Inverse

Most of the statistical procedures in meta-analysis are based on the estimation of average effect sizes from a set of primary studies. The optimal weight for averaging a set of independent effect sizes is the inverse variance of each effect size, but in practice these weights have to be estimated, being affected by sampling error. When assuming a random-effects model, there are two alternative procedures for averaging independent effect sizes: Hunter and Schmidt’s estimator, which consists of weighting by sample size as an approximation to the optimal weights; and Hedges and Vevea’s estimator, which consists of weighting by an estimation of the inverse variance of each effect size. In this article, the bias and mean squared error of the two estimators were assessed via Monte Carlo simulation of meta-analyses with the standardized mean difference as the effect-size index. Hedges and Vevea’s estimator, although slightly biased, achieved the best performance in terms of the mean square...

This article examines the divergent voice systems of a selection of Malay/Indonesian varieties. I will show that the voice systems of the different Malay/Indonesian varieties largely (but not completely) reflect the voice systems in the languages in which that variety is spoken. In this way Malay/Indonesian, in its different varieties, can be seen as a mirror on the development of voice systems in Austronesian languages. While many languages show a syntactically privileged 'subject', in many western Austronesian languages (including Malay/Indonesian) some subject properties accrue according to argument structure position, and some other of these properties accrue to the argument that is morphologically marked as 'special' in the clause. At the same time, those Austronesian languages belonging to the (eastern) Oceanic branch lack voice alternations, or else show a simple active/passive dichotomy. The change in the presence and nature voice systems follows the migration path of the Austronesians, moving the highly marked diathesis to a more 'normal' diathesis. The voice systems of the different Malay varieties vary greatly, encompassing almost all the variation that is found across the Austronesian languages. I propose a model in terms of the speakers' access to universal grammar in determining the grammar of the new variety of Malay/Indonesian.

Effective flocculation and dewatering of mineral processing streams containing colloidal clays has become increasingly urgent. Release of water from slurries in tailings streams and dam beds for recycle water consumption, is usually slow and incomplete. To achieve fast settling and minimization of retained water, individual particles need to be bound, in the initial stages of thickening, into large, high-density aggregates, which may sediment more rapidly with lower intra-aggregate water content. Quantitative cryo-SEM image analysis shows that the structure of aggregates formed before flocculant addition has a determinative effect on these outcomes. Without flocculant addition, 3 stages occur in the mechanism of primary dewatering of kaolinite at pH 8: initially, the dispersed structures already show edgeedge (EE) and edge-face (EF) inter-particle associations but these are open, loose and easily disrupted; in the hindered settling region, aggregates are in adherent, chain-like structures of EE and stairstep face-face (FF) associations; this network structure slowly partially rearranges from EE chains to more compact face-face (FF) contacts densifying the aggregates with increased settling rates. During settling, the sponge-like network structure with EE and FF string-like aggregates, limits dewatering because the steric effects in the resulting partially-gelled aggregate structures are dominant. With flocculant addition, the internal structure and networking of the pre-aggregates is largely preserved but they are rapidly and effectively bound together by the aggregate-bridging action of the flocculant. The effects of initial pH and Ca ion addition on these structures are also analyzed. Statistical analysis from cryo-SEM imaging shows that there is an inverse correlation of intra-aggregate porosity with Darcian inter-aggregate permeability whereas there is a strong positive correlation of Darcian permeability with settling and primary dewatering rate as a function of pH in suspension. Graphs of partial void contributions also suggest that it is not total porosity that dominates permeability in these systems but the abundance of larger intra-aggregate voids.

The so-called passive' participle in NENA dialects is said to function as both passive and active. This apory is resolved once it is shown that it is neither one or the other, namely that the opposition is not diathetic to begin with but aspectual. Tha so-called passive participle is perfect(ive) and the so-called active one is imperfect(ive). Transitivity, or rather valency, is narrowly linked to that, and in this language so are ergativity and case.

The inverses of r-banded matrices, for r = 1, 2, 3 have been thoroughly investigated as one can see from the references we provide. Let B r,n (1 ≤ r ≤ n) be an n × n matrix of entries {a i j }, −r ≤ i ≤ r, 1 ≤ j ≤ r, with the remaining un-indexed entries all zeros. In this paper, generalizing a method of Mallik (1999) [5], we give the LU factorization and the inverse of the matrix B r,n (if it exists). Our results are valid for an arbitrary square matrix (taking r = n), and so, we will give a new approach for computing the inverse of an invertible square matrix. Our method is based on Hessenberg submatrices associated to B r,n .

Chalcogenide opal and inverse opal photonic crystals were successfully fabricated by low-cost and lowtemperature solution-based process, which is well developed in polymer films processing. Highly ordered silica colloidal crystal films were successfully infilled with nano-colloidal solution of the high refractive index As 30 S 70 chalcogenide glass by using spin-coating method. The silica/As-S opal film was etched in HF acid to dissolve the silica opal template and fabricate the inverse opal As-S photonic crystal. Both, the infilled silica/As-S opal film (Dn $ 0.84 near k = 770 nm) and the inverse opal As-S photonic structure (Dn $ 1.26 near k = 660 nm) had significantly enhanced reflectivity values and wider photonic bandgaps in comparison with the silica opal film template (Dn $ 0.434 near k = 600 nm). The key aspects of opal film preparation by spin-coating of nano-colloidal chalcogenide glass solution are discussed. The solution fabricated ''inorganic polymer" opal and the inverse opal structures exceed photonic properties of silica or any organic polymer opal film. The fabricated photonic structures are proposed for designing novel flexible colloidal crystal laser devices, photonic waveguides and chemical sensors.

We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium.

The surface properties of chemical vapor deposition (CVD)-grown, multiwalled carbon nanotubes (CNTs) have been studied using inverse gas chromatography (IGC). By adapting known IGC methodologies to these challenging materials, the surface character of a broad range of CNT materials can be reliably compared and quantified in terms of dispersive and specific surface energies, electron acceptor and donor numbers, and adsorption capacities. The effect of CNT surface modification by high temperature annealing, thermal oxidation, and grafting of methyl methacrylate was explored. The IGC surface characterization of these materials was consistent with results from other surface-sensitive analytical techniques, including X-ray photoelectron spectroscopy (XPS), titration, and electron microscopy, confirming the validity and sensitivity of our approaches. The same IGC methodologies were successfully applied to characterize three as-received CNT materials which differed significantly in their specific surface areas and functional surface group concentrations.

In this study, without using the assumption a-1 > 0, it is shown that E is lattice - and algebra - isometric isomorphic to the reals R whenever E is a Banach lattice f-algebra with unit e, |e| = 1, in which for every a > 0 the inverse a-1 exists. Subsequently, an alternative proof to a result of Huijsmans is given for Banach lattice algebras.

In this paper we study the 0-1 inverse maximum stable set problem, denoted by IS {0,1} . Given a graph and a stable set (not necessarily maximum), it is to delete a minimum number of vertices to make the given stable set maximum in the new graph. We also consider IS {0,1} against a specific algorithm such as Greedy and 2opt, which is denoted by IS {0,1},greedy and IS {0,1},2opt , respectively. We prove the NP-hardness of these problems and an approximation ratio of 2 − Θ( 1 √ log∆ ) for IS {0,1},2opt . In addition, we restrict IS {0,1} to some classes of perfect graphs such as comparability and chordal graphs, and we study its tractability. Finally, we compare the hardness of IS {0,1} and IS {0,1},2opt for some other classes of graphs.

This paper describes the application of the adjoint method to the history matching problem in reservoir engineering. The history matching problem consists in adjusting a set of parameters, in this case the permeability distribution, in order to match the data obtained with the simulator to the actual production data in the reservoir. Several numerical experiments are presented which show that

We develop the Inverse Scattering Transform (IST) method for the Degasperis-Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method are presented.

In this paper, we introduce the one-two descriptor. The one-two descriptors is the sum of the vertex contributions such that each pendant vertex contributes 1, each vertex of degree two adjacent to pendant vertex contributes 2, and each vertex of degree higher than two also contributes 2. We test this descriptor on the benchmark data set of the octane isomers proposed by the International Academy of Mathematical Chemistry. We show that this descriptor is a good predictor of the heat capacity at P constant (CP) and of the total surface area (TSA). Linear model predictions for both these properties are better then predictions of any of the benchmark descriptors proposed by International Academy of Mathematical Chemistry. Linear model predictions of TSA are also better then predictions of any of Adriatic descriptors, while linear model predictions of CP are not as good as predictions by Adriatic descriptor called inverse sum lordeg index. We also analyze the mathematical properties of this descriptor and we find tight upper and lower bounds in the families of the trees with n vertices and the chemical trees with n vertices.

Systems biology is a new discipline built upon the premise that an understanding of how cells and organisms carry out their functions cannot be gained by looking at cellular components in isolation. Instead, consideration of the interplay between the parts of systems is indispensable for analyzing, modeling, and predicting systems' behavior. Studying biological processes under this premise, systems biology combines experimental techniques and computational methods in order to construct predictive models. Both in building and utilizing models of biological systems, inverse problems arise at several occasions, for example, (i) when experimental time series and steady state data are used to construct biochemical reaction networks, (ii) when model parameters are identified that capture underlying mechanisms or (iii) when desired qualitative behavior such as bistability or limit cycle oscillations is engineered by proper choices of parameter combinations. In this paper we review principles of the modeling process in systems biology and illustrate the ill-posedness and regularization of parameter identification problems in that context. Furthermore, we discuss the methodology of qualitative inverse problems and demonstrate how sparsity enforcing regularization allows the determination of key reaction mechanisms underlying the qualitative behavior.

We tested the hypothesis of synchronous interannual changes in forage fish dynamics around the North Pacific Rim. To do this, we sampled forage fish communities using a seabird predator, the rhinoceros auklet (Cerorhinca monocerata), at six coastal study sites from Japan to California. We investigated whether take of forage fishes was related to local marine conditions as indexed by sea surface temperature (SST). SST was concordant across sites in the eastern Pacific, but inversely correlated between east and west. Forage fish communities consisted of anchovy (Engraulis spp.), sandlance (Ammodytes spp.), capelin (Mallotus spp.), and juvenile rockfish (Sebastes spp.), among others, and take of forage fish varied in response to interannual and possibly lower-frequency oceanographic variability. Take of primary forage species were significantly related to changes in SST only at the eastern sites. We found synchrony in interannual variation of primary forage fishes across several regions in the eastern Pacific, but no significant east-west correlations. Specifically in the Japan Sea, factors other than local SST or interannual variability may more strongly influence forage fishes. Predator diet sampling offers a fishery-independent, large-scale perspective on forage fish dynamics that may be difficult to obtain using conventional means of study.

The distorted Born iterative method (DBI) is used to solve the inverse scattering problem in the ultrasound tomography with the objective of determining a scattering function that is related to the acoustical properties of the region of interest (ROI) from the disturbed waves measured by transducers outside the ROI. Since the method is iterative, we use Born approximation for the first estimate of the scattering function. The main problem with the DBI is that the linear system of the inverse scattering equations is ill-posed. To deal with that, we use two different algorithms and compare the relative errors and execution times. The first one is Truncated Total Least Squares (TTLS). The second one is Regularized Total Least Squares method (RTLS-Newton) where the parameters for regularization were found by solving a nonlinear system with Newton method. We simulated the data for the DBI method in a way that leads to the overdetermined system. The advantage of RTLS-Newton is that the computation of singular value decomposition for a matrix is avoided, so it is faster than TTLS, but it still solves the similar minimization problem. For the exact scattering function we used Modified Shepp-Logan phantom. For finding the Born approximation, RTLS-Newton is 10 times faster than TTLS. In addition, the relative error in L2-norm is smaller using RTLS-Newton than TTLS after 10 iterations of the DBI method and it takes less time.

An ever present, common sense idea in language modelling research is that, for a word to be a valid phrase, it should comply with multiple constraints at once. A new language definition model is studied, based on agreement or consensus between similar strings. Considering a regular set of strings over a bipartite alphabet made by pairs of unmarked/marked symbols, a match relation is introduced, in order to specify when such strings agree. Then a regular set over the bipartite alphabet can be interpreted as specifying another language over the unmarked alphabet, called the consensual language. A word is in the consensual language if a set of corresponding matching strings is in the original language. The family thus defined includes the regular languages and also interesting non-semilinear ones. The word problem can be solved in NLOGSPACE, hence in P time. The emptiness problem is undecidable. Closure properties are proved for intersection with regular sets and inverse alphabetical homomorphism. Several conditions for a consensual definition to yield a regular language are presented, and it is shown that the size of a consensual specification of regular languages can be in a logarithmic ratio with respect to a DFA. The family is incomparable with context-free and tree-adjoining grammar families.

Abstract. We prove that we can uniquely recover the coefficient of a one dimensional heat equation from a finite set of measurements and provide a constructive procedure for its recovery. The algorithm is based on the well known Gelfand-Levitan-Gasymov inverse spectral theory of Sturm-...

Inverse gas chromatography (IGC) is presented as a representative tool for the investigation of nanomaterials: Aerosil200V and two iron oxides (nanohematite and nanogoethite). IGC was used for characterization of the surface properties of materials. Parameters describing their surface properties are calculated from the retention data of test solutes injected into a column filled with the solid of interest. It is possible to determine the surface activity and the Hamaker constants of different nanomaterials.

Today many different natural materials are being effectively used in the acoustics and noise control domain. In this study, the acoustical characterization of three different types of natural jute felt material is performed by an experimental method and by using the Dunn and Davern model, along with an inverse characterization method. There are many empirical models available in the literature which describes the acoustical behavior of specific material accurately, as they are specially developed for that material. In this study, the possibility of using only the air flow resistivity based Delany–Bazley model and the Dunn–Davern model for acoustical performance prediction of jute material is tested. However, these two models do not show good matching with the experimental data throughout the frequency range of interest. Particularly in the low frequency region, the level of mismatch between experimental and model data is high. Therefore the inverse prediction of the coefficients [Fo...

We investigated how thermal stress may alter the locomotor phenotype of barramundi, Lates calcarifer , from genetically distinct northern (low latitude) and southern (high latitude) populations in tropical Australia. Following early growth and development under native (25 °C and 30 °C) and non-native (20 °C and 35 °C) temperatures, we observed distinct differences in the swimming performance of northern and southern individuals that were consistent with expectations based on local thermal adaptation. Southern population fish exhibited significantly faster swimming speeds (32.10 ± 0.33 cm·s–1, mass-adjusted mean ± 95% confidence limit) than their northern counterparts (28.58 ± 0.64 cm·s–1) under cold-stress (20 °C) conditions. Conversely, northern population fish performed significantly better (51.63 ± 2.1 cm·s–1) than their southern counterparts (44.18 ± 3.11 cm·s–1) under heat-stress (35 °C) conditions. We conclude that L. calcarifer display locomotor phenotypes thermally adapted t...

We present in this paper a novel statistical based focalized reconstruction method for the underdetermined EEG (electroencephalogram) inverse problem. The algorithm is based on the representation of non-Gaussian distributions as an Infinite Mixture of Gaussians (IMG) and relies on an iterative procedure consisting out of alternated variance estimation/ linear inversion operations. By taking into account noise statistics, it performs implicit spurious data rejection and produces robust focalized solutions allowing for straightforward discrimination of active/non-active brain regions. We apply the proposed reconstruction procedure to average evoked potentials EEG data and compare the reconstruction results with the corresponding known physiological responses.

In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may lead to detection of false positive QTL. To improve the robustness of Bayesian QTL mapping methods, the normal distribution for residuals is replaced with a skewed Student-t distribution. The latter distribution is able to account for both heavy tails and skewness, and both components are each controlled by a single parameter. The Bayesian QTL mapping method using a skewed Student-t distribution is evaluated with simulated data sets under five different scenarios of residual error distributions and QTL effects.

We consider two complementary operations: Hairpin completion introduced in [D. Cheptea, C. Martin-Vide, V. Mitrana, A new operation on words suggested by DNA biochemistry: Hairpin completion, in: Proc. Transgressive Computing, 2006, pp. 216-228] with motivations coming from DNA biochemistry and hairpin reduction as the inverse operation of the hairpin completion. Both operations are viewed here as formal operations on words and languages. We settle the closure properties of the classes of regular and linear context-free languages under hairpin completion in comparison with hairpin reduction. While the class of linear context-free languages is exactly the weak-code image of the class of the hairpin completion of regular languages, rather surprisingly, the weak-code image of the class of the hairpin completion of linear context-free languages is a class of mildly context-sensitive languages. The closure properties with respect to the hairpin reduction of some time and space complexity classes are also studied. We show that the factors found in the general cases are not necessary for regular and context-free languages. This part of the paper completes the results given in the earlier paper, where a similar investigation was made for hairpin completion. Finally, we briefly discuss the iterated variants of these operations.

Let T be an aperiodic and repetitive tiling of Rd with finite local complexity. Let Ω be its tiling space with canonical transversal Ξ. The tiling equivalence relation RΞ is the set of pairs of tilings in Ξ which are translates of each others, with a certain (étale) topology. In this paper RΞ is reconstructed as a generalized “tail equivalence ” on a Bratteli dia-gram, with its standard AF-relation as a subequivalence relation. Using a generalization of the Anderson–Putnam complex (Bellissard et al. in Commun. Math. Phys. 261:1–41, 2006) Ω is identified with the inverse limit of a sequence of finite CW-complexes. A Bratteli diagram B is built from this sequence, and its set of infinite paths ∂B is homeomorphic to Ξ. The diagram B is endowed with a horizontal structure: additional edges that encode the adjacencies of patches in T. This allows to define an étale equivalence relation RB on ∂B which is homeomorphic to RΞ, and contains the AF-relation of “tail equivalence”.

Effective flocculation and dewatering of mineral processing streams containing colloidal clays has become increasingly urgent. Release of water from slurries in tailings streams and dam beds for recycle water consumption, is usually slow and incomplete. To achieve fast settling and minimization of retained water, individual particles need to be bound, in the initial stages of thickening, into large, high-density aggregates, which may sediment more rapidly with lower intra-aggregate water content. Quantitative cryo-SEM image analysis shows that the structure of aggregates formed before flocculant addition has a determinative effect on these outcomes. Without flocculant addition, 3 stages occur in the mechanism of primary dewatering of kaolinite at pH 8: initially, the dispersed structures already show edgeedge (EE) and edge-face (EF) inter-particle associations but these are open, loose and easily disrupted; in the hindered settling region, aggregates are in adherent, chain-like structures of EE and stairstep face-face (FF) associations; this network structure slowly partially rearranges from EE chains to more compact face-face (FF) contacts densifying the aggregates with increased settling rates. During settling, the sponge-like network structure with EE and FF string-like aggregates, limits dewatering because the steric effects in the resulting partially-gelled aggregate structures are dominant. With flocculant addition, the internal structure and networking of the pre-aggregates is largely preserved but they are rapidly and effectively bound together by the aggregate-bridging action of the flocculant. The effects of initial pH and Ca ion addition on these structures are also analyzed. Statistical analysis from cryo-SEM imaging shows that there is an inverse correlation of intra-aggregate porosity with Darcian inter-aggregate permeability whereas there is a strong positive correlation of Darcian permeability with settling and primary dewatering rate as a function of pH in suspension. Graphs of partial void contributions also suggest that it is not total porosity that dominates permeability in these systems but the abundance of larger intra-aggregate voids.

We consider a simple (but fully three-dimensional) mathematical model for the electromagnetic exploration of buried, perfect electrically conducting objects within the soil underground. Moving an electric device parallel to the ground at constant height in order to generate a magnetic field, we measure the induced magnetic field within the device, and factor the underlying mathematics into a product of three operations which correspond to the primary excitation, some kind of reflection on the surface of the buried object(s) and the corresponding secondary excitation, respectively. Using this factorization we are able to give a justification of the so-called sampling method from inverse scattering theory for this particular setup.

A schema mapping is a specification that describes how data from a source schema is to be mapped to a target schema. Once the data has been transferred from the source to the target, a natural question is whether one can undo the process and recover the initial data, or at least part of it. In fact, it would be desirable to find a reverse schema mapping from target to source that specifies how to bring the exchanged data back.

Male bowerbirds collect and decorate their bowers with coloured objects that influence female choice. A recent version of the sensory drive hypothesis claims that female food colour preferences have driven the evolution of female preferences for the colour of male display traits. This hypothesis predicts a positive correlation between male display and food colour preferences. A positive correlation between food and decoration preferences could also arise because of sensory biases built into bowerbirds or the environment. Here we test hypotheses that (1) male and female satin bowerbirds show well-defined food colour preferences, (2) these preferences correlate with independently assessed preferences for bower decorations, and, in a cross-species comparison, (3) food items were used as the first bower decorations. We found that male and female satin bowerbirds, Ptilonorhynchus violaceus, preferentially use long wavelength and were colours as food items. Male decoration preferences were biased towards colours of short wavelength and were negatively correlated with food colour preferences. Our reconstruction of ancestral character states is most consistent with the hypothesis that the original bower decorations were inedible objects and were thus unlikely to have been dual-use traits that also functioned as food items. Our results do not support the hypothesis that food colour preferences have driven the evolution of bower decoration colour preferences nor that sensory drive has caused similar food and decoration preferences, but instead suggest that different factors have shaped female preferences for male display and food colour preferences in bowerbirds.

With the help of some techniques based upon certain inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Srivastava's hypergeometric functions H A , H B and H C in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By means of these operator identities, as many as 15 decomposition formulas are then found, which express the aforementioned triple hypergeometric functions in terms of such simpler functions as the products of the Gauss and Appell hypergeometric functions. Other closely-related results are also considered briefly.

The categorization of evidence through an "inverse inference" model is a preliminary attempt to organize the manner in which the ordinary language user perceives the use of evidence. While discussions on the nature of evidence have an important place in the realm of the theoretician and methodologist, this model attempts to explain how naive observers interpret and make sense of their world. The model begins with the assumption that individuals interpret events within a relatively stable frame of references. Ordinary language users treat as evidence those interpretations of phenomena which allow them to create meaningful classifications or apply them. The inferential process of connecting evidence with the interpretation of phenomena requires acceptance of several assumptions: evidence is inferred; evidence requiring less inference is preferred to evidence which requires greater inference; the frame of reference through which evidence is interpreted is subjective; and the frame of reference in relatively stable, even though it is subject to change. Three levels of evidence (in order of least inference required to most required) emerge for categorizing evidence types through the mndel: (1) evidence only requiring a perceptual inference; (2) evidence requiring both a perceptual inference and at least one level of logical inference by the observer; and (3) evidence requiring multiple levels of logical inference without a direct perceptual inference by the observer. Future elaboration of the model will explain the heuristic rules employed. (Contains 16 references.) (RS)

This paper presents a computationally efficient source estimation algorithm that localizes cortical oscillations and their phase relationships. The proposed method employs wavelet-transformed magnetoencephalography (MEG) data and uses anatomical MRI to constrain the current locations to the cortical mantle. In addition, the locations of the sources can be further confined with the help of functional MRI (fMRI) data. As a result, we obtain spatiotemporal maps of spectral power and phase relationships. As an example, we show how the phase locking value (PLV), that is, the trial-by-trial phase relationship between the stimulus and response, can be imaged on the cortex. We apply the method to spontaneous, evoked, and driven cortical oscillations measured with MEG. We test the method of combining MEG, structural MRI, and fMRI using simulated cortical oscillations along Heschl's gyrus (HG). We also analyze sustained auditory gammaband neuromagnetic fields from MEG and fMRI measurements. Our results show that combining the MEG recording with fMRI improves source localization for the non-noise-normalized wavelet power. In contrast, noise-normalized spectral power or PLV localization may not benefit from the fMRI constraint. We show that if the thresholds are not properly chosen, noise-normalized spectral power or PLV estimates may contain false (phantom) sources, independent of the inclusion of the fMRI prior information. The proposed algorithm can be used for evoked MEG/EEG and block-designed or event-related fMRI paradigms, or for spontaneous MEG data sets. Spectral spatiotemporal imaging of cortical oscillations and interactions in the human brain can provide further understanding of large-scale neural activity and communication between different brain regions.

Magnetoencephalography (MEG) can be used to reconstruct neuronal activity with high spatial and temporal resolution. However, this reconstruction problem is ill-posed, and requires the use of prior constraints in order to produce a unique solution. At present there are a multitude of inversion algorithms, each employing different assumptions, but one major problem when comparing the accuracy of these different approaches is that often the true underlying electrical state of the brain is unknown. In this study, we explore one paradigm, retinotopic mapping in the primary visual cortex (V1), for which the ground truth is known to a reasonable degree of accuracy, enabling the comparison of MEG source reconstructions with the true electrical state of the brain. Specifically, we attempted to localize, using a beanforming method, the induced responses in the visual cortex generated by a high contrast, retinotopically varying stimulus. Although well described in primate studies, it has been an open question whether the induced gamma power in humans due to high contrast gratings derives from V1 rather than the prestriate cortex (V2). We show that the beanformer source estimate in the gamma and theta bands does vary in a manner consistent with the known retinotopy of V1. However, these peak locations, although retinotopically organized, did not accurately localize to the cortical surface. We considered possible causes for this discrepancy and suggest that improved MEG/magnetic resonance imaging co-registration and the use of more accurate source models that take into account the spatial extent and shape of the active cortex may, in future, improve the accuracy of the source reconstructions.

Systems biology is a new discipline built upon the premise that an understanding of how cells and organisms carry out their functions cannot be gained by looking at cellular components in isolation. Instead, consideration of the interplay between the parts of systems is indispensable for analyzing, modeling, and predicting systems' behavior. Studying biological processes under this premise, systems biology combines experimental techniques and computational methods in order to construct predictive models. Both in building and utilizing models of biological systems, inverse problems arise at several occasions, for example, (i) when experimental time series and steady state data are used to construct biochemical reaction networks, (ii) when model parameters are identified that capture underlying mechanisms or (iii) when desired qualitative behavior such as bistability or limit cycle oscillations is engineered by proper choices of parameter combinations. In this paper we review principles of the modeling process in systems biology and illustrate the ill-posedness and regularization of parameter identification problems in that context. Furthermore, we discuss the methodology of qualitative inverse problems and demonstrate how sparsity enforcing regularization allows the determination of key reaction mechanisms underlying the qualitative behavior.

ABSTRACT In the present work, the application of reversed-flow inverse gas chromatography (RF-IGC) to adsorption studies related to heterogeneous catalytic processes on noble metal supported catalysts is reviewed. RF-IGC methodologies are technically simple and they are combined with suitable mathematical treatments which give the possibility for studying the kinetics of catalyzed surface reactions, as well as the topography and the nature of the active sites of solid catalysts. Adsorption parameters, such as rate constants, adsorption energies, adsorption entropies, local isotherms, surface diffusion coefficients, lateral interaction energies and energy distribution functions, are simultaneously determined by RF-IGC. The potential of the novel methodologies has been evaluated by utilising as model systems CO adsorption/oxidation over well-studied Pt–Rh/SiO2 and nanosized-Au/γ-Al2O3 catalysts. The main findings are presented and future goals are also discussed.

The present work is concerned with the extension of the factorization method to the inverse elastic scattering problem by penetrable isotropic bodies embedded in an isotropic host environment for time-harmonic plane wave incidence. Although the former method has been successfully employed for the shape reconstruction problem in the field of elastodynamic scattering by rigid bodies or cavities, no corresponding results have been recorded, so far, for the very interesting (both from a theoretical and a practical point of view) case of isotropic elastic inclusions. This paper aims at closing this gap by developing the theoretical framework which is necessary for the application of the factorization method to the inverse transmission problem in elastodynamics. As in the previous works referring to the particular reconstruction method, the main outcome is the construction of a binary criterion which determines whether a given point is inside or outside the scattering obstacle by using only the spectral data of the far-field operator.