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Concept: Hilbert space



The assessment of body hydration is a complex process, and no measurement is valid for all situations. Bioelectrical impedance vector analysis (BIVA) has emerged as a relatively novel technique for assessing hydration status in sports. We applied BIVA a) to determine hydration changes evoked by an intense synchronized swimming (SS) training session; b) to characterize the sample of young elite swimmers in relation with a nonathletic reference population; and c) to generate its 50%, 75% and 95% percentiles of the bioelectrical variables.

Concepts: Measurement, Psychometrics, Hilbert space, 2000s music groups, Complex number, 1990s music groups, Swimming, Synchronized swimming


A combined stress-vibration sensor was developed to measure stress and vibration simultaneously based on fiber Bragg grating (FBG) technology. The sensor is composed of two FBGs and a stainless steel plate with a special design. The two FBGs sense vibration and stress and the sensor can realize temperature compensation by itself. The stainless steel plate can significantly increase sensitivity of vibration measurement. Theoretical analysis and Finite Element Method (FEM) were used to analyze the sensor’s working mechanism. As demonstrated with analysis, the obtained sensor has working range of 0-6000 Hz for vibration sensing and 0-100 MPa for stress sensing, respectively. The corresponding sensitivity for vibration is 0.46 pm/g and the resulted stress sensitivity is 5.94 pm/MPa, while the nonlinearity error for vibration and stress measurement is 0.77% and 1.02%, respectively. Compared to general FBGs, the vibration sensitivity of this sensor is 26.2 times higher. Therefore, the developed sensor can be used to concurrently detect vibration and stress. As this sensor has height of 1 mm and weight of 1.15 g, it is beneficial for minimization and integration.

Concepts: Finite element method, Hilbert space, Bragg diffraction, Steel, Partial differential equation, Stainless steel, Bragg's law, Fiber Bragg grating


In the present study, we examined the ability of the recombinant spidroin to serve as a substrate for the cardiac tissue engineering. For this purpose, isolated neonatal rat cardiomyocytes were seeded on the electrospun spidroin fiber matrices and cultured to form the confluent cardiac monolayers. Besides the adhesion assay and immunostaining analysis, we tested the ability of the cultured cardiomyocytes to form a functional cardiac syncytium by studying excitation propagation in the cultured tissue with the aid of optical mapping. It was demonstrated that recombinant spidroin fiber meshes are directly suitable for the adherence and growth of the cardiomyocytes without additional coating with the attachment factors, such as fibronectin.

Concepts: Present, Blood, Extracellular matrix, Cardiac muscle, Engineering, Hilbert space, Functional analysis, Calculus of variations


To improve understanding of the internal structure of the proximal phalanx (P1), response of the bone to load and possible relation to the pathogenesis of fractures in P1.

Concepts: Finite element method, Hilbert space, Set theory, Partial differential equation, Finite element method in structural mechanics, Discrete mathematics


BACKGROUND: Gene Set Analysis (GSA) has proven to be a useful approach to microarray analysis. However, most of the method development for GSA has focused on the statistical tests to be used rather than on the generation of sets that will be tested. Existing methods of set generation are often overly simplistic. The creation of sets from individual pathways (in isolation) is a poor reflection of the complexity of the underlying metabolic network. We have developed a novel approach to set generation via the use of Principal Component Analysis of the Laplacian matrix of a metabolic network. We have analysed a relatively simple data set to show the difference in results between our method and the current state of the art pathway-based sets. RESULTS: The sets generated with this method are semi-exhaustive and capture much of the topological complexity of the metabolic network. This semi-exhaustive nature of this method has also allowed us to design a hypergeometric enrichment test to determine which genes are likely responsible for set significance. We show that our method finds significant aspects of biology that would be missed (i.e. false negatives) and addresses the false positive rates found with the use of simple pathway-based sets. CONCLUSIONS: The set generation step for GSA is often neglected but is a crucial part of the analysis as it defines the full context for the analysis. As such, set generation methods should be robust and yield as complete a representation of the extant biological knowledge as possible. The method reported here achieves this goal and is demonstrably superior to previous set analysis methods.

Concepts: Gene, Statistics, Biology, Type I and type II errors, Hilbert space, Principal component analysis, Graph theory, Statistical hypothesis testing


The management of enterocutaneous fistulae (ECF) is complex and challenging. We have examined factors associated with fistula healing at a National Intestinal Failure Centre, and have devised the first scoring system to predict spontaneous fistula healing prior to surgery.

Concepts: Multivariate statistics, Ulcerative colitis, Hilbert space, Manifold, Fistula, Multivariate analysis, Anal fistula


We present an ab initio potential for the H-CO(X ^2 A') complex in which the CO bond length is varied and the long range interactions between H and CO are accurately represented. It was computed using the spin-unrestricted open-shell single and double excitation coupled cluster method with perturbative triples [UCCSD(T)]. Three doubly augmented correlation-consistent basis sets were utilized to extrapolate the correlation energy to the complete basis set limit. More than 4400 data points were calculated and used for an analytic fit of the potential: long range terms with inverse power dependence on the H-CO distance R were fit to the data points for large R, the reproducing kernel Hilbert space (RKHS) method was applied to the data at smaller distances. Our potential was compared with previous calculations and with some data extracted from spectroscopy. Furthermore, it was used in three-dimensional discrete variable representation (DVR) calculations of the vibrational frequencies and rotational constants of HCO, which agree very well with the most recently measured data. Also the dissociation energy D_0 = 0.623 eV of HCO into H + CO obtained from these calculations agrees well with experimental values. Finally, we made preliminary two-dimensional (2D) calculations of the cross sections for rotationally inelastic H-CO collisions with the CO bond length fixed and obtained good agreement with recently published 2D results.

Concepts: Energy, Computational chemistry, Hilbert space, Quantum chemistry, Basis set, Distance, Analytic geometry, Reproducing kernel Hilbert space


Kernel machines traditionally arise from an elegant formulation based on measuring the smoothness of the admissible solutions by the norm in the reproducing kernel Hilbert space (RKHS) generated by the chosen kernel. It was pointed out that they can be formulated in a related functional framework, in which the Green’s function of suitable differential operators is thought of as a kernel. In this letter, our own picture of this intriguing connection is given by emphasizing some relevant distinctions between these different ways of measuring the smoothness of admissible solutions. In particular, we show that for some kernels, there is no associated differential operator. The crucial relevance of boundary conditions is especially emphasized, which is in fact the truly distinguishing feature of the approach based on differential operators. We provide a general solution to the problem of learning from data and boundary conditions and illustrate the significant role played by boundary conditions with examples. It turns out that the degree of freedom that arises in the traditional formulation of kernel machines is indeed a limitation, which is partly overcome when incorporating the boundary conditions. This likely holds true in many real-world applications in which there is prior knowledge about the expected behavior of classifiers and regressors on the boundary.

Concepts: Hilbert space, Vector space, Derivative, Operator, Functional analysis, Kernel trick, Reproducing kernel Hilbert space, Differential operator


BACKGROUND: This study aims to clarify the effect of various designs of reverse shoulder prosthesis (RSP) on stress variation of its glenoid component using 2-dimensional (2D) finite element analysis (FEA). This FEA study provides future reference for the optimal design of glenoid component of RSP. MATERIALS AND METHODS: In this study, a 2D finite element (FE) model of human shoulder with implementation of RSP was developed by commercial FE software. The proper material properties were adopted in our model. Various design factors were simulated and all the mechanical profile data were investigated by FEA. RESULTS: Both distal placement and increased lateral offset of glenosphere induce higher stress over glenoid-baseplate junction. Increased thickness of graft, inferiorly tilting of the baseplate, and adoption of BIO-RSA (bony increased-offset reverse shoulder arthroplasty) incur higher stresses over glenoid screws. The inferior screw attains more stress than superior screw. Maximum stress occurs at the base of inferior screw. CONCLUSION: Increased eccentric offset and lateral offset of glenosphere, although being able to reduce notching, may pay the penalty of significant stress concentration over glenoid and its subsequent loosening. Maximum stress occurs at the base of inferior screw elucidate the direct contact failure mode at the middle of inferior screw. This study provides an alternative tool for the optimal design of glenoid component of RSP in the future.

Concepts: Engineering, Finite element method, Hilbert space, Shoulder, Partial differential equation, Finite element method in structural mechanics, Structural analysis