Nonorthogonal wavelet approximation with rates of deterministic signals

An nth order asymptotic expansion is produced for the L2-error in a nonorthogonal (in general) wavelet approximation at resolution 2−k of deterministic signals f. These signals over the whole real line are assumed to have n continuous derivatives of bounded variation. The engaged nonorthogonal (in general) scale function ϕ fulfills the partition of unity property, and it is of compact support. The asymptotic expansion involves only even terms of products of integrals involving ϕ with integrals of squares of (the first [ only) derivatives of f

Psyche, Signals and Systems

For a century or so, the multidisciplinary nature of neuroscience has left the field fractured into distinct areas of research. In particular, the subjects of consciousness and perception present unique challenges in the attempt to build a unifying understanding bridging between the micro-, meso-, and macro-scales of the brain and psychology. This chapter outlines an integrated view of the neurophysiological systems, psychophysical signals, and theoretical considerations related to consciousness. First, we review the signals that correlate to consciousness during psychophysics experiments. We then review the underlying neural mechanisms giving rise to these signals. Finally, we discuss the computational and theoretical functions of such neural mechanisms, and begin to outline means in which these are related to ongoing theoretical research

Spike-timing control by dendritic plateau potentials in the presence of synaptic barrages

Apical and tuft dendrites of pyramidal neurons support regenerative electrical potentials, giving rise to long-lasting (approximately hundreds of milliseconds) and strong (~50 mV from rest) depolarizations. Such plateau events rely on clustered glutamatergic input, can be mediated by calcium or by NMDA currents, and often generate somatic depolarizations that last for the time course of the dendritic plateau event. We address the computational significance of such single-neuron processing via reduced but biophysically realistic modeling. We introduce a model based on two discrete integration zones, a somatic and a dendritic one, that communicate from the dendritic to the somatic compartment via a long plateau-conductance. We show principled differences in the way dendritic vs. somatic inhibition controls spike timing, and demonstrate how this could implement a mechanism of spike time control in the face of barrages of synaptic inputs

Transient down-regulation of beta1 integrin subtypes on kidney carcinoma cells is induced by mechanical contact with endothelial cell membranes

Adhesion molecules of the integrin beta1 family are thought to be involved in the malignant progression renal cell carcinoma (RCC). Still, it is not clear how they contribute to this process. Since the hematogenous phase of tumour dissemination is the rate-limiting step in the metastatic process, we explored beta1 integrin alterations on several RCC cell lines (A498, Caki1, KTC26) before and after contacting vascular endothelium in a tumour-endothelium (HUVEC) co-culture assay. Notably, alpha2, alpha3 and alpha5 integrins became down-regulated immediately after the tumour cells attached to HUVEC, followed by re-expression shortly thereafter. Integrin down-regulation on RCC cells was caused by direct contact with endothelial cells, since the isolated endothelial membrane fragments but not the cell culture supernatant contributed to the observed effects. Integrin loss was accompanied by a reduced focal adhesion kinase (FAK) expression, FAK activity and diminished binding of tumour cells to matrix proteins. Furthermore, intracellular signalling proteins RCC cells were altered in the presence of HUVEC membrane fragments, in particular 14-3-3 epsilon, ERK2, PKCdelta, PKCepsilon and RACK1, which are involved in regulating tumour cell motility. We, therefore, speculate that contact of RCC cells with the vascular endothelium converts integrin-dependent adhesion to integrin-independent cell movement. The process of dynamic integrin regulation may be an important part in tumour cell migration strategy, switching the cells from being adhesive to becoming motile and invasive

Physiology of Layer 5 Pyramidal Neurons in Mouse Primary Visual Cortex: Coincidence Detection through Bursting

L5 pyramidal neurons are the only neocortical cell type with dendrites reaching all six layers of cortex, casting them as one of the main integrators in the cortical column. What is the nature and mode of computation performed in mouse primary visual cortex (V1) given the physiology of L5 pyramidal neurons? First, we experimentally establish active properties of the dendrites of L5 pyramidal neurons of mouse V1 using patch-clamp recordings. Using a detailed multi-compartmental model, we show this physiological setup to be well suited for coincidence detection between basal and apical tuft inputs by controlling the frequency of spike output. We further show how direct inhibition of calcium channels in the dendrites modulates such coincidence detection. To establish the singe-cell computation that this biophysics supports, we show that the combination of frequency-modulation of somatic output by tuft input and (simulated) calcium-channel blockage functionally acts as a composite sigmoidal function. Finally, we explore how this computation provides a mechanism whereby dendritic spiking contributes to orientation tuning in pyramidal neurons

Soliton transverse instabilities in anisotropic nonlocal self-focusing media

We study, both theoretically and experimentally, the transverse modulational instability of spatial stripe solitons in anisotropic nonlocal photorefractive media. We demonstrate that the instability scenarios depend strongly on the stripe orientation, but the anisotropy-induced features are largely suppressed for spatial solitons created by self-trapping of partially incoherent light.Comment: 3 pages including 4 figures (2 theoretical and 2 experimental). submitted to Optics Letter

Partially incoherent optical vortices in self-focusing nonlinear media

We observe stable propagation of spatially localized single- and double-charge optical vortices in a self-focusing nonlinear medium. The vortices are created by self-trapping of partially incoherent light carrying a phase dislocation, and they are stabilized when the spatial incoherence of light exceeds a certain threshold. We confirm the vortex stabilization effect by numerical simulations and also show that the similar mechanism of stabilization applies to higher-order vortices.Comment: 4 pages and 6 figures (including 3 experimental figures

Exact soliton solutions, shape changing collisions and partially coherent solitons in coupled nonlinear Schroedinger equations

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schroedinger equations (N-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyse the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partial coherent solitons (PCS) discussed in the literature are special cases of the higher order bright soliton solutions of the N-CNLS equations.Comment: 4 pages, RevTex, 1 EPS figure To appear in Physical Review Letter

Grouping time series by pairwise measures of redundancy

A novel approach is proposed to group redundant time series in the frame of causality. It assumes that (i) the dynamics of the system can be described using just a small number of characteristic modes, and that (ii) a pairwise measure of redundancy is sufficient to elicit the presence of correlated degrees of freedom. We show the application of the proposed approach on fMRI data from a resting human brain and gene expression profiles from HeLa cell culture.Comment: 4 pages, 8 figure

Expansion of anti-AFP Th1 and Tc1 responses in hepatocellular carcinoma occur in different stages of disease

Copyright @ 2010 Cancer Research UK. This work is licensed under the Creative Commons Attribution-NonCommercial-Share Alike 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/.Background: α-Fetoprotein (AFP) is a tumour-associated antigen in hepatocellular carcinoma (HCC) and is a target for immunotherapy. However, there is little information on the pattern of CD4 (Th1) and CD8 (Tc1) T-cell response to AFP in patients with HCC and their association with the clinical characteristics of patients. Methods: We therefore analysed CD4 and CD8 T-cell responses to a panel of AFP-derived peptides in a total of 31 HCC patients and 14 controls, using an intracellular cytokine assay for IFN-γ. Results: Anti-AFP Tc1 responses were detected in 28.5% of controls, as well as in 25% of HCC patients with Okuda I (early tumour stage) and in 31.6% of HCC patients with stage II or III (late tumour stages). An anti-AFP Th1 response was detected only in HCC patients (58.3% with Okuda stage I tumours and 15.8% with Okuda stage II or III tumours). Anti-AFP Th1 response was mainly detected in HCC patients who had normal or mildly elevated serum AFP concentrations (P=0.00188), whereas there was no significant difference between serum AFP concentrations in these patients and the presence of an anti-AFP Tc1 response. A Th1 response was detected in 44% of HCC patients with a Child–Pugh A score (early stage of cirrhosis), whereas this was detected in only 15% with a B or C score (late-stage cirrhosis). In contrast, a Tc1 response was detected in 17% of HCC patients with a Child–Pugh A score and in 46% with a B or C score. Conclusion: These results suggest that anti-AFP Th1 responses are more likely to be present in patients who are in an early stage of disease (for both tumour stage and liver cirrhosis), whereas anti-AFP Tc1 responses are more likely to be present in patients with late-stage liver cirrhosis. Therefore, these data provide valuable information for the design of vaccination strategies against HCC.Association for International Cancer Research and Polkemmet Fund, London Clinic