Derived categories and Grothendieck duality

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The Euler characteristic of a category

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Möbius inversion from posets to categories.

Object recognition for autonomous objects: comparison of two approaches

Report for the scientific sojourn at the Swiss Federal Institute of Technology Zurich, Switzerland, between September and December 2007. In order to make robots useful assistants for our everyday life, the ability to learn and recognize objects is of essential importance. However, object recognition in real scenes is one of the most challenging problems in computer vision, as it is necessary to deal with difficulties. Furthermore, in mobile robotics a new challenge is added to the list: computational complexity. In a dynamic world, information about the objects in the scene can become obsolete before it is ready to be used if the detection algorithm is not fast enough. Two recent object recognition techniques have achieved notable results: the constellation approach proposed by Lowe and the bag of words approach proposed by Nistér and Stewénius. The Lowe constellation approach is the one currently being used in the robot localization project of the COGNIRON project. This report is divided in two main sections. The first section is devoted to briefly review the currently used object recognition system, the Lowe approach, and bring to light the drawbacks found for object recognition in the context of indoor mobile robot navigation. Additionally the proposed improvements for the algorithm are described. In the second section the alternative bag of words method is reviewed, as well as several experiments conducted to evaluate its performance with our own object databases. Furthermore, some modifications to the original algorithm to make it suitable for object detection in unsegmented images are proposed.

Cluster algebras, quiver representations and triangulated categories

This is an introduction to some aspects of Fomin-Zelevinsky’s cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer schools held in 2006 (Bavaria)and 2008 (Jerusalem). In addition to by now classical material, we present the outline of a proof of the periodicity conjecture for pairs of Dynkin diagrams (details will appear elsewhere) and recent results on the interpretation of mutations as derived equivalences.

On the homotopy theory of spectral categories

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A Thomason model structure on the category of small n-fold categories

We construct a cofibrantly generated Thomason model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, the unit and counit of the adjunction between simplicial sets and n-fold categories are natural weak equivalences.

Finiteness obstructions and Euler characteristics of categories

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Fear assessment in pigs exposed to a novel object test

The experiment aimed to study approach and locomotive behaviour as indicators of fear in a novel object test carried out in pigs. Thirty post-weaning (30 kg) and 30 finishing (90 kg) pigs were exposed to visual, auditory and olfactory novel stimuli during 2 different experiments. The facilities consisted of a test pen in which a trough was located. The trough contained chopped apples. Once the animals were trained to enter the test pen individually they were subjected to 3 different fear stimuli. These stimuli were applied in the test pen and next to the trough. The variables studied were feeding behaviour, approach behaviour (the distance and position of the animal with respect to the trough) and locomotive behaviour (general activity, reluctance to move, turning back and retreat attempts). Two groups were studied: saline and midazolam treated group. Twenty minutes before the start of the sessions, 15 post-weaning and finishing pigs received an intramuscular injection of 0.20 and 0.15 mg/kg, respectively, midazolam (Dormicum1). The saline pigs (15 animals per group) were injected with saline. The administration of midazolam increased the feeding behaviour and approaching behaviour, and reduced the locomotive behaviour. In front of the visual and olfactory stimuli post-weaning pigs showed a higher general activity than finishing pigs, but the contrary was found when the auditory stimulus was applied. The olfactory stimulus was more related to the turning back behaviour, whereas the visual stimulus was more related to retreat attempts. Although it could be concluded that reluctant to move was the most common response to the different fear stimuli applied in our study regardless of the age of animals, the combination of reluctant to move and turning back would be a good criterion to assess fear in domestic pigs. The use of midazolam as anxiolytic for studies of fear in commercial conditions in pigs is recommended.

The role of multisensory memories in unisensory object discrimination.

Past multisensory experiences can influence current unisensory processing and memory performance. Repeated images are better discriminated if initially presented as auditory-visual pairs, rather than only visually. An experience's context thus plays a role in how well repetitions of certain aspects are later recognized. Here, we investigated factors during the initial multisensory experience that are essential for generating improved memory performance. Subjects discriminated repeated versus initial image presentations intermixed within a continuous recognition task. Half of initial presentations were multisensory, and all repetitions were only visual. Experiment 1 examined whether purely episodic multisensory information suffices for enhancing later discrimination performance by pairing visual objects with either tones or vibrations. We could therefore also assess whether effects can be elicited with different sensory pairings. Experiment 2 examined semantic context by manipulating the congruence between auditory and visual object stimuli within blocks of trials. Relative to images only encountered visually, accuracy in discriminating image repetitions was significantly impaired by auditory-visual, yet unaffected by somatosensory-visual multisensory memory traces. By contrast, this accuracy was selectively enhanced for visual stimuli with semantically congruent multisensory pasts and unchanged for those with semantically incongruent multisensory pasts. The collective results reveal opposing effects of purely episodic versus semantic information from auditory-visual multisensory events. Nonetheless, both types of multisensory memory traces are accessible for processing incoming stimuli and indeed result in distinct visual object processing, leading to either impaired or enhanced performance relative to unisensory memory traces. We discuss these results as supporting a model of object-based multisensory interactions.

Interoperability issues between learning object repositories and metadata harvesters

In this paper we describe an open learning object repository on Statistics based on DSpace which contains true learning objects, that is, exercises, equations, data sets, etc. This repository is part of a large project intended to promote the use of learning object repositories as part of the learning process in virtual learning environments. This involves the creation of a new user interface that provides users with additional services such as resource rating, commenting and so. Both aspects make traditional metadata schemes such as Dublin Core to be inadequate, as there are resources with no title or author, for instance, as those fields are not used by learners to browse and search for learning resources in the repository. Therefore, exporting OAI-PMH compliant records using OAI-DC is not possible, thus limiting the visibility of the learning objects in the repository outside the institution. We propose an architecture based on ontologies and the use of extended metadata records for both storing and refactoring such descriptions.

Dukes B colorectal cancer: distinct genetic categories and clinical outcome based on proximal or distal tumor location.

PURPOSE: The aim of this study was to determine whether tumor location proximal or distal to the splenic flexure is associated with distinct molecular patterns and can predict clinical outcome in a homogeneous group of patients with Dukes B (T3-T4, N0, M0) colorectal cancer. It has been hypothesized that proximal and distal colorectal cancer may arise through different pathogenetic mechanisms. Although p53 and Ki-ras gene mutations occur frequently in distal tumors, another form of genomic instability associated with defective DNA mismatch repair has been predominantly identified in the proximal colon. To date, however, the clinical usefulness of these molecular characteristics remains unproven. METHODS: A total of 126 patients with a lymph node-negative sporadic colon or rectum adenocarcinoma were prospectively assessed with the endpoint of death by cancer. No patient received either radiotherapy or chemotherapy. p53 protein was studied by immunohistochemistry using DO-7 monoclonal antibody, and p53 and Ki-ras gene mutations were detected by single strand conformation polymorphism assay. RESULTS: During a mean follow-up of 67 months, the overall five-year survival was 70 percent. Nuclear p53 staining was found in 57 tumors (47 percent), and was more frequent in distal than in proximal tumors (55 vs. 21 percent; chi-squared test, P < 0.001). For the whole group, p53 protein expression correlated with poor survival in univariate and multivariate analysis (log-rank test, P = 0.01; hazard ratio = 2.16; 95 percent confidence interval = 1.12-4.11, P = 0.02). Distal colon tumors and rectal tumors exhibited similar molecular patterns and showed no difference in clinical outcome. In comparison with distal colorectal cancer, proximal tumors were found to be statistically significantly different on the following factors: mucinous content (P = 0.008), degree of histologic differentiation (P = 0.012), p53 protein expression, and gene mutation (P = 0.001 and 0.01 respectively). Finally, patients with proximal tumors had a marginally better survival than those with distal colon or rectal cancers (log-rank test, P = 0.045). CONCLUSION: In this series of Dukes B colorectal cancers, p53 protein expression was an independent factor for survival, which also correlated with tumor location. Eighty-six percent of p53-positive tumors were located in the distal colon and rectum. Distal colon and rectum tumors had similar molecular and clinical characteristics. In contrast, proximal neoplasms seem to represent a distinct entity, with specific histopathologic characteristics, molecular patterns, and clinical outcome. Location of the neoplasm in reference to the splenic flexure should be considered before group stratification in future trials of adjuvant chemotherapy in patients with Dukes B tumors.

La reconnaissance des objets sonores chez l'humain

Abstract : This thesis investigated the spatio-temporal brain mechanisms of three processes involved in recognizing environmental sounds produced by living (animal vocalisations) and man-made (manufactured) objects: their discrimination, their plasticity, and the involvement of action representations. Results showed rapid brain discrimination between these categories beginning at ~70ms. Then, beginning at ~150ms, effects of plasticity are observed, without any influence of the categories of sounds. Both of these processes of discrimination and repetition priming involved brain structures located in temporal and frontal lobes. Activation of brain areas BA21 and BA22 suggest an access to semantic representations and/or linked to object manipulation. To investigate the involvement of action representations in sound recognition, analyses were restricted to sounds produced by man-made objects. Results suggest an access to representations linked to action functionally related to sound rather than to representations linked to action that produced sound. These effects occurred at ~300ms post-stimulus onset and involved differential activity brain regions attributed to the mirror neuron system. These data are discussed in regard to motor preparation of actions functionally linked to sounds. Collectively these data showed a sequential progression of cerebral activity underlying the recognizing of environmental sounds. The processes occurred firstly in a shared network of brain areas before propagating elsewhere and/or leading to differential activity in these structures. Cerebral responses observed in this work allowed establishing a dynamic model of discrimination of sounds produced by living and man-made objects.

Monads in double categories

We extend the basic concepts of Street's formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a double category C and dene what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads.

Euler characteristics of categories and homotopy colimits

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