Developing a numerical inverse-theory-based extraction of orientation-dependent relaxation rates from partially- relaxed spectra

Second-rank tensor interactions, such as quadrupolar interactions between the spin- 1 deuterium nuclei and the electric field gradients created by chemical bonds, are affected by rapid random molecular motions that modulate the orientation of the molecule with respect to the external magnetic field. In biological and model membrane systems, where a distribution of dynamically averaged anisotropies (quadrupolar splittings, chemical shift anisotropies, etc.) is present and where, in addition, various parts of the sample may undergo a partial magnetic alignment, the numerical analysis of the resulting Nuclear Magnetic Resonance (NMR) spectra is a mathematically ill-posed problem. However, numerical methods (de-Pakeing, Tikhonov regularization) exist that allow for a simultaneous determination of both the anisotropy and orientational distributions. An additional complication arises when relaxation is taken into account. This work presents a method of obtaining the orientation dependence of the relaxation rates that can be used for the analysis of the molecular motions on a broad range of time scales. An arbitrary set of exponential decay rates is described by a three-term truncated Legendre polynomial expansion in the orientation dependence, as appropriate for a second-rank tensor interaction, and a linear approximation to the individual decay rates is made. Thus a severe numerical instability caused by the presence of noise in the experimental data is avoided. At the same time, enough flexibility in the inversion algorithm is retained to achieve a meaningful mapping from raw experimental data to a set of intermediate, model-free

Constrains on the structure of Maio Island (Cape Verde) by a three-dimensional gravity model: Imaging partially exhumed magma chambers

We propose a 3-D gravity model for the volcanic structure of the island of Maio (Cape Verde archipelago) with the objective of solving some open questions concerning the geometry and depth of the intrusive Central Igneous Complex. A gravity survey was made covering almost the entire surface of the island. The gravity data was inverted through a non-linear 3-D approach which provided a model constructed in a random growth process. The residual Bouguer gravity field shows a single positive anomaly presenting an elliptic shape with a NWSE trending long axis. This Bouguer gravity anomaly is slightly off-centred with the island but its outline is concordant with the surface exposure of the Central Igneous Complex. The gravimetric modelling shows a high-density volume whose centre of mass is about 4500 m deep. With increasing depth, and despite the restricted gravimetric resolution, the horizontal sections of the model suggest the presence of two distinct bodies, whose relative position accounts for the elongated shape of the high positive Bouguer gravity anomaly. These bodies are interpreted as magma chambers whose coeval volcanic counterparts are no longer preserved. The orientation defined by the two bodies is similar to that of other structures known in the southern group of the Cape Verde islands, thus suggesting a possible structural control constraining the location of the plutonic intrusions.

Estudos experimentais sôbre a origem do milho

1) It may seem rather strange that, in spite of the efforts of a considerable number of scientists, the problem of the origin of indian corn or maize still has remained an open question. There are no fossil remains or archaeological relics except those which are quite identical with types still existing. (Fig. 1). The main difficulty in finding the wild ancestor- which may still exist - results from the fact that it has been somewhat difficult to decide what it should be like and also where to look for it. 2) There is no need to discuss the literature since an excellent review has recently been published by MANGELSDORF and REEVES (1939). It may be sufficient to state that there are basically two hypotheses, that of ST. HILAIRE (1829) who considered Brazilian pod corn as the nearest relative of wild corn still existing, and that of ASCHERSON (1875) who considered Euchlaena from Central America as the wild ancestor of corn. Later hypotheses represent or variants of these two hypotheses or of other concepts, howewer generally with neither disproving their predecessors nor showing why the new hypotheses were better than the older ones. Since nearly all possible combinations of ideas have thus been put forward, it har- dly seems possible to find something theoretically new, while it is essential first to produce new facts. 3) The studies about the origin of maize received a new impulse from MANGELSDORF and REEVES'S experimental work on both Zea-Tripsacum and Zea-Euchlaena hybrids. Independently I started experiments in 1937 with the hope that new results might be obtained when using South American material. Having lost priority in some respects I decided to withold publication untill now, when I can put forward more concise ideas about the origin of maize, based on a new experimental reconstruction of the "wild type". 4) The two main aspects of MANGELSDORF and REEVES hypothesis are discussed. We agree with the authors that ST. HILAIRE's theory is probably correct in so far as the tunicata gene is a wild type relic gene, but cannot accept the reconstruction of wild corn as a homozygous pod corn with a hermaphroditic tassel. As shown experimentally (Fig. 2-3) these tassels have their central spike transformed into a terminal, many rowed ear with a flexible rachis, while possessing at the same time the lateral ear. Thus no explanation is given of the origin of the corn ear, which is the main feature of cultivated corn (BRIEGER, 1943). The second part of the hypothesis referring to the origin of Euchlaena from corn, inverting thus ASCHERSON's theory, cannot be accepted for several reasons, stated in some detail. The data at hand justify only the conclusion that both genera, Euchlaena and Zea, are related, and there is as little proof for considering the former as ancestor of the latter as there is for the new inverse theory. 5) The analysis of indigenous corn, which will be published in detail by BRIEGER and CUTLER, showed several very primitive characters, but no type was found which was in all characters sufficiently primitive. A genetical analysis of Paulista Pod Corn showed that it contains the same gene as other tunicates, in the IV chromosome, the segregation being complicated by a new gametophyte factor Ga3. The full results of this analysis shall be published elsewhere. (BRIEGER). Selection experiments with Paulista Pod Corn showed that no approximation to a wild ancestor may be obtained when limiting the studies to pure corn. Thus it seemed necessary to substitute "domesticated" by "wild type" modifiers, and the only means for achieving this substitution are hybridizations with Euchlaena. These hybrids have now been analysed init fourth generation, including backcrosses, and, again, the full data will be published elsewhere, by BRIEGER and ADDISON. In one present publication three forms obtained will be described only, which represent an approximation to wild type corn. 6) Before entering howewer into detail, some arguments against ST. HILAIRE's theory must be mentioned. The premendelian argument, referring to the instability of this character, is explained by the fact that all fertile pod corn plants are heterozygous for the dominant Tu factor. But the sterility of the homozygous TuTu, which phenotypically cannot be identified, is still unexplained. The most important argument against the acceptance of the Tunicata faetor as wild type relic gene was removed recently by CUTLER (not yet published) who showed that this type has been preserved for centuries by the Bolivian indians as a mystical "medicine". 7) The main botanical requirements for transforming the corn ear into a wild type structure are stated, and alternative solutions given. One series of these characters are found in Tripsacum and Euchlaena : 2 rows on opposite sides of the rachis, protection of the grains by scales, fragility of the rachis. There remains the other alternative : 4 rows, possibly forming double rows of female and male spikelets, protection of kernels by their glumes, separation of grains at their base from the cob which is thin and flexible. 8) Three successive stages in the reconstruction of wild corn, obtained experimentally, are discussed and illustrated, all characterized by the presence of the Tu gene. a) The structure of the Fl hybrids has already been described in 1943. The main features of the Tunicata hybrids (Fig. -8), when compared with non-tunicate hybrids (Fig. 5-6), consist in the absence of scaly protections, the fragility of the rachis and finally the differentiation of the double rows into one male and one female spikelet. As has been pointed out, these characters represent new phenotypic effects of the tunicate factor which do not appear in the presence of pure maize modifiers. b) The next step was observed among the first backcross to teosinte (Fig. 9). As shown in the photography, Fig. 9D, the features are essencially those of the Fl plants, except that the rachis is more teosinte like, with longer internodes, irregular four-row-arrangement and a complete fragility on the nodes. c) In the next generation a completely new type appeared (Fig. 10) which resembles neither corn nor teosinte, mainly in consequence of one character: the rachis is thin and flexible and not fragile, while the grains have an abscission layer at the base, The medium sized, pointed, brownish and hard granis are protected by their well developed corneous glumes. This last form may not yet be the nearest approach to a wild grass, and I shall try in further experiments to introduce other changes such as an increase of fertile flowers per spikelet, the reduction of difference between terminal and lateral inflorescences, etc.. But the nature of the atavistic reversion is alveadwy such that it alters considerably our expectation when looking for a still existing wild ancestor of corn. 9) The next step in our deductions must now consist in an reversion of our question. We must now explain how we may obtain domesticated corn, starting from a hypothetical wild plant, similar to type c. Of the several changes which must have been necessary to attract the attention of the Indians, the following two seem to me the most important: the disappearance of all abscission layers and the reduction of the glumes. This may have been brought about by an accumulation of mutations. But it seems much more probable to assume that some crossing with a tripsacoid grass or even with Tripsacum australe may have been responsible. In such a cross, the two types of abscission layer would be counterbalanced as shown by the Flhybrids of corn, Tripsacum and Euchlaena. Furthermore in later generations a.tu-allele of Tripsacum may become homozygous and substitute the wild tunicate factor of corn. The hypothesis of a hybrid origin of cultivated corn is not completely new, but has been discussed already by HARSHBERGER and COLLINS. Our hypothesis differs from that of MANGELSDORF and REEVES who assume that crosses with Tripsacum are responsible only for some features of Central and North American corn. 10) The following arguments give indirects evidence in support of our hypothesis: a) Several characters have been observed in indigenous corn from the central region of South America, which may be interpreted as "tripsacoid". b) Equally "zeoid" characters seem to be present in Tripsacum australe of central South-America. c) A system of unbalanced factors, combined by the in-tergeneric cross, may be responsible for the sterility of the wild type tunicata factor when homozygous, a result of the action of modifiers, brought in from Tripsacum together with the tuallele. d) The hybrid theory may explain satisfactorily the presence of so many lethals and semilethals, responsible for the phenomenon of inbreeding in cultivated corn. It must be emphasized that corn does not possess any efficient mechanism to prevent crossing and which could explain the accumulation of these mutants during the evolutionary process. Teosinte which'has about the same mechanism of sexual reproduction has not accumulated such genes, nor self-sterile plants in spite of their pronounced preference for crossing. 11) The second most important step in domestication must have consisted in transforming a four rowed ear into an ear with many rows. The fusion theory, recently revived byLANGHAM is rejected. What happened evidently, just as in succulent pXants (Cactus) or in cones os Gymnosperms, is that there has been a change in phyllotaxy and a symmetry of longitudinal rows superimposed on the original spiral arrangement. 12) The geographical distribution of indigenous corn in South America has been discussed. So far, we may distinguish three zones. The most primitive corn appears in the central lowlands of what I call the Central Triangle of South America: east of the Andies, south of the Amazone-Basin, Northwest of a line formed by the rivers São Prancisco-Paraná and including the Paraguay-Basin. The uniformity of the types found in this extremely large zone is astonishing (BRIEGER and CUTLER). To the west, there is the well known Andian region, characterized by a large number of extremely diverse types from small pop corn to large Cuszco, from soft starch to modified sweet corn, from large cylindrical ears to small round ears, etc.. The third region extends along the atlantic coast in the east, from the Caribean Sea to the Argentine, and is characterized by Cateto, an orange hard flint corn. The Andean types must have been obtained very early, and undoubtedly are the result of the intense Inca agriculture. The Cateto type may be obtained easily by crosses, for instance, of "São Paulo Pointed Pop" to some orange soft corn of the central region. The relation of these three South American zones to Central and North America are not discussed, and it seems essential first to study the intermediate region of Ecuador, Colombia and Venezuela. The geograprical distribution of chromosome knobs is rapidly discussed; but it seems that no conclusions can be drawn before a large number of Tripsacum species has been analysed.

Focused time-lapse inversion of radio and audio magnetotelluric data

Geoelectrical techniques are widely used to monitor groundwater processes, while surprisingly few studies have considered audio (AMT) and radio (RMT) magnetotellurics for such purposes. In this numerical investigation, we analyze to what extent inversion results based on AMT and RMT monitoring data can be improved by (1) time-lapse difference inversion; (2) incorporation of statistical information about the expected model update (i.e., the model regularization is based on a geostatistical model); (3) using alternative model norms to quantify temporal changes (i.e., approximations of l(1) and Cauchy norms using iteratively reweighted least-squares), (4) constraining model updates to predefined ranges (i.e., using Lagrange Multipliers to only allow either increases or decreases of electrical resistivity with respect to background conditions). To do so, we consider a simple illustrative model and a more realistic test case related to seawater intrusion. The results are encouraging and show significant improvements when using time-lapse difference inversion with non l(2) model norms. Artifacts that may arise when imposing compactness of regions with temporal changes can be suppressed through inequality constraints to yield models without oscillations outside the true region of temporal changes. Based on these results, we recommend approximate l(1)-norm solutions as they can resolve both sharp and smooth interfaces within the same model. (C) 2012 Elsevier B.V. All rights reserved.

Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data

Numerous sources of evidence point to the fact that heterogeneity within the Earth's deep crystalline crust is complex and hence may be best described through stochastic rather than deterministic approaches. As seismic reflection imaging arguably offers the best means of sampling deep crustal rocks in situ, much interest has been expressed in using such data to characterize the stochastic nature of crustal heterogeneity. Previous work on this problem has shown that the spatial statistics of seismic reflection data are indeed related to those of the underlying heterogeneous seismic velocity distribution. As of yet, however, the nature of this relationship has remained elusive due to the fact that most of the work was either strictly empirical or based on incorrect methodological approaches. Here, we introduce a conceptual model, based on the assumption of weak scattering, that allows us to quantitatively link the second-order statistics of a 2-D seismic velocity distribution with those of the corresponding processed and depth-migrated seismic reflection image. We then perform a sensitivity study in order to investigate what information regarding the stochastic model parameters describing crustal velocity heterogeneity might potentially be recovered from the statistics of a seismic reflection image using this model. Finally, we present a Monte Carlo inversion strategy to estimate these parameters and we show examples of its application at two different source frequencies and using two different sets of prior information. Our results indicate that the inverse problem is inherently non-unique and that many different combinations of the vertical and lateral correlation lengths describing the velocity heterogeneity can yield seismic images with the same 2-D autocorrelation structure. The ratio of all of these possible combinations of vertical and lateral correlation lengths, however, remains roughly constant which indicates that, without additional prior information, the aspect ratio is the only parameter describing the stochastic seismic velocity structure that can be reliably recovered.

Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

Upper-mantle seismic structure beneath SE and Central Brazil from P- and S-wave regional traveltime tomography

We present models for the upper-mantle velocity structure beneath SE and Central Brazil using independent tomographic inversions of P- and S-wave relative arrival-time residuals (including core phases) from teleseismic earthquakes. The events were recorded by a total of 92 stations deployed through different projects, institutions and time periods during the years 1992-2004. Our results show correlations with the main tectonic structures and reveal new anomalies not yet observed in previous works. All interpretations are based on robust anomalies, which appear in the different inversions for P-and S-waves. The resolution is variable through our study volume and has been analyzed through different theoretical test inversions. High-velocity anomalies are observed in the western portion of the Sao Francisco Craton, supporting the hypothesis that this Craton was part of a major Neoproterozoic plate (San Franciscan Plate). Low-velocity anomalies beneath the Tocantins Province (mainly fold belts between the Amazon and Sao Francisco Cratons) are interpreted as due to lithospheric thinning, which is consistent with the good correlation between intraplate seismicity and low-velocity anomalies in this region. Our results show that the basement of the Parana Basin is formed by several blocks, separated by suture zones, according to model of Milani & Ramos. The slab of the Nazca Plate can be observed as a high-velocity anomaly beneath the Parana Basin, between the depths of 700 and 1200 km. Further, we confirm the low-velocity anomaly in the NE area of the Parana Basin which has been interpreted by VanDecar et al. as a fossil conduct of the Tristan da Cunha Plume related to the Parana flood basalt eruptions during the opening of the South Atlantic.

Retrieval of kinetic rates in reactions with semi batch liquid phase using ill-posed inverse problem theory

A neural network procedure to solve inverse chemical kinetic problems is discussed in this work. Rate constants are calculated from the product concentration of an irreversible consecutive reaction: the hydrogenation of Citral molecule, a process with industrial interest. Simulated and experimental data are considered. Errors in the simulated data, up to 7% in the concentrations, were assumed to investigate the robustness of the inverse procedure. Also, the proposed method is compared with two common methods in nonlinear analysis; the Simplex and Levenberg-Marquardt approaches. In all situations investigated, the neural network approach was numerically stable and robust with respect to deviations in the initial conditions or experimental noises.

Inverse problems in neural field theory

We study inverse problems in neural field theory, i.e., the construction of synaptic weight kernels yielding a prescribed neural field dynamics. We address the issues of existence, uniqueness, and stability of solutions to the inverse problem for the Amari neural field equation as a special case, and prove that these problems are generally ill-posed. In order to construct solutions to the inverse problem, we first recast the Amari equation into a linear perceptron equation in an infinite-dimensional Banach or Hilbert space. In a second step, we construct sets of biorthogonal function systems allowing the approximation of synaptic weight kernels by a generalized Hebbian learning rule. Numerically, this construction is implemented by the Moore–Penrose pseudoinverse method. We demonstrate the instability of these solutions and use the Tikhonov regularization method for stabilization and to prevent numerical overfitting. We illustrate the stable construction of kernels by means of three instructive examples.

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (α-turbulence models) simulated at resolution 8192x8192. We consider α=1 (surface quasigeostrophic flow), α=2 (2D Euler flow) and α=3. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both α=1 and α=2. The active scalar field for α=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction −(7−α)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for α=1 and α=2, while the α=3 inverse cascade is much closer to Gaussian and non-intermittent. For α=3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling ℰ(k)∝k−2 (α=1) and ℰ(k)∝k−5/3 (α=2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (α=1 and α=2) and non-realizability (α=3) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for α=1 and α=2.

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.

Theory and application of inverse problems in groundwater: numerical, laboratory and field studies.

Aquifers are a vital water resource whose quality characteristics must be safeguarded or, if damaged, restored. The extent and complexity of aquifer contamination is related to characteristics of the porous medium, the influence of boundary conditions, and the biological, chemical and physical processes. After the nineties, the efforts of the scientists have been increased exponentially in order to find an efficient way for estimating the hydraulic parameters of the aquifers, and thus, recover the contaminant source position and its release history. To simplify and understand the influence of these various factors on aquifer phenomena, it is common for researchers to use numerical and controlled experiments. This work presents some of these methods, applying and comparing them on data collected during laboratory, field and numerical tests. The work is structured in four parts which present the results and the conclusions of the specific objectives.

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.