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On Judgment Aggregation in Abstract Argumentation Caminada, Martin ; Pigozzi, Gabriella in Autonomous Agents & Multi-Agent Systems (2011), 22(1), 64102 Judgment aggregation is a field in which individuals are required to vote for or against a certain decision (the conclusion) while providing reasons for their choice. The reasons and the conclusion are ... [more ▼] Judgment aggregation is a field in which individuals are required to vote for or against a certain decision (the conclusion) while providing reasons for their choice. The reasons and the conclusion are logically connected propositions. The problem is how a collective judgment on logically interconnected propositions can be defined from individual judgments on the same propositions. It turns out that, despite the fact that the individuals are logically consistent, the aggregation of their judgments may lead to an inconsistent group outcome, where the reasons do not support the conclusion. However, in this paper we claim that collective irrationality should not be the only worry of judgment aggregation. For example, judgment aggregation would not reject a consistent combination of reasons and conclusion that no member voted for. In our view this may not be a desirable solution. This motivates our research about when a social outcome is ‘compatible’ with the individuals’ judgments. The key notion that we want to capture is that any individual member has to be able to defend the collective decision. This is guaranteed when the group outcome is compatible with its members views. Judgment aggregation problems are usually studied using classical propositional logic. However, for our analysis we use an argumentation approach to judgment aggregation problems. Indeed the question of how individual evaluations can be combined into a collective one can also be addressed in abstract argumentation. We introduce three aggregation operators that satisfy the condition above, and we offer two definitions of compatibility. Not only does our proposal satisfy a good number of standard judgment aggregation postulates, but it also avoids the problem of individual members of a group having to become committed to a group judgment that is in conflict with their own individual positions. [less ▲] Detailed reference viewed: 76 (1 UL)On L2 error bounds between systems ; ; Goncalves, Jorge Scientific Conference (2006) Detailed reference viewed: 28 (1 UL)On minimal realisations of dynamical structure functions ; ; Goncalves, Jorge in Automatica (2015), 55 Motivated by the fact that transfer functions do not contain structural information about networks, dynamical structure functions were introduced to capture causal relationships between measured nodes in ... [more ▼] Motivated by the fact that transfer functions do not contain structural information about networks, dynamical structure functions were introduced to capture causal relationships between measured nodes in networks. From the dynamical structure functions, a) we show that the actual number of hidden states can be larger than the number of hidden states estimated from the corresponding transfer function; b) we can obtain partial information about the true state-space equation, which cannot in general be obtained from the transfer function. Based on these properties, this paper proposes algorithms to find minimal realisations for a given dynamical structure function. This helps to estimate the minimal number of hidden states, to better understand the complexity of the network, and to identify potential targets for new measurements. [less ▲] Detailed reference viewed: 163 (16 UL)On multistability of delayed genetic regulatory networks with multivariable regulation functions Pan, Wei ; ; et al in Mathematical Biosciences (2010), 228(1), 100-109 Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and ... [more ▼] Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and multivariable regulation functions are usually inevitable in such GRNs. In this paper, multistability of GRNs is analyzed by applying the control theory and mathematical tools. This study is to provide a theoretical tool to facilitate the design of synthetic gene circuit with multistability in the perspective of control theory. By transforming such GRNs into a new and uniform mathematical formulation, we put forward a general sector-like regulation function that is capable of quantifying the regulation effects in a more precise way. By resorting to up-to-date techniques, a novel Lyapunov–Krasovskii functional (LKF) is introduced for achieving delay dependence to ensure less conservatism. New conditions are then proposed to ensure the multistability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the delays. Our multistability conditions are applicable to several frequently used regulation functions especially the multivariable ones. Two examples are employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲] Detailed reference viewed: 68 (0 UL)On numerical integration of discontinuous approximations in partition of unity finite elements ; Bordas, Stéphane ; in IUTAM Bookseries (2010), 19 This contribution presents two advances in the formulation of discontinuous approximations in finite elements. The first method relies on Schwarz-Christoffel mapping for integration on arbitrary polygonal ... [more ▼] This contribution presents two advances in the formulation of discontinuous approximations in finite elements. The first method relies on Schwarz-Christoffel mapping for integration on arbitrary polygonal domains [1]. When an element is split into two subdomains by a piecewise continuous discontinuity, each of these polygonal domains is mapped onto a unit disk on which cubature rules are utilized. This suppresses the need for the usual two-level isoparametric mapping. The second method relies on strain smoothing applied to discontinuous finite element approximations. By writing the strain field as a non-local weighted average of the compatible strain field, integration on the surface of the finite elements is transformed into boundary integration, so that the usual subdivision into integration cells is not required, an isoparametric mapping is not needed and the derivatives of the shape (enrichment) functions do not need to be computed. Results in fracture mechanics and composite materials are presented and both methods are compared in terms of accuracy and simplicity. The interested reader is referred to [1,6,13] for more details and should contact the authors to receive a version of the MATLAB codes used to obtain the results herein. © 2010 Springer Science+Business Media B.V. [less ▲] Detailed reference viewed: 158 (1 UL)On the approximation in the smoothed finite element method (SFEM) Bordas, Stéphane ; in International Journal for Numerical Methods in Engineering (2010), 81(5), 660-670 This letter aims at resolving the issues raised in the recent short communication (Int. J. Numer. Meth. Engng 2008; 76(8):1285-1295. DOI: 10.1002/nme.2460) and answered by (Int. J. Numer. Meth. Engng 2009 ... [more ▼] This letter aims at resolving the issues raised in the recent short communication (Int. J. Numer. Meth. Engng 2008; 76(8):1285-1295. DOI: 10.1002/nme.2460) and answered by (Int. J. Numer. Meth. Engng 2009; DOI: 10.1002/nme.2587) by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique advantages of the smoothed finite element method (SFEM) (Comput. Mech. 2007; 39(6):859-877. DOI: 10.1007/s00466-006-0075-4; Commun. Numer. Meth. Engng 2009; 25(1):19-34. DOI: 10.1002/cnm.1098; Int. J. Numer. Meth. Engng 2007; 71(8):902-930; Comput. Meth. Appl. Mech. Engng 2008; 198(2):165-177. DOI: 10.1016/j.cma.2008.05.029; Comput. Meth. Appl. Mech. Engng 2007; submitted; Int. J. Numer. Meth. Engng 2008; 74(2):175-208. DOI: 10.1002/nme.2146; Comput. Meth. Appl. Mech. Engng 2008; 197 (13-16):1184-1203. DOI: 10.1016/j.cma.2007.10.008) and resolve the existence, linearity and positivity deficiencies pointed out in (Int. J. Numer. Meth. Engng 2008; 76(8):1285-1295). We show that Wachspress interpolants (A Rational Basis for Function Approximation. Academic Press, Inc.: New York, 1975) computed in the physical coordinate system are very well suited to the SFEM, especially when elements are heavily distorted (obtuse interior angles). The proposed approximation leads to results that are almost identical to those of the SFEM initially proposed in (Comput. Mech. 2007; 39(6):859-877. DOI: 10.1007/s00466-006-0075-4). These results suggest that the proposed approximation scheme forms a strong and rigorous basis for the construction of SFEMs. © 2009 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 149 (4 UL)On the consistency between travelers’ satisfaction and utility: the case of the University of Luxembourg Sprumont, François ; ; Viti, Francesco Scientific Conference (2015, July) Detailed reference viewed: 80 (7 UL)On the convergence of stresses in fretting fatigue ; Bordas, Stéphane ; Tomar, Satyendra et al in Materials (2016), 9(8), Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce ... [more ▼] Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce the service life of a component due to fretting fatigue. In this regard, the analysis of stresses at contact is of great importance for predicting the lifetime of components. However, due to the complexity of the fretting phenomenon, analytical solutions are available for very selective situations and finite element (FE) analysis has become an attractive tool to evaluate stresses and to study fretting problems. Recent laboratory studies in fretting fatigue suggested the presence of stress singularities in the stick-slip zone. In this paper, we constructed finite element models, with different element sizes, in order to verify the existence of stress singularity under fretting conditions. Based on our results, we did not find any singularity for the considered loading conditions and coefficients of friction. Since no singularity was found, the present paper also provides some comments regarding the convergence rate. Our analyses showed that the convergence rate in stress components depends on coefficient of friction, implying that this rate also depends on the loading condition. It was also observed that errors can be relatively high for cases with a high coefficient of friction, suggesting the importance of mesh refinement in these situations. Although the accuracy of the FE analysis is very important for satisfactory predictions, most of the studies in the literature rarely provide information regarding the level of error in simulations. Thus, some recommendations of mesh sizes for those who wish to perform FE analysis of fretting problems are provided for different levels of accuracy. [less ▲] Detailed reference viewed: 81 (2 UL)On the effect of grains interface parameters on the macroscopic properties of polycrystalline materials ; ; Bordas, Stéphane in Computers & Structures (2018), 196 In this paper, the influence of microscopic parameters on the macroscopic behaviour of polycrystalline materials under different loading configuration is investigated. Linear elastic grains with zero ... [more ▼] In this paper, the influence of microscopic parameters on the macroscopic behaviour of polycrystalline materials under different loading configuration is investigated. Linear elastic grains with zero thickness cohesive interfaces are considered at the microscale with in depth introduction of effective parameters. A multiscale method based on homogenisation technique is employed to bridge the scales. In order to minimize the homogenisation error, a representative volume element (RVE) of the microscopic structure is statistically determined to be used in the numerical analysis. For each loading condition of the RVE, several numerical examinations are conducted to illustrate the relationship between the microscopic parameters. Finally, the effects of microscopic critical fracture energies, maximum tensile and shear strengths of grain interfaces on the mechanical properties, i.e. stress-strain curve and yield surface at the macroscale are discussed in details. It is shown that macroscopic yield surface and stress strain curves can be used to characterise the microscopic properties. [less ▲] Detailed reference viewed: 124 (3 UL)On the equivalence between the cell-based smoothed finite element method and the virtual element method ; Bordas, Stéphane ; E-print/Working paper (2014) We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity ... [more ▼] We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEMis combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D. [less ▲] Detailed reference viewed: 409 (10 UL)On the impacts of transport policies and urban form on traffic-induced air pollution (extended abstract) Schindler, Mirjam ; Caruso, Geoffrey in Hesse, Markus; Caruso, Geoffrey; Gerber, Philippe (Eds.) et al Proceedings of the BIVEC-GIBET Transport Research Days 2013 (2013) Air pollution is a major concern in urban areas worldwide. It is not only a hazard to the environment but also on human health. Many argue that a compact city is the desirable urban form in the context of ... [more ▼] Air pollution is a major concern in urban areas worldwide. It is not only a hazard to the environment but also on human health. Many argue that a compact city is the desirable urban form in the context of sustainability due to shorter travelling distances and reduced conversion of land. If considering not only the environmental pillar of sustainability in terms of total emissions but also the social one comprising human exposure and social well-being, the argumentation might change. The question we ask is whether selected common transport policies are efficient solutions to overcome the environmental and social challenge? In order to investigate this question, we developed a modelling system in order to test the impacts of different transport policies, either on the urban structure itself or on traffic flows and respectively on air quality. [less ▲] Detailed reference viewed: 101 (15 UL)On the link between activity patterns and traffic within-day demand profiles: empirical analysis and application to demand estimation Cantelmo, Guido ; Viti, Francesco Scientific Conference (2015, September) Detailed reference viewed: 89 (16 UL)On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM) Bordas, Stéphane ; ; et al in International Journal for Numerical Methods in Engineering (2011), 86(4-5), 637-666 By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25:137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39 ... [more ▼] By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25:137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6):859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). © 2011 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 182 (1 UL)On the role of enrichment and statistical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods ; ; Bordas, Stéphane et al in Engineering Computations (2012), 29(8), 814-841 Purpose - The purpose of this paper is to assess the effect of the statistical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also ... [more ▼] Purpose - The purpose of this paper is to assess the effect of the statistical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also the accuracy, local and global effectivity of recovery-based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM). Design/methodology/approach - The authors study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR-CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution. Findings - Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz-Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statistically admissible recovered solutions. Originality/value - The paper shows that both extended recovery procedures and statistical admissibility are key to an accurate assessment of the quality of enriched finite element approximations. © Emerald Group Publishing Limited. [less ▲] Detailed reference viewed: 82 (3 UL)On the structure of a new superhard hexagonal carbon phase ; ; et al in AIP Conference Proceedings (2010), 1233(PART 1), 489-493 Molecular dynamics simulations show that graphite will transform into a superhard phase under cold compression. Recent experiments show that there is a sp 3-rich hexagonal carbon polymorph (a 0=2.496 Å, c ... [more ▼] Molecular dynamics simulations show that graphite will transform into a superhard phase under cold compression. Recent experiments show that there is a sp 3-rich hexagonal carbon polymorph (a 0=2.496 Å, c 0=4.123Å) with a bulk modulus of 447 GPa and average density about 3.6g/cm 3, restricted to the space group of P-62c (No. 190), but the detailed atomic structure was not obtained [Wang et al., P. Natl. Acad. Sci. 101(38), 13699]. Here we set carbon atoms occupying P-62c 4f Wyckoff positions of P-62c, and calculate the total energy of the different structures changing the internal parameter z by first-principles calculations using geometry optimisation algorithm in CASTEP code, which shows that the stable structures in energy (at local minimum points) are hexagonal carbon (z=1/4) and hexagonal diamond (z=1/16). The calculated mechanical properties and lattice parameters of the structure P-62c 4f (z=1/4) are in good agreement with those of the new hexagonal carbon proposed by Wang et al., which indicates that the atomic structure is a possible candidate. © 2010 American Institute of Physics. [less ▲] Detailed reference viewed: 77 (0 UL)On the substitutability of traffic light and pricing controllers in transportation networks Mazur, Xavier ; Rinaldi, Marco ; Viti, Francesco Scientific Conference (2019, June) Detailed reference viewed: 42 (1 UL)On the use of recovery techniques for accurate error estimation and error bounding in XFEM ; ; et al in Bordas, Stéphane; Kerfriden, Pierre (Eds.) 2nd International Conference on the Extended Finite Element Method (2011) Detailed reference viewed: 64 (1 UL)On three-dimensional modelling of crack growth using partition of unity methods ; Bordas, Stéphane ; in Computers & Structures (2010), 88(23-24), 1391-1411 This paper reviews different crack tracking techniques in three-dimensions applicable in the context of partition of unity methods, especially meshfree methods. Issues such as describing and tracking the ... [more ▼] This paper reviews different crack tracking techniques in three-dimensions applicable in the context of partition of unity methods, especially meshfree methods. Issues such as describing and tracking the crack surface are addressed. A crack tracking procedure is proposed in detail and implemented in the context of the extended element-free Galerkin method (XEFG). Several three-dimensional cracking examples are compared to other results from the literature or the experimental data and show good agreement. [less ▲] Detailed reference viewed: 124 (8 UL)On time integration in the XFEM ; Zilian, Andreas in International Journal for Numerical Methods in Engineering (2009), 79(1), 69-93 The extended finite element method (XFEM) is often used in applications that involve moving interfaces. Examples are the propagation of cracks or the movement of interfaces in two-phase problems. This ... [more ▼] The extended finite element method (XFEM) is often used in applications that involve moving interfaces. Examples are the propagation of cracks or the movement of interfaces in two-phase problems. This work focuses on time integration in the XFEM. The performance of the discontinuous Galerkin method in time (space-time finite elements (FEs)) and time-stepping schemes are analyzed by convergence studies for different model problems. It is shown that space-time FE achieve optimal convergence rates. Special care is required for time stepping in the XFEM due to the time dependence of the enrichment functions. In each time step, the enrichment functions have to be evaluated at different time levels. This has important consequences in the quadrature used for the integration of the weak form. A time-stepping scheme that leads to optimal or only slightly sub-optimal convergence rates is systematically constructed in this work. © 2009 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 77 (3 UL)A one point integration rule over star convex polytopes ; ; et al in Computers and Structures (2019), 215 In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it ... [more ▼] In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it requires only one integration point within each n-sided polytope as opposed to 3n in Francis et al. (2017) and 13n integration points in the conventional approach for numerically integrating the weak form in two dimensions. The essence of the proposed technique is to approximate the compatible strain by a linear smoothing function and evaluate the smoothed nodal derivatives by the discrete form of the divergence theorem at the geometric center. This is done by Taylor’s expansion of the weak form which facilitates the use of the smoothed nodal derivatives acting as the stabilization term. This translates to 50% and 30% reduction in the overall computational time in the two and three dimensions, respectively, whilst preserving the accuracy and the convergence rates. The convergence properties, the accuracy and the efficacy of the one point integration scheme are discussed by solving few benchmark problems in elastostatics. [less ▲] Detailed reference viewed: 36 (0 UL) |
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