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Preprint de J. Araújo, W. Bentz, P.J. Cameron, M. Kinyon, J. Konieczny, “Matrix Theory for Independence Algebras”, Linear Algebra and its Applications 642 (2022), 221-250. A universal algebra A with underlying set A is said to be a matroid algebra if (A, 〈·〉), where 〈·〉 denotes the operator subalgebra generated by, is a matroid. A matroid algebra is said to be an independence algebra if every mapping α : X → A defined on a minimal generating X of A can be extended to an endomorphism of A. These algebras are particularly well-behaved generalizations of vector spaces, and hence they naturally appear in several branches of mathematics, such as model theory, group theory, and semigroup theory. It is well known that matroid algebras have a well-defined notion of dimension. Let A be any independence algebra of finite dimension n, with at least two elements. Denote by End(A) the monoid of endomorphisms of A. In the 1970s, Glazek proposed the problem of extending the matrix theory for vector spaces to a class of universal algebras which included independence algebras. In this paper, we answer that problem by developing a theory of matrices for (almost all) finite-dimensional independence algebras. In the process of solving this, we explain the relation between the classification of inde- pendence algebras obtained by Urbanik in the 1960s, and the classification of finite indepen- dence algebras up to endomorphism-equivalence obtained by Cameron and Szab ́o in 2000. (This answers another question by experts on independence algebras.) We also extend the classification of Cameron and Szab ́o to all independence algebras. The paper closes with a number of questions for experts on matrix theory, groups, semi- groups, universal algebra, set theory or model theory. This work was funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020, UIDP/00297/2020 (Center for Mathematics and Applications) and PTDC/MAT/PUR/31174/2017. info:eu-repo/semantics/publishedVersion

Preprint de J. Araújo, J.P. Araújo, W. Bentz, P.J. Cameron, and P. Spiga, “A Transversal Property for Permutation Groups Motivated by Partial Transformations”, Journal of Algebra 573 (2021), 741-759. In this paper we introduce the definition of the (k, l)-universal transversal property for permutation groups, which is a refinement of the definition of k-universal transversal property, which in turn is a refine- ment of the classical definition of k-homogeneity for permutation groups. In particular, a group possesses the (2, n)-universal transversal property if and only if it is primitive; it possesses the (2, 2)-universal transversal property if and only if it is 2-homogeneous. Up to a few undecided cases, we give a classification of groups satisfying the (k, l)-universal transversal property, for k ≥ 3. Then we apply this result for studying regular semigroups of partial transformations. The first and third authors were partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through projects UIDB/00297/2020 (Center for Mathematics and Applications) and CEMAT-CIÊNCIAS UID/Multi/04621/2013, and also by the Fundacão para a Ciência e a Tecnologia through project PTDC/MAT-PUR/31174/2017. The second author was partially supported by Fundação Calouste Gulbenkian, Programa Talentos Inteligência Artificial. The fourth author was partially supported by Fundação para a Ciência e a Tecnologia (Portuguese Founda- tion for Science and Technology) through project CEMAT-CIÊNCIAS UID/Multi/04621/2013. info:eu-repo/semantics/publishedVersion

Preprint de J. Araújo, W. Bentz, and P.J. Cameron, “Primitive Permutation Groups and Strongly Factorizable Transformation Semigroups”, Journal of Algebra 565 (2021), 513-530. Let Ω be a finite set and T (Ω) be the full transformation monoid on Ω. The rank of a transformation t ∈ T (Ω) is the natural number |Ωt|. Given A ⊆ T (Ω), denote by 〈A〉 the semigroup generated by A. Let k be a fixed natural number such that 2 ≤ k ≤ |Ω|. In the first part of this paper we (almost) classify the permutation groups G on Ω such that for all rank k transformations t ∈ T (Ω), every element in St := 〈G, t〉 can be written as a product eg, where e2 = e ∈ St and g ∈ G. In the second part we prove, among other results, that if S ≤ T (Ω) and G is the normalizer of S in the symmetric group on Ω, then the semigroup SG is regular if and only if S is regular. (Recall that a semigroup S is regular if for all s ∈ S there exists s′ ∈ S such that s = ss′s.) The paper ends with a list of problems. The first author was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UIDB/00297/2020 (Centro de Matemtica e Aplicaes), PTDC/MAT-PUR/31174/2017, UIDB/04621/2020 and UIDP/04621/2020. info:eu-repo/semantics/publishedVersion

Ruberto, S., Vanneschi, L., & Castelli, M. (2019). Genetic programming with semantic equivalence classes. Swarm and Evolutionary Computation, 44(February), 453-469. DOI: 10.1016/j.swevo.2018.06.001 In this paper, we introduce the concept of semantics-based equivalence classes for symbolic regression problems in genetic programming. The idea is implemented by means of two different genetic programming systems, in which two different definitions of equivalence are used. In both systems, whenever a solution in an equivalence class is found, it is possible to generate any other solution in that equivalence class analytically. As such, these two systems allow us to shift the objective of genetic programming: instead of finding a globally optimal solution, the objective is now to find any solution that belongs to the same equivalence class as a global optimum. Further, we propose improvements to these genetic programming systems in which, once a solution that belongs to a particular equivalence class is generated, no other solution in that class is accepted in the population during the evolution anymore. We call these improved versions filtered systems. Experimental results obtained via seven complex real-life test problems show that using equivalence classes is a promising idea and that filters are generally helpful for improving the systems' performance. Furthermore, the proposed methods produce individuals with a much smaller size with respect to geometric semantic genetic programming. Finally, we show that filters are also useful to improve the performance of a state-of-the-art method, not explicitly based on semantic equivalence classes, like linear scaling. authorsversion published

As an important humanitarian relief material after disaster, blood has its distinguishing characteristics like perishability and time-sensitivity. During the post-disaster emergency blood collection, the location and allocation of mobile blood collecting facilities directly influence the timely supply of blood. This paper proposes a two-stage bi-objective mixed integer location-allocation model for mobile blood collecting facilities. An augmented e-constraint combined with Lagrangian relaxation method is applied. Finally numerical experiments based on blood collection process in Shanghai is provided.

Emergency blood supply plays an important role in disaster relief. However, large fluctuations in blood demand make precise blood forecasting a challenge. The demand for blood and information about transportation disruption are dynamically revealed over time. A discrete-time Mixed Integer Linear Programming (MILP) mathematical formulation will be developed to cope with the underlying uncertainty through a rolling horizon approach with the purpose to optimally manage the blood supply chain system in disaster relief (i.e., determining the amount of blood collection, location of the blood collection stations, transport and storage needed to meet the demand in the worst-case scenario and minimize the total response time and total operational costs). The model also takes blood characteristics and blood emergency supply constraints into consideration. The performance of the proposed model and solution method is then investigated in a real case study from the 2008 Wenchuan earthquake and the results are discussed in detail.

Let H be a quasi-Hopf algebra. We apply results obtained in [8] to give necessary and sufficient conditions for the forgetful functor from Doi–Hopf modules, two-sided Hopf modules or Yetter–Drinfeld modules over H to representations of the underlying algebra to be Frobenius (resp. separable). We show that in some situations these conditions reduce to the unimodularity and/or (co)semisimplicity of the quasi-Hopf algebra H.

Hexapod robots are easy to realize walking in complicated environments and have the characteristic of high redundancy. It is well worth taking advantage of hexapod robots’ versatility, such as using legs to do manipulation or carry objects. In this paper, several methods are proposed to deal with issues of carrying objects by transforming one or two legs as arms while walking on other legs for hexapod robots. Firstly, practical gaits for one-legged carrying and two-legged carrying are presented respectively. Secondly, problems existing in gait planning, for instance how to estimate the mass of object and how to calculate joint motions according to desired center of gravity (COG) trajectory, are solved by dynamic analysis and a kinematic method based on COG Jacobian. Finally, the effectiveness of our methods to implement carrying objects is demonstrated by two successful experiments of carrying a bottle of water and a box.

Recently, the development of collaborative robots that have to work in a cooperative way with humans, has become an important trend both in academia and in the industry. Thereby, safety has increasingly become an essential research aspect. Today, the main techniques to ensure safety are based on reducing 1) the stiffness of the actuators and/or links, 2) the speed of the robot when it approaches humans or obstacles, and 3) the weight of the robot. In all these techniques, the robot's end-effector position is measured by position sensors on the joints, whereby the robot's limbs have to be as rigid as possible. This method has as possible drawbacks that the limbs have to carry unnecessary load (i.e. the robot's weight), and that the position errors increase with increased payload so that the robot can only be used for low payloads. To tackle these problems, we proposed a novel error compensation method based on the use of an additional measurement arm in parallel with the main load bearing arm, whereby the two arms are only coupled between the base and the end-effector. We designed a proof of concept robotic arm and validated the feasibility of our method. This paper presents the End-Effector Position Measuring (EEPM) method and introduces the Independent Load And Measurement Arm (ILAMA) to demonstrate the EEPM concept. With this novel method, the robot can be designed by strength instead of by stiffness. As a consequence, the weight of the limbs can drastically be reduced and the payload to mass ratio can be increased to a value that is bigger than one, while preserving the high end-effector position accuracy, as shown in the experiments. These advantages make the EEPM method very promising to use in collaborative robots or in mobile robot arms. Future works will investigate the feasibility of the proposed concept for real industrial robots with 6 to 7 DOF.

Bakurov, I., Castelli, M., Fontanella, F., Scotto Di Freca, A., & Vanneschi, L. (2022). A novel binary classification approach based on geometric semantic genetic programming. Swarm and Evolutionary Computation, 69(March), 1-12. [101028]. https://doi.org/10.1016/j.swevo.2021.101028 ------Funding Information: This work was supported by national funds through the FCT (Fundação para a Ciência e a Tecnologia) by the projects GADgET (DSAIPA/DS/0022/2018), BINDER (PTDC/CCIINF/29168/2017), and AICE (DSAIPA/DS/0113/2019). Mauro Castelli acknowledges the financial support from the Slovenian Research Agency (research core funding no. P5-0410). Geometric semantic genetic programming (GSGP) is a recent variant of genetic programming. GSGP allows the landscape of any supervised regression problem to be transformed into a unimodal error surface, thus it has been applied only to this kind of problem. In a previous paper, we presented a novel variant of GSGP for binary classification problems that, taking inspiration from perceptron neural networks, uses a logistic-based activation function to constrain the output value of a GSGP tree in the interval [0,1]. This simple approach allowed us to use the standard RMSE function to evaluate the train classification error on binary classification problems and, consequently, to preserve the intrinsic properties of the geometric semantic operators. The results encouraged us to investigate this approach further. To this aim, in this paper, we present the results from 18 test problems, which we compared with those achieved by eleven well-known and widely classification schemes. We also studied how the parameter settings affect the classification performance and the use of the -score function to deal with imbalanced data. The results confirmed the effectiveness of the proposed approach. authorsversion published

Given $x\in(0, 1]$, let $\mathcal U(x)$ be the set of bases $q\in(1,2]$ for which there exists a unique sequence $(d_i)$ of zeros and ones such that $x=\sum_{i=1}^\infty d_i/q^i$. L\"{u}, Tan and Wu (2014) proved that $\mathcal U(x)$ is a Lebesgue null set of full Hausdorff dimension. In this paper, we show that the algebraic sum $\mathcal U(x)+\lambda\mathcal U(x)$ and product $\mathcal U(x)\cdot\mathcal U(x)^\lambda$ contain an interval for all $x\in(0, 1]$ and $\lambda\ne 0$. As an application we show that the same phenomenon occurs for the set of non-matching parameters studied by the first author and Kalle (2017)., Comment: 21 pages, 1 figure. To appear in Indag. Math

C. I. Lewis invented modern modal logic as a theory of "strict implication". Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive power than the box and allows to make distinctions invisible in the ordinary syntax. In particular, the logic determined by the most popular semantics of intuitionistic K becomes a proper extension of the minimal normal logic of the binary connective. Even an extension of this minimal logic with the "strength" axiom, classically near-trivial, preserves the distinction between the binary and the unary setting. In fact, this distinction and the strong constructive strict implication itself has been also discovered by the functional programming community in their study of "arrows" as contrasted with "idioms". Our particular focus is on arithmetical interpretations of the intuitionistic strict implication in terms of preservativity in extensions of Heyting's Arithmetic., Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years later"

Let $G$ be connected reductive algebraic group defined over an algebraically closed field of characteristic $p > 0$ and suppose that $p$ is a good prime for the root system of $G$, the derived subgroup of $G$ is simply connected and the Lie algebra $\mathfrak{g} = \operatorname{Lie}(G)$ admits a non-degenerate Ad$(G)$-invariant symmetric bilinear form. Given a linear function $\chi$ on $\mathfrak{g}$ we denote by $U_\chi(\mathfrak{g})$ the reduced enveloping algebra of $\mathfrak{g}$ associated with $\chi$. By the Kac-Weisfeiler conjecture (now a theorem), any irreducible $U_\chi(\mathfrak{g})$-module has dimension divisible by $p^{d(\chi)}$ where $2d(\chi)$ is the dimension of the coadjoint $G$-orbit containing $\chi$. In this paper we give a positive answer to the natural question raised in the 1990s by Kac, Humphreys and the first-named author and show that any algebra $U_\chi(\mathfrak{g})$ admits a module of dimension $p^{d(\chi)}$., Comment: The present version is accepted for publication

The present manuscript describes the combined effect of using a parallel spring in conjunction with a variable-stiffness actuator to reduce the torque and power requirements of an ankle–foot prosthesis during normal walking. The behavior of both elements is analyzed in terms of the reduction of the required motor peak power, energy and torque with respect to a conventional actuator. The proposed actuator is based on the Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator concept. The advantages and disadvantages of the referred actuation scheme are discussed and experimental results are used to illustrate the actual reduction of motor torque requirements.

We propose a tool-body assimilation model that considers grasping during motor babbling for using tools. A robot with tool-use skills can be useful in humanrobot symbiosis because this allows the robot to expand its task performing abilities. Past studies that included tool-body assimilation approaches were mainly focused on obtaining the functions of the tools, and demonstrated the robot starting its motions with a tool pre-attached to the robot. This implies that the robot would not be able to decide whether and where to grasp the tool. In real life environments, robots would need to consider the possibilities of tool-grasping positions, and then grasp the tool. To address these issues, the robot performs motor babbling by grasping and nongrasping the tools to learn the robots body model and tool functions. In addition, the robot grasps various parts of the tools to learn different tool functions from different grasping positions. The motion experiences are learned using deep learning. In model evaluation, the robot manipulates an object task without tools, and with several tools of different shapes. The robot generates motions after being shown the initial state and a target image, by deciding whether and where to grasp the tool. Therefore, the robot is capable of generating the correct motion and grasping decision when the initial state and a target image are provided to the robot.

Humanoid robots are expected to be integrated into daily life. This requires the robots to perform human-like actions that are easily understandable by humans. Learning by imitation is an effective framework that enables the robots to generate the same motions that humans do. However, it is generally not useful for the robots to generate motions that are precisely the same as learned motions because the environment is likely to be different from the environment where the motions were learned. The humanoid robot should synthesize motions that are adaptive to the current environment by modifying learned motions. Previous research encoded captured human whole-body motions into hidden Markov models, which are hereafter referred to as motion primitives, and generated human-like motions based on the acquired motion primitives. The contact between the body and the environment also needs to be controlled, so that the humanoid robots whole-body motion can be realized in its current environment. This paper proposes a novel approach to synthesizing kinematic data using the motion primitive and controlling the torques of all the joints in the humanoid robot to achieve the desired whole-body motions and contact forces. The experiments demonstrate the validity of the proposed approach to synthesizing and controlling whole-body motions by humanoid robots. This paper proposes the synthesis of whole body motions from stochastic motion primitives.The joint torques are computed during preserving the profile of the synthesized motion and controlling the reaction forces.Simulation demonstrates the validity of the motion synthesis and force control.

A 3PRR parallel precision positioning system, driven by three ultrasonic linear motors, was designed for use as the object stage of a scanning electron microscope (SEM). To improve the tracking accuracy of the parallel platform, the positioning control algorithms for the drive joints needed to be studied. The dead-zone phenomenon caused by static friction reduces the trajectory tracking accuracy significantly. Linear control algorithms such as PID (Proportion Integration Differentiation) are unable to compensate effectively for the dead-zone nonlinearity. To address this problem, two types of feedforward compensation control algorithms have been investigated. One is constant feedforward with the integral separation PID; the other is adaptive feedback and feedforward based on the model reference adaptive control (MRAC). Simulations and experiments were conducted using these two control algorithms. The results demonstrated that the constant feedforward with integral separation PID algorithm can compensate for the time-invariant system after identifying the dead-zone depth, while the adaptive feedback and feedforward algorithm is more suitable for the time-varying system. The experimental results show good agreement with the simulation results for these two control algorithms. For the dead-zone nonlinearity caused by the static friction, the adaptive feedback and feedforward algorithm can effectively improve the trajectory tracking accuracy. A positioning system has been built for the driven joints of the 3-PRR in SEM.The dead-zone of the system has been identified and applied to compensation.The proposed control algorithm improves the tracking precision significantly.

International audience; The time discretization of gradient flows in metric spaces uses variants of the celebrated implicit Euler-type scheme of Jordan, Kinderlehrer and Otto. We propose in this Note a different approach which allows to construct two second-order in time numerical schemes. In a metric space framework, we show that the schemes are well defined and prove the convergence for one of them under some regularity assumptions. For the particular case of a Fokker–Planck gradient flow in the Wasserstein space, we obtain (theoretically and numerically) the second-order convergence.; La discrétisation temporelle des flots de gradient dans des espaces métriques utilise des variantes du schéma d’Euler implicite issu du travail séminal de Jordan, Kinderlehrer et Otto. Nous proposons dans cette Note une approche différente permettant de construire deux schémas numériques d’ordre deux en temps. Dans le cadre d’un espace métrique, nous montrons que les schémas sont bien définis et prouvons la convergence de l’un d’entre eux sous des hypothèses de régularité. Pour le cas particulier d’un flot de gradient Fokker–Planck dans l’espace de Wasserstein, nous obtenons (théoriquement et numériquement) la convergence à l’ordre deux.

We introduce partial $r$-Bell polynomials in three combinatorial Hopf algebras. We prove a factorization formula for the generating functions which is a consequence of the Zassenhauss formula., Comment: 7 pages

We propose the analogues of boundary layer potentials for the sub-Laplacian on homogeneous Carnot groups/stratified Lie groups and prove continuity results for them. In particular, we show continuity of the single layer potential and establish the Plemelj type jump relations for the double layer potential. We prove sub-Laplacian adapted versions of the Stokes theorem as well as of Green's first and second formulae on homogeneous Carnot groups. Several applications to boundary value problems are given. As another consequence, we derive formulae for traces of the Newton potential for the sub-Laplacian to piecewise smooth surfaces. Using this we construct and study a nonlocal boundary value problem for the sub-Laplacian extending to the setting of the homogeneous Carnot groups M. Kac's “principle of not feeling the boundary”. We also obtain similar results for higher powers of the sub-Laplacian. Finally, as another application, we prove refined versions of Hardy's inequality and of the uncertainty principle.

In this note, we characterize the solution of a system of elliptic integro-differential equations describing a phe-notypically structured population subject to mutation, selection and migration. Generalizing an approach based on Hamilton-Jacobi equations, we identify the dominant terms of the solution when the mutation term is small (but nonzero). This method was initially used, for different problems from evolutionary biology, to identify the asymptotic solutions, while the mutations vanish, as a sum of Dirac masses. A key point is a uniqueness property related to the weak KAM theory. This method allows to go further than the Gaussian approximation commonly used by biologists and is an attempt to fill the gap between the theories of adaptive dynamics and quantitative genetics., Comment: arXiv admin note: substantial text overlap with arXiv:1612.06193

Resume On modelise un solide elastique fragile (pouvant developper des fractures) comme limite d'un modele d'endommagement et proposons une methode numerique afin de determiner l'evolution quasi-statique d'une fracture dans l'esprit des travaux de Francfort et Marigo [3] et Allaire et al. [1] , [2] .

In this work, we will establish local in time dispersive estimates for solutions to the model-case Dirichlet wave equation inside a cylindrical convex domain Ω ⊂ R 3 with a smooth boundary ∂ Ω ≠ ∅ . Let us recall that dispersive estimates are key ingredients to prove Strichartz estimates. Nonoptimal Strichartz estimates for waves inside an arbitrary domain Ω have been proved by Blair–Smith–Sogge [1] , [2] . Better estimates in strictly convex domains have been obtained in [4] . Our case of cylindrical domains is an extension of the result of [4] in the case where the curvature radius ≥0 depends on the incident angle and vanishes in some directions.

We give conditions under which the intersection between two attracting immediate basins boundaries of a rational map contains at least one periodic point.

International audience; We use the formalism of the Rényi entropies to establish the symmetry range of extremal functions in a family of subcriti-cal Caffarelli-Kohn-Nirenberg inequalities. By extremal functions we mean functions which realize the equality case in the inequalities, written with optimal constants. The method extends recent results on critical Caffarelli-Kohn-Nirenberg inequalities. Using heuristics given by a nonlinear diffusion equation, we give a variational proof of a symmetry result, by establishing a rigidity theorem: in the symmetry region, all positive critical points have radial symmetry and are therefore equal to the unique positive, radial critical point, up to scalings and multiplications. This result is sharp. The condition on the parameters is indeed complementary of the condition which determines the region in which symmetry breaking holds as a consequence of the linear instability of radial optimal functions. Compared to the critical case, the subcritical range requires new tools. The Fisher information has to be replaced by Rényi entropy powers, and since some invariances are lost, the estimates based on the Emden-Fowler transformation have to be modified.

We address the topology of the set of singularities of a solution to a Hamilton–Jacobi equation. For this, we will apply the idea of the first two authors (Cannarsa and Cheng, Generalized characteristics and Lax–Oleinik operators: global result, preprint, arXiv:1605.07581 , 2016) to use the positive Lax–Oleinik semi-group to propagate singularities.

In this paper, we identify the moduli space for germs of generic unfoldings of nonresonant linear differential systems with an irregular singularity of Poincar\'e rank $k$ at the origin, under analytic equivalence. The modulus of a given family was determined in \cite{HLR}: it comprises a formal part depending analytically on the parameters, and an analytic part given by unfoldings of the Stokes matrices. These unfoldings are given on "Douady-Sentenac" (DS) domains in the parameter space covering the generic values of the parameters corresponding to Fuchsian singular points. Here we identify exactly which moduli can be realized. A necessary condition on the analytic part, called compatibility condition, is saying that the unfoldings define the same monodromy group (up to conjugacy) for the different presentations of the modulus on the intersections of DS domains. With the additional requirement that the corresponding cocycle is trivial and good limit behavior at some boundary points of the DS domains, this condition becomes sufficient. In particular we show that any modulus can be realized by a $k$-parameter family of systems of rational linear differential equations over $\mathbb C\mathbb P^1$ with $k+1$, $k+2$ or $k+3$ singular points (with multiplicities). Under the generic condition of irreducibility, there are precisely $k+2$ singular points which are Fuchsian as soon as simple. This in turn implies that any unfolding of an irregular singularity of Poincar\'e rank $k$ is analytically equivalent to a rational system of the form $y'=\frac{A(x)}{p_\epsilon(x)}\cdot y$, with $A(x)$ polynomial of degree at most $k$ and $p_\epsilon(x)$ is the generic unfolding of the polynomial $x^{k+1}$., Comment: 45 pages, 19 figures

Consideration of resources such as fuel, battery charge, and storage space, is a crucial requirement for the successful persistent operation of autonomous systems. The Stochastic Collection and Replenishment (SCAR) scenario is motivated by mining and agricultural scenarios where a dedicated replenishment agent transports a resource between a centralised replenishment point to agents using the resource in the field. The agents in the field typically operate within fixed areas (for example, benches in mining applications, and fields or orchards in agricultural scenarios), and the motion of the replenishment agent may be restricted by a road network. Existing research has typically approached the problem of scheduling the actions of the dedicated replenishment agent from a short-term and deterministic angle. This paper introduces a method of incorporating uncertainty in the schedule optimisation through a novel prediction framework, and a branch and bound optimisation method which uses the prediction framework to minimise the downtime of the agents. The prediction framework makes use of several Gaussian approximations to quickly calculate the risk-weighted cost of a schedule. The anytime nature of the branch and bound method is exploited within an MPC-like framework to outperform existing optimisation methods while providing reasonable calculation times in large scenarios., Comment: Revision 1

International audience; This paper introduces the notion of a metric for a simplex. Such a metric is a key ingredient when solving a PDE system by means of a Finite Element Method. Both mesh generation methods and error estimates (as far as interpolation error is considered) are concerned. Moreover, this metric gives information about the geometry of the corresponding element, typically about its shape quality in any Euclidean space.; Ce papier introduit la notion de métrique liée à un élément géométrique simplicial (un simplexe). Cette métrique est utilisée dans la résolution par la méthode des éléments finis d'équations aux dérivées partielles, à la fois pour la génération de maillages et les estimateurs d'erreur basés sur l'erreur d'interpolation. En outre, cette métrique renseigne sur la géométrie de l'élément et, en particulier, sur sa qualité en forme dans un espace euclidien quelconque.

According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity. At the opposite extremity of the nilpotent cone, the closure of the minimal nilpotent orbit is also an isolated symplectic singularity, called a minimal singularity. For classical Lie algebras, Kraft and Procesi showed that these two types of singularities suffice to describe all generic singularities of nilpotent orbit closures: specifically, any such singularity is either a simple surface singularity, a minimal singularity, or a union of two simple surface singularities of type $A_{2k-1}$. In the present paper, we complete the picture by determining the generic singularities of all nilpotent orbit closures in exceptional Lie algebras (up to normalization in a few cases). We summarize the results in some graphs at the end of the paper. In most cases, we also obtain simple surface singularities or minimal singularities, though often with more complicated branching than occurs in the classical types. There are, however, six singularities which do not occur in the classical types. Three of these are unibranch non-normal singularities: an $SL_2(\mathbb C)$-variety whose normalization is ${\mathbb A}^2$, an $Sp_4(\mathbb C)$-variety whose normalization is ${\mathbb A}^4$, and a two-dimensional variety whose normalization is the simple surface singularity $A_3$. In addition, there are three 4-dimensional isolated singularities each appearing once. We also study an intrinsic symmetry action on the singularities, in analogy with Slodowy's work for the regular nilpotent orbit., 56 pages (5 figures). Minor corrections. Accepted in Advances in Math

We consider the energy critical semilinear heat equation ∂ t u = Δ u + | u | 4 d − 2 u , x ∈ R d in dimension d ≥ 3 . We propose a self-contained proof of the stability of solutions u blowing-up in finite time with type-I ODE blow-up ‖ u ‖ L ∞ ∼ κ ( T − t ) d − 2 4 , T > 0 , κ : = ( d − 2 4 ) d − 2 4 which adapts to the energy critical case the proof of Fermanian, Merle, Zaag [4] .

We show that separable, nuclear and strongly purely infinite C*-algebras have finite nuclear dimension. In fact, the value is at most three. This exploits a deep structural result of Kirchberg and R{\o}rdam on strongly purely infinite C*-algebras that are homotopic to zero in an ideal-system preserving way., Comment: 7 pages; v2 a few minor stylistic changes in the intro. This version is going to appear in Advances in Mathematics

Current state of the art scan registration algorithms which use only position information often fall victim to correspondence ambiguity and degeneracy in the optimization solutions. Other methods which use additional channels, such as color or intensity, often use only a small fraction of the available information and ignore the underlying structural information of the added channels. The proposed method incorporates the additional channels directly into the scan registration formulation to provide information within the plane of the surface. This is achieved by calculating the uncertainty both along and perpendicular to the local surface at each point and calculating nearest neighbor correspondences in the higher dimensional space. The proposed method reduces instances of degenerate transformation estimates and improves both registration accuracy and convergence rate. The method is tested on the Ford Vision and Lidar dataset using both color and intensity channels, as well as with Microsoft Kinect data from the Freiburg RGBD Office dataset and data obtained from the University of Waterloo campus.

Nous montrons que les \'equations du rep\`ere mobile des surfaces de Bonnet conduisent \`a une paire de Lax matricielle isomonodromique d'ordre deux pour la sixi\`eme \'equation de Painlev\'e. We show that the moving frame equations of Bonnet surfaces can be extrapolated to a second order, isomonodromic matrix Lax pair of the sixth Painlev\'e equation., Comment: in French. Formula (14) added. Two paragraphs added p 5-6. Old ref 1 removed, ref 7 added. To appear, Comptes rendus Acad. sciences Paris

In the perspective of estimating main effects of model inputs, two approaches are studied to iteratively construct replicated designs based on Sobol' sequences. Space-filling properties of the resulting designs are studied based on two criteria.

This is an Open Access article Abstract. How can we best identify, understand, and deal with ethical and societal issues raised by healthcare robotics? This paper argues that next to ethical analysis, classic technology assessment, and philosophical speculation we need forms of reflection, dialogue, and experiment that come, quite literally, much closer to innovation practices and contexts of use. The authors discuss a number of ways how to achieve that.. Informed by their experience with “embedded” ethics in technical projects and with various tools and methods of responsible research and innovation, the paper identifies “internal” and “external” forms of dialogical research and innovation and reflects on the possibilities and limitations of these forms of ethical-technological forms of innovation and explores a number of ways how they can be supported by policy at national and supranational level.

Drawing is a way of visually expressing our feelings, knowledge, and situation. People draw pictures to share information with other human beings. This study investigates visuomotor memory (VM), which is a reusable memory storing drawing behavioral data. We propose a neural network-based model for acquiring a computational memory that can replicate VM through self-organized learning of a robot’s actual drawing experiences. To design the model, we assume that VM has the following two characteristics: (1) it is formed by bottom-up learning and integration of temporal drawn pictures and motion data, and (2) it allows the observers to associate drawing motions from pictures. The proposed model comprises a deep neural network for dimensionally compressing temporal drawn images and a continuous-time recurrent neural network for integration learning of drawing motions and temporal drawn images. Two experiments are conducted on unicursal shape learning to investigate whether the proposed model can learn the function without any shape information for visual processing. Based on the first experiment, the model can learn 15 drawing sequences for three types of pictures, acquiring associative memory for drawing motions through the bottom-up learning process. Thus, it can associate drawing motions from untrained drawn images. In the second experiment, four types of pictures are trained, with four distorted variations per type. In this case, the model can organize the different shapes based on their distortions by utilizing both the image information and the drawing motions, even if visual characteristics are not shared.

C. R. Math. Acad. Sci. Paris.http://dx.doi.org/10.1016/j.crma.2016.06.007Open access; International audience; In this Note, we present a new version of the vector penalty-projection splitting method described in [1] (Angot et al., 2012) for the fast numerical computation of incompressible flows with variable density and viscosity. We show that the velocity correction can be made completely independent on the mass density ρ. Hence, this step is purely kinematic using the fast Helmholtz-Hodge decompositions proposed in [2] (Angot et al., 2013). Then, it is shown that the dynamic step of pressure gradient correction can be fast and locally consistent on edge-based generalized MAC-type unstructured meshes which naturally verify the compatibility condition in the proposed discrete setting. By the way, a new accurate front-tracking Lagrangian-advection technique is also introduced for multiphase flows. This new method preserves the fully vector formulation of both the prediction and correction steps of the original scheme, the primary unknowns being (v, Grad p) and ρ by advection, since the pressure Neumann-Poisson problem remains eliminated. The efficiency of the present method is demonstrated through numerical results on sharp test cases.; Résumé. Une méthode cinématique de pénalité-projection vectorielle pour l' écoulement incompressiblè à densité variable. On présente dans cette Note une nouvelle version de la méthode de splitting par pénalité-projection vectorielle décrite dans [1] pour le calcul des écoulements incompressibles à masse volumique et viscosité variables. Le principal résultat est de rendre la correction vectorielle de vitesse complètement indépendante de la masse volumique ρ. Cette étape devient donc purement cinématique et correspond à une décomposition rapide de Helmholtz-Hodge proposée dans [2]. On montre que l' étape dynamique de correction du gradient de pression peut être rapide et localement consistante sur des maillages généralisés de type MAC non structurés. Version française abrégée. L'idée clé pour la construction de cette nouvelle méthode (K-VPP ε) repose sur les décompositions rapides de Helmholtz-Hodge en domaine borné proposées dans [2] et analysées dans [3]. L'étape de correction vectorielle en vitesse v est rendue purement cinématique. Elle correspond à une méthode de projection à divergence nulle approchée pour obtenir la composante irrotationnelle $\widehat{v} := Grad φ$ du champ de vitesse prédit $\widetilde{v}$. L'étape dynamique de correction du gradient de pression est alors obtenue en introduisant le concept de densité inertielle $\bar{ρ}$ calculée sur chaque arête du maillage principal et reliant les sommets des inconnues scalaires p, φ et ρ. On montre qu'il existe $\bar{ρ}$ satisfaisant l'équation de consistance locale : $Grad(\bar{ρ} φ) = ρ Grad φ = ρ \widehat{v}$, et permettant de recouvrer un gradient de pression entre les sommets. En pratique, comme la condition de compatibilité associée est naturellement satisfaite pour les maillages de type MAC, le calcul de $\bar{ρ}$ est effectué facilement et de façon rapide à partir de ρ et d'une fonction de partage α, tandis que φ est reconstruit à partir de son gradient connu sur les arêtes.

The goal of this note is to announce certain results in orbit equivalence theory, especially concerning the approximation of p.m.p. standard equivalence relations by increasing sequences of sub-relations, with application to the behavior of the Bernoulli percolation on Cayley graphs at the threshold p u .

We study endomorphism algebras of 2-term silting complexes in derived categories of hereditary finite dimensional algebras, or more generally of $\mathop{\rm Ext}\nolimits$-finite hereditary abelian categories. Module categories of such endomorphism algebras are known to occur as hearts of certain bounded $t$-structures in such derived categories. We show that the algebras occurring are exactly the algebras of small homological dimension, which are algebras characterized by the property that each indecomposable module either has injective dimension at most one, or it has projective dimension at most one., Comment: Fix some typos, to appear in Adv. Math

In this paper we consider a punctured Riemann surface endowed with a Hermitian metric which equals the Poincar\'e metric near the punctures and a holomorphic line bundle which polarizes the metric. We show that the Bergman kernel can be localized around the singularities and its local model is the Bergman kernel of the punctured unit disc endowed with the standard Poincar\'e metric. As a consequence, we obtain an optimal uniform estimate of the supremum norm of the Bergman kernel, involving a fractional growth order of the tensor power., Comment: 42 pages, 2 figures; v.2 is a final update to agree with the published paper

Large-scale offshore wind turbine blades need careful dimensional inspection at the production stage. This paper aims to establish an accurate measurement technique using Coherent Laser Radar technology combined with B-Spline point generation and alignment. Through varying the Degrees of Freedom (DoF), used for data point transformation, within the Spatial Analyser software package, erroneous inspection results generated by unconstrained blade flexing can be eradicated. The paper concludes that implementing a single B-Spline point generation and alignment method, whilst allowing transformation with DoF in X, Y and Rz, provides confidence to wind turbine blade manufacturers that inspection data is accurate. The experimental procedure described in this paper can also be applied to the precision inspection of other large-scale non-rigid, unconstrained objects.

International audience; Mould calculus is a powerful combinatorial tool that often provides some explicit formulae when there are no other available computational methods. It has a well-known interpretation/dictionary in terms of Hopf algebras. But this dictionary does not provide any equivalent of formal moulds. Thus, we present here such an interpretation and give a generic way to prove mould symmetries of formal moulds.; Le calcul moulien est un outil combinatoire puissant, qui fournit souvent des formules explicites, alors que d'autres moyens de calcul n'aboutissent pas. Il en existe une interprétation/un dictionnaire en termes d'algèbres de Hopf. Mais ce dictionnaire n'a pas été développé jusqu'aux moules formels. Nous présentons ici une telle interprétation et donnons alors une méthode générique permettant de prouver les symétries de moules formels.

Our results and examples show how transformations between self-similar sets may be continuous almost everywhere with respect to measures on the sets and may be used to carry well known notions from analysis and functional analysis, for example flows and spectral analysis, from familiar settings to new ones. The focus of this paper is on a number of surprising applications including what we call fractal Fourier analysis, in which the graphs of the basis functions are Cantor sets, discontinuous at a countable dense set of points, yet have good approximation properties. In a sequel, the focus will be on Lebesgue measure-preserving flows whose wave-fronts are fractals. The key idea is to use fractal transformations to provide unitary transformations between Hilbert spaces defined on attractors of iterated function systems.

In this paper we study multiserial and special multiserial algebras. These algebras are a natural generalization of biserial and special biserial algebras to algebras of wild representation type. We define a module to be multiserial if its radical is the sum of uniserial modules whose pairwise intersection is either 0 or a simple module. We show that all finitely generated modules over a special multiserial algebra are multiserial. In particular, this implies that, in analogy to special biserial algebras being biserial, special multiserial algebras are multiserial. We then show that the class of symmetric special multiserial algebras coincides with the class of Brauer configuration algebras, where the latter are a generalization of Brauer graph algebras. We end by showing that any symmetric algebra with radical cube zero is special multiserial and so, in particular, it is a Brauer configuration algebra., Minor revision, to appear in Advances in Mathematics

A Laurent polynomial ring R 0 [ t , t − 1 ] with coefficients in a unital ring determines a category of quasi-coherent sheaves on the projective line over R 0 ; its K-theory is known to split into a direct sum of two copies of the K-theory of R 0 . In this paper, the result is generalised to the case of an arbitrary strongly Z -graded ring R in place of the Laurent polynomial ring. The projective line associated with R is indirectly defined by specifying the corresponding category of quasi-coherent sheaves. Notions from algebraic geometry like sheaf cohomology and twisting sheaves are transferred to the new setting, and the K-theoretical splitting is established.

International audience; This note introduces reflective tomography in a mathematical framework. The effect of the filtered backprojection on reflective-kind projections is studied: a reflective projection is defined, tomographic filtering of such a projection is analysed, and so is the filtered backprojection. The results emphasize the role of the contrasts: we get a decomposition in which the contributions of the discontinuities and of the tangential variations are enlightened.

We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear wave equations posed on a curved space, when wave equations and Klein–Gordon equations are coupled. This method is based on a ( 3 + 1 ) foliation (of the interior of a future light cone in Minkowski spacetime) by spacelike and asymptotically hyperboloidal hypersurfaces. In the new formulation of the method, we succeed to cover wave-Klein–Gordon systems containing “strong interaction” terms at the level of the metric, and then generalize our method in order to establish a new existence theory for the Einstein equations of general relativity. Following pioneering work by Lindblad and Rodnianski on the Einstein equations in wave coordinates, we establish the nonlinear stability of Minkowski spacetime for self-gravitating massive scalar fields.

In this note, we prove the non-degeneracy of the Kobayashi–Eisenman volume measure of a singular directed varieties (X,V), i.e. the Kobayashi measure hyperbolicity of (X,V), as long as the canonical sheaf KV of V is big in the sense of Demailly.