Noise resistant generalized parametric validity index of clustering for gene expression data

This article has been made available through the Brunel Open Access Publishing Fund.Validity indices have been investigated for decades. However, since there is no study of noise-resistance performance of these indices in the literature, there is no guideline for determining the best clustering in noisy data sets, especially microarray data sets. In this paper, we propose a generalized parametric validity (GPV) index which employs two tunable parameters α and β to control the proportions of objects being considered to calculate the dissimilarities. The greatest advantage of the proposed GPV index is its noise-resistance ability, which results from the flexibility of tuning the parameters. Several rules are set to guide the selection of parameter values. To illustrate the noise-resistance performance of the proposed index, we evaluate the GPV index for assessing five clustering algorithms in two gene expression data simulation models with different noise levels and compare the ability of determining the number of clusters with eight existing indices. We also test the GPV in three groups of real gene expression data sets. The experimental results suggest that the proposed GPV index has superior noise-resistance ability and provides fairly accurate judgements

Accretion disk around the rotating Damour-Solodukhin wormhole

A new rotating generalization of the Damour-Solodukhin wormhole (RDSWH), called Kerr-like wormhole, has recently been proposed and investigated by Bueno \textit{et al} for echoes in the gravitational wave signal. We show a novel feature of the RDSWH, viz., that the kinematic properties such as the ISCO\ or marginally stable radius $r_{\text{ms}}$, efficiency $\epsilon$ and the disk potential $V_{\text{eff}}$ are \textit{independent} of $\lambda$ (which means they are identical to their KBH counterparts for any given spin). Differences however appear in the emissivity properties for higher values $0.1<\lambda\leq 1$ (say) and for the extreme spin $a_{\star}=0.998$. The kinematic and emissivity are generic properties as variations of the wormhole mass and the rate of accretion within the model preserve these properties. Specifically, the behavior of the luminosity peak is quite opposite to each other for the two objects, which could be useful from the viewpoint of observations. Apart from this, an estimate of the difference $\Delta_{\lambda}$ in the maxima of flux of radiation $F(r)$ shows non-zero values but is too tiny to be observable at present for $\lambda < 10^{-3}$ permitted by the strong lensing bound. The broad conclusion is that RDSWH\ are experimentally indistinguishable from KBH by accretion characteristics.Comment: 9 pages, 3 tables, 13 figure

Spectral Signatures of Winds from Accretion Disks Around Black Holes

We show that with the wind/jet activity, the spectral index of hard X-ray is changed in galactic microquasars. When mass loss takes place, the spectrum becomes softer and when mass gain takes place, the spectrum becomes harder. We present examples of such changes in GRS1915+105.Comment: 4 pages, 2 figures To be published in the Proceedings of 10th Marcel Grossman Meeting, Ed. R. Ruffini et al. (World Scientific: Singapore

Field Theories on Null Manifolds

We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed an action for the electric sector of the theory. This action is the first example for an interacting conformal Carrollian Field Theory. The proposed action respects the finite and infinite conformal Carrollian symmetries in d = 4. We calculate conserved charges corresponding to these finite and infinite symmetries and then rewrite the conserved charges in terms of the canonical variables. We finally compute the Poisson brackets for these charges and confirm that infinite Carrollian conformal algebra is satisfied at the level of charges

Dual-layer network representation exploiting information characterization

In this paper, a logical dual-layer representation approach is proposed to facilitate the analysis of directed and weighted complex networks. Unlike the single logical layer structure, which was widely used for the directed and weighted flow graph, the proposed approach replaces the single layer with a dual-layer structure, which introduces a provider layer and a requester layer. The new structure provides the characterization of the nodes by the information, which they provide to and they request from the network. Its features are explained and its implementation and visualization are also detailed. We also design two clustering methods with different strategies respectively, which provide the analysis from different points of view. The effectiveness of the proposed approach is demonstrated using a simplified example. By comparing the graph layout with the conventional directed graph, the new dual-layer representation reveals deeper insight into the complex networks and provides more opportunities for versatile clustering analysis.The National Institute for Health Research (NIHR) under its Programme Grants for Applied Research Programme (Grant Reference Number RP-PG-0310-1004)

Comment on "Layering transition in confined molecular thin films: Nucleation and growth"

When fluid is confined between two molecularly smooth surfaces to a few molecular diameters, it shows a large enhancement of its viscosity. From experiments it seems clear that the fluid is squeezed out layer by layer. A simple solution of the Stokes equation for quasi-two-dimensional confined flow, with the assmption of layer-by-layer flow is found. The results presented here correct those in Phys. Rev. B, 50, 5590 (1994), and show that both the kinematic viscosity of the confined fluid and the coefficient of surface drag can be obtained from the time dependence of the area squeezed out. Fitting our solution to the available experimental data gives the value of viscosity which is ~7 orders of magnitude higher than that in the bulk.Comment: 4 pages, 2 figure