Influence of the implanted pulse generator as reference electrode in finite element model of monopolar deep brain stimulation.

Electrical deep brain stimulation (DBS) is an efficient method to treat movement disorders. Many models of DBS, based mostly on finite elements, have recently been proposed to better understand the interaction between the electrical stimulation and the brain tissues. In monopolar DBS, clinically widely used, the implanted pulse generator (IPG) is used as reference electrode (RE). In this paper, the influence of the RE model of monopolar DBS is investigated. For that purpose, a finite element model of the full electric loop including the head, the neck and the superior chest is used. Head, neck and superior chest are made of simple structures such as parallelepipeds and cylinders. The tissues surrounding the electrode are accurately modelled from data provided by the diffusion tensor magnetic resonance imaging (DT-MRI). Three different configurations of RE are compared with a commonly used model of reduced size. The electrical impedance seen by the DBS system and the potential distribution are computed for each model. Moreover, axons are modelled to compute the area of tissue activated by stimulation. Results show that these indicators are influenced by the surface and position of the RE. The use of a RE model corresponding to the implanted device rather than the usually simplified model leads to an increase of the system impedance (+48%) and a reduction of the area of activated tissue (-15%).

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Integral cohomology of finite postnikov towers

Depuis le séminaire H. Cartan de 1954-55, il est bien connu que l'on peut trouver des éléments de torsion arbitrairement grande dans l'homologie entière des espaces d'Eilenberg-MacLane K(G,n) où G est un groupe abélien non trivial et n>1. L'objectif majeur de ce travail est d'étendre ce résultat à des H-espaces possédant plus d'un groupe d'homotopie non trivial. Dans le but de contrôler précisément le résultat de H. Cartan, on commence par étudier la dualité entre l'homologie et la cohomologie des espaces d'Eilenberg-MacLane 2-locaux de type fini. On parvient ainsi à raffiner quelques résultats qui découlent des calculs de H. Cartan. Le résultat principal de ce travail peut être formulé comme suit. Soit X un H-espace ne possédant que deux groupes d'homotopie non triviaux, tous deux finis et de 2-torsion. Alors X n'admet pas d'exposant pour son groupe gradué d'homologie entière réduite. On construit une large classe d'espaces pour laquelle ce résultat n'est qu'une conséquence d'une caractéristique topologique, à savoir l'existence d'un rétract faible X K(G,n) pour un certain groupe abélien G et n>1. On généralise également notre résultat principal à des espaces plus compliqués en utilisant la suite spectrale d'Eilenberg-Moore ainsi que des méthodes analytiques faisant apparaître les nombres de Betti et leur comportement asymptotique. Finalement, on conjecture que les espaces qui ne possédent qu'un nombre fini de groupes d'homotopie non triviaux n'admettent pas d'exposant homologique. Ce travail contient par ailleurs la présentation de la « machine d'Eilenberg-MacLane », un programme C++ conçu pour calculer explicitement les groupes d'homologie entière des espaces d'Eilenberg-MacLane. <br/><br/>By the work of H. Cartan, it is well known that one can find elements of arbitrarilly high torsion in the integral (co)homology groups of an Eilenberg-MacLane space K(G,n), where G is a non-trivial abelian group and n>1. The main goal of this work is to extend this result to H-spaces having more than one non-trivial homotopy groups. In order to have an accurate hold on H. Cartan's result, we start by studying the duality between homology and cohomology of 2-local Eilenberg-MacLane spaces of finite type. This leads us to some improvements of H. Cartan's methods in this particular case. Our main result can be stated as follows. Let X be an H-space with two non-vanishing finite 2-torsion homotopy groups. Then X does not admit any exponent for its reduced integral graded (co)homology group. We construct a wide class of examples for which this result is a simple consequence of a topological feature, namely the existence of a weak retract X K(G,n) for some abelian group G and n>1. We also generalize our main result to more complicated stable two stage Postnikov systems, using the Eilenberg-Moore spectral sequence and analytic methods involving Betti numbers and their asymptotic behaviour. Finally, we investigate some guesses on the non-existence of homology exponents for finite Postnikov towers. We conjecture that Postnikov pieces do not admit any (co)homology exponent. This work also includes the presentation of the "Eilenberg-MacLane machine", a C++ program designed to compute explicitely all integral homology groups of Eilenberg-MacLane spaces. <br/><br/>Il est toujours difficile pour un mathématicien de parler de son travail. La difficulté réside dans le fait que les objets qu'il étudie sont abstraits. On rencontre assez rarement un espace vectoriel, une catégorie abélienne ou une transformée de Laplace au coin de la rue ! Cependant, même si les objets mathématiques sont difficiles à cerner pour un non-mathématicien, les méthodes pour les étudier sont essentiellement les mêmes que celles utilisées dans les autres disciplines scientifiques. On décortique les objets complexes en composantes plus simples à étudier. On dresse la liste des propriétés des objets mathématiques, puis on les classe en formant des familles d'objets partageant un caractère commun. On cherche des façons différentes, mais équivalentes, de formuler un problème. Etc. Mon travail concerne le domaine mathématique de la topologie algébrique. Le but ultime de cette discipline est de parvenir à classifier tous les espaces topologiques en faisant usage de l'algèbre. Cette activité est comparable à celle d'un ornithologue (topologue) qui étudierait les oiseaux (les espaces topologiques) par exemple à l'aide de jumelles (l'algèbre). S'il voit un oiseau de petite taille, arboricole, chanteur et bâtisseur de nids, pourvu de pattes à quatre doigts, dont trois en avant et un, muni d'une forte griffe, en arrière, alors il en déduira à coup sûr que c'est un passereau. Il lui restera encore à déterminer si c'est un moineau, un merle ou un rossignol. Considérons ci-dessous quelques exemples d'espaces topologiques: a) un cube creux, b) une sphère et c) un tore creux (c.-à-d. une chambre à air). a) b) c) Si toute personne normalement constituée perçoit ici trois figures différentes, le topologue, lui, n'en voit que deux ! De son point de vue, le cube et la sphère ne sont pas différents puisque ils sont homéomorphes: on peut transformer l'un en l'autre de façon continue (il suffirait de souffler dans le cube pour obtenir la sphère). Par contre, la sphère et le tore ne sont pas homéomorphes: triturez la sphère de toutes les façons (sans la déchirer), jamais vous n'obtiendrez le tore. Il existe un infinité d'espaces topologiques et, contrairement à ce que l'on serait naïvement tenté de croire, déterminer si deux d'entre eux sont homéomorphes est très difficile en général. Pour essayer de résoudre ce problème, les topologues ont eu l'idée de faire intervenir l'algèbre dans leurs raisonnements. Ce fut la naissance de la théorie de l'homotopie. Il s'agit, suivant une recette bien particulière, d'associer à tout espace topologique une infinité de ce que les algébristes appellent des groupes. Les groupes ainsi obtenus sont appelés groupes d'homotopie de l'espace topologique. Les mathématiciens ont commencé par montrer que deux espaces topologiques qui sont homéomorphes (par exemple le cube et la sphère) ont les même groupes d'homotopie. On parle alors d'invariants (les groupes d'homotopie sont bien invariants relativement à des espaces topologiques qui sont homéomorphes). Par conséquent, deux espaces topologiques qui n'ont pas les mêmes groupes d'homotopie ne peuvent en aucun cas être homéomorphes. C'est là un excellent moyen de classer les espaces topologiques (pensez à l'ornithologue qui observe les pattes des oiseaux pour déterminer s'il a affaire à un passereau ou non). Mon travail porte sur les espaces topologiques qui n'ont qu'un nombre fini de groupes d'homotopie non nuls. De tels espaces sont appelés des tours de Postnikov finies. On y étudie leurs groupes de cohomologie entière, une autre famille d'invariants, à l'instar des groupes d'homotopie. On mesure d'une certaine manière la taille d'un groupe de cohomologie à l'aide de la notion d'exposant; ainsi, un groupe de cohomologie possédant un exposant est relativement petit. L'un des résultats principaux de ce travail porte sur une étude de la taille des groupes de cohomologie des tours de Postnikov finies. Il s'agit du théorème suivant: un H-espace topologique 1-connexe 2-local et de type fini qui ne possède qu'un ou deux groupes d'homotopie non nuls n'a pas d'exposant pour son groupe gradué de cohomologie entière réduite. S'il fallait interpréter qualitativement ce résultat, on pourrait dire que plus un espace est petit du point de vue de la cohomologie (c.-à-d. s'il possède un exposant cohomologique), plus il est intéressant du point de vue de l'homotopie (c.-à-d. il aura plus de deux groupes d'homotopie non nuls). Il ressort de mon travail que de tels espaces sont très intéressants dans le sens où ils peuvent avoir une infinité de groupes d'homotopie non nuls. Jean-Pierre Serre, médaillé Fields en 1954, a montré que toutes les sphères de dimension >1 ont une infinité de groupes d'homotopie non nuls. Des espaces avec un exposant cohomologique aux sphères, il n'y a qu'un pas à franchir...

Kumar's algorithm for solving Toeplitz systems of equations over finite fields

Adaptació de l'algorisme de Kumar per resoldre sistemes d'equacions amb matrius de Toeplitz sobre els reals a cossos finits en un temps 0 (n log n).

A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

A novel procedure for establishing clinching parameters for high strength steel sheet

The building industry has a particular interest in using clinching as a joining method for frame constructions of light-frame housing. Normally many clinch joints are required in joining of frames.In order to maximise the strength of the complete assembly, each clinch joint must be as sound as possible. Experimental testing is the main means of optimising a particular clinch joint. This includes shear strength testing and visual observation of joint cross-sections. The manufacturers of clinching equipment normally perform such experimental trials. Finite element analysis can also be used to optimise the tool geometry and the process parameter, X, which represents the thickness of the base of the joint. However, such procedures require dedicated software, a skilled operator, and test specimens in order to verify the finite element model. In addition, when using current technology several hours' computing time may be necessary. The objective of the study was to develop a simple calculation procedure for rapidly establishing an optimum value for the parameter X for a given tool combination. It should be possible to use the procedure on a daily basis, without stringent demands on the skill of the operator or the equipment. It is also desirable that the procedure would significantly decrease thenumber of shear strength tests required for verification. The experimental workinvolved tests in order to obtain an understanding of the behaviour of the sheets during clinching. The most notable observation concerned the stage of the process in which the upper sheet was initially bent, after which the deformation mechanism changed to shearing and elongation. The amount of deformation was measured relative to the original location of the upper sheet, and characterised as the C-measure. By understanding in detail the behaviour of the upper sheet, it waspossible to estimate a bending line function for the surface of the upper sheet. A procedure was developed, which makes it possible to estimate the process parameter X for each tool combination with a fixed die. The procedure is based on equating the volume of material on the punch side with the volume of the die. Detailed information concerning the behaviour of material on the punch side is required, assuming that the volume of die does not change during the process. The procedure was applied to shear strength testing of a sample material. The sample material was continuously hot-dip zinc-coated high-strength constructional steel,with a nominal thickness of 1.0 mm. The minimum Rp0.2 proof stress was 637 N/mm2. Such material has not yet been used extensively in light-frame housing, and little has been published on clinching of the material. The performance of the material is therefore of particular interest. Companies that use clinching on a daily basis stand to gain the greatest benefit from the procedure. By understanding the behaviour of sheets in different cases, it is possible to use data at an early stage for adjusting and optimising the process. In particular, the functionality of common tools can be increased since it is possible to characterise the complete range of existing tools. The study increases and broadens the amount ofbasic information concerning the clinching process. New approaches and points of view are presented and used for generating new knowledge.

Volcanoes of l-isogenies of elliptic curves over finite fields: the case l=3

This paper is devoted to the study of the volcanoes of l-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the l-Sylow subgroup of an elliptic curve and the level of the volcano where it is placed. The particular case l = 3 is studied in detail, giving an algorithm to determine the volcano of 3-isogenies of a given elliptic curve. Experimental results are also provided.

A prospective observational study comparing a non-operator dependent automatic PWV analyser to pulse pressure, in assessing arterial stiffness in hemodialysis.

BACKGROUND: Chronic kidney disease (CKD) accelerates vascular stiffening related to age. Arterial stiffness may be evaluated measuring the carotid-femoral pulse wave velocity (PWV) or more simply, as recommended by KDOQI, monitoring pulse pressure (PP). Both correlate to survival and incidence of cardiovascular disease. PWV can also be estimated on the brachial artery using a Mobil-O-Graph; a non-operator dependent automatic device. The aim was to analyse whether, in a dialysis population, PWV obtained by Mobil-O-Graph (MogPWV) is more sensitive for vascular aging than PP. METHODS: A cohort of 143 patients from 4 dialysis units has been followed measuring MogPWV and PP every 3 to 6 months and compared to a control group with the same risk factors but an eGFR > 30 ml/min. RESULTS: MogPWV contrarily to PP did discriminate the dialysis population from the control group. The mean difference translated in age between the two populations was 8.4 years. The increase in MogPWV, as a function of age, was more rapid in the dialysis group. 13.3% of the dialysis patients but only 3.0% of the control group were outliers for MogPWV. The mortality rate (16 out of 143) was similar in outliers and inliers (7.4 and 8.0%/year). Stratifying patients according to MogPWV, a significant difference in survival was seen. A high parathormone (PTH) and to be dialysed for a hypertensive nephropathy were associated to a higher baseline MogPWV. CONCLUSIONS: Assessing PWV on the brachial artery using a Mobil-O-Graph is a valid and simple alternative, which, in the dialysis population, is more sensitive for vascular aging than PP. As demonstrated in previous studies PWV correlates to mortality. Among specific CKD risk factors only PTH is associated with a higher baseline PWV. TRIAL REGISTRATION: ClinicalTrials.gov Identifier: NCT02327962.

Design of User Authentication System for Multi-operator wireless LANs

Langattomat lähiverkot ovat viime vuosikymmeninä saavuttaneet suuren suosion. Tässä työssä käsitellään käyttäjien todentamisjärjestelmän suunnittelua ja kehitystä langattomaan monioperaattoriverkkoon. Langattomassa monioperaattoriverkossa käyttäjillä on mahdollisuus käyttää eri operaattoreiden palveluita. Aluksi käsitellään olemassa olevia todentamismenetelmiä ja -järjestelmiä. minkä jälkeen kuvaillaan todentamisjärjestelmä langattomille monioperaattoriverkoille. Todentamisjärjestelmän ratkaisuvaihtoehtoja esitellään kaksi, niin sanotut moni- istunto - ja yksittäisistuntomalli. Moni-istuntomalli on normaali lähestymistapa käyttäjien todentamiseen tietokonejärjestelmissä. Siinä käyttäjän pitää tunnistautua ja todentaa itsensä jokaiselle verkon palvelulle erikseen. Yksittäisistuntomallissa pyritään parempaan luotettavuuteen ja käytettävyyteen. Siinä käyttäjä todentaa itsensä vain kerran ja voi sen jälkeen päästä useisiin palveluihin. Työn loppuosassa kuvaillaan suunnitellun järjestelmän toteutusta. Lisäksi ehdotetaan vaihtoehtoisia toteutustapoja, analysoidaan järjestelmän heikkouksia ja kerrotaan jatkokehitysmahdoillisuuksista.

Ecuaciones de recurrencia estocásticas en el cálculo de la prima de reaseguro Finite Risk

RESUMEN: El objetivo de este trabajo es calcular el importe de la prima pura periódica que debe cobrar el reasegurador a la cedente en un reaseguro finite risk en ambiente financiero estocástico. El problema de la convolución de las diferentes variables aleatorias que intervienen en el cálculo de la prima lo hemos solucionado simulando, por Monte-Carlo, trayectorias de siniestralidad para el reasegurador aplicando posteriormente, en cada trayectoria simulada, los criterios de decisión financieros, esperanza, varianza y desviación. En los criterios de la varianza y de la desviación proponemos utilizar una ecuación de recurrencia estocástica para evitar el problema de la dependencia que existe entre los factores de capitalización estocásticos, obteniendo la prima de reaseguro en función del nivel de aversión al riesgo del reasegurador y de la volatilidad del tipo de interés. Palabras clave: Finite risk, ambiente estocástico, ecuación de recurrencia, simulación de Monte-Carlo, prima pura periódica.

A method for decision making with the OWA operator

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices

Quartz Tuning Fork (QTF)-based Scanning Probe Microscopy (SPM) is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement.

The induced generalized OWA operator

We present the induced generalized ordered weighted averaging (IGOWA) operator. It is a new aggregation operator that generalizes the OWA operator by using the main characteristics of two well known aggregation operators: the generalized OWA and the induced OWA operator. Then, this operator uses generalized means and order inducing variables in the reordering process. With this formulation, we get a wide range of aggregation operators that include all the particular cases of the IOWA and the GOWA operator, and a lot of other cases such as the induced ordered weighted geometric (IOWG) operator and the induced ordered weighted quadratic averaging (IOWQA) operator. We further generalize the IGOWA operator by using quasi-arithmetic means. The result is the Quasi-IOWA operator. Finally, we also develop a numerical example of the new approach in a financial decision making problem.

The connection between distortion risk measures and ordered weighted averaging operators

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.