'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Combined affinity labelling and mass spectrometry analysis of differential cell surface protein expression in normal and prostate cancer cells

Differences in the expression of cell surface proteins between a normal prostate epithelial (1542-NP2TX) and a prostate cancer cell line (1542-CP3TX) derived from the same patient were investigated. A combination of affinity chromatographic purification of biotin-tagged surface proteins with mass spectrometry analysis identified 26 integral membrane proteins and 14 peripheral surface proteins. The findings confirm earlier reports of altered expression in prostate cancer for several cell surface proteins, including ALCAM/CD166, the Ephrin type A receptor, EGFR and the prostaglandin F2 receptor regulatory protein. In addition, several novel findings of differential expression were made, including the voltage-dependent anion selective channel proteins Porin 1 and 2, ecto-5'-nucleotidase (CD73) and Scavenger receptor B1. Cell surface protein expression changed both qualitatively and quantitatively when the cells were grown in the presence of either or both interferon INF alpha and INF gamma. Costimulation with type I and II interferons had additive or synergistic effects on the membrane density of several, mainly peripherally attached surface proteins. Concerted upregulation of surface exposed antigens may be of benefit in immuno-adjuvant-based treatment of interferon-responsive prostate cancer. In conclusion, this study demonstrates that differences in the expression of membrane proteins between normal and prostate cancer cells are reproducibly detectable following vectorial labelling with biotin, and that detailed analysis of extracellular-induced surface changes can be achieved by combining surface-specific labelling with high-resolution two-dimensional gel electrophoresis and mass spectrometry.

Mapping fibre orientation in complex-shaped biological systems with micrometre resolution by scanning X-ray microdiffraction

A fully automated procedure to extract and to image local fibre orientation in biological tissues from scanning X-ray diffraction is presented. The preferred chitin fibre orientation in the flow sensing system of crickets is determined with high spatial resolution by applying synchrotron radiation based X-ray microbeam diffraction in conjunction with advanced sample sectioning using a UV micro-laser. The data analysis is based on an automated detection of azimuthal diffraction maxima after 2D convolution filtering (smoothing) of the 2D diffraction patterns. Under the assumption of crystallographic fibre symmetry around the morphological fibre axis, the evaluation method allows mapping the three-dimensional orientation of the fibre axes in space. The resulting two-dimensional maps of the local fibre orientations - together with the complex shape of the flow sensing system - may be useful for a better understanding of the mechanical optimization of such tissues.

Facial feature extraction and selection by Gabor wavelets and boosting

In this paper, we present a feature selection approach based on Gabor wavelet feature and boosting for face verification. By convolution with a group of Gabor wavelets, the original images are transformed into vectors of Gabor wavelet features. Then for individual person, a small set of significant features are selected by the boosting algorithm from a large set of Gabor wavelet features. The experiment results have shown that the approach successfully selects meaningful and explainable features for face verification. The experiments also suggest that for the common characteristics such as eyes, noses, mouths may not be as important as some unique characteristic when training set is small. When training set is large, the unique characteristics and the common characteristics are both important.

An improved digital deconvolution equation

This paper first points out the important fact that the rectangle formulas of continuous convolution discretization, which was widely used in conventional digital deconvolution algorithms, can result in zero-time error. Then, an improved digital deconvolution equation is suggested which is equivalent to the trapezoid formulas of continuous convolution discretization and can overcome the disadvantage of conventional equation satisfactorily. Finally, a simulation in computer is given, thus confirming the theoretical result.

Deconvolution method for removing the distortion from time jitter in equivalent-time waveform samplers

A sampling oscilloscope is one of the main units in automatic pulse measurement system (APMS). The time jitter in waveform samplers is an important error source that affect the precision of data acquisition. In this paper, this kind of error is greatly reduced by using the deconvolution method. First, the probability density function (PDF) of time jitter distribution is determined by the statistical approach, then, this PDF is used as convolution kern to deconvolve with the acquired waveform data with additional averaging, and the result is the waveform data in which the effect of time jitter has been removed, and the measurement precision of APMS is greatly improved. In addition, some computer simulations are given which prove the success of the method given in this paper.

Early and late stimulus-evoked cortical hemodynamic responses provide insight into the neurogenic nature of neurovascular coupling

Understanding neurovascular coupling is a prerequisite for the interpretation of results obtained from modern neuroimaging techniques. This study investigated the hemodynamic and neural responses in rat somatosensory cortex elicited by 16 seconds electrical whisker stimuli. Hemodynamics were measured by optical imaging spectroscopy and neural activity by multichannel electrophysiology. Previous studies have suggested that the whisker-evoked hemodynamic response contains two mechanisms, a transient ‘backwards’ dilation of the middle cerebral artery, followed by an increase in blood volume localized to the site of neural activity. To distinguish between the mechanisms responsible for these aspects of the response, we presented whisker stimuli during normocapnia (‘control’), and during a high level of hypercapnia. Hypercapnia was used to ‘predilate’ arteries and thus possibly ‘inhibit’ aspects of the response related to the ‘early’ mechanism. Indeed, hemodynamic data suggested that the transient stimulus-evoked response was absent under hypercapnia. However, evoked neural responses were also altered during hypercapnia and convolution of the neural responses from both the normocapnic and hypercapnic conditions with a canonical impulse response function, suggested that neurovascular coupling was similar in both conditions. Although data did not clearly dissociate early and late vascular responses, they suggest that the neurovascular coupling relationship is neurogenic in origin.

Long duration stimuli and nonlinearities in the neural–haemodynamic coupling

Recent studies have shown that the haemodynamic responses to brief (<2 secs) stimuli can be well characterised as a linear convolution of neural activity with a suitable haemodynamic impulse response. In this paper, we show that the linear convolution model cannot predict measurements of blood flow responses to stimuli of longer duration (>2 secs), regardless of the impulse response function chosen. Modifying the linear convolution scheme to a nonlinear convolution scheme was found to provide a good prediction of the observed data. Whereas several studies have found a nonlinear coupling between stimulus input and blood flow responses, the current modelling scheme uses neural activity as an input, and thus implies nonlinearity in the coupling between neural activity and blood flow responses. Neural activity was assessed by current source density analysis of depth-resolved evoked field potentials, while blood flow responses were measured using laser Doppler flowmetry. All measurements were made in rat whisker barrel cortex after electrical stimulation of the whisker pad for 1 to 16 secs at 5 Hz and 1.2 mA (individual pulse width 0.3 ms).

The hemodynamic impulse response to a single neural event

This article investigates the relation between stimulus-evoked neural activity and cerebral hemodynamics. Specifically, the hypothesis is tested that hemodynamic responses can be modeled as a linear convolution of experimentally obtained measures of neural activity with a suitable hemodynamic impulse response function. To obtain a range of neural and hemodynamic responses, rat whisker pad was stimulated using brief (less than or equal to2 seconds) electrical stimuli consisting of single pulses (0.3 millisecond, 1.2 mA) combined both at different frequencies and in a paired-pulse design. Hemodynamic responses were measured using concurrent optical imaging spectroscopy and laser Doppler flowmetry, whereas neural responses were assessed through current source density analysis of multielectrode recordings from a single barrel. General linear modeling was used to deconvolve the hemodynamic impulse response to a single "neural event" from the hemodynamic and neural responses to stimulation. The model provided an excellent fit to the empirical data. The implications of these results for modeling schemes and for physiologic systems coupling neural and hemodynamic activity are discussed.

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.