Response to comment on "the geometric structure of the brain fiber pathways".

In response to Catani et al., we show that corticospinal pathways adhere via sharp turns to two local grid orientations; that our studies have three times the diffusion resolution of those compared; and that the noted technical concerns, including crossing angles, do not challenge the evidence of mathematically specific geometric structure. Thus, the geometric thesis gives the best account of the available evidence.

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.

Geometric Structure of the Adaptive Controller of the Human Arm

The objects with which the hand interacts with may significantly change the dynamics of the arm. How does the brain adapt control of arm movements to this new dynamic? We show that adaptation is via composition of a model of the task's dynamics. By exploring generalization capabilities of this adaptation we infer some of the properties of the computational elements with which the brain formed this model: the elements have broad receptive fields and encode the learned dynamics as a map structured in an intrinsic coordinate system closely related to the geometry of the skeletomusculature. The low--level nature of these elements suggests that they may represent asset of primitives with which a movement is represented in the CNS.

A closer look at chaotic advection in the stratosphere: part I: geometric structure

The relevance of chaotic advection to stratospheric mixing and transport is addressed in the context of (i) a numerical model of forced shallow-water flow on the sphere, and (ii) a middle-atmosphere general circulation model. It is argued that chaotic advection applies to both these models if there is suitable large-scale spatial structure in the velocity field and if the velocity field is temporally quasi-regular. This spatial structure is manifested in the form of “cat’s eyes” in the surf zone, such as are commonly seen in numerical simulations of Rossby wave critical layers; by analogy with the heteroclinic structure of a temporally aperiodic chaotic system the cat’s eyes may be thought of as an “organizing structure” for mixing and transport in the surf zone. When this organizing structure exists, Eulerian and Lagrangian autocorrelations of the velocity derivatives indicate that velocity derivatives decorrelate more rapidly along particle trajectories than at fixed spatial locations (i.e., the velocity field is temporally quasi-regular). This phenomenon is referred to as Lagrangian random strain.

More maximal arcs in Desarguesian projective planes and their geometric structure

In a previous paper R. Mathon gave a new construction method for maximal arcs in finite Desarguesian projective planes via closed sets of conics, as well as giving many new examples of maximal arcs. In the current paper, new classes of maximal arcs are constructed, and it is shown that every maximal arc so constructed gives rise to an infinite class of maximal arcs. Apart from when they are of Denniston type or dual hyperovals, closed sets of conics are shown to give maximal arcs that are not isomorphic to the known constructions. An easy characterisation of when a closed set of conics is of Denniston type is given. Results on the geometric structure of the maximal arcs and their duals are proved, as well as on elements of their collineation stabilisers.

A geometric approach to cosmological boundary conditions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Synthesis, structure, and stability of metal-organic frameworks

Metal-organic frameworks (MOFs) obtained much attention because of their unusual structures and properties as well as their potential applications. This dissertation research was focused on (1) the effects of synthesis conditions on the structures of MOFs, (2) the thermal stability of MOFs, (3) pressure-induced amorphization, and (4) the effect of high-valent ions on the structure of a MOF. This research demonstrated that the crystal structure of MOF-5 could be controlled by drying solvents. If the vacuum solvent is dimethylformamide (DMF), the crystal structure of MOF-5 is tetragonal. In contrast, if the DMF is displaced by CH2Cl2 before the vacuum, the obtained MOF-5 occupies a cubic structure. Furthermore, it was found that the tetragonal MOF-5 exhibited a mediate surface area (300-1000 m2/g). The surface area of tetragonal MOF-5 is also dependent on Zn(NO3)2/H2BDC (H2BDC: terephthalic acid) molar ratios used for its synthesis. The optimum ratio is 1.38, at which synthesized tetragonal MOF-5 exhibits the highest crystallinity and surface area (1297 m2/g). The thermal stability and decomposition of MOF-5 were systematically investigated. The thermal decomposition of cubic and tetragonal MOF-5s resulted in the same products: CO2, benzene, amorphous carbon, and crystal ZnO. The thermal decomposition is due to breaking carboxylic bridges between benzene rings and Zn4O clusters. Identifying structural relationships between crystalline and noncrystalline states is of fundamental interest in materials research. Currently, amorphization of solid materials at ambient temperature requires an ultra-high pressure (several GPa). However, this research demonstrated that MOF-5 and IRMOF-8 can be irreversibly amorphized at ambient temperature by employing a low compressing pressure of 3.5 MPa, which is 100 times lower than that required for amorphization of other solids. Furthermore, the pressure-induced amorphization (PIA) of MOFs is strongly dependent on the changeability of bond angles. If the geometric structure of a MOF can allow bond angles to be changed without breaking bonds, it can easily be amorphized by compression. This can explain why MOF-5 and IRMOF-8 can easily be amorphized via compression than Cu-BTC. It is generally recognized that zeolitic imidazolate frameworks (ZIFs) occupy much higher stability than other types of MOFs. The representative of ZIFs is Zn(2-methylimidazole)2 (ZIF-8) exhibiting high-decomposition temperature and high chemical resistance to various solvents. However, so far, it is still unknown whether the high stability of ZIF-8 can be challenged by ions, which is important for its modification by doping ions. In this research, we performed aqueous salt solution treatment on ZIF-8, and the results showed that anions (Cl¯ and NO3¯) in a solution exhibited no effect on the crystal structure of ZIF-8. However, the effect of cations (in a solution) on structure of ZIF-8 strongly depends on the cation valences. The univalent metal cations showed no effect on the structure of ZIF-8, whereas the bivalent or higher-valent metal cations caused the collapse of ZIF-8 crystal structure. Therefore, structure stability of ZIF-8 is considered when it is subjected to the application, in which high-valent metal cations are involved.

Multiple correspondence analysis of a subset of response categories

In the analysis of multivariate categorical data, typically the analysis of questionnaire data, it is often advantageous, for substantive and technical reasons, to analyse a subset of response categories. In multiple correspondence analysis, where each category is coded as a column of an indicator matrix or row and column of Burt matrix, it is not correct to simply analyse the corresponding submatrix of data, since the whole geometric structure is different for the submatrix . A simple modification of the correspondence analysis algorithm allows the overall geometric structure of the complete data set to be retained while calculating the solution for the selected subset of points. This strategy is useful for analysing patterns of response amongst any subset of categories and relating these patterns to demographic factors, especially for studying patterns of particular responses such as missing and neutral responses. The methodology is illustrated using data from the International Social Survey Program on Family and Changing Gender Roles in 1994.

Estudio estructural del MoO3 y sus planos cristalinos

In the present work we present geometric models of the most studied MoO3 surfaces, which were obtained using the DTMM 2.0 Molecular Modeller software. MoO3 has an orthorhombic layered structure, with each layer comprised of two interleaved planes of MoO6 octahedral. These layers are parallel to the (010) crystal plane and only oxygen ions are exposed on their surfaces. This situation results in weak van der Waals bonding between layers and in a relatively inert surface. In our approach to surface geometric structure we consider "ideal" crystal surface, in which the bulk atomic arrangement is maintained. These surfaces were generated by imaginary cleavage along appropriate planes in the bulk crystal structure.

On Vessiot's Theory of Partial Differential Equations

The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.

The Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach

The algebraic-geometric structure of the simplex, known as Aitchison geometry, is used to look at the Dirichlet family of distributions from a new perspective. A classical Dirichlet density function is expressed with respect to the Lebesgue measure on real space. We propose here to change this measure by the Aitchison measure on the simplex, and study some properties and characteristic measures of the resulting density

Novas fases amorfas de carbono produzidas por irradiação iônica de filmes de C/sub 60/, [alfa]-C e [alfa]-C:H

Neste trabalho estuda-se a formação de novas fases de carbono amorfo através da irradiação iônica de filmes de fulereno, a-C e a-C:H polimérico. Os efeitos da irradiação iônica na modificação das propriedades ópticas e mecânicas dos filmes de carbono irradiados são analisados de forma correlacionada com as alterações estruturais a nivel atômico. O estudo envolve tanto a análise dos danos induzidos no fulereno pela irradiação iônica a baixas fluências, correspondendo a baixas densidades de energia depositada, quanto a investigação das propriedades físico-químicas das fases amorfas obtidas após irradiações dos filmes de fulereno, a-C e a-C:H com altas densidades de energia depositada. As propriedades ópticas, mecânicas e estruturais das amostras são analisadas através de técnicas de espectroscopia Raman e infravermelho, espectrofotometria UV-VIS-NIR, microscopias ópticas e de força atômica, nanoindentação e técnicas de análise por feixe de íons, tais como retroespalhamento Rutherford e análises por reação nuclear. As irradiações produzem profundas modificações nas amostras de fulereno, a-C e a-C:H, e por conseqüência significativas alterações em suas propriedades ópticas e mecânicas. Após máximas fluências de irradiação fases amorfas rígidas (com dureza de 14 e 17 GPa) e com baixos gaps ópticos (0,2 e 0,5 eV) são formadas. Estas estruturas não usuais correspondem a arranjos atômicos com 90 a 100% de estados sp2. Em geral fases sp2 são planares e apresentam baixa dureza, como predito pelo modelo de “cluster”. Entretanto, os resultados experimentais mostram que as propriedades elásticas das novas fases formadas são alcançadas através da criação de uma estrutura sp2 tridimensional. A indução de altas distorções angulares, através da irradiação iônica, possibilita a formação de anéis de carbono não hexagonais, tais como pentágonos e heptágonos, permitindo assim a curvatura da estrutura. Utilizando um modelo de contagem de vínculos é feita uma análise comparativa entre a topologia (estrutura geométrica) de ligações C-sp2 e as propriedades nanomecânicas. São comparados os efeitos de estruturas sp2 planares e tridimensionais (aleatórias) no processo de contagem de vínculos e, conseqüentemente, nas propriedades elásticas de cada sistema. Os resultados mostram que as boas propriedades mecânicas das novas fases de carbono formadas seguem as predições do modelo de vínculos para uma rede atômica sp2 tridimensional. A formação de uma fase amorfa dura e 100% sp2 representa uma importante conquista na procura de novas estruturas rígidas de carbono. A síntese da estrutura desordenada sp2 tridimensional e vinculada aqui apresentada é bastante incomum na literatura. O presente trabalho mostra que o processo de não-equilíbrio de deposição de energia durante a irradiação iônica permite a formação de distorções angulares nas ligações sp2-C, possibilitando a criação de estruturas grafíticas tridimensionais.

Efeito do campo elétrico em nanocones formados por aln e BN: um estudo por primeiros princípios

The development of computers and algorithms capable of making increasingly accurate and rapid calculations as well as the theoretic foundation provided by quantum mechanics has turned computer simulation into a valuable research tool. The importance of such a tool is due to its success in describing the physical and chemical properties of materials. One way of modifying the electronic properties of a given material is by applying an electric field. These effects are interesting in nanocones because their stability and geometric structure make them promising candidates for electron emission devices. In our study we calculated the first principles based on the density functional theory as implemented in the SIESTA code. We investigated aluminum nitride (AlN), boron nitride (BN) and carbon (C), subjected to external parallel electric field, perpendicular to their main axis. We discuss stability in terms of formation energy, using the chemical potential approach. We also analyze the electronic properties of these nanocones and show that in some cases the perpendicular electric field provokes a greater gap reduction when compared to the parallel field

LEAST ACTION PRINCIPLE and THE INCOMPRESSIBLE EULER EQUATIONS WITH VARIABLE DENSITY

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Proposição de rotina morfológica para detecção de malha viária em imagens orbitais

The outdating of cartographic products affects planning. It is important to propose methods to help detect changes in surface. Thus, the combined use of remote sensing image and techniques of digital image processing has contributed significantly to minimize such outdating. Mathematical morphology is an image processing technique which describes quantitatively geometric structures presented in the image and provides tools such as edge detectors and morphological filters. Previous studies have shown that the technique has potential on the detection of significant features. Thus, this paper proposes a routine of morphological operators to detect a road network. The test area corresponds to an excerpt Quickbird image and has as a feature of interest an avenue of the city of Presidente Prudente, SP. In the processing, the main morphological operators used were threshad, areaopen, binary and erosion. To estimate the accuracy with which the linear features were detected, it was done the analysis of linear correlation between vectors of the features detected and the corresponding topographical map of the region. The results showed that the mathematical morphology can be used in cartography, aiming to use them in conventional cartographic updating processes.