Efficient Kernel Computation for Volterra Filter Structure Evaluation

Despite their generality, conventional Volterra filters are inadequate for some applications, due to the huge number of parameters that may be needed for accurate modelling. When a state-space model of the target system is known, this can be assessed by computing its kernels, which also provides valuable information for choosing an adequate alternate Volterra filter structure, if necessary, and is useful for validating parameter estimation procedures. In this letter, we derive expressions for the kernels by using the Carleman bilinearization method, for which an efficient algorithm is given. Simulation results are presented, which confirm the usefulness of the proposed approach.

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm

Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

Nutritive value of palm kernel meal in diets for growing rabbits

The aim of this work was to determine the nutritive value of palm kernel meal (PKM) in diets for growing rabbits. In Experiment 1, 20 New Zealand × Californian growing rabbits 50 d-old were used to determine energy, crude protein, fibre and fat digestibility of PKM. The nutritive value was estimated by the difference method using a basal diet and another diet made by substituting 200 g/kg of basal diet with PKM. Energy, crude protein, ether extract and neutral detergent fibre of PKM digestibilities were, respectively, 0.549 (±0.056, SE), 0.541 (±0.069), 0.850 (±0.048) and 0.430 (±0.101), and the digestible energy concentration was 10.9 MJ/kg (±1.03) DM. In Experiment 2, 412 rabbits were allocated at random to the two experimental diets to measure growing performance. Inclusion of 200 g PKM/kg in the diet did not affect feed or digestible energy intake but decreased slightly (by around 5%) average daily gain (P = 0.003) and feed efficiency (P < 0.001). Neither mortality nor Clostridium perfringens counts in soft faeces were affected by type of diet. Palm kernel meal can be considered a palatable source of fibre, protein and fat for rabbits and can substitute significant amounts of other fibrous ingredients in the diet without adverse effects on growth performance.

Bernstein polynomials in element-free Galerkin method

In the recent decades, meshless methods (MMs), like the element-free Galerkin method (EFGM), have been widely studied and interesting results have been reached when solving partial differential equations. However, such solutions show a problem around boundary conditions, where the accuracy is not adequately achieved. This is caused by the use of moving least squares or residual kernel particle method methods to obtain the shape functions needed in MM, since such methods are good enough in the inner of the integration domains, but not so accurate in boundaries. This way, Bernstein curves, which are a partition of unity themselves,can solve this problem with the same accuracy in the inner area of the domain and at their boundaries.

Representations of Inverse Functions by the Integral Transform with the Sign Kernel

Mathematics Subject Classification: Primary 30C40

An edge-based matching kernel through discrete-time quantum walks

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

Monte Carlo Method for Reconstruction of Densities

2000 Mathematics Subject Classification: 65C05

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method

2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.

Heat kernel and worldline path integrals for the Proca theory

In this thesis we study the heat kernel, a useful tool to analyze various properties of different quantum field theories. In particular, we focus on the study of the one-loop effective action and the application of worldline path integrals to derive perturbatively the heat kernel coefficients for the Proca theory of massive vector fields. It turns out that the worldline path integral method encounters some difficulties if the differential operator of the heat kernel is of non-minimal kind. More precisely, a direct recasting of the differential operator in terms of worldline path integrals, produces in the classical action a non-perturbative vertex and the path integral cannot be solved. In this work we wish to find ways to circumvent this issue and to give a suggestion to solve similar problems in other contexts.

A Highly Improved Method For Sensitive Determination Of Amitriptyline In Pharmaceutical Formulations Using An Unmodified Carbon Nanotube Electrode In The Presence Of Sulfuric Acid.

The present paper describes a novel, simple and reliable differential pulse voltammetric method for determining amitriptyline (AMT) in pharmaceutical formulations. It has been described for many authors that this antidepressant is electrochemically inactive at carbon electrodes. However, the procedure proposed herein consisted in electrochemically oxidizing AMT at an unmodified carbon nanotube paste electrode in the presence of 0.1 mol L(-1) sulfuric acid used as electrolyte. At such concentration, the acid facilitated the AMT electroxidation through one-electron transfer at 1.33 V vs. Ag/AgCl, as observed by the augmentation of peak current. Concerning optimized conditions (modulation time 5 ms, scan rate 90 mV s(-1), and pulse amplitude 120 mV) a linear calibration curve was constructed in the range of 0.0-30.0 μmol L(-1), with a correlation coefficient of 0.9991 and a limit of detection of 1.61 μmol L(-1). The procedure was successfully validated for intra- and inter-day precision and accuracy. Moreover, its feasibility was assessed through analysis of commercial pharmaceutical formulations and it has been compared to the UV-vis spectrophotometric method used as standard analytical technique recommended by the Brazilian Pharmacopoeia.

Influence Of Delivery Method On Neuroprotection By Bone Marrow Mononuclear Cell Therapy Following Ventral Root Reimplantation With Fibrin Sealant.

The present work compared the local injection of mononuclear cells to the spinal cord lateral funiculus with the alternative approach of local delivery with fibrin sealant after ventral root avulsion (VRA) and reimplantation. For that, female adult Lewis rats were divided into the following groups: avulsion only, reimplantation with fibrin sealant; root repair with fibrin sealant associated with mononuclear cells; and repair with fibrin sealant and injected mononuclear cells. Cell therapy resulted in greater survival of spinal motoneurons up to four weeks post-surgery, especially when mononuclear cells were added to the fibrin glue. Injection of mononuclear cells to the lateral funiculus yield similar results to the reimplantation alone. Additionally, mononuclear cells added to the fibrin glue increased neurotrophic factor gene transcript levels in the spinal cord ventral horn. Regarding the motor recovery, evaluated by the functional peroneal index, as well as the paw print pressure, cell treated rats performed equally well as compared to reimplanted only animals, and significantly better than the avulsion only subjects. The results herein demonstrate that mononuclear cells therapy is neuroprotective by increasing levels of brain derived neurotrophic factor (BDNF) and glial derived neurotrophic factor (GDNF). Moreover, the use of fibrin sealant mononuclear cells delivery approach gave the best and more long lasting results.

Uv-vis Spectra As An Alternative To The Lowry Method For Quantify Hair Damage Induced By Surfactants.

It is well known that long term use of shampoo causes damage to human hair. Although the Lowry method has been widely used to quantify hair damage, it is unsuitable to determine this in the presence of some surfactants and there is no other method proposed in literature. In this work, a different method is used to investigate and compare the hair damage induced by four types of surfactants (including three commercial-grade surfactants) and water. Hair samples were immersed in aqueous solution of surfactants under conditions that resemble a shower (38 °C, constant shaking). These solutions become colored with time of contact with hair and its UV-vis spectra were recorded. For comparison, the amount of extracted proteins from hair by sodium dodecyl sulfate (SDS) and by water were estimated by the Lowry method. Additionally, non-pigmented vs. pigmented hair and also sepia melanin were used to understand the washing solution color and their spectra. The results presented herein show that hair degradation is mostly caused by the extraction of proteins, cuticle fragments and melanin granules from hair fiber. It was found that the intensity of solution color varies with the charge density of the surfactants. Furthermore, the intensity of solution color can be correlated to the amount of proteins quantified by the Lowry method as well as to the degree of hair damage. UV-vis spectrum of hair washing solutions is a simple and straightforward method to quantify and compare hair damages induced by different commercial surfactants.

Graded Meshes In Bio-thermal Problems With Transmission-line Modeling Method.

In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems.