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The study described herein represents an initial, exploratory attempt to understand what it means to translate between external representation systems. Researchers have traditionally considered translation as an all-or-none activity. We hypothesize that translation is comprised of both knowledge and skill components, and accordingly construe translation as an activity that our framework allows us to define as partial or complete. We examined the effects of part–whole knowledge in change unknown subtraction situations and the structure of three different external representations on first grade students’ ability to translate in a partitioning task. Based on three interviews conducted with each student, results from our mixed methods analysis showed that translation skill was affected by what students knew about subtraction and the structure of the ER. Further, whereas high knowledge students demonstrated greater difficulty with translating to the ERs, low knowledge students had difficulty translating from the problem statement as well as translating to the ERs.

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

Augmented reality is considered one of the enabling technologies of the fourth industrial revolution, within the Industry 4.0 program and beyond. Indeed, augmented reality solutions can increase the working quality and the productivity and allow a better use of the human resources. This technology can help the operator in the industrial applications during the crucial phases of the processes. Since the quality assessment of the surfaces is recognized to be a key phase in the polishing process, in this paper we propose a novel method that exploits augmented reality to support the operators during this phase. The metrology data measured by a surface measurement system are directly projected on the polished component through an augmented reality headset worn by the operators and used to assess the quality of the worked surfaces. Rather than imagine how a certain parameter change can affect the result achieved, the information is directly there on the component’s surface. Users can see from the data where refinements are required and make better and faster decisions, which is compelling for its potential beyond industrial polishing. The proposed method is implemented and validated on an industrial cell, where the robot automatically perform the polishing task and move the head of the surface measurement system along the surface to measure the metrology parameters. Thanks to the proposed approach, the end-user and the operator can directly see on the component if the quality reached satisfies the specifications or if some parts of the surface require further refinements through additional polishing steps.

We prove the existence of the fundamental solution of the degenerate second order partial differential equation related to Geman–Yor stochastic processes, that arise in models for option pricing theory in finance. We then prove pointwise lower and upper bounds for such fundamental solution. Lower bounds are obtained by using repeatedly an invariant Harnack inequality and by solving an associated optimal control problem with quadratic cost. Upper bounds are obtained by the fact that the cost satisfies a specific Hamilton–Jacobi–Bellman equation.

We study the perfect conductivity problem when two perfectly conducting inclusions are closely located to each other in an anisotropic background medium. We establish optimal upper and lower gradient bounds for the solution in any dimension which characterize the singular behavior of the electric field as the distance between the inclusions goes to zero.

We prove that weak solutions obtained as limits of certain numerical space-time discretizations are suitable in the sense of Scheffer and Caffarelli-Kohn-Nirenberg. More precisely, in the space-periodic setting, we consider a full discretization in which the theta-method is used to discretize the time variable, while in the space variables we consider appropriate families of finite elements. The main result is the validity of the so-called local energy inequality., Comment: 16 pages

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

Manufacturing ergonomics refers to the application of ergonomic principles and human factors analysis to the design of manufacturing tasks with the final aim to optimize the workers’ wellbeing and guarantee the expected process performance. Traditional design approaches are based on the observation of individual workers performing their jobs, the detection of unnatural postures (e.g., bending, twisting, overextending, rotating), and the definition of late corrective actions according to ergonomic guidelines. Recently, computer-integrated simulations based on virtual prototypes and digital human models (DHMs) can be used to assess manufacturing ergonomics on virtual manikins operating in digital workplaces. Such simulations allow validating different design alternatives and optimizing the workstation design before the creation, and pave the way to a new approach to manufacturing system design. The present paper aims at comparing different computer-integrated set-ups to support the design of human-centred manufacturing workstations. It defines a protocol analysis to support workstation design by analysing both physical and cognitive aspects, and applies the protocol within different digital set-ups. In particular, the study investigates a 2D desktop set-up using standardized DHMs and a 3D immersive mixed reality set-up based on motion capture of real workers’ acting into a mixed environment, comparing them with the traditional approach. An industrial case study focusing on design optimization of a manufacturing workstation in the energy industry is used to test the effectiveness of the two digital set-ups for the definition of re-design actions.

We provide an existence result for stationary fractional mean field game systems, with fractional exponent greater than 1/2. In the case in which the coupling is a nonlocal regularizing potential, we obtain existence of solutions under general assumptions on the Hamiltonian. In the case of local coupling, we restrict to the subcritical regime, that is the case in which the diffusion part of the operator dominates the Hamiltonian term. We consider both the case of local bounded coupling and of local unbounded coupling with power-type growth. In this second regime, we impose some conditions on the growth of the coupling and on the growth of the Hamiltonian with respect to the gradient term., Comment: 19 pages

In this paper we study the asymptotic behaviour of an exact controllability problem for a second order linear evolution equation defined in a two-component composite with e-periodic disconnected inclusions of size e. On the interface we prescribe a jump of the solution that varies according to a real parameter γ. In particular, we suppose that − 1 γ ≤ 1 . The case γ = 1 is the most interesting and delicate one, since the homogenized problem is represented by a coupled system of a P.D.E. and an O.D.E., giving rise to a memory effect. Our approach to exact controllability consists in applying the Hilbert Uniqueness Method, introduced by J.-L. Lions, which leads us to the construction of the exact control as the solution of a transposed problem. Our main result proves that the exact control and the corresponding solution of the e-problem converge to the exact control of the homogenized problem and to the corresponding solution respectively.

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.

We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon estimates for heat semigroups and applies to Gaussian and RCD(K,∞) spaces. As a consequence, we obtain quantitative stability for regular Lagrangian flows in Gaussian settings. We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon estimates for heat semigroups and applies to Gaussian and RCD(K,∞) spaces. As a consequence, we obtain quantitative stability for regular Lagrangian flows in Gaussian settings.

In this work, we describe an approach for estimation and tracking of the skeleton of the human body from camera networks exploiting only depth data. The algorithm takes advantage of multiple views by building and merging together the 3D point clouds. The final skeleton is computed from a virtual depth image generated from this point cloud by means of back-projection to a reference camera image plane. Before the back-projection, the person point cloud is frontalized with respect to the reference camera, so that the virtual depth image represents the person from a frontal viewpoint and the accuracy of the skeleton estimation algorithm is maximized. Our experiments show how the proposed approach boosts the performance with respect to other state-of-the-art approaches. Moreover, the proposed algorithm requires low computational burden, thus running in real-time.

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.

For every $\tau\in\mathbb{R}$ and every integer $N$, let $\mathfrak{m}_N(\tau)$ be the minimum of the distance of $\tau$ from the sums $\sum_{n=1}^N s_n/n$, where $s_1, \ldots, s_n \in \{-1, +1\}$. We prove that $\mathfrak{m}_N(\tau) < \exp\!\big(-C(\log N)^2\big)$, for all sufficiently large positive integers $N$ (depending on $C$ and $\tau$), where $C$ is any positive constant less than $1/\log 4$., Comment: minor corrections to the text, a small improvement to Proposition 2.7

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

We introduce and analyze a class of models with nonlocal point constraints for traffic flow through bottlenecks, such as exits in the context of pedestrians traffic and reduction of lanes on a road under construction in vehicular traffic. Constraints are defined based on data collected from non-local in space and/or in time observations of the flow. We propose a theoretical analysis and discretization framework that permits to include different data acquisition strategies; a numerical comparison is provided. Nonlocal constraint allows to model, e.g., the irrational behavior (" panic ") near the exit observed in dense crowds and the capacity drop at tollbooth in vehicular traffic. Existence and uniqueness of solutions are shown under suitable and " easy to check " assumptions on the constraint operator. A numerical scheme for the problem, based on finite volume methods, is designed, its convergence is proved and its validation is done with an explicit solution. Numerical examples show that nonlocally constrained models are able to reproduce important features in traffic flow such as self-organization.

We consider a Cournot duopoly with isoelastic demand function and constant marginal costs. We assume that both producers have naive expectations but one of them reacts with delay to the move of its competitors, due to a “less efficient” production process of a competitor with respect to its opponent. The model is described by a 3D map having the so-called “cube separate property”, that is its third iterate has separate components. We show that many cycles may coexist and, through global analysis, we characterize their basins of attraction. We also study the chaotic dynamics generated by the model, showing that the attracting set is either a parallelepiped or the union of coexisting parallelepipeds. We also prove that such attracting sets coexist with chaotic surfaces, having the shape of generalized cylinders, and with different chaotic curves.

Among the existing global optimization algorithms, Particle Swarm Optimization (PSO) is one of the most effective methods for non-linear and complex high-dimensional problems. Since PSO performance strongly depends on the choice of its settings (i.e., inertia, cognitive and social factors, minimum and maximum velocity), Fuzzy Logic (FL) was previously exploited to select these values. So far, FL-based implementations of PSO aimed at the calculation of a unique settings for the whole swarm. In this work we propose a novel self-tuning algorithm—called Fuzzy Self-Tuning PSO (FST-PSO)—which exploits FL to calculate the inertia, cognitive and social factor, minimum and maximum velocity independently for each particle, thus realizing a complete settings-free version of PSO. The novelty and strength of FST-PSO lie in the fact that it does not require any expertise in PSO functioning, since the behavior of every particle is automatically and dynamically adjusted during the optimization. We compare the performance of FST-PSO with standard PSO, Proactive Particles in Swarm Optimization, Artificial Bee Colony, Covariance Matrix Adaptation Evolution Strategy, Differential Evolution and Genetic Algorithms. We empirically show that FST-PSO can basically outperform all tested algorithms with respect to the convergence speed and is competitive concerning the best solutions found, noticeably with a reduced computational effort.

This paper proposes the theory and the experimental assessment of a robust model-based trajectory planning algorithm for underactuated nonlinear systems in point-to-point motion. The method has been developed to increase the insensitivity of the resulting trajectory to parametric uncertainties of the plant. The proposed method is based on an augmented model that considers an approximate dynamics of the servo-controlled axis driving the actuated degrees of freedom. Trajectory planning is accomplished by computing the motion reference for the actuated degrees of freedom to reduce the effects of the uncertainty on the dynamic model. By exploiting an indirect variational formulation method, the necessary optimality conditions deriving from the Pontryagin’s minimum principle are imposed, thus leading to a differential Two-Point Boundary Value Problem (TPBVP). Numerical solution of the latter is accomplished by means of collocation techniques to handle model nonlinearities. Robustness is achieved by including additional conditions on the sensitivity functions for the initial and final points of the trajectory. The experimental evaluation of the effectiveness of the proposed method is performed on a double-pendulum crane, by comparing the transient and residual vibration. A comparison is provided with three well-established input-shaping methods, and robustness against unmodeled parametric perturbations and tracking errors is evaluated. The experimental evidence indicates that the inclusion of the additional constrains results in an effective reduction of the residual vibration, and that the proposed method is well suited to perform high speed motion.

In [1] , even if f only belongs to L 1 ( Ω ) , we proved that the assumption | f ( x ) | ≤ Q a ( x ) ∈ L 1 ( Ω ) , Q ∈ R + , implies the existence of a bounded solution of boundary value problems, whose simplest example is the linear problem { − div ( M ( x ) ∇ u ) + a ( x ) u = f ( x ) , in Ω ; u = 0 , on ∂ Ω ; where Ω is a bounded open set of R N and M is a bounded elliptic matrix. In this paper, we continue the study of the regularizing effect on the solutions, in some nonlinear Dirichlet problems, when we have L q interaction between the coefficient a ( x ) and the datum f ( x ) (i.e. Q is now a function in L q ( Ω ) ).

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 growing market demand for a wide variety of product models and small batch production makes flexible robotized production systems an emerging need in industry. Today, in manufacturing applications, general purpose grippers are not very considered, and robot end effectors are properly designed for the specific task with a strongly limited versatility. Flexibility is thus usually obtained by using a different tool for each family of parts: a tool changing system allows the robot to rapidly replace the tool on the end effector; tools are stored in a tool magazine allocated in the workcell. However, such systems are expensive and their use can affect the working cycle-time. This paper presents the design and testing of a variable-aperture, cost-effective gripper, capable of adapting its aperture (grasp width) to different handling demands, without affecting the working-cycle time of the production system. The solution proposed consists of (1) an electrically-actuated mechanism, which allows it to satisfy flexibility requirements, by regulating the aperture in hidden time; (2) a pneumatically-actuated mechanism to achieve high performance in open/close operations. Simulations and preliminary tests showed that this type of design can be a suitable solution to increase flexibility in robotized workcells without increasing the cycle time.

We consider the nonlinear nonlocal beam evolution equation introduced by Woinowsky- Krieger. We study the existence and behavior of periodic solutions: these are called nonlinear modes. Some solutions only have two active modes and we investigate whether there is an energy transfer between them. The answer depends on the geometry of the energy function which, in turn, depends on the amount of compression compared to the spatial frequencies of the involved modes. Our results are complemented with numerical experiments, overall, they give a complete picture of the instabilities that may occur in the beam. We expect these results to hold also in more complicated dynamical system, Comment: Journal-Mathematiques-Pures-Appliquees, 2017

Given ρ ∈ [ 0 , 1 ] , we consider for e ∈ ( 0 , 1 ] the nonautonomous viscoelastic equation with a singularly oscillating external force ∂ t t u − κ ( 0 ) Δ u − ∫ 0 ∞ κ ′ ( s ) Δ u ( t − s ) d s + f ( u ) = g 0 ( t ) + e − ρ g 1 ( t / e ) together with the averaged equation ∂ t t u − κ ( 0 ) Δ u − ∫ 0 ∞ κ ′ ( s ) Δ u ( t − s ) d s + f ( u ) = g 0 ( t ) . Under suitable assumptions on the nonlinearity and on the external force, the related solution processes S e ( t , τ ) acting on the natural weak energy space H are shown to possess uniform attractors A e . Within the further assumption ρ 1 , the family A e turns out to be bounded in H , uniformly with respect to e ∈ [ 0 , 1 ] . The convergence of the attractors A e to the attractor A 0 of the averaged equation as e → 0 is also established.

This article represents an attempt to characterise the dynamics of a nonlinear duopoly with price competition and horizontal product differentiation by accounting for non-negativity constraints (on profits and the market demand). The model is set up by following the tradition led by Bischi et al. (1998), according to which players have limited information. The article shows several local and global phenomena of a two-dimensional discrete time system when the price demand elasticity varies. It also points out the differences from both a mathematical and economic point of views in terms of dynamic outcomes when the non-negativity constraints are not binding and when they are binding. This is done by combining mathematical techniques and simulation exercises.

Minkowski’s question mark function is the distribution function of a singular continuous measure: we study this measure from the point of view of logarithmic potential theory and orthogonal polynomials. We conjecture that it is regular, in the sense of Ullman–Saff–Stahl–Totik and moreover that it belongs to a Nevai class; we provide numerical evidence of the validity of these conjectures. In addition, we study the zeros of its orthogonal polynomials and the associated Christoffel functions, for which asymptotic formulae are derived. As a by-product, we compute upper and lower bounds to the Hausdorff dimension of Minkowski’s measure. Rigorous results and numerical techniques are based upon Iterated Function Systems composed of Mobius maps.

We devise a new geometric approach to study the propagation of disturbance – compactly supported data – in reaction–diffusion equations. The method builds a bridge between the propagation of disturbance and of almost planar solutions. It applies to very general reaction–diffusion equations. The main consequences we derive in this paper are: a new proof of the classical Freidlin–Gartner formula for the asymptotic speed of spreading for periodic Fisher–KPP equations; extension of the formula to the monostable, combustion and bistable cases; existence of the asymptotic speed of spreading for equations with almost periodic temporal dependence; derivation of multi-tiered propagation for multistable equations.

Powered lower-limb prostheses require a natural, and an easy-to-use, interface for communicating amputee’s motor intention in order to select the appropriate motor program in any given context, or simply to commute from active (powered) to passive mode of functioning. To be widely accepted, such an interface should not put additional cognitive load at the end-user, it should be reliable and minimally invasive. In this paper we present a one such interface based on a robust method for detecting and recognizing motor actions from a low-cost wearable sensor network mounted on a sound leg providing inertial (accelerometer, gyrometer and magnetometer) data in real-time. We assume that the sensor measurement trajectories – in a given temporal window – can be represented as the output of a linear time invariant system. We describe such set of trajectories via a Hankel matrix, which embeds the observability matrix of the LTI system generating the set of trajectories. The use of Hankel matrices (known as Hankelets) avoids the burden of performing system identification while providing a computationally convenient descriptor for the dynamics of a time-series. For the recognition of actions, we use two off-the-shelf classifiers, nearest neighbor (NN) and support vector machines (SVM), in cross-subject validation. We present results using either the joint angles or the raw sensor data showing a net improvement of the Hankelet-based approach against a baseline method. In addition, we compare results on action recognition using joint angles provided by trakSTAR, a high-accuracy motion tracking unit, demonstrating – somewhat surprisingly – that best results (in terms of average recognition accuracy over different actions) are provided by raw inertial data, paving the way towards a wider usage of our method in the field of active prosthetics, in particular, and motor intention recognition, in general.

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.

In this paper we present a case study in which a 14-year-old, right-handed stroke patient with severe weakness, spasticity, and motor dysfunction of the left upper extremity participated in a three-month distal robotic training program. The robotic device was compliant to the patient’s movements and was able to modulate the level of assistance continuously throughout the trial (i.e., online adaptive modulation). Standard clinical and robotic evaluations of upper extremity motor performance were conducted before and after robotic training. There were improvements in upper extremity spasticity and motor functions. In addition, robotic training lead to positive changes in wrist active range of motion and kinematics: movements were smoother and there was a noticeable decrease in the level of robotic intervention required to complete each trial. In sum, results of the present case study demonstrate that distal upper extremity robotic rehabilitation that features the proposed adaptive control algorithm promoted positive changes in upper limb motor coordination and function after pediatric stroke.

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.

Visual perception is a fundamental component for most robotics systems operating in human environments. Specifically, visual recognition is a prerequisite to a large variety of tasks such as tracking, manipulation, human–robot interaction. As a consequence, the lack of successful recognition often becomes a bottleneck for the application of robotics system to real-world situations. In this paper we aim at improving the robot visual perception capabilities in a natural, human-like fashion, with a very limited amount of constraints to the acquisition scenario. In particular our goal is to build and analyze a learning system that can rapidly be re-trained in order to incorporate new evidence if available. To this purpose, we review the state-of-the-art coding–pooling pipelines for visual recognition and propose two modifications which allow us to improve the quality of the representation, while maintaining real-time performances: a coding scheme, Best Code Entries (BCE), and a new pooling operator, Mid-Level Classification Weights (MLCW). The former focuses entirely on sparsity and improves the stability and computational efficiency of the coding phase, the latter increases the discriminability of the visual representation, and therefore the overall recognition accuracy of the system, by exploiting data supervision. The proposed pipeline is assessed from a qualitative perspective on a Human–Robot Interaction (HRI) application on the iCub platform. Quantitative evaluation of the proposed system is performed both on in-house robotics data-sets (iCubWorld) and on established computer vision benchmarks (Caltech-256, PASCAL VOC 2007). As a byproduct of this work, we provide for the robotics community an implementation of the proposed visual recognition pipeline which can be used as perceptual layer for more complex robotics applications.

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.