A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Observability analysis of electric networks considering branch impedance

This paper presents an analytical method to analyze the effect of X to R ratio as well as impedance value of branches on observability of a network based on un-decoupled formulation of state estimation (SE) and null space of matrices. The results showed that the X to R ratio of branches had no effect on the observability of networks. In addition, it was shown that observability of some networks was affected by impedance values while some others were not affected. In addition, for branch observability analysis of radial network, a simple and quick method is developed. Illustrative examples of the network under transmission and distribution voltages demonstrate the effectiveness of the proposed methods.

Kinematics of pantograph masts

This paper deals with the kinematics of pantograph masts. Pantograph masts have widespread use in space application as deployable structures. They are over constrained mechanisms with degree-of-freedom, evaluated by the Grübler–Kutzback formula, as less than one. In this paper, a numerical algorithm is used to evaluate the degree-of-freedom of pantograph masts by obtaining the null space of a constraint Jacobian matrix. In the process redundant joints in the masts are obtained. A method based on symbolic computation, to obtain the closed-form kinematics equations of triangular and box shaped pantograph masts, is presented. In the process, the various configurations such masts can attain during deployment, are obtained. The closed-form solution also helps in identifying the redundant joints in the masts. The symbolic computations involving the Jacobian matrix also leads to a method to evaluate the global degree-of-freedom for these masts.

XOR-based hash functions

Bank conflicts can severely reduce the bandwidth of an interleaved multibank memory and conflict misses increase the miss rate of a cache or a predictor. Both occurrences are manifestations of the same problem: Objects which should be mapped to different indices are accidentally mapped to the same index. Suitable chosen hash functions can avoid conflicts in each of these situations by mapping the most frequently occurring patterns conflict-free. A particularly interesting class of hash functions are the XOR-based hash functions, which compute each set index bit as the exclusive-or of a subset of the address bits. When implementing an XOR-based hash function, it is extremely important to understand what patterns are mapped conflict-free and how a hash function can be constructed to map the most frequently occurring patterns without conflicts. Hereto, this paper presents two ways to reason about hash functions: by their null space and by their column space. The null space helps to quickly determine whether a pattern is mapped conflict-free. The column space is more useful for other purposes, e. g., to reduce the fan-in of the XOR-gates without introducing conflicts or to evaluate interbank dispersion in skewed-associative caches. Examples illustrate how these ideas can be applied to construct conflict-free hash functions.

Highly accurate and efficient evaluation of randomising set index functions

Randomising set index functions can reduce the number of conflict misses in data caches by spreading the cache blocks uniformly over all sets. Typically, the randomisation functions compute the exclusive ors of several address bits. Not all randomising set index functions perform equally well, which calls for the evaluation of many set index functions. This paper discusses and improves a technique that tackles this problem by predicting the miss rate incurred by a randomisation function, based on profiling information. A new way of looking at randomisation functions is used, namely the null space of the randomisation function. The members of the null space describe pairs of cache blocks that are mapped to the same set. This paper presents an analytical model of the error made by the technique and uses this to propose several optimisations to the technique. The technique is then applied to generate a conflict-free randomisation function for the SPEC benchmarks. (C) 2003 Elsevier Science B.V. All rights reserved.

Designing optimal fault tolerant Jacobian for robotic manipulators

Fault tolerance of robotic manipulators is determined based on the fault tolerance measures. In this study a Jacobian of a 7DOF optimal fault tolerant manipulator is designed based on optimality of worse case relative manipulability and worse case dexterity from geometric perspective instead of numerical solution of constrained optimisation problem or construction of optimal Jacobean through a desired null space. The proposed Jacobean matrix is optimal and equally fault tolerant for a single joint failure within any joint of the manipulators.

A class of optimal fault tolerant Jacobian for minimal redundant manipulators based on symmetric geometries

Design of locally optimal fault tolerant manipulators has been recently addressed via using the constraints of the desired null space for the Jacobian matrix of the manipulators. In the present paper the Jacobian matrices for optimal fault tolerance are presented based on geometric properties of column vectors instead of the null space. They are equally fault tolerant to a single joint failure from the worst-case relative manipulability and worst-case dexterity points of view. The optimality is achieved through a symmetric distribution of points on spheres.

Optimal fault tolerant Jacobian matrix generators for redundant manipulators

The design of locally optimal fault-tolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian matrix is obtained. In this study, an optimal fault-tolerant Jacobian matrix generator is introduced from geometric properties instead of the null space properties. The proposed generator provides equally fault-tolerant Jacobian matrices in R3 that are optimally fault tolerant for one or two locked joint failures. It is shown that the proposed optimal Jacobian matrices are directly obtained via regular pyramids. The geometric approach and zonotopes are used as a novel tool for determining relative manipulability in the context of fault-tolerant robotics and for bringing geometric insight into the design of optimal fault-tolerant manipulators.

Análise de resolução em tomografia interpoços em 3-D

A aplicação de métodos de inversão aos dados de múltiplos levantamentos sísmicos interpoços permite a reconstrução de modelos de vagarosidade em 3-D de alta resolução adequados para monitoramento de processos de recuperação avançada de petróleo e caracterização de reservatórios. Entretanto, a falta de cobertura volumétrica uniforme de raios de levantamentos interpoços exige informação adicional ao sistema tomográfico para obtenção de soluções estáveis. A discretização do modelo em uma malha 3-D com células prismáticas triangulares e a decomposição em valores singulares são utilizadas para avaliar a reconstrução tomográfica em 3-D. O ângulo da projeção de modelos-alvo no subespaço ortogonal ao espaço nulo efetivo da matriz tomográfica é um critério adequado para se otimizar a malha de discretização do modelo interpretativo e a geometria de aquisição dos dados de modo a melhorar o condicionamento da reconstrução tomográfica. Esta abordagem pode ser utilizada durante as iterações lineares para redefinir a malha ou avaliar a necessidade de informação a priori adicional ao sistema tomográfico.

Coordinated Control of Robotic Swarms in Unknown Environments

This thesis gathers the work carried out by the author in the last three years of research and it concerns the study and implementation of algorithms to coordinate and control a swarm of mobile robots moving in unknown environments. In particular, the author's attention is focused on two different approaches in order to solve two different problems. The first algorithm considered in this work deals with the possibility of decomposing a main complex task in many simple subtasks by exploiting the decentralized implementation of the so called \emph{Null Space Behavioral} paradigm. This approach to the problem of merging different subtasks with assigned priority is slightly modified in order to handle critical situations that can be detected when robots are moving through an unknown environment. In fact, issues can occur when one or more robots got stuck in local minima: a smart strategy to avoid deadlock situations is provided by the author and the algorithm is validated by simulative analysis. The second problem deals with the use of concepts borrowed from \emph{graph theory} to control a group differential wheel robots by exploiting the Laplacian solution of the consensus problem. Constraints on the swarm communication topology have been introduced by the use of a range and bearing platform developed at the Distributed Intelligent Systems and Algorithms Laboratory (DISAL), EPFL (Lausanne, CH) where part of author's work has been carried out. The control algorithm is validated by demonstration and simulation analysis and, later, is performed by a team of four robots engaged in a formation mission. To conclude, the capabilities of the algorithm based on the local solution of the consensus problem for differential wheel robots are demonstrated with an application scenario, where nine robots are engaged in a hunting task.

The underlying pathway structure of biochemical reaction networks

Bioinformatics is yielding extensive, and in some cases complete, genetic and biochemical information about individual cell types and cellular processes, providing the composition of living cells and the molecular structure of its components. These components together perform integrated cellular functions that now need to be analyzed. In particular, the functional definition of biochemical pathways and their role in the context of the whole cell is lacking. In this study, we show how the mass balance constraints that govern the function of biochemical reaction networks lead to the translation of this problem into the realm of linear algebra. The functional capabilities of biochemical reaction networks, and thus the choices that cells can make, are reflected in the null space of their stoichiometric matrix. The null space is spanned by a finite number of basis vectors. We present an algorithm for the synthesis of a set of basis vectors for spanning the null space of the stoichiometric matrix, in which these basis vectors represent the underlying biochemical pathways that are fundamental to the corresponding biochemical reaction network. In other words, all possible flux distributions achievable by a defined set of biochemical reactions are represented by a linear combination of these basis pathways. These basis pathways thus represent the underlying pathway structure of the defined biochemical reaction network. This development is significant from a fundamental and conceptual standpoint because it yields a holistic definition of biochemical pathways in contrast to definitions that have arisen from the historical development of our knowledge about biochemical processes. Additionally, this new conceptual framework will be important in defining, characterizing, and studying biochemical pathways from the rapidly growing information on cellular function.

Strings vs. spins on the null orbifold

We study the null orbifold singularity in 2+1 d flat space higher spin theory as well as string theory. Using the Chern-Simons formulation of 2+1 d Einstein gravity, we first observe that despite the singular nature of this geometry, the eigenvalues of its Chern-Simons holonomy are trivial. Next, we construct a resolution of the singularity in higher spin theory: a Kundt spacetime with vanishing scalar curvature invariants. We also point out that the UV divergences previously observed in the 2-to-2 tachyon tree level string amplitude on the null orbifold do not arise in the at alpha' -> infinity limit. We find all the divergences of the amplitude and demonstrate that the ones remaining in the tensionless limit are physical IR-type divergences. We conclude with a discussion on the meaning and limitations of higher spin (cosmological) singularity resolution and its potential connection to string theory.

Towards accurate estimation of the proportion of true null hypotheses in multiple testing

Background

Biomedical researchers are now often faced with situations where it is necessary to test a large number of hypotheses simultaneously, eg, in comparative gene expression studies using high-throughput microarray technology. To properly control false positive errors the FDR (false discovery rate) approach has become widely used in multiple testing. The accurate estimation of FDR requires the proportion of true null hypotheses being accurately estimated. To date many methods for estimating this quantity have been proposed. Typically when a new method is introduced, some simulations are carried out to show the improved accuracy of the new method. However, the simulations are often very limited to covering only a few points in the parameter space.

Results

Here I have carried out extensive in silico experiments to compare some commonly used methods for estimating the proportion of true null hypotheses. The coverage of these simulations is unprecedented thorough over the parameter space compared to typical simulation studies in the literature. Thus this work enables us to draw conclusions globally as to the performance of these different methods. It was found that a very simple method gives the most accurate estimation in a dominantly large area of the parameter space. Given its simplicity and its overall superior accuracy I recommend its use as the first choice for estimating the proportion of true null hypotheses in multiple testing.

On purely gravito-magnetic vacuum space-times

It is shown that there are no purely magnetic, vacuum, spacetime metrics where any one of the following conditions holds: (a) the ratio of any two eigenvalues of the Weyl tensor is constant, (b) both of the Riemann principal null directions, defining the time-like blade, are nonrotating, (c) the shear tensor possesses an eigenvector v^a which is defined by one of the space-like Riemann principal directions, (d) the vorticity is parallel to v^a, where v^a is defined by one of the space-like Riemann principal directions.

Avaliação de um método de cromatografia em fase gasosa head space e estudo da estabilidade do etanol em amostras de sangue

The ethanol is the most overused psychoactive drug over the world; this fact makes it one of the main substances required in toxicological exams nowadays. The development of an analytical method, adaptation or implementation of a method known, involves a process of validation that estimates its efficiency in the laboratory routine and credibility of the method. The stability is defined as the ability of the sample of material to keep the initial value of a quantitative measure for a defined period within specific limits when stored under defined conditions. This study aimed to evaluate the method of Gas chromatography and study the stability of ethanol in blood samples, considering the variables time and temperature of storage, and the presence of preservative and, with that check if the conditions of conservation and storage used in this study maintain the quality of the sample and preserve the originally amount of analyte present. Blood samples were collected from 10 volunteers to evaluate the method and to study the stability of ethanol. For the evaluation of the method, part of the samples was added to known concentrations of ethanol. In the study of stability, the other side of the pool of blood was placed in two containers: one containing the preservative sodium fluoride 1% and the anticoagulant heparin and the other only heparin, was added ethanol at a concentration of 0.6 g/L, fractionated in two bottles, one being stored at 4ºC (refrigerator) and another at -20ºC (freezer), the tests were performed on the same day (time zero) and after 1, 3, 7, 14, 30 and 60 days of storage. The assessment found the difference in results during storage in relation to time zero. It used the technique of headspace associated with gas chromatography with the FID and capillary column with stationary phase of polyethylene. The best analysis of chromatographic conditions were: temperature of 50ºC (column), 150ºC (jet) and 250ºC (detector), with retention time for ethanol from 9.107 ± 0.026 and the tercbutanol (internal standard) of 8.170 ± 0.081 minutes, the ethanol being separated properly from acetaldehyde, acetone, methanol and 2-propanol, which are potential interfering in the determination of ethanol. The technique showed linearity in the concentration range of 0.01 and 3.2 g/L (0.8051 x + y = 0.6196; r2 = 0.999). The calibration curve showed the following equation of the line: y = x 0.7542 + 0.6545, with a linear correlation coefficient equal to 0.996. The average recovery was 100.2%, the coefficients of variation of accuracy and inter intra test showed values of up to 7.3%, the limit of detection and quantification was 0.01 g/L and showed coefficient of variation within the allowed. The analytical method evaluated in this study proved to be fast, efficient and practical, given the objective of this work satisfactorily. The study of stability has less than 20% difference in the response obtained under the conditions of storage and stipulated period, compared with the response obtained at time zero and at the significance level of 5%, no statistical difference in the concentration of ethanol was observed between analysis. The results reinforce the reliability of the method of gas chromatography and blood samples in search of ethanol, either in the toxicological, forensic, social or clinic