A Geometric Characterization of Interpolation in $\hat{\E}^\prime(\R)$

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

An evaluation of volume-based morphometry for prediction of mild cognitive impairment and Alzheimer's disease.

Voxel-based morphometry from conventional T1-weighted images has proved effective to quantify Alzheimer's disease (AD) related brain atrophy and to enable fairly accurate automated classification of AD patients, mild cognitive impaired patients (MCI) and elderly controls. Little is known, however, about the classification power of volume-based morphometry, where features of interest consist of a few brain structure volumes (e.g. hippocampi, lobes, ventricles) as opposed to hundreds of thousands of voxel-wise gray matter concentrations. In this work, we experimentally evaluate two distinct volume-based morphometry algorithms (FreeSurfer and an in-house algorithm called MorphoBox) for automatic disease classification on a standardized data set from the Alzheimer's Disease Neuroimaging Initiative. Results indicate that both algorithms achieve classification accuracy comparable to the conventional whole-brain voxel-based morphometry pipeline using SPM for AD vs elderly controls and MCI vs controls, and higher accuracy for classification of AD vs MCI and early vs late AD converters, thereby demonstrating the potential of volume-based morphometry to assist diagnosis of mild cognitive impairment and Alzheimer's disease.

Influence of magnetic field strength and image registration strategy on voxel-based morphometry in a study of Alzheimer's disease.

Multi-centre data repositories like the Alzheimer's Disease Neuroimaging Initiative (ADNI) offer a unique research platform, but pose questions concerning comparability of results when using a range of imaging protocols and data processing algorithms. The variability is mainly due to the non-quantitative character of the widely used structural T1-weighted magnetic resonance (MR) images. Although the stability of the main effect of Alzheimer's disease (AD) on brain structure across platforms and field strength has been addressed in previous studies using multi-site MR images, there are only sparse empirically-based recommendations for processing and analysis of pooled multi-centre structural MR data acquired at different magnetic field strengths (MFS). Aiming to minimise potential systematic bias when using ADNI data we investigate the specific contributions of spatial registration strategies and the impact of MFS on voxel-based morphometry in AD. We perform a whole-brain analysis within the framework of Statistical Parametric Mapping, testing for main effects of various diffeomorphic spatial registration strategies, of MFS and their interaction with disease status. Beyond the confirmation of medial temporal lobe volume loss in AD, we detect a significant impact of spatial registration strategy on estimation of AD related atrophy. Additionally, we report a significant effect of MFS on the assessment of brain anatomy (i) in the cerebellum, (ii) the precentral gyrus and (iii) the thalamus bilaterally, showing no interaction with the disease status. We provide empirical evidence in support of pooling data in multi-centre VBM studies irrespective of disease status or MFS.

Francisci Maurolyci, Siculi, demonstratio algebrae ; sive potiùs, regulae calculi litteralis ad inveniendum terminum quemlibet proportionis geometricè continuae.

Colbertinus

1.° Francisci Maurolyci de centro solidi parabolae demonstratio : praemittuntur catalogus ejusdem operum et observationes de ordine quo singula legenda sunt. — 2.° Descriptio hyperbolarum contrapositarum, diametrorum, tangentium, linearum continuè proportionalium et triangulorum aequalium : authore eodem. — 3.° Ejusdem algebra, sive potiùs, regulae calculi litteralis ad inveniendum terminum quemlibet proportionis geometricè continuae.

Colbertinus

The geometric structure of the brain fiber pathways.

The structure of the brain as a product of morphogenesis is difficult to reconcile with the observed complexity of cerebral connectivity. We therefore analyzed relationships of adjacency and crossing between cerebral fiber pathways in four nonhuman primate species and in humans by using diffusion magnetic resonance imaging. The cerebral fiber pathways formed a rectilinear three-dimensional grid continuous with the three principal axes of development. Cortico-cortical pathways formed parallel sheets of interwoven paths in the longitudinal and medio-lateral axes, in which major pathways were local condensations. Cross-species homology was strong and showed emergence of complex gyral connectivity by continuous elaboration of this grid structure. This architecture naturally supports functional spatio-temporal coherence, developmental path-finding, and incremental rewiring with correlated adaptation of structure and function in cerebral plasticity and evolution.

Maintenance of Traffic for Innovative Geometric Design Work Zones, 2015

Currently there are no guidelines within the Manual on Uniform Traffic Control Devices (MUTCD) on construction phasing and maintenance of traffic (MOT) for retrofit construction and maintenance projects involving innovative geometric designs. The research presented in this report addressed this gap in existing knowledge by investigating the state of the practice of construction phasing and MOT for several types of innovative geometric designs including the roundabout, single point urban interchange (SPUI), diverging diamond interchange (DDI), restricted-crossing left turn (RCUT), median U-turn (MUT), and displaced left turn (DLT). This report provides guidelines for transportation practitioners in developing construction phasing and MOT plans for innovative geometric designs. This report includes MOT Phasing Diagrams to assist in the development of MOT strategies for innovative designs. The MOT Phasing Diagrams were developed through a review of literature, survey, interviews with practitioners, and review of plans from innovative geometric design projects. These diagrams are provided as a tool to assist in improving work zone safety and mobility through construction of projects with innovative geometric designs. The aforementioned synthesis of existing knowledge documented existing practices for these types of designs.

Constrained peptidomimetics reveal detailed geometric requirements of covalent prolyl oligopeptidase inhibitors.

Prolyl oligopeptidases cleave peptides on the carboxy side of internal proline residues and their inhibition has potential in the treatment of human brain disorders. Using our docking program fitted, we have designed a series of constrained covalent inhibitors, built from a series of bicyclic scaffolds, to study the optimal shape required for these small molecules. These structures bear nitrile functional groups that we predicted to covalently bind to the catalytic serine of the enzyme. Synthesis and biological assays using human brain-derived astrocytic cells and endothelial cells and human fibroblasts revealed that these compounds act as selective inhibitors of prolyl oligopeptidase activity compared to prolyl-dipeptidyl-aminopeptidase activity, are able to penetrate the cells and inhibit intracellular activities in intact living cells. This integrated computational and experimental study shed light on the binding mode of inhibitors in the enzyme active site and will guide the design of future drug-like molecules.

Quantitative morphometry analysis of the fetal brain using clinical MR imaging

In vivo fetal magnetic resonance imaging provides aunique approach for the study of early human braindevelopment [1]. In utero cerebral morphometry couldpotentially be used as a marker of the cerebralmaturation and help to distinguish between normal andabnormal development in ambiguous situations. However,this quantitative approach is a major challenge becauseof the movement of the fetus inside the amniotic cavity,the poor spatial resolution provided by very fast MRIsequences and the partial volume effect. Extensiveefforts are made to deal with the reconstruction ofhigh-resolution 3D fetal volumes based on severalacquisitions with lower resolution [2,3,4]. Frameworkswere developed for the segmentation of specific regionsof the fetal brain such as posterior fossa, brainstem orgerminal matrix [5,6], or for the entire brain tissue[7,8], applying the Expectation-Maximization MarkovRandom Field (EM-MRF) framework. However, many of theseprevious works focused on the young fetus (i.e. before 24weeks) and use anatomical atlas priors to segment thedifferent tissue or regions. As most of the gyraldevelopment takes place after the 24th week, acomprehensive and clinically meaningful study of thefetal brain should not dismiss the third trimester ofgestation. To cope with the rapidly changing appearanceof the developing brain, some authors proposed a dynamicatlas [8]. To our opinion, this approach however faces arisk of circularity: each brain will be analyzed /deformed using the template of its biological age,potentially biasing the effective developmental delay.Here, we expand our previous work [9] to proposepost-processing pipeline without prior that allow acomprehensive set of morphometric measurement devoted toclinical application. Data set & Methods: Prenatal MRimaging was performed with a 1-T system (GE MedicalSystems, Milwaukee) using single shot fast spin echo(ssFSE) sequences (TR 7000 ms, TE 180 ms, FOV 40 x 40 cm,slice thickness 5.4mm, in plane spatial resolution1.09mm). For each fetus, 6 axial volumes shifted by 1 mmwere acquired under motherâeuro?s sedation (about 1min pervolume). First, each volume is segmentedsemi-automatically using region-growing algorithms toextract fetal brain from surrounding maternal tissues.Inhomogeneity intensity correction [10] and linearintensity normalization are then performed. Brain tissues(CSF, GM and WM) are then segmented based on thelow-resolution volumes as presented in [9]. Ahigh-resolution image with isotropic voxel size of 1.09mm is created as proposed in [2] and using B-splines forthe scattered data interpolation [11]. Basal gangliasegmentation is performed using a levet setimplementation on the high-resolution volume [12]. Theresulting white matter image is then binarized and givenas an input in FreeSurfer software(http://surfer.nmr.mgh.harvard.edu) to providetopologically accurate three-dimensional reconstructionsof the fetal brain according to the local intensitygradient. References: [1] Guibaud, Prenatal Diagnosis29(4) (2009). [2] Rousseau, Acad. Rad. 13(9), 2006. [3]Jiang, IEEE TMI 2007. [4] Warfield IADB, MICCAI 2009. [5]Claude, IEEE Trans. Bio. Eng. 51(4) 2004. [6] Habas,MICCAI 2008. [7] Bertelsen, ISMRM 2009. [8] Habas,Neuroimage 53(2) 2010. [9] Bach Cuadra, IADB, MICCAI2009. [10] Styner, IEEE TMI 19(39 (2000). [11] Lee, IEEETrans. Visual. And Comp. Graph. 3(3), 1997. [12] BachCuadra, ISMRM 2010.

Structural changes induced by daily music listening in the recovering brain after middle cerebral artery stroke: a voxel-based morphometry study

Music is a highly complex and versatile stimulus for the brain that engages many temporal, frontal, parietal, cerebellar, and subcortical areas involved in auditory, cognitive, emotional, and motor processing. Regular musical activities have been shown to effectively enhance the structure and function of many brain areas, making music a potential tool also in neurological rehabilitation. In our previous randomized controlled study, we found that listening to music on a daily basis can improve cognitive recovery and improve mood after an acute middle cerebral artery stroke. Extending this study, a voxel-based morphometry (VBM) analysis utilizing cost function masking was performed on the acute and 6-month post-stroke stage structural magnetic resonance imaging data of the patients (n = 49) who either listened to their favorite music [music group (MG), n = 16] or verbal material [audio book group (ABG), n = 18] or did not receive any listening material [control group (CG), n = 15] during the 6-month recovery period. Although all groups showed significant gray matter volume (GMV) increases from the acute to the 6-month stage, there was a specific network of frontal areas [left and right superior frontal gyrus (SFG), right medial SFG] and limbic areas [left ventral/subgenual anterior cingulate cortex (SACC) and right ventral striatum (VS)] in patients with left hemisphere damage in which the GMV increases were larger in the MG than in the ABG and in the CG. Moreover, the GM reorganization in the frontal areas correlated with enhanced recovery of verbal memory, focused attention, and language skills, whereas the GM reorganization in the SACC correlated with reduced negative mood. This study adds on previous results, showing that music listening after stroke not only enhances behavioral recovery, but also induces fine-grained neuroanatomical changes in the recovering brain.