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The human subthalamic area is a region of high anatomical complexity, tightly packed with tiny fiber bundles. Some of them, including the pallidothalamic, cerebello-thalamic, and mammillothalamic tracts, are relevant targets in functional neurosurgery for various brain diseases. Diffusion-weighted imaging-based tractography has been suggested as a useful tool to map white matter pathways in the human brain in vivo and non-invasively, though the reconstruction of these specific fiber bundles is challenging due to their small dimensions and complex anatomy. To the best of our knowledge, a population-based, in vivo probabilistic atlas of subthalamic white matter tracts is still missing. In the present work, we devised an optimized tractography protocol for reproducible reconstruction of the tracts of subthalamic area in a large data sample from the Human Connectome Project repository. First, we leveraged the super-resolution properties and high anatomical detail provided by short tracks track-density imaging (stTDI) to identify the white matter bundles of the subthalamic area on a group-level template. Tracts identification on the stTDI template was also aided by visualization of histological sections of human specimens. Then, we employed this anatomical information to drive tractography at the subject-level, optimizing tracking parameters to maximize between-subject and within-subject similarities as well as anatomical accuracy. Finally, we gathered subject level tracts reconstructed with optimized tractography into a large-scale, normative population atlas. We suggest that this atlas could be useful in both clinical anatomy and functional neurosurgery settings, to improve our understanding of the complex morphology of this important brain region.

The contribution of structural connectivity to functional connectivity dynamics is still far from being fully elucidated. Herein, we applied track-weighted dynamic functional connectivity (tw-dFC), a model integrating structural, functional, and dynamic connectivity, on high quality diffusion weighted imaging and resting-state fMRI data from two independent repositories. The tw-dFC maps were analyzed using independent component analysis, aiming at identifying spatially independent white matter components which support dynamic changes in functional connectivity. Each component consisted of a spatial map of white matter bundles that show consistent fluctuations in functional connectivity at their endpoints, and a time course representative of such functional activity. These components show high intra-subject, inter-subject, and inter-cohort reproducibility. We provided also converging evidence that functional information about white matter activity derived by this method can capture biologically meaningful features of brain connectivity organization, as well as predict higher-order cognitive performance.

The striatum represents the major hub of the basal ganglia, receiving projections from the entire cerebral cortex and it is assumed to play a key role in a wide array of complex behavioral tasks. Despite being extensively investigated during the last decades, the topographical organization of the striatum is not well understood yet. Ongoing efforts in neuroscience are focused on analyzing striatal anatomy at different spatial scales, to understand how structure relates to function and how derangements of this organization are involved in various neuropsychiatric diseases. While being subdivided at the macroscale level into dorsal and ventral divisions, at a mesoscale level the striatum represents an anatomical continuum sharing the same cellular makeup. At the same time, it is now increasingly ascertained that different striatal compartments show subtle histochemical differences, and their neurons exhibit peculiar patterns of gene expression, supporting functional diversity across the whole basal ganglia circuitry. Such diversity is further supported by afferent connections which are heterogenous both anatomically, as they originate from distributed cortical areas and subcortical structures, and biochemically, as they involve a variety of neurotransmitters. Specifically, the cortico-striatal projection system is topographically organized delineating a functional organization which is maintained throughout the basal ganglia, subserving motor, cognitive and affective behavioral functions. While such functional heterogeneity has been firstly conceptualized as a tripartite organization, with sharply defined limbic, associative and sensorimotor territories within the striatum, it has been proposed that such territories are more likely to fade into one another, delineating a gradient-like organization along medio-lateral and ventro-dorsal axes. However, the molecular and cellular underpinnings of such organization are less understood, and their relations to behavior remains an open question, especially in humans. In this review we aimed at summarizing the available knowledge on striatal organization, especially focusing on how it links structure to function and its alterations in neuropsychiatric diseases. We examined studies conducted on different species, covering a wide array of different methodologies: from tract-tracing and immunohistochemistry to neuroimaging and transcriptomic experiments, aimed at bridging the gap between macroscopic and molecular levels.

The periaqueductal gray is a mesencephalic structure involved in modulation of responses to stressful stimuli. Structural connections between the periaqueductal gray and the cerebellum have been described in animals and in a few diffusion tensor imaging studies. Nevertheless, these periaqueductal gray–cerebellum connectivity patterns have yet to be fully investigated in humans. The objective of this study was to qualitatively and quantitatively characterize such pathways using high-resolution, multi-shell data of 100 healthy subjects from the open-access Human Connectome Project repository combined with constrained spherical deconvolution probabilistic tractography. Our analysis revealed robust connectivity density profiles between the periaqueductal gray and cerebellar nuclei, especially with the fastigial nucleus, followed by the interposed and dentate nuclei. High-connectivity densities have been observed between vermal (Vermis IX, Vermis VIIIa, Vermis VIIIb, Vermis VI, Vermis X) and hemispheric cerebellar regions (Lobule IX). Our in vivo study provides for the first time insights on the organization of periaqueductal gray–cerebellar pathways thus opening new perspectives on cognitive, visceral and motor responses to threatening stimuli in humans.

The subthalamic nucleus (STN) is commonly used as a surgical target for deep brain stimulation in movement disorders such as Parkinson’s Disease. Tractography-derived connectivity-based parcellation (CBP) has been recently proposed as a suitable tool for non-invasive in vivo identification and pre-operative targeting of specific functional territories within the human STN. However, a well-established, accurate and reproducible protocol for STN parcellation is still lacking. The present work aims at testing the effects of different tractography-based approaches for the reconstruction of STN functional territories.We reconstructed functional territories of the STN on the high-quality dataset of 100 unrelated healthy subjects and on the test-retest dataset of the Human Connectome Project (HCP) repository. Connectivity-based parcellation was performed with a hypothesis-driven approach according to cortico-subthalamic connectivity, after dividing cortical areas into three groups: associative, limbic and sensorimotor. Four parcellation pipelines were compared, combining different signal modeling techniques (single-fiber vs multi-fiber) and different parcellation approaches (winner takes all parcellation vs fiber density thresholding). We tested these procedures on STN regions of interest obtained from three different, commonly employed, subcortical atlases. We evaluated the pipelines both in terms of between-subject similarity, assessed on the cohort of 100 unrelated healthy subjects, and of within-subject similarity, using a second cohort of 44 subjects with available test-retest data. We found that each parcellation provides converging results in terms of location of the identified parcels, but with significative variations in size and shape. Higher between-subject similarity was found with multi-fiber signal modeling techniques combined with fiber density thresholding. All the pipelines obtained very high within-subject similarity, with tensor-based approaches outperforming multi-fiber pipelines. We suggest that a fine-tuning of tractography-based parcellation may lead to higher reproducibility and aid the development of an optimized surgical targeting protocol.

The subthalamic nucleus (STN) is commonly used as a surgical target for deep brain stimulation in movement disorders such as Parkinson's Disease. Tractography-derived connectivity-based parcellation (CBP) has been recently proposed as a suitable tool for non-invasive in vivo identification and pre-operative targeting of specific functional territories within the human STN. However, a well-established, accurate and reproducible protocol for STN parcellation is still lacking. The present work aims at testing the effects of different tractography-based approaches for the reconstruction of STN functional territories. We reconstructed functional territories of the STN on the high-quality dataset of 100 unrelated healthy subjects and on the test-retest dataset of the Human Connectome Project (HCP) repository. Connectivity-based parcellation was performed with a hypothesis-driven approach according to cortico-subthalamic connectivity, after dividing cortical areas into three groups: associative, limbic and sensorimotor. Four parcellation pipelines were compared, combining different signal modeling techniques (single-fiber vs multi-fiber) and different parcellation approaches (winner takes all parcellation vs fiber density thresholding). We tested these procedures on STN regions of interest obtained from three different, commonly employed, subcortical atlases. We evaluated the pipelines both in terms of between-subject similarity, assessed on the cohort of 100 unrelated healthy subjects, and of within-subject similarity, using a second cohort of 44 subjects with available test-retest data. We found that each parcellation provides converging results in terms of location of the identified parcels, but with significative variations in size and shape. All pipelines obtained very high within-subject similarity, with tensor-based approaches outperforming multi-fiber pipelines. On the other hand, higher between-subject similarity was found with multi-fiber signal modeling techniques combined with fiber density thresholding. We suggest that a fine-tuning of tractography-based parcellation may lead to higher reproducibility and aid the development of an optimized surgical targeting protocol.

The development of novel techniques for the in vivo, non-invasive visualization and identification of thalamic nuclei has represented a major challenge for human neuroimaging research in the last decades. Thalamic nuclei have important implications in various key aspects of brain physiology and many of them show selective alterations in various neurologic and psychiatric disorders. In addition, both surgical stimulation and ablation of specific thalamic nuclei have been proven to be useful for the treatment of different neuropsychiatric diseases. The present work aimed at describing a novel protocol for histologically-guided delineation of thalamic nuclei based on short-tracks track-density imaging (stTDI), which is an advanced imaging technique that exploits high angular resolution diffusion tractography to obtain super-resolved white matter maps with high anatomical information. We tested this protocol on i) six healthy individual 3T MRI scans from the Human Connectome Project database, and on ii) a group population template reconstructed by averaging 100 unrelated healthy subjects scans from the same repository. We demonstrated that this approach can identify up to 13 distinct thalamic nuclei bilaterally with very high reliability (intraclass correlation coefficient: 0.996, 95% CI: 0.993-0.998; total accumulated overlap: 0.43) and that both subject-based and group-level thalamic parcellation show a fair share of similarity to a recent standard-space histological thalamic atlas. Finally, we showed that stTDI-derived thalamic maps can be successfully employed to study thalamic structural and functional connectivity, and may have potential implications both for basic and translational research, as well as for pre-surgical planning purposes.

The Ventral intermediate nucleus (Vim) of thalamus is the most targeted structure for the treatment of drug-refractory tremors. Since methodological differences across existing studies are remarkable and no gold-standard pipeline is available, in this study, we tested different parcellation pipelines for tractography-derived putative Vim identification.Thalamic parcellation was performed on a high quality, multi-shell dataset and a downsampled, clinical-like dataset using two different diffusion signal modeling techniques and two different voxel classification criteria, thus implementing a total of four parcellation pipelines. The most reliable pipeline in terms of inter-subject variability has been picked and parcels putatively corresponding to motor thalamic nuclei have been selected by calculating similarity with a histology-based mask of Vim. Then, spatial relations with optimal stimulation points for the treatment of essential tremor have been quantified. Finally, effect of data quality and parcellation pipelines on a volumetric index of connectivity clusters has been assessed.We found that the pipeline characterized by higher-order signal modeling and threshold-based voxel classification criteria was the most reliable in terms of inter-subject reliability regardless data quality. The maps putatively corresponding to Vim were those derived by precentral- and dentate nucleus-thalamic connectivity. However, tractography-derived functional targets showed remarkable differences in shape and sizes when compared to a ground truth model based on histochemical staining on seriate sections of human brain. Thalamic voxels connected to contralateral dentate nucleus resulted to be the closest to literature-derived stimulation points for essential tremor but at the same time showing the most remarkable inter-subject variability. Finally, the volume of connectivity parcels resulted to be significantly influenced by data quality and parcellation pipelines. Hence, caution is warranted when performing thalamic connectivity-based segmentation for stereotacting targeting.

The red nucleus (RN) is a large subcortical structure located in the ventral midbrain. Although it originated as a primitive relay between the cerebellum and the spinal cord, during its phylogenesis the RN shows a progressive segregation between a magnocellular part, involved in the rubrospinal system, and a parvocellular part, involved in the olivocerebellar system. Despite exhibiting distinct evolutionary trajectories, these two regions are strictly tied together and play a prominent role in motor and non-motor behavior in different animal species. However, little is known about their function in the human brain. This lack of knowledge may have been conditioned both by the notable differences between human and non-human RN and by inherent difficulties in studying this structure directly in the human brain, leading to a general decrease of interest in the last decades. In the present review, we identify the crucial issues in the current knowledge and summarize the results of several decades of research about the RN, ranging from animal models to human diseases. Connecting the dots between morphology, experimental physiology and neuroimaging, we try to draw a comprehensive overview on RN functional anatomy and bridge the gap between basic and translational research.

Background and objectives: Functional deregulation of dopaminergic midbrain regions is a core feature of schizophrenia pathophysiology. Anatomical research on primates suggests that these regions may be subdivided into distinct, topographically organized functional territories according to their connectivity to the striatum. The aim of the present work was the reconstruction of dopaminergic midbrain subregions in healthy subjects and schizophrenic patients and the evaluation of their structural connectivity profiles. Materials and Methods: A hypothesis-driven connectivity-based parcellation derived from diffusion tractography was applied on 24 healthy subjects and 30 schizophrenic patients to identify distinct territories within the human dopaminergic midbrain in vivo and non-invasively. Results: We identified a tripartite subdivision of dopaminergic midbrain, including limbic, prefrontal and sensorimotor territories. No significant differences in structural features or connectivity were found between subjects and patients. Conclusions: The parcellation scheme proposed herein may help to achieve detailed characterization of structural and functional anomalies of the dopaminergic midbrain in schizophrenic patients.

Background and objectives: The internal (GPi) and external segments (GPe) of the globus pallidus represent key nodes in the basal ganglia system. Connections to and from pallidal segments are topographically organized, delineating limbic, associative and sensorimotor territories. The topography of pallidal afferent and efferent connections with brainstem structures has been poorly investigated. In this study we sought to characterize in-vivo connections between the globus pallidus and the pedunculopontine nucleus (PPN) via diffusion tractography. Materials and Methods: We employed structural and diffusion data of 100 subjects from the Human Connectome Project repository in order to reconstruct the connections between the PPN and the globus pallidus, employing higher order tractography techniques. We assessed streamline count of the reconstructed bundles and investigated spatial relations between pallidal voxels connected to the PPN and pallidal limbic, associative and sensorimotor functional territories. Results: We successfully reconstructed pallidotegmental tracts for the GPi and GPe in all subjects. The number of streamlines connecting the PPN with the GPi was greater than the number of those joining it with the GPe. PPN maps within pallidal segments exhibited a distinctive spatial organization, being localized in the ventromedial portion of the GPi and in the ventral-anterior portion in the GPe. Regarding their spatial relations with tractography-derived maps of pallidal functional territories, the highest value of percentage overlap was noticed between PPN maps and the associative territory. Conclusions: We successfully reconstructed the anatomical course of the pallidotegmental pathways and comprehensively characterized their topographical arrangement within both pallidal segments. PPM maps were localized in the ventromedial aspect of the GPi, while they occupied the anterior pole and the most ventral portion of the GPe. A better understanding of the spatial and topographical arrangement of the pallidotegmental pathways may have pathophysiological and therapeutic implications in movement disorders.

Internal and external segments of globus pallidus (GP) exert different functions in basal ganglia circuitry, despite their main connectional systems share the same topographical organization, delineating limbic, associative, and sensorimotor territories. The identification of internal GP sensorimotor territory has therapeutic implications in functional neurosurgery settings. This study is aimed at assessing the spatial coherence of striatopallidal, subthalamopallidal, and pallidothalamic pathways by using tractography‐derived connectivity‐based parcellation (CBP) on high quality diffusion MRI data of 100 unrelated healthy subjects from the Human Connectome Project. A two‐stage hypothesis‐driven CBP approach has been carried out on the internal and external GP. Dice coefficient between functionally homologous pairs of pallidal maps has been computed. In addition, reproducibility of parcellation according to different pathways of interest has been investigated, as well as spatial relations between connectivity maps and existing optimal stimulation points for dystonic patients. The spatial organization of connectivity clusters revealed anterior limbic, intermediate associative and posterior sensorimotor maps within both internal and external GP. Dice coefficients showed high degree of coherence between functionally similar maps derived from the different bundles of interest. Sensorimotor maps derived from the subthalamopallidal pathway resulted to be the nearest to known optimal pallidal stimulation sites for dystonic patients. Our findings suggest that functionally homologous afferent and efferent connections may share similar spatial territory within the GP and that subcortical pallidal connectional systems may have distinct implications in the treatment of movement disorders., The identification of internal globus pallidus (GP) sensorimotor territory has therapeutic implications in functional neurosurgery settings. This study is aimed at assessing the spatial coherence of striatopallidal, subthalamopallidal and pallidothalamic pathways by using tractography‐derived connectivity‐based parcellation. Our results suggest that the general topographical organization of connectivity parcels is highly consistent across the internal and external GP, regardless the bundle of interest, corroborating the hypothesis that different pathways, running parallel and in series to one other, may share the same spatial organization pattern. Indeed, we found high similarity among functionally homologous connectivity maps derived from the striatopallidal, subthalamopallidal and pallidothalamic tracts. In other words, we show neuroimaging evidences suggesting the presence of partially segregated yet integrated functional territories within the GP, derived from connectivity patterns that maintain a consistent topographical arrangement throughout the entire cortico‐basal ganglia‐thalamo‐cortical circuitry.

Background Diffusion tensor imaging (DTI) is a non-invasive MR technique widely employed to study muscle anatomy. DTI parameters have been used to investigate microstructural changes dependent on demographic factors or transient condition such as exercise. The present study is aimed at investigating the diffusion parameters changes of the human calf muscles after a 3-months strength training protocol. Methods Ten young men were trained for improving size and strength of the medial (GCM), lateral gastrocnemius (GCL) and soleus (SL) three times a week, with at least 24 hours between training sessions, for a period of three months. Diffusion weighted magnetic resonance images were acquired at the beginning of the training period (TPRE) and at three months (TPOST) using a 3T scanner. The fractional anisotropy (FA), mean diffusivity (MD) and tensor eigenvalues (λ1, λ2, λ3) were derived from the diffusion weighted imaging data. Results We found a significant increase in λ1, λ2, λ3 and MD values and muscle volumes between TPRE and TPOST in all the examined muscles both for the left and right side. No significant differences were highlighted for FA. Conclusions DTI enables the investigation of muscle microstructure, allowing for the assessment of diffusion parameters variation of the muscle tissue in response to training thus being a useful tool to investigate physiological and pathological changes in skeletal muscle microstructure which could be employed to test the outcomes and the effectiveness of a given training protocol.

Background Understanding the topographical organization of the cortico-basal ganglia circuitry is of pivotal importance because of the spreading of techniques such as DBS and, more recently, MR-guided focused ultrasound for the treatment of movement disorders. A growing body of evidence has described both direct cortico- and dento-pallidal connections, although the topographical organization in vivo of these pathways in the human brain has never been reported. Objective To investigate the topographical organization of cortico- and dento-pallidal pathways by means of diffusion MRI tractography and connectivity based parcellation. Methods High-quality data from 100 healthy subjects from the Human Connectome Project repository were utilized. Constrained spherical deconvolution-based tractography was used to reconstruct structural cortico- and dento-pallidal connectivity. Connectivity-based parcellation was performed with a hypothesis-driven approach at three different levels: functional regions (limbic, associative, sensorimotor, and other), lobes, and gyral subareas. Results External globus pallidus segregated into a ventral associative cluster, a dorsal sensorimotor cluster, and a caudal "other" cluster on the base of its cortical connectivity. Dento-pallidal connections clustered only in the internal globus pallidus, where also associative and sensorimotor clusters were identified. Lobar parcellation revealed the presence in the external globus pallidus of dissociable clusters for each cortical lobe (frontal, parietal, temporal, and occipital), whereas in internal globus pallidus only frontal and parietal clusters were found out. Conclusion We mapped the topographical organization of both internal and external globus pallidus according to cortical and cerebellar connections. These anatomical data could be useful in DBS, radiosurgery and MR-guided focused ultrasound targeting for treating motor and nonmotor symptoms in movement disorders. © 2019 The Authors. Movement Disorders published by Wiley Periodicals, Inc. on behalf of International Parkinson and Movement Disorder Society.

The amygdala plays a key role in gathering social cues to context-appropriate responses that require refined motor behavior, involving either direct or indirect connections with sensorimotor-related areas. Although, several studies investigated the structural and functional limbic connectivity of the amygdala both in animals and in humans, less is known about the limbic modulation on sensorimotor-related areas. However, recent evidences suggest the amygdala as a possible cornerstone in the limbic-motor interface. Herein, we used high-resolution diffusion data of the Massachusetts General Hospital-University of Southern California (MGH-USC) Adult Diffusion Dataset, constrained spherical deconvolution-based signal modeling and probabilistic tractography aimed at identifying and reconstructing the connectivity patterns linking the amygdala to the limbic- and sensorimotor-related areas. As regards the limbic network, our results showed that the amygdala has high probability to be connected with the fusiform gyrus and the lateral orbitofrontal cortex. On the other hand, our connectomic analysis revealed a close interplay between the amygdala and the inferior parietal lobule, followed by the postcentral gyrus, the precentral gyrus and the paracentral lobule. The findings of the present study are in line with previous literature and reinforce the idea of the existence of a limbic-motor interface, which is likely to be involved in the emotional modulation of complex functions such as spatial perception and movement computation. Considering that these pathways may play an important role, not on in physiological conditions, but also in pathological context, further studies should be fostered in order to confirm the existence of a limbic-motor interface and its precise functional meaning.

The aim of this study is to underline the necessity of a better knowledge of pedicles anatomy in order to improve surgical treatment of spine disorders such us low back pain, spinal fractures and scholiosis. A classification of pedicles lateral tilt which could help surgeons before the application of screws during transpedicular fixation is reported. Anatomical differences in the orientiation of the pedicles of L5 and L4 have been found. For each patient that met the inclusion criteria underwent: Radiography of the lumbo-sacral region, CT examination, MRI acquisition. Patients were divided into three categories thanks to 3D direct volume rendering of CT scan. Subjects belonged to W-Type, V-Type and U-type depending on their morphometric features. The subdivision was further implemented with measurements of the distance between pedicles and adjacent nervous structures. Concerning L5, W-Type (WT) exhibited a lateral tilt of L5 larger than 36°, V-Type exhibited a lateral tilt of L5 from 30° to 36°, U-type exhibited a lateral tilt of L5 smaller than 30°. Concerning L4, WT exhibited a lateral tilt of 28.4°, VT exhibited a lateral tilt of of 25.1, UT exhibited a lateral tilt of 22.2°; we assume that the degree of lateralization of L4 depends on the one of L5. The way the screw is applied during surgical treatment is clinically relevant, thus our classification may be very useful in order to decrease surgical risk and improve conditions of patients after surgical treatment.

In humans, vertical posture acquisition caused several changes in bones and muscles which can be assumed as verticalization. Pelvis, femur, and vertebral column gain an extension position which decreases muscular work by paravertebral muscles in the latter. It’s widely known that six different morphological categories exist; each category differs from the others by pelvic parameters and vertebral column curvatures. Both values depend on the Pelvic Incidence, calculated as the angle between the axes passing through the rotation centre of the two femur heads and the vertical axis passing through the superior plate of the sacrum. The aim of this study is to evaluate the distribution of stress and the resulting strain along the axial skeleton using finite element analysis. The use of this computational method allows performing different analyses investigating how different bony geometries and skeletal structures can behavior under specific loading conditions. A computerized tomography (CT) of artificial bones, carried on at 1.5 mm of distance along sagittal, coronal and axial planes with the knee at 0° flexion (accuracy 0.5 mm), was used to obtain geometrical data of the model developed. Lines were imported into a commercial code (Hypermesh by Altair®) in order to interpolate main surfaces and create the solid version of the model. In particular six different models were created according Roussoly’s classification, by arranging geometrical position of the skeletal components. Loading conditions were obtained by applying muscular forces components to T1 till to L5, according to a reference model (Daniel M. 2011), and a fixed constrain was imposed on the lower part of the femurs. Materials were assumed as elastic with an Elastic modulus of 15 GPa, a Shear Modulus of 7 GPa for bony parts, and an Elastic modulus of 6 MPa, a Shear Modulus of 3 MPa for cartilaginous parts. Six different simulations have been carried out in order to evaluate the mechanical behavior of the human vertebral column arranged according to the Russoly’s classification; results confirm higher solicitations obtained varying configurations from case I to case VI. In particular way, first three cases seem to supply the different loading configurations spreading stresses in almost all the bony parts of the column, while the remaining others three cases produce an higher concentration of stress around the lower part of spine (L3, L4, L5). Results confirm a good agreement with those present in literature (Winkle et al., 1999), an equivalent Von Mises average stress was of 0,55 MPa was found on the intervertebral disks with the higher values reached on the lower part of the column. A comparison of results obtained for Case I with literature (Galbusera et al., and El Rich et al., 2004), shows a good agreement in terms of normal compressive force, while more evident differences with Galbusera’s results can be found for shear force and sagittal moment. The results underline a relationship between PI increase, and accordingly of PT and LL, and the distribution of load forces. Load forcesi is exerted mainly on distal vertebrae, especially on L4 and L5.

Apres avoir defini le concept de representativite d'un echantillon aleatoire, l'auteur propose une mesure de combien l'echantillon observe represente la distribution parente. Cette mesure est dite Fonction de Representativite. Pour un echantillon donne la fonction donne les valeurs de l'indice pour toutes le distributions de la famille consideree, tandis que, pour une distribution donnee, elle donne la mesure de la representativite de chaque possible echantillon. La Fonction de Representativite peut etre employee dans les problemes d'inference statistique justement comme la fonction de vraisemblance, puisque elle donne a chaque distribution le "support experimental" produit par l'echantillon observe. La measure est a distribution libre et on demontre que elle est une tranformation de la bien connue statistique de Cramer-von Mises. En utilisant le proprietes de la dite statistique, on introduit des criteres pour obtenir estimateur ensemblistes et test d'hypothese. L'utilization de la fonction de representativite dans plusieurs problemes statistique est montree par des examples. La qualite des decisions inferentielles peut etre evaluee par les techniques usuelles (MSE, fonction de puissance, probabilites de couverture). Les examples les plus interessant sont ceux qui concerne les situations "non regulieres", par exemple l'estimation de parametres qui figurent dans le support de la population parente, ou situations moins explorees (choix du modele).

The stochastic method has recently received much attention from researchers and seems to be a useful and efficient tool for implementing multiregional forecasting at a local level. In the paper the results are presented of a project financed by the Province of Rome to make a multiple stochastic population forecast of the Rome Metropolitan Area using the so-called Bertino-Sonnino method, based on micro-simulations of birthdeath- emigration-immigration point event processes. This forecast is based on a range of assumptions referring to the future demographic dynamics over the period 2009-24 and forming three variants. The outcome of the stochastic method is compared with deterministic multiregional forecasting to verify the efficiency of both methodologies. This two-step strategy allows control to be maintained over the assumed future demographic variants, at the same time linking in a probability level.

In this paper the minimum of the expected value of the product of three random variables is studied as their joint distribution function varies in the Frechet class associated to the three given marginal distribution functions. The general problem is studied for three positive valued random variables and a lower bound for the minimum is provided. The case of three uniformly distributed random variables in [0, 1] is analyzed in more detail and an upper bound for the minimum is given. The Author conjectures that the distribution correspondent to the upper bound is a solution of the problem.

A study of the demographic trends in a group of Latium municipalities between the 17th and 19th centuries1, conducted with the Stochastic Inverse Projection (SIP) technique2, has enabled us to achieve a detailed reconstruction of the reproductive systems in these populations. In this study, the time patterns of the population dynamics in twelve communities have been analysed on the basis of the period analysis of fertility and mortality rates. The paper then re-examines these reconstructions in order to make a detailed analysis of the reproductive processes followed by the female cohorts of four small towns: Segni, Cori, Norma and Velletri. The illustrated results utilise the average values of the fertility and mortality estimates by generations (cohort analysis) obtained by thirty simulations of the dynamics of these populations. These simulations were conducted for each of the municipalities, applying the SIPIN computer programme for stochastic backward inverse projection.

The techniques aimed at the reconstruction of population structures from parish register in historical periods have widely developed in the last three decades. R. Lee [10] was the first to suggest a method known as the Inverse Projection (IP) to estimate the structural evolution of a population during a determined period of time, given the time series of births and deaths and the size and composition by age of the population at the first year of the studied period. R.McCaa has implemented IP in the easy-to-use programme Populate.