls). 168 polyps and 411 additional disease controls were also evaluated. Based on the training study SEPT9-based classification detected 120/252 CRCs (48%) and 7/102 controls (7%). In the test study 73/126 CRCs (58%) and 18/183 control samples (10%) were positive for SEPT9 validating the training set results. Inclusion of an additional measurement replicate increased the sensitivity of the assay in the testing set to 72% (90/125 CRCs detected) while maintaining 90% specificity (19/183 for controls). Positive rates for plasmas from the other cancers (11/96) and non-cancerous conditions (41/315) were low. The rate of polyp detection (>1 cm) was approximately 20%. CONCLUSIONS/SIGNIFICANCE: Analysis of SEPT9 DNA methylation in plasma represents a straightforward, minimally invasive method to detect all stages of CRC with potential to satisfy unmet needs for increased compliance in the screening population. Further clinical testing is warranted

Antiflow of kaons in relativistic heavy ion collisions

We compare relativistic transport model calculations to recent data on the sideward flow of neutral strange K^0_s mesons for Au+Au collisions at 6 AGeV. A soft nuclear equation of state is found to describe very well the positive proton flow data measured in the same experiment. In the absence of kaon potential, the K^0 flow pattern is similar to that of protons. The kaon flow becomes negative if a repulsive kaon potential determined from the impulse approximation is introduced. However, this potential underestimates the data which exhibits larger antiflow. An excellent agreement with the data is obtained when a relativistic scalar-vector kaon potential, that has stronger density dependence, is used. We further find that the transverse momentum dependence of directed and elliptic flow is quite sensitive to the kaon potential in dense matter.Comment: 5 pages, Revtex, 4 figure

The dissipative potential induced by QCD at finite temperature and density

In the framework of QCD at finite temperature we have obtained dissipative terms for the effective potential between $q$ and $\bar q$ which would partly explain the $J/\psi$ suppression in the Quark Gluon Plasma (QGP). The derivation of the dissipative potential for QGP is presented and the case for Hadron Matter (HM) is briefly discussed. The suppression effects are estimated based on simple approximations.Comment: 13 page