On the trace of an endofunctor of a small category

The trace of a square matrix can be defined by a universal property which, appropriately generalized yields the concept of "trace of an endofunctor of a small category". We review the basic definitions of this general concept and give a new construction, the "pretrace category", which allows us to obtain the trace of an endofunctor of a small category as the set of connected components of its pretrace. We show that this pretrace construction determines a finite-product preserving endofunctor of the category of small categories, and we deduce from this that the trace inherits any finite-product algebraic structure that the original category may have. We apply our results to several examples from Representation Theory obtaining a new (indirect) proof of the fact that two finite dimensional linear representations of a finite group are isomorphic if and only if they have the same character.

Impact of a Cleft Lip and/or Palate on Maternal Stress and Attachment Representations.

Objective : The announcement, prenatally or at birth, of a cleft lip and/or palate represents a challenge for the parents. The purpose of this study is to identify parental working internal models of the child (parental representations of the child and relationship in the context of attachment theory) and posttraumatic stress disorder symptoms in mothers of infants born with a cleft. Method : The study compares mothers with a child born with a cleft (n  =  22) and mothers with a healthy infant (n  =  36). Results : The study shows that mothers of infants with a cleft more often experience insecure parental working internal models of the child and more posttraumatic stress symptoms than mothers of the control group. It is interesting that the severity or complexity of the cleft is not related to parental representations and posttraumatic stress disorder symptoms. The maternal emotional involvement, as expressed in maternal attachment representations, is higher in mothers of children with a cleft who had especially high posttraumatic stress disorder symptoms, as compared with mothers of children with a cleft having fewer posttraumatic stress disorder symptoms. Discussion : Mothers of children with a cleft may benefit from supportive therapy regarding parent-child attachment, even when they express low posttraumatic stress disorder symptoms.

Donor's and organ representations in liver, kidney, heart and lung transplantation : a qualitative longitudinal study

Purpose: Organ transplantation is a biological and psychological challenge and graft acceptance is an important achievement for patients. Patients' concerns toward the deceased donor and the organ may contribute to this process. Method: Forty-seven patients involved in heart (N=9), liver (N=8), lung (N=14) and kidney (N=16) transplantation participated in IRB-approved longitudinal semi-structured interviews: (T1) registered on the waiting-list, (T2) six months and (T3) twelve months after transplantation. Qualitative pattern analysis (QUAPA) was carried out on the verbatim transcripts and concerns about the donor and the organ were then analysed. Results: - Donor's representation: At T1, patients were reluctant to talk about the donor: 27% expressed culpability and 19% accepted the clause of anonymity. At T2, intense emotions were associated with the reminiscing about the donor and 45% highlighted the generosity of his/her act. In addition, heart, lung and kidney recipients were concerned about the donor's identity: 42% challenged the clause of anonymity. Liver recipients complained about anonymity, but could nevertheless cope with it. At T3, 47% of heart, lung and kidney recipients thought daily of the donor and 33% were still looking for information about him/her. Liver recipients rarely have thoughts about the donor. - Organ representation: At T1, organ descriptions were biomedical (49% of the interviewees) and more rarely, mainly heart candidates, referred to the symbolic meaning of the organ. After transplantation (T2-T3), function was underlined. Acceptance and organ integration were associated with post-operative outcomes (23%) and psychological well-being (45%). Some patients (32%) inferred the donor's personality from the organ quality and felt privileged having received an organ in such a good state. Conclusion: Donor's representations should be explored during the transplantation process as they play an important role in the psychological acceptance of the graft.

Improved temporal resolution for functional studies with reduced number of segments with three-dimensional echo planar imaging.

PURPOSE: To introduce a new k-space traversal strategy for segmented three-dimensional echo planar imaging (3D EPI) that encodes two partitions per radiofrequency excitation, effectively reducing the number excitations used to acquire a 3D EPI dataset by half. METHODS: The strategy was evaluated in the context of functional MRI applications for: image quality compared with segmented 3D EPI, temporal signal-to-noise ratio (tSNR) (the ability to detect resting state networks compared with multislice two-dimensional (2D) EPI and segmented 3D EPI, and temporal resolution (the ability to separate cardiac- and respiration-related fluctuations from the desired blood oxygen level-dependent signal of interest). RESULTS: Whole brain images with a nominal voxel size of 2 mm isotropic could be acquired with a temporal resolution under half a second using traditional parallel imaging acceleration up to 4× in the partition-encode direction and using novel data acquisition speed-up of 2× with a 32-channel coil. With 8× data acquisition speed-up in the partition-encode direction, 3D reduced excitations (RE)-EPI produced acceptable image quality without introduction of noticeable additional artifacts. Due to increased tSNR and better characterization of physiological fluctuations, the new strategy allowed detection of more resting state networks compared with multislice 2D-EPI and segmented 3D EPI. CONCLUSION: 3D RE-EPI resulted in significant increases in temporal resolution for whole brain acquisitions and in improved physiological noise characterization compared with 2D-EPI and segmented 3D EPI. Magn Reson Med 72:786-792, 2014. © 2013 Wiley Periodicals, Inc.

Values, Multiculturalism and Representations

The theory of values is underdeveloped within economics with very few theoretical models explaining how values are created and propagated through a population. Those models that do exist are limited in how well they explain the role of values and how they behave. This paper argues that the theory of values needs to be fundamentally rethought, incorporating basic ideas from psychology, anthropology and philosophy that have largely been ignored in the literature. The resulting model is applied to answer some fundamental issues surrounding the notion of multiculturalism.

Persistent bundles over a two dimensional compact set

"Vegeu el resum a l'inici del document del fitxer adjunt."

Representations and the Corruption of Goods

The traditional view of the economic agent is of an individual who is self-interested, rational and perceives the world “correctly”. However, there is a lot of experimental and other evidence that undermines this view of agents. It is argued that an attempt to model these agents properly requires the cognitive science idea of a mental representation- a mental state with content. It is shown that this idea gives economists resources to discuss critiques of economics by Sandel (2012) and Grant (2012). In particular, it allows us to think clearly about the notion of goods being “corrupted” by a change in context from a non-market to a market situation.

Amino acid coevolution reveals three-dimensional structure and functional domains of insect odorant receptors.

Insect odorant receptors (ORs) comprise an enormous protein family that translates environmental chemical signals into neuronal electrical activity. These heptahelical receptors are proposed to function as ligand-gated ion channels and/or to act metabotropically as G protein-coupled receptors (GPCRs). Resolving their signalling mechanism has been hampered by the lack of tertiary structural information and primary sequence similarity to other proteins. We use amino acid evolutionary covariation across these ORs to define restraints on structural proximity of residue pairs, which permit de novo generation of three-dimensional models. The validity of our analysis is supported by the location of functionally important residues in highly constrained regions of the protein. Importantly, insect OR models exhibit a distinct transmembrane domain packing arrangement to that of canonical GPCRs, establishing the structural unrelatedness of these receptor families. The evolutionary couplings and models predict odour binding and ion conduction domains, and provide a template for rationale structure-activity dissection.

Differentiation of rat striatal embryonic stem cells in vitro: monolayer culture vs. three-dimensional coculture with differentiated brain cells.

Several groups have demonstrated the existence of self-renewing stem cells in embryonic and adult mouse brain. In vitro, these cells proliferate in response to epidermal growth factor, forming clusters of nestin-positive cells that may be dissociated and subcultured repetitively. Here we show that, in stem cell clusters derived from rat embryonic striatum, cell proliferation decreased with increasing number of passages and in response to elevated concentrations of potassium (30 mM KCl). In monolayer culture, the appearance of microtubule-associated protein type-5-immunoreactive (MAP-5(+)) cells (presumptive neurons) in response to basic fibroblast growth factor (bFGF) was reduced at low cell density and with increasing number of passages. In the presence of bFGF, elevated potassium caused a more differentiated neuronal phenotype, characterized by an increased proportion of MAP-5(+) cells, extensive neuritic branching, and higher specific activity of glutamic acid decarboxylase. Dissociated stem cells were able to invade cultured brain cell aggregates containing different proportions of neurons and glial cells, whereas they required the presence of a considerable proportion of glial cells in the host cultures to become neurofilament H-positive. The latter observation supports the view that astrocyte-derived factors influence early differentiation of the neuronal cell lineage.

Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

A three dimensional signed small ball inequality

"Vegeu el resum a l'inici del document del fitxer adjunt."

Three-dimensional slope stability analysis of South Peak, Crowsnest Pass, Alberta, Canada

South Peak is a 7-Mm3 potentially unstable rock mass located adjacent to the 1903 Frank Slide on Turtle Mountain, Alberta. This paper presents three-dimensional numerical rock slope stability models and compares them with a previous conceptual slope instability model based on discontinuity surfaces identified using an airborne LiDAR digital elevation model (DEM). Rock mass conditions at South Peak are described using the Geological Strength Index and point load tests, whilst the mean discontinuity set orientations and characteristics are based on approximately 500 field measurements. A kinematic analysis was first conducted to evaluate probable simple discontinuity-controlled failure modes. The potential for wedge failure was further assessed by considering the orientation of wedge intersections over the airborne LiDAR DEM and through a limit equilibrium combination analysis. Block theory was used to evaluate the finiteness and removability of blocks in the rock mass. Finally, the complex interaction between discontinuity sets and the topography within South Peak was investigated through three-dimensional distinct element models using the code 3DEC. The influence of individual discontinuity sets, scale effects, friction angle and the persistence along the discontinuity surfaces on the slope stability conditions were all investigated using this code.

Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system

We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods.

Three-dimensional cholangio-spiral CT demonstration of a post-traumatic bile leak in a child.

Bilioma is a rare complication of traumatic liver injury, and the precise site of bile leak is often difficult to demonstrate with a non-invasive technique. We report a case of post-traumatic bile leak in a 15-year-old girl in whom spiral CT after intravenous cholangiography allowed excellent preoperative demonstration of the extent of the liver rupture and an exact location of the bile leak. We think that spiral-CT cholangiography could be an accurate, non-invasive technique to investigate the biliary system in cases of paediatric liver trauma.