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Additive Manufacturing (AM) allows for the manufacturing of complex geometry parts as a single object regardless of their geometric complexity. However, manufacturing a consolidate object is not always to be better than the assembly approach. There are several practical scenarios which often require an assembly approach, i.e., (1) to achieve specific mechanical functionality in the product and aesthetic aspects; (2) to fit a product component in a predefined buildable space, particularly the case where large-scale products are required to be fitted with a developing platform space; and (3) to improve the additive manufacturing productivity (by minimizing processing time, improving product quality, surface finish and reducing material/support cost). In this paper, a computational framework is proposed to decompose the initial object design into several assemblies with the aim to minimize the total AM processing time. The decomposed components can be arranged into a minimum printing height space, thus it reduces the number of printing layer significantly, yielding to a build-up time reduction even if some time is spent in required assembling operations. Computation framework is implemented for three medium size object geometries. The presented study points out that the part decomposition and assembling approach can considerably reduce the total AM processing time. The methodology supports AM to be extended for a broad range of medium size products, and leads to strengthening the customizability of the products.

When adopting the matching method of the least squares image based on object-patch to match tilted images, problems like the low degree of connection points for images with the discontinuity of depth or the discrepancy in elevation or low availability of aerotriangulation points would frequently appear. To address such problems, a tilted-image-matching algorithm based on an adaptive initial object-patch is proposed by this paper. By means of the existing initial values of the interior and exterior orientation elements of the tilted image and the information of object points generated in the matching process, the algorithm takes advantage of the method of multi-patch forward intersection and object variance partition so as to adaptively calculate the elevation of the object-patch and the initial value of the normal vector direction angle. Furthermore, this algorithm aims to solve the problem of difficulties in matching the tilted image with its corresponding points brought about by the low accuracy of the initial value of the tilted image when adopting the matching method of the least squares image based on object-patch to match the tilted image with high discrepancy in elevation. We adopt the algorithm as proposed in this paper and the least squares image matching method in which the initial state of the object-patch is horizontal to the object-patch respectively to conduct the verification process of comparing and matching two groups of tilted images. Finally, the effectiveness of the algorithm as proposed in this paper is verified by the testing results.

In the first part of the paper, we clarify the connections between several algebraic objects appearing in matroid theory: both partial fields and hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are compatible with the respective matroid theories. Moreover, fuzzy rings are ordered blueprints and lie in the intersection of tracts with ordered blueprints; we call the objects of this intersection pastures. In the second part, we construct moduli spaces for matroids over pastures. We show that, for any non-empty finite set $E$, the functor taking a pasture $F$ to the set of isomorphism classes of rank-$r$ $F$-matroids on $E$ is representable by an ordered blue scheme $Mat(r,E)$, the moduli space of rank-$r$ matroids on $E$. In the third part, we draw conclusions on matroid theory. A classical rank-$r$ matroid $M$ on $E$ corresponds to a $\mathbb{K}$-valued point of $Mat(r,E)$ where $\mathbb{K}$ is the Krasner hyperfield. Such a point defines a residue pasture $k_M$, which we call the universal pasture of $M$. We show that for every pasture $F$, morphisms $k_M\to F$ are canonically in bijection with $F$-matroid structures on $M$. An analogous weak universal pasture $k_M^w$ classifies weak $F$-matroid structures on $M$. The unit group of $k_M^w$ can be canonically identified with the Tutte group of $M$. We call the sub-pasture $k_M^f$ of $k_M^w$ generated by ``cross-ratios' the foundation of $M$,. It parametrizes rescaling classes of weak $F$-matroid structures on $M$, and its unit group is coincides with the inner Tutte group of $M$. We show that a matroid $M$ is regular if and only if its foundation is the regular partial field, and a non-regular matroid $M$ is binary if and only if its foundation is the field with two elements. This yields a new proof of the fact that a matroid is regular if and only if it is both binary and orientable., 85 pages; some additional material, e.g. a new section 5.6; the terminology has been adapted to the usage in follow-up papers

The characteristic is a simple yet important invariant of an algebra. In this paper, we study the characteristic of a Rota–Baxter algebra, called the Rota–Baxter characteristic. We introduc...

This paper presents the development of a control system for vision-guided pick-and-place tasks using a robot arm equipped with a 3D camera. The main steps include camera intrinsic and extrinsic calibration, hand-eye calibration, initial object pose registration, objects pose alignment algorithm, and pick-and-place execution. The proposed system allows the robot be able to to pick and place object with limited times of registering a new object and the developed software can be applied for new object scenario quickly. The integrated system was tested using the hardware combination of kuka iiwa, Robotiq grippers (two finger gripper and three finger gripper) and 3D cameras (Intel realsense D415 camera, Intel realsense D435 camera, Microsoft Kinect V2). The whole system can also be modified for the combination of other robotic arm, gripper and 3D camera.

In this paper, we explore generalizable, perception-to-action robotic manipulation for precise, contact-rich tasks. In particular, we contribute a framework for closed-loop robotic manipulation that automatically handles a category of objects, despite potentially unseen object instances and significant intra-category variations in shape, size and appearance. Previous approaches typically build a feedback loop on top of a real-time 6-DOF pose estimator. However, representing an object with a parameterized transformation from a fixed geometric template does not capture large intra-category shape variation. Hence we adopt the keypoint-based object representation proposed in kPAM for category-level pick-and-place, and extend it to closed-loop manipulation policies with contact-rich tasks. We first augment keypoints with local orientation information. Using the oriented keypoints, we propose a novel object-centric action representation in terms of regulating the linear/angular velocity or force/torque of these oriented keypoints. This formulation is surprisingly versatile -- we demonstrate that it can accomplish contact-rich manipulation tasks that require precision and dexterity for a category of objects with different shapes, sizes and appearances, such as peg-hole insertion for pegs and holes with significant shape variation and tight clearance. With the proposed object and action representation, our framework is also agnostic to the robot grasp pose and initial object configuration, making it flexible for integration and deployment., IEEE Robotics and Automation Letter. The video demo is on https://sites.google.com/view/kpam2/

We construct a functor, from the category of schemes to the category of graded rings, that is an initial object for having a theory of Chern classes with an additive first Chern class. For any scheme $X$, the graded ring that our functor associates to $X$ is related to the associated graded ring of the $\gamma$-filtration on the Grothendieck ring of finite rank locally free sheaves on $X$ via a Grothendieck-Riemann-Roch type theorem., Comment: 14 Pages. To appear in Journal of Algebra

The category of all idempotent generated semigroups with a prescribed structure E of their idempotents E (called the biordered set) has an initial object called the free idempotent generated semigroup over E, defined by a presentation over alphabet E, and denoted by IG(E). Recently, much effort has been put into investigating the structure of semigroups of the form IG(E), especially regarding their maximal subgroups. In this paper we take these investigations in a new direction by considering the word problem for IG(E). We prove two principal results, one positive and one negative. We show that, for a finite biordered set E, it is decidable whether a given word w ∈ E∗represents a regular element; if in addition one assumes that all maximal subgroups of IG(E) have decidable word problems, then the word problem in IG(E) restricted to regular words is decidable. On the other hand, we exhibit a biorder E arising from a finite idempotent semigroup S, such that the word problem for IG(E) is undecidable, even though all the maximal subgroups have decidable word problems. This is achieved by relating the word problem of IG(E) to the subgroup membership problem in finitely presented groups.

In this work, we study 'reduction monads', which are essentially the same as monads relative to the free functor from sets into multigraphs. Reduction monads account for two aspects of the lambda calculus: on the one hand, in the monadic viewpoint, the lambda calculus is an object equipped with a well-behaved substitution; on the other hand, in the graphical viewpoint, it is an oriented multigraph whose vertices are terms and whose edges witness the reductions between two terms. We study presentations of reduction monads. To this end, we propose a notion of 'reduction signature'. As usual, such a signature plays the role of a virtual presentation, and specifies arities for generating operations---possibly subject to equations---together with arities for generating reduction rules. For each such signature, we define a category of models; any model is, in particular, a reduction monad. If the initial object of this category of models exists, we call it the 'reduction monad presented (or specified) by the given reduction signature'. Our main result identifies a class of reduction signatures which specify a reduction monad in the above sense. We show in the examples that our approach covers several standard variants of the lambda calculus., POPL 2020

Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $\sigma$-class. In this enriched signature, the class of all $F$-inverse monoids forms a variety of algebraic structures. We describe universal objects in several classes of $F$-inverse monoids, in particular free $F$-inverse monoids. More precisely, for every $X$-generated group $G$ we describe the initial object in the category of all $X$-generated $F$-inverse monoids $F$ for which $F/\sigma=G$., Comment: 21 pages

For any biordered set of idempotents [Formula: see text] there is an initial object [Formula: see text], the free idempotent generated semigroup over[Formula: see text], in the category of semigroups generated by a set of idempotents biorder-isomorphic to [Formula: see text]. Recent research on [Formula: see text] has focused on the behavior of the maximal subgroups. Inspired by an example of Brittenham, Margolis and Meakin, several proofs have been offered that any group occurs as a maximal subgroup of some [Formula: see text], the latest being that of Dolinka and Ruškuc, who show that [Formula: see text] can be taken to be a band. From a result of Easdown, Sapir and Volkov, periodic elements of any [Formula: see text] lie in subgroups. However, little else is known of the “global” properties of [Formula: see text], other than that it need not be regular, even where [Formula: see text] is a semilattice. The aim of this paper is to deepen our understanding of the overall structure of [Formula: see text] in the case where [Formula: see text] is a biordered set with trivial products (for example, the biordered set of a poset) or where [Formula: see text] is the biordered set of a band [Formula: see text]. Since its introduction by Fountain in the late 1970s, the study of abundant and related semigroups has given rise to a deep and fruitful research area. The class of abundant semigroups extends that of regular semigroups in a natural way and itself is contained in the class of weakly abundant semigroups. Our main results show that (1) if [Formula: see text] is a biordered set with trivial products then [Formula: see text] is abundant and (if [Formula: see text] is finite) has solvable word problem, and (2) for any band [Formula: see text], the semigroup [Formula: see text] is weakly abundant and moreover satisfies a natural condition called the congruence condition. Further, [Formula: see text] is abundant for a normal band [Formula: see text] for which [Formula: see text] satisfies a given technical condition, and we give examples of such [Formula: see text]. On the other hand, we give an example of a normal band [Formula: see text] such that [Formula: see text] is not abundant.

A convergence class is introduced on every object of a given category by using certain generalized nets for expressing the convergence. The obtained concrete category is then investigated whose objects are the pairs consisting of objects of the original category and convergence classes on them and whose morphisms are the morphisms of the original category that preserve the convergence. We define, in a natural way, separation and compactness of objects of the concrete category under investigation and study their behavior.

For a given category KAC 2 , the present paper deals with the existence problem for the category DTC 2 (k), which is equivalent to KAC 2 , where DTC 2 (k) is the category whose objects are simple closed K-curves with even number l of elements in Z n , l ≠ 6, and morphisms are (digitally) K-continuous maps, and KAC 2 is a category whose objects are simple closed A-curves and morphisms are A-maps. To address this issue, the paper starts from the category denoted by KAC 1 whose objects are connected nD Khalimsky topological subspaces with Khalimsky adjacency and morphisms are A-maps in [S. E. Han and A. Sostak, Comput. Appl. Math., 32, 521–536 (2013)]. Based on this approach, in KAC 1 the paper proposes the notions of A-homotopy and A-homotopy equivalence and classifies the spaces in KAC 1 or KAC 2 in terms of the A-homotopy equivalence. Finally, the paper proves that, for Sa given category KAC 2 , there is DTC 2 (k), which is equivalent to KAC 2 .

It is known that an Ehresmann monoid P ( T , Y ) may be constructed from a monoid T acting via order-preserving maps on both sides of a semilattice Y with identity, such that the actions satisfy an appropriate compatibility criterion. Our main result shows that if T is cancellative and equidivisible (as is the case for the free monoid X ⁎ ), the monoid P ( T , Y ) not only is Ehresmann but also satisfies the stronger property of being adequate. Fixing T, Y and the actions, we characterise P ( T , Y ) as being unique in the sense that it is the initial object in a suitable category of Ehresmann monoids. We also prove that the operator P defines an expansion of Ehresmann monoids.

Given a model category C enriched over groupoids, we study and characterize the class of strongly fibered objects F ( K ) in terms of homotopy limits, with respect to a suitable subcategory K of C . We also show that the strong shape category for the pair ( C , K ) turns out to be isomorphic to the usual shape category for the pair ( C , F ( K ) ) . This applies, in particular, to topological shape and strong shape.

We show that every exact fully faithful functor from the category of perfect complexes on the spectrum of dual numbers to the bounded derived category of a noetherian separated scheme is of Fourier-Mukai type. The kernel turns out to be an object of the bounded derived category of coherent complexes on the product of the two schemes. We also study the space of stability conditions on the derived category of the spectrum of dual numbers., 23 pages, Final version to appear in J. Algebra

We study the properties of the relative derived category $D_{\mathscr{C}}^{b}$($\mathscr{A}$) of an abelian category $\mathscr{A}$ relative to a full and additive subcategory $\mathscr{C}$. In particular, when $\mathscr{A}=A{\text -}\mod$ for a finite-dimensional algebra $A$ over a field and $\mathscr{C}$ is a contravariantly finite subcategory of $A$-$\mod$ which is admissible and closed under direct summands, the $\mathscr{C}$-singularity category $D_{\mathscr{C}{\text sg}}$($\mathscr{A}$)=$D_{\mathscr{C}}^{b}$($\mathscr{A}$)/$K^{b}(\mathscr{C})$ is studied. We give a sufficient condition when this category is triangulated equivalent to the stable category of the Gorenstein category $\mathscr{G}(\mathscr{C})$ of $\mathscr{C}$., 17 pages, to appear in Journal of Pure and Applied Algebra

The (usual) Caldero–Chapoton map is a map from the set of objects of a category to a Laurent polynomial ring over the integers. In the case of a cluster category, it maps reachable indecomposable objects to the corresponding cluster variables in a cluster algebra. This formalizes the idea that the cluster category is a categorification of the cluster algebra. The definition of the Caldero–Chapoton map requires the category to be 2-Calabi-Yau, and the map depends on a cluster-tilting object in the category. We study a modified version of the Caldero–Chapoton map which requires only that the category have a Serre functor and depends only on a rigid object in the category. It is well known that the usual Caldero–Chapoton map gives rise to so-called friezes, for instance, Conway–Coxeter friezes. We show that the modified Caldero–Chapoton map gives rise to what we call generalized friezes and that, for cluster categories of Dynkin type A, it recovers the generalized friezes introduced by combinatorial means in recent work by the authors and Bessenrodt.

We developed a top-down and bottom-up segmentation ofobjects using shape contours through a two-stage procedure. First, the object was identified using an edge-based contour feature and then the object contour was obtained using a constraint optimization procedure based on the results from the earlier identified contours. The initial object detection provides object category specific information for the contour completion to be effected. We argue that top-down bottom-up interaction architecture has plausible neurological correlates. This method has an advantage in that it does not require learning boundaries with large datasets.

Unsupervised object modeling is important in robotics, especially for handling a large set of objects. We present a method for unsupervised 3D object discovery, reconstruction, and localization that exploits multiple instances of an identical object contained in a single RGB-D image. The proposed method does not rely on segmentation, scene knowledge, or user input, and thus is easily scalable. Our method aims to find recurrent patterns in a single RGB-D image by utilizing appearance and geometry of the salient regions. We extract keypoints and match them in pairs based on their descriptors. We then generate triplets of the keypoints matching with each other using several geometric criteria to minimize false matches. The relative poses of the matched triplets are computed and clustered to discover sets of triplet pairs with similar relative poses. Triplets belonging to the same set are likely to belong to the same object and are used to construct an initial object model. Detection of remaining instances with the initial object model using RANSAC allows to further expand and refine the model. The automatically generated object models are both compact and descriptive. We show quantitative and qualitative results on RGB-D images with various objects including some from the Amazon Picking Challenge. We also demonstrate the use of our method in an object picking scenario with a robotic arm. ispartof: pages:431-439 ispartof: Proceedings International Conference on 3D Vision pages:431-439 ispartof: International Conference on 3D Vision location:Qingdao, China date:10 Oct - 12 Oct 2017 status: published

We find a partial solution to the longstanding problem of Kostant concerning description of the so-called locally finite endomorphisms of highest weight irreducible modules. The solution is obtained by means of its reduction to a far-reaching extension of the quantization problem. While the classical quantization problem consists in finding *product deformations of the commutative algebras of functions, we consider the case when the initial object is already a noncommutative algebra, the algebra of functions within q-calculus.

In this paper, we present a method of pattern recognition based on obtaining the photoanisotropic copies of object images. Such copies are induced on the dynamic polarization-sensitive material when the amplitude image of the object formed by a spatial light modulator is transilluminated by linearly polarized light with a wavelength actinic for the used material. In this case, the distribution of the intensities over the amplitude image is converted into the distribution of photoanisotropy over the sample of a polarization-sensitive material. In the recognition process, this copy is illuminated by parallel circularly polarized nonactinic light. The distribution of elliptical polarization occurs directly behind the photoanisotropic copy, and it is reduced to a summary ellipse in the Fraunhofer diffraction region. It has been shown that the parameters of this ellipse are related to the characteristics of the object and uniquely identify the initial object. The polarization-holographic diffraction element that we developed enables determining the polarization state of a summary ellipse to obtain all the Stokes parameters in real time. The obtained results were compared with the Stokes parameters of the recognizable object in the database. The method invariance with regard to the position, scale, and rotation of the pattern were investigated. In addition, the resolution and sensitivity of this method were determined. The polarization-sensitive materials used to obtain copies are reversible, with practically an unlimited number of recording-deleting cycles. To obtain a photoanisotropic copy of another object on the same material, the previous copy should be deleted with a pulse of circularly polarized actinic light, and then the next copy can be recorded. A laboratory model of the recognition device and the appropriate software were created, and a theoretical model was developed. Databases were obtained for the images of various objects.

The popular multiresolution segmentation (MRS) algorithm is time and memory consuming when dealing with large images because it uses the pixel-grid for the initial object representation. In this study, we have tested a new workflow for image segmentation of remote sensing data, starting the MRS (using the ESP2 tool) from the superpixel level (using SLIC superpixels) and aiming at dramatically reducing the amount of time and computational resources needed to automatically partition relatively large datasets of very high resolution (VHR) remote sensing images. Tests were done on Quickbird and WorldView-2 data and the results show that the proposed workflow outperforms the traditional approach (MRS starting from pixels). The computational time was reduced in all cases, the biggest improvement being from 5h 35min to 13 min, for a WorldView-2 scene with 8 bands and an extent of 12.2 million pixels. This also comes with a slight improvement of the geometric accuracy of the extracted objects. This approach has the potential to enhance the automation of big remote sensing data analysis and processing, especially when time is an important constraint.

A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for distinct objects c,c'. If we keep in place the latter axiom but allow for more than one morphism between objects, we have a sort of generalized poset in which there are multiplicities attached to covering relations, and possibly nontrivial automorphism groups. We call such a category an "updown category". In this paper we give a precise definition of such categories and develop a theory for them. We also give a detailed account of ten examples, including updown categories of integer partitions, integer compositions, planar rooted trees, and rooted trees., arXiv admin note: substantial text overlap with arXiv:math/0402450

There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely eliminated. Category theory seems to be the correct mathematical theory for clarifying conceptual possibilities in this respect. In this theory, objects acquire their identity either by definition, when in defining category we postulate the existence of objects, or formally by the existence of identity morphisms. We show that it is perfectly possible to get rid of the identity of objects by definition, but the formal identity of objects remains as an essential element of the theory. This can be achieved by defining category exclusively in terms of morphisms and identity morphisms (objectless, or object free, category) and, analogously, by defining category theory entirely in terms of functors and identity functors (categoryless, or category free, category theory). With objects and categories eliminated, we focus on the "philosophy of arrows" and the roles various identities play in it (identities as such, identities up to isomorphism, identities up to natural isomorphism...). This perspective elucides a contrast between "set ontology" and "categorical ontology"., Comment: 13 pages, no figures

This paper proposes a new real-time object tracking algorithm using particle filters with color and texture features in moving CCD camera images. If the user selects an initial object, this region is declared as a target particle and an initial state is modeled. Then, N particles are generated based on random distribution and CS-LBP (Centre Symmetric Local Binary Patterns) for texture model and weighted color distribution is modeled from each particle. For observation likelihoods estimation, Bhattacharyya distance between particles and their feature models are calculated and this observation likelihoods are used for weights of individual particles. After weights estimation, a new particle which has the maximum weight is selected and new particles are re-sampled using the maximum particle. For performance comparison, we tested a few combinations of features and particle filters. The proposed algorithm showed best object tracking performance when we used color and texture model simultaneously for likelihood estimation.

Substantially nonlinear objects function at limitations of arbitrary kind. These limitations are not necessarily «convex» areas. For such objects the construction of area of the fully the fully-controlled state area is a serious problem. In the article it has been suggested to replace this task the task of the fully-controlled state area estimation from within. The secure estimation method of the fully-controlled state area has been developed for this purpose. Other dynamic system has been used as a «tester» (measure) of the fully-controlled state area. Construction and estimation of controllability and accessibility area of this dynamic system well methodically validate and deserved researchers confession. The descriptions concordance requirements of this new object with properties of initial object must be executed and provide property of «immersion» of new object in an initial object. Possibility is thus opened on the the fully-controlled state area of new object to define the the fully-controlled state area of the initial system

We give a characterization of those finitely complete categories with initial object and pushouts of split monomorphisms that admit categorical semidirect products. As an application we examine the case of groupoids with fixed set of objects. Further, we extend this to the internal case. (C) 2010 Elsevier B.V. All rights reserved.

One of the new area of research emerging in the field of statistics is the shape analysis. Shape is defined as all the geometrical information of an object whose location, scale and orientation is not of interest. Diffusion in shape analysis can be studied via either perturbation of the key coordi- nates identifying the initial object or random evolution of the shape itself. Reviewing the first case, we mainly consider the second case and particularly define a new family of diffusion processes. It can be used to model diffusion phenomena represented by shape evolution such as cell motion.

We show that in a finitely accessible additive category every class of objects closed under direct limits and pure epimorphic images is covering. In particular, the classes of flat objects in a locally finitely presented additive category and of absolutely pure objects in a locally coherent category are covering.

Given a category C, a certain category pro*-C on inverse systems in C is constructed, such that the usual pro-category pro-C may be considered as a subcategory of pro*-C. By simulating the (abstract) shape category construction, Sh(C, D), an (abstract) coarse shape category Sh*(C, D) is obtained. An appropriate functor of the shape category to the coarse shape category exists. In the case of topological spaces, C = HTop and D = HPol or D = HANR, he corresponding realizing category for Sh* is pro*-HPol or pro*-HANR respectively. Concerning an operative characterization of a coarse shape isomorphism, a full analogue of the well known Morita lemma is proved, while in the case of inverse sequences, a useful sufficient condition is established. It is proved by examples that for C = Grp (groups) and C = HTop, the classification of inverse systems in pro*-C is strictly coarser than in pro-C. Therefore, the underlying coarse shape theory for topological spaces makes sense.

The notion of a universal building associated with a point in the Hitchin base is introduced. This is a building equipped with a harmonic map from a Riemann surface that is initial among harmonic maps which induce the given cameral cover of the Riemann surface. In the rank one case, the universal building is the leaf space of the quadratic differential defining the point in the Hitchin base. The main conjectures of this paper are: (1) the universal building always exists; (2) the harmonic map to the universal building controls the asymptotics of the Riemann-Hilbert correspondence and the non-abelian Hodge correspondence; (3) the singularities of the universal building give rise to Spectral Networks; and (4) the universal building encodes the data of a 3d Calabi-Yau category whose space of stability conditions has a connected component that contains the Hitchin base. The main theorem establishes the existence of the universal building, conjecture (3), as well as the Riemann-Hilbert part of conjecture (2), in the case of the rank two example introduced in the seminal work of Berk-Nevins-Roberts on higher order Stokes phenomena. It is also shown that the asymptotics of the Riemann-Hilbert correspondence is always controlled by a harmonic map to a certain building, which is constructed as the asymptotic cone of a symmetric space., Comment: Preliminary version. Comments are welcome

International audience; Shape idealization transformations are very common operations when adapting a CAD component to FEA requirements. Here, an idealization approach is proposed that is based on generative shape processes used to decompose an initial B-Rep solid, i.e., extru-sion processes with material addition are used to seg-ment a solid. The corresponding extrusion primitives form the basis of candidate sub domains for idealiza-tion and their connections conveyed through the gen-erative processes they belong to, bring robustness to set up the appropriate connections between idealized sub domains. This is made possible because the con-nections between extrusion primitives have an explicit geometric representation and can be used to bound the connections between idealized sub domains. Taking ad-vantage of an existing construction tree as available in a CAD software does not help much because it may be complicated to use it for idealization processes because this tree structure is not unique. Using generative pro-cesses attached to an object that are no longer reduced to a single construction tree but to a graph containing all non trivial construction trees, is more useful for the engineer to evaluate variants of idealization. From this automated decomposition, each primitive is subjected to a morphological analysis to define whether it can idealized or not. Subsequently, geometric interfaces be-tween primitives form also a graph that can be used to process the connections between the idealized sub do-mains generated from the primitives. These interfaces are taken into account to determine more precisely the idealizable sub domains and their contours when primi-tives are incrementally merged to come back to produce the global morphological analysis of the initial object. A user defined threshold is used to tune the morpho-logical analysis with respect to further user parameters. Finally, the idealizable sub domains and their connec-tions are processed to locate the mid-surfaces and con-nect them using generic criteria that the user can tune locally using complementary criteria.

We investigate the categories of weak maps associated to an algebraic weak factorisation system (AWFS) in the sense of Grandis-Tholen. For any AWFS on a category with an initial object, cofibrant replacement forms a comonad, and the category of (left) weak maps associated to the AWFS is by definition the Kleisli category of this comonad. We exhibit categories of weak maps as a kind of "homotopy category", that freely adjoins a section for every "acyclic fibration" (=right map) of the AWFS; and using this characterisation, we give an alternate description of categories of weak maps in terms of spans with left leg an acyclic fibration. We moreover show that the 2-functor sending each AWFS on a suitable category to its cofibrant replacement comonad has a fully faithful right adjoint: so exhibiting the theory of comonads, and dually of monads, as incorporated into the theory of AWFS. We also describe various applications of the general theory: to the generalised sketches of Kinoshita-Power-Takeyama, to the two-dimensional monad theory of Blackwell-Kelly-Power, and to the theory of dg-categories., 30 pages, final journal version

Given a proper morphism X → S X\to S , we show that a large class of objects in the derived category of X X naturally form an Artin stack locally of finite presentation over S S . This class includes S S -flat coherent sheaves and, more generally, contains the collection of all S S -flat objects which can appear in the heart of a reasonable sheaf of t t -structures on X X . In this sense, this is the Mother of all Moduli Spaces (of sheaves). The proof proceeds by studying the finite presentation properties, deformation theory, and Grothendieck existence theorem for objects in the derived category, and then applying Artin’s representability theorem.

[EN] A fuzzy category is a certain superstructure over an ordinary category in which ”potential” objects and ”potential” morphisms could be such to a certain degree. The aim of this paper is to introduce a fuzzy category FTOP(L,M) extending the category TOP(L,M) of M-valued L- topological spaces which in its turn is an extension of the category TOP(L) of L-fuzzy topological spaces in Kubiak-Sostak’s sense. Basic properties of the fuzzy category FTOP(L,M) and its objects are studied.

We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x_0. The process stops when all the fragments have sizes smaller than x_0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m=m_c. For mm_c they are anomalously large and non-Gaussian. We apply this general result to analyze two different search algorithms in computer science., Comment: 5 pages RevTeX, 3 figures (.eps)

Existing methods of object tracking use template matching, re-detection of object boundaries or motion information. The template matching method requires very long computation time. The re-detection of object boundaries may produce false edges. The method using motion information shows poor tracking performance in moving camera. In this paper, a robust object tracking algorithm is proposed, using projected motion and histogram intersection. The initial object image is constructed by selecting the regions of interest after image segmentation. From the selected object, the approximate displacement of the object is computed by using 1-dimensional intensity projection in horizontal and vortical direction. Based on the estimated displacement, various template masks are constructed for possible orientations and scales of the object. The best template is selected by using the modified histogram intersection method. The robustness of the proposed tracking algorithm has been verified by experimental results.

Consider a push-out diagram of spaces C B, construct the homotopy push-out, and then the homotopy pull-back of the diagram one gets by forgetting the initial object A. We compare the difference between A and this homotopy pull-back. This difference is measured in terms of the homotopy fibers of the original maps. Restricting our attention to the connectivity of these maps, we recover the classical Blakers-Massey Theorem., Comment: 22 pages, we took special care in this revised version in distinguishing fiber sets from single fibers, in indicating what we mean by the loop space on a possibly non-connected and unpointed space, thus smoothing the exposition

The objects around us constantly move and interact, and the perceptual system needs to monitor on-line these interactions and to update the object's status accordingly. Gestalt grouping principles, such as proximity and common fate, play a fundamental role in how we perceive and group these objects. Here, we investigated situations in which the initial object representation as a separate item was updated by a subsequent Gestalt grouping cue (i.e., proximity or common fate). We used a version of the color change detection paradigm, in which the objects started to move separately, then met and stayed stationary, or moved separately, met, and then continued to move together. We monitored the object representations on-line using the contralateral delay activity (CDA; an ERP component indicative of the number of maintained objects), during their movement, and after the objects disappeared and became working memory representations. The results demonstrated that the objects' representations (as indicated by the CDA amplitude) persisted as being separate, even after a Gestalt proximity cue (when the objects “met” and remained stationary on the same position). Only a strong common fate Gestalt cue (when the objects not just met but also moved together) was able to override the objects' initial separate status, creating an integrated representation. These results challenge the view that Gestalt principles cause reflexive grouping. Instead, the object initial representation plays an important role that can override even powerful grouping cues.

This paper suggests a new method to extract the initial movement of moving objects in digital image data obtained in visual sensor networks. First, consecutive images are received as input. Then, the frames are partitioned into nonoverlapping square blocks of pixels, and finally, the block-based motion vectors, which represent the movement information between two adjacent frames, are extracted from the received images using a block-matching algorithm. The extracted motion vectors are subsequently applied to an outlier-elimination algorithm called robust estimation to discriminate between the background motion vectors and those of noise or moving objects. The motion vectors corresponding to the noise or objects are clustered with an unsupervised clustering algorithm to segment the individual moving objects. Experimental results prove that the proposed method can effectively detect the initial movement of objects in various indoor and outdoor environments.

We study slicing functions, which are called direct connections in the smooth category, and parallel displacements along sequences in a topological connection theory. We define holonomy groups for such parallel displacements, and prove a holonomy reduction theorem and related results. In particular, we study a category of principal bundles with parallel displacements over a fixed base space. Assuming the existence of an initial object of a category of principal $G$-bundles, we obtain a classification theorem of topological principal $G$-bundles in terms of topological group homomorphisms. It is shown that a certain object is an initial object if it is the holonomy reduction of itself with respect to the identification topology. The result is applied to the universal bundle over a countable simplicial complex constructed by Milnor.

We investigate a categorical framework for the semantics of asynchronous communication in networks of parallel processes. Abstracting from a category of asynchronous labeled transition systems, we formulate the notion of a categorical model of asynchrony as a uniformly traced monoidal category with diagonals, such that every morphism is total and the focus is equivalent to a category of complete partial orders. We present a simple, non-deterministic, cpo-based model that satisfies these requirements, and we discuss how to refine this model by an observational congruence. We also present a general construction of passing from deterministic to non-deterministic models, and more generally, from non-linear to linear structure on a category.

The geometrical description of deformation quantization based on quantum duality principle makes it possible to introduce deformed Lie-Poisson structure. It serves as a natural analogue of classical Lie bialgebra for the case when the initial object is a quantized group. The explicit realization of the deformed Lie-Poisson structure is a difficult problem. We study the special case of such constructions characterized by quite a simple form of tangent vector fields. In this case 4 Lie compositions define 2 deformations of the first order and 4 Lie bialgebras and give rise to 2 families of deformed Lie-Poisson structures. The explicit example is studied.

We define the notion of componentwise regularity and study some of its basic properties. We prove an analogue, when working with weight orders, of Buchberger's criterion to compute Gr\"obner bases; the proof of our criterion relies on a strengthening of a lifting lemma of Buchsbaum and Eisenbud. This criterion helps us to show a stronger version of Green's crystallization theorem in a quite general setting, according to the componentwise regularity of the initial object. Finally we show a necessary condition, given a submodule $M$ of a free one over the polynomial ring and a weight such that $in(M)$ is componentwise linear, for the existence of an $i$ such that $\beta_i(M)=\beta_i(in(M))$., Comment: Minor changes to the introduction. Added Corollary 5.6. Strengthened conclusion of Theorem 5.7

Anticipatory force planning during grasping is based on visual cues about the object's physical properties and sensorimotor memories of previous actions with grasped objects. Vision can be used to estimate object mass based on the object size to identify and recall sensorimotor memories of previously manipulated objects. It is not known whether subjects can use density cues to identify the object's center of mass (CM) and create compensatory moments in an anticipatory fashion during initial object lifts to prevent tilt. We asked subjects (n = 8) to estimate CM location of visually symmetric objects of uniform densities (plastic or brass, symmetric CM) and non-uniform densities (mixture of plastic and brass, asymmetric CM). We then asked whether subjects can use density cues to scale fingertip forces when lifting the visually symmetric objects of uniform and non-uniform densities. Subjects were able to accurately estimate an object's center of mass based on visual density cues. When the mass distribution was uniform, subjects could scale their fingertip forces in an anticipatory fashion based on the estimation. However, despite their ability to explicitly estimate CM location when object density was non-uniform, subjects were unable to scale their fingertip forces to create a compensatory moment and prevent tilt on initial lifts. Hefting object parts in the hand before the experiment did not affect this ability. This suggests a dichotomy between the ability to accurately identify the object's CM location for objects with non-uniform density cues and the ability to utilize this information to correctly scale their fingertip forces. These results are discussed in the context of possible neural mechanisms underlying sensorimotor integration linking visual cues and anticipatory control of grasping.

This paper presents a grasp execution strategy for grasping an object with one trial when there is uncertainty in the object position. This strategy is based on three grasping components: 1) robust grasp trajectory planning which can cope with reasonable amount of initial object position error, 2) sensor-based grasp adaptation, and 3) compliant characteristics of the under actuated mechanism. This strategy is implemented and tested on the iCub humanoid robot. Two experiments and a demo of the iCub robot playing the Towers of Hanoi game are carried out to verify our system. The results demonstrate that the iCub using this approach can successfully grasp objects under certain position error with its under-actuated anthropomorphic hand. © 2012 IEEE.

Our purpose in this work is to boost the performance of object classifiers learned using the self-training paradigm. We exploit the multi-modal nature of tagged images found in social networks, to optimize the process of region selection when retraining the initial model. More specifically, the proposed approach uses a small number of manually labelled regions to train the initial object detection classifiers. Then, a large number of loosely tagged images, pre-segmented by an automatic segmentation algorithm, is used to enhance the initial training set with additional image regions. However, in contrast to the typical case of self-training where the image regions are selected based solely on how well they fit to the original classification model, our approach aims at optimizing this selection by making combined use of both visual and textual information. The experimental results show that the object detection classifiers generated using the proposed approach outperform the classifiers generated using the typical self-training paradigm.

25 p; International audience; Müger proved in 2003 that the center of a spherical fusion category C of non-zero dimension over an algebraically closed field is a modular fusion category whose dimension is the square of that of C. We generalize this theorem to a pivotal fusion category C over an arbitrary commutative ring K, without any condition on the dimension of the category. (In this generalized setting, modularity is understood as 2-modularity in the sense of Lyubashenko.) Our proof is based on an explicit description of the Hopf algebra structure of the coend of the center of C. Moreover we show that the dimension of C is invertible in K if and only if any object of the center of C is a retract of a 'free' half-braiding. As a consequence, if K is a field, then the center of C is semisimple (as an abelian category) if and only if the dimension of C is non-zero. If in addition K is algebraically closed, then this condition implies that the center is a fusion category, so that we recover Müger's result.

We present an approach for propagation of user interests in ontology- based user models taking into account the properties declared for the concepts in the ontology. Starting from initial user feedback on an object, we calculate user interest in this particular object and its properties and further propagate user interest to other objects in the ontology, similar or related to the initial object. The similarity and relatedness of objects depends on the number of properties they have in common and their corresponding values. The approach we propose can support finer recommendation modalities, considering the user interest in the objects, as well as in singular properties of objects in the recommendation process. We tested our approach for interest propagation with a real adaptive application and obtained an improvement with respect to IS-A-propagation of interest values.