Cubic spline population density functions and subcentre delimitation. The case of Barcelona

The presence of subcentres cannot be captured by an exponential function. Cubic spline functions seem more appropriate to depict the polycentricity pattern of modern urban systems. Using data from Barcelona Metropolitan Region, two possible population subcentre delimitation procedures are discussed. One, taking an estimated derivative equal to zero, the other, a density gradient equal to zero. It is argued that, in using a cubic spline function, a delimitation strategy based on derivatives is more appropriate than one based on gradients because the estimated density can be negative in sections with very low densities and few observations, leading to sudden changes in estimated gradients. It is also argued that using as a criteria for subcentre delimitation a second derivative with value zero allow us to capture a more restricted subcentre area than using as a criteria a first derivative zero. This methodology can also be used for intermediate ring delimitation.

The density of injective endomorphisms of a free group

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Cortical origin of functional recovery in the somatosensory cortex of the adult mouse after thalamic lesion

Résumé L'accident vasculaire cérébral sensoriel pur est un des syndromes lacunaires, dû à l'occlusion de petits vaisseaux cérébraux, souvent dans le cadre d'une lésion intéressant le noyau ventro-caudal du thalamus. Il produit un hémisyndrome sensitif pur, et parfois un syndrome douloureux se développe à distance de l'événement aigu. Afin d'étudier la récupération fonctionnelle dans le cortex somatosensoriel (SI) après une telle lésion dans le thalamus, un modèle de lésion excitotoxique a été développé dans le système somatosensoriel de la souris adulte, caractérisé par la présence de formations cytoarchitectoniques dans SI appelées "tonneaux". Chacun de ces tonneaux correspond à la représentation corticale d'une vibrisse du museau. L'activité métabolique a été mesurée dans SI à différents intervalles après la lésion, à l'aide de déoxyglucose marqué radioactivement. Dans les deux premiers jours suivant celle-ci, l'activité métabolique diminue de manière importante dans toutes les couches corticales, avec une atteinte plus marquée dans la couche IV, principale projection des axones thalamo-corticaux. Une récupération de l'activité métabolique se produit ensuite, d'autant plus marquée que le délai après la lésion est grand. Cette récupération s'observe dans toutes les couches coticales, les couches I et Vb récupérant plus rapidement que les couches II, III, IV, Va et VI. Cinq semaines après la lésion, l'absence des vibrisses correspondant à la partie déafférentée de SI diminue l'activité métabolique corticale de 32% et démontre l'activation par la périphérie de cette partie de l'écorce, malgré la perte des axones thalamo-corticaux provenant du noyau ventro-caudal. Des expériences de traçage rétrograde ont montré une augmentation des projections intracorticales sur la partie déafférentée de l'écorce, en particulier de longue distance, ainsi que des projections interhémisphériques, mais n'ont pas permis de mettre en évidence de nouvelle projection thalamique, indiquant une origine corticale à la récupération fonctionnelle observée. Abstract To study the degree and time course of the functional recovery in the somatosensory cortex (SI) after an excitotoxic lesion in the adult mouse thalamus, metabolic activity was determined in SI at various times points post lesion. Immediately after the lesion, metabolic activity in the thalamically deafferented part of SI was at its lowest value but increased progressively at subsequent time points. This was seen in all cortical layers, however, layers I and Vb recover more rapidly than layers II, III, IV, Va and VI. Removal of the mystacial whiskers corresponding to the deafferented area, 5 weeks after cortical recovery, produced a subsequent 32% drop in metabolic activity, demonstrating peripheral sensory activation of this part of the cortex. Tracing experiments revealed that the deafferented cortex did not receive a novel thalamic input, but cortico-cortical and contralateral barrel cortex projections to this area were reinforced. We conclude that the cortical functional recovery after a thalamic lesion is, at least partially, due to modified cortico-cortical and callosal projections to the deafferented cortical area.

Alveolar echinococcosis of the liver: Diffusion-weighted MRI findings and potential role in lesion characterisation

PURPOSE: To report the diffusion-weighted MRI findings in alveolar echinococcosis (AE) of the liver and evaluate the potential role of apparent diffusion coefficients (ADCs) in the characterisation of lesions. MATERIALS AND METHODS: We retrospectively included 22 patients with 63 AE liver lesions (≥1cm), examined with 3-T liver MRI, including a free-breathing diffusion-weighted single-shot echo-planar imaging sequence (b-values=50, 300 and 600s/mm(2)). Two radiologists jointly assessed the following lesion features: size, location, presence of cystic and/or solid components (according to Kodama's classification system), relative contrast enhancement, and calcifications (on CT). The ADCtotal, ADCmin and ADCmax were measured in each lesion and the surrounding liver parenchyma. RESULTS: Three type 1, 19 type 2, 17 type 3, three type 4 and 21 type 5 lesions were identified. The mean (±SD) ADCtotal, ADCmin and ADCmax for all lesions were 1.73±0.50, 0.76±0.38 and 2.63±0.76×10(-3)mm(2)/s, respectively. The mean ADCtotal for type 1, type 2, type 3, type 4 and type 5 lesions were 1.97±1.01, 1.76±0.53, 1.73±0.41, 1.15±0.42 and 1.76±0.44×10(-3)mm(2)/s, respectively. No significant differences were found between the five lesion types, except for type 4 (p=0.0363). There was a significant correlation between the presence of a solid component and low ADCmin (r=0.39, p=0.0016), whereas an inverse correlation was found between the relative contrast enhancement and ADCtotal (r=-0.34, p=0.0072). CONCLUSION: The ADCs of AE lesions are relatively low compared to other cystic liver lesions, which may help in the differential diagnosis. Although ADCs are of little use to distinguish between the five lesion types, their low value reflects the underlying solid component.

Skeletal Muscle Mitochondrial and Lipid Droplet Volume Density: Validity of Electron Microscopy Point-counting Measurements

Mitochondrial (M) and lipid droplet (L) volume density (vd) are often used in exercise research. Vd is the volume of muscle occupied by M and L. The means of calculating these percents are accomplished by applying a grid to a 2D image taken with transmission electron microscopy; however, it is not known which grid best predicts these values. PURPOSE: To determine the grid with the least variability of Mvd and Lvd in human skeletal muscle. METHODS: Muscle biopsies were taken from vastus lateralis of 10 healthy adults, trained (N=6) and untrained (N=4). Samples of 5-10mg were fixed in 2.5% glutaraldehyde and embedded in EPON. Longitudinal sections of 60 nm were cut and 20 images were taken at random at 33,000x magnification. Vd was calculated as the number of times M or L touched two intersecting grid lines (called a point) divided by the total number of points using 3 different sizes of grids with squares of 1000x1000nm sides (corresponding to 1µm2), 500x500nm (0.25µm2) and 250x250nm (0.0625µm2). Statistics included coefficient of variation (CV), 1 way-BS ANOVA and spearman correlations. RESULTS: Mean age was 67 ± 4 yo, mean VO2peak 2.29 ± 0.70 L/min and mean BMI 25.1 ± 3.7 kg/m2. Mean Mvd was 6.39% ± 0.71 for the 1000nm squares, 6.01% ± 0.70 for the 500nm and 6.37% ± 0.80 for the 250nm. Lvd was 1.28% ± 0.03 for the 1000nm, 1.41% ± 0.02 for the 500nm and 1.38% ± 0.02 for the 250nm. The mean CV of the three grids was 6.65% ±1.15 for Mvd with no significant differences between grids (P>0.05). Mean CV for Lvd was 13.83% ± 3.51, with a significant difference between the 1000nm squares and the two other grids (P<0.05). The 500nm squares grid showed the least variability between subjects. Mvd showed a positive correlation with VO2peak (r = 0.89, p < 0.05) but not with weight, height, or age. No correlations were found with Lvd. CONCLUSION: Different size grids have different variability in assessing skeletal muscle Mvd and Lvd. The grid size of 500x500nm (240 points) was more reliable than 1000x1000nm (56 points). 250x250nm (1023 points) did not show better reliability compared with the 500x500nm, but was more time consuming. Thus, choosing a grid with square size of 500x500nm seems the best option. This is particularly relevant as most grids used in the literature are either 100 points or 400 points without clear information on their square size.

Conjugate eye deviation due to traumatic striatal-subthalamic lesion.

We report the case of a 22-year-old man after severe cranial trauma, who was noted to have conjugate eye deviation (CED) to the left. A magnetic resonance imaging (MRI) scan demonstrated a lesion in the left (ipsilateral) striatal-subthalamic region. The involvement of supranuclear fibres from the left frontal eye field (FEF) traveling to the right parapontine reticular formation (PPRF) could explain this clinical finding. Alternatively, involvement of deep brain nuclei, such as the striatum and the subthalamic nucleus, could be responsible for this phenomenon. This neurological presentation is unusual after severe cranial trauma.

On the density distribution across space: a probabilistic approach

This paper aims at providing a Bayesian parametric framework to tackle the accessibility problem across space in urban theory. Adopting continuous variables in a probabilistic setting we are able to associate with the distribution density to the Kendall's tau index and replicate the general issues related to the role of proximity in a more general context. In addition, by referring to the Beta and Gamma distribution, we are able to introduce a differentiation feature in each spatial unit without incurring in any a-priori definition of territorial units. We are also providing an empirical application of our theoretical setting to study the density distribution of the population across Massachusetts.

Factors conditioning the habitat and the density of Biomphalaria tenagophila (Orbigny, 1835) in an isolated schistosomiasis focus in Rio de Janeiro city

The present work was carried out in a watercress garden in Alto da Boa Vista, in the city of Rio de Janeiro, Brazil. The investigation was carried out in two phases. The first one (1985-86) involved the sampling of Biomphalaria tenegophila in two areas to determine its relative populational densities. The results showed that the populations presented similar densities and dynamics. The second phase (1988-89) involved the study of the influence of some environmental factors on the establishment of B. tenagophila in watercress garden. Two factors were identified as responsible for the establishment of B. tenagophila in the garden: (1) the quality of the water entering the irrigation system, to which domestic sewage is added, and (2) alterations in the nature of the substrate, due to inadequate fertilization techniques, which employ organic matter from adjacent pigsties. Aquatic plants and hydrological parameters of the irrigation system were subsidiary factors to the establishment of B. tenagophila in the garden.

Sobolev mappings: Lipschitz density is not an isometric invariant of the target

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Effects of unilateral motor cortex lesion on ipsilesional hand's reach and grasp performance in monkeys: relationship with recovery in the contralesional hand.

Manual dexterity, a prerogative of primates, is under the control of the corticospinal (CS) tract. Because 90-95% of CS axons decussate, it is assumed that this control is exerted essentially on the contralateral hand. Consistently, unilateral lesion of the hand representation in the motor cortex is followed by a complete loss of dexterity of the contralesional hand. During the months following lesion, spontaneous recovery of manual dexterity takes place to a highly variable extent across subjects, although largely incomplete. In the present study, we tested the hypothesis that after a significant postlesion period, manual performance in the ipsilesional hand is correlated with the extent of functional recovery in the contralesional hand. To this aim, ten adult macaque monkeys were subjected to permanent unilateral motor cortex lesion. Monkeys' manual performance was assessed for each hand during several months postlesion, using our standard behavioral test (modified Brinkman board task) that provides a quantitative measure of reach and grasp ability. The ipsilesional hand's performance was found to be significantly enhanced over the long term (100-300 days postlesion) in six of ten monkeys, with the six exhibiting the best, though incomplete, recovery of the contralesional hand. There was a statistically significant correlation (r = 0.932; P < 0.001) between performance in the ipsilesional hand after significant postlesion period and the extent of recovery of the contralesional hand. This observation is interpreted in terms of different possible mechanisms of recovery, dependent on the recruitment of motor areas in the lesioned and/or intact hemispheres.