Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean {\it coordinate} system (X$^i$,$\tau$) as the quantum statistical system of N quantum (statistical) variables (X$^i$) and one {\it Euclidean time} variable ($\tau$). Introducing paths (lines or hypersurfaces) in this space (X$^i$,$\tau$), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the {\it mechanical} system. The system Hamiltonian appears as the {\it area}. We show quantization is realized by the {\it minimal area principle} in the present geometric approach. When we take a {\it line} as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a {\it hyper-surface} as the path, the system Hamiltonian is given by the {\it area} of the {\it hyper-surface} which is defined as a {\it closed-string configuration} in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.Comment: 20 pages, 8 figures, Proceedings of ICFS2010 (2010.9.13-18, Ise-Shima, Mie, Japan

Moment inversion problem for piecewise D-finite functions

We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation with polynomial coefficients on each continuity interval. Therefore, they may be specified by a finite amount of information. This reconstruction problem has practical importance in Signal Processing and other applications. It is somewhat of a ``folklore'' that the sequence of the moments of such ``piecewise D-finite''functions satisfies a linear recurrence relation of bounded order and degree. We derive this recurrence relation explicitly. It turns out that the coefficients of the differential operator which annihilates every piece of the function, as well as the locations of the discontinuities, appear in this recurrence in a precisely controlled manner. This leads to the formulation of a generic algorithm for reconstructing a piecewise D-finite function from its moments. We investigate the conditions for solvability of the resulting linear systems in the general case, as well as analyze a few particular examples. We provide results of numerical simulations for several types of signals, which test the sensitivity of the proposed algorithm to noise

Non-parametric directionality analysis: extension for removal of a single common predictor and application to time series

BACKGROUND: The ability to infer network structure from multivariate neuronal signals is central to computational neuroscience. Directed network analyses typically use parametric approaches based on auto-regressive (AR) models, where networks are constructed from estimates of AR model parameters. However, the validity of using low order AR models for neurophysiological signals has been questioned. A recent article introduced a non-parametric approach to estimate directionality in bivariate data, non-parametric approaches are free from concerns over model validity. NEW METHOD: We extend the non-parametric framework to include measures of directed conditional independence, using scalar measures that decompose the overall partial correlation coefficient summatively by direction, and a set of functions that decompose the partial coherence summatively by direction. A time domain partial correlation function allows both time and frequency views of the data to be constructed. The conditional independence estimates are conditioned on a single predictor. RESULTS: The framework is applied to simulated cortical neuron networks and mixtures of Gaussian time series data with known interactions. It is applied to experimental data consisting of local field potential recordings from bilateral hippocampus in anaesthetised rats. COMPARISON WITH EXISTING METHOD(S): The framework offers a non-parametric approach to estimation of directed interactions in multivariate neuronal recordings, and increased flexibility in dealing with both spike train and time series data. CONCLUSIONS: The framework offers a novel alternative non-parametric approach to estimate directed interactions in multivariate neuronal recordings, and is applicable to spike train and time series data

Non-Agonistic Bivalent Antibodies That Promote c-MET Degradation and Inhibit Tumor Growth and Others Specific for Tumor Related c-MET

The c-MET receptor has a function in many human cancers and is a proven therapeutic target. Generating antagonistic or therapeutic monoclonal antibodies (mAbs) targeting c-MET has been difficult because bivalent, intact anti-Met antibodies frequently display agonistic activity, necessitating the use of monovalent antibody fragments for therapy. By using a novel strategy that included immunizing with cells expressing c-MET, we obtained a range of mAbs. These c-MET mAbs were tested for binding specificity and anti-tumor activity using a range of cell-based techniques and in silico modeling. The LMH 80 antibody bound an epitope, contained in the small cysteine-rich domain of c-MET (amino acids 519–561), that was preferentially exposed on the c-MET precursor. Since the c-MET precursor is only expressed on the surface of cancer cells and not normal cells, this antibody is potentially tumor specific. An interesting subset of our antibodies displayed profound activities on c-MET internalization and degradation. LMH 87, an antibody binding the loop connecting strands 3d and 4a of the 7-bladed β-propeller domain of c-MET, displayed no intrinsic agonistic activity but promoted receptor internalization and degradation. LMH 87 inhibited HGF/SF-induced migration of SK-OV-3 ovarian carcinoma cells, the proliferation of A549 lung cancer cells and the growth of human U87MG glioma cells in a mouse xenograft model. These results indicate that c-MET antibodies targeting epitopes controlling receptor internalization and degradation provide new ways of controlling c-MET expression and activity and may enable the therapeutic targeting of c-MET by intact, bivalent antibodies

Review of the methods of determination of directed connectivity from multichannel data

The methods applied for estimation of functional connectivity from multichannel data are described with special emphasis on the estimators of directedness such as directed transfer function (DTF) and partial directed coherence. These estimators based on multivariate autoregressive model are free of pitfalls connected with application of bivariate measures. The examples of applications illustrating the performance of the methods are given. Time-varying estimators of directedness: short-time DTF and adaptive methods are presented

Seizure prediction : ready for a new era

Acknowledgements: The authors acknowledge colleagues in the international seizure prediction group for valuable discussions. L.K. acknowledges funding support from the National Health and Medical Research Council (APP1130468) and the James S. McDonnell Foundation (220020419) and acknowledges the contribution of Dean R. Freestone at the University of Melbourne, Australia, to the creation of Fig. 3.Peer reviewedPostprin

Disrupted Thalamus White Matter Anatomy and Posterior Default Mode Network Effective Connectivity in Amnestic Mild Cognitive Impairment

Alzheimer’s disease (AD) and its prodromal state amnestic mild cognitive impairment (aMCI) are characterized by widespread abnormalities in inter-areal white matter fiber pathways and parallel disruption of default mode network (DMN) resting state functional and effective connectivity. In healthy subjects, DMN and task positive network interaction are modulated by the thalamus suggesting that abnormal task-based DMN deactivation in aMCI may be a consequence of impaired thalamo-cortical white matter circuitry. Thus, this article uses a multimodal approach to assess white matter integrity between thalamus and DMN components and associated effective connectivity in healthy controls (HCs) relative to aMCI patients. Twenty-six HC and 20 older adults with aMCI underwent structural, functional and diffusion MRI scanning using the high angular resolution diffusion-weighted acquisition protocol. The DMN of each subject was identified using independent component analysis (ICA) and resting state effective connectivity was calculated between thalamus and DMN nodes. White matter integrity changes between thalamus and DMN were investigated with constrained spherical deconvolution (CSD) tractography. Significant structural deficits in thalamic white matter projection fibers to posterior DMN components posterior cingulate cortex (PCC) and lateral inferior parietal lobe (IPL) were identified together with significantly reduced effective connectivity from left thalamus to left IPL. Crucially, impaired thalamo-cortical white matter circuitry correlated with memory performance. Disrupted thalamo-cortical structure was accompanied by significant reductions in IPL and PCC cortico-cortical effective connectivity. No structural deficits were found between DMN nodes. Abnormal posterior DMN activity may be driven by changes in thalamic white matter connectivity; a view supported by the close anatomical and functional association of thalamic nuclei effected by AD pathology and the posterior DMN nodes. We conclude that dysfunctional posterior DMN activity in aMCI is consistent with disrupted cortico-thalamo-cortical processing and thalamic-based dissemination of hippocampal disease agents to cortical hubs

Catenarity in quantum nilpotent algebras

In this paper, it is established that quantum nilpotent algebras (also known as CGL extensions) are catenary, i.e., all saturated chains of inclusions of prime ideals between any two given prime ideals $P \subsetneq Q$ have the same length. This is achieved by proving that the prime spectra of these algebras have normal separation, and then establishing the mild homological conditions necessary to apply a result of Lenagan and the first author. The work also recovers the Tauvel height formula for quantum nilpotent algebras, a result that was first obtained by Lenagan and the authors through a different approach.Comment: 11 page