Semivariogram methods for modeling Whittle-Mat\'ern priors in Bayesian inverse problems

We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance operators defined by the Mat\'ern covariance function and Gaussian processes with precision (inverse-covariance) operators defined by the Green's functions of a class of elliptic stochastic partial differential equations (SPDEs). We present a detailed mathematical description of this connection. We will show that there is an equivalence between these two Gaussian processes when the domain is infinite -- for us, $\mathbb{R}^2$ -- which breaks down when the domain is finite due to the effect of boundary conditions on Green's functions of PDEs. We show how this connection can be re-established using extended domains. We then introduce the semivariogram method for estimating the Mat\'ern covariance parameters, which specify the Gaussian prior needed for stabilizing the inverse problem. Results are extended from the isotropic case to the anisotropic case where the correlation length in one direction is larger than another. Finally, we consider the situation where the correlation length is spatially dependent rather than constant. We implement each method in two-dimensional image inpainting test cases to show that it works on practical examples

Opportunistic Collaborative Beamforming with One-Bit Feedback

An energy-efficient opportunistic collaborative beamformer with one-bit feedback is proposed for ad hoc sensor networks over Rayleigh fading channels. In contrast to conventional collaborative beamforming schemes in which each source node uses channel state information to correct its local carrier offset and channel phase, the proposed beamforming scheme opportunistically selects a subset of source nodes whose received signals combine in a quasi-coherent manner at the intended receiver. No local phase-precompensation is performed by the nodes in the opportunistic collaborative beamformer. As a result, each node requires only one-bit of feedback from the destination in order to determine if it should or shouldn't participate in the collaborative beamformer. Theoretical analysis shows that the received signal power obtained with the proposed beamforming scheme scales linearly with the number of available source nodes. Since the the optimal node selection rule requires an exhaustive search over all possible subsets of source nodes, two low-complexity selection algorithms are developed. Simulation results confirm the effectiveness of opportunistic collaborative beamforming with the low-complexity selection algorithms.Comment: Proceedings of the Ninth IEEE Workshop on Signal Processing Advances in Wireless Communications, Recife, Brazil, July 6-9, 200

Geoid undulations and gravity anomalies over the Aral Sea, the Black Sea and the Caspian Sea from a combined GEOS-3/SEASAT/GEOSAT altimeter data set

Satellite-based altimetric data taken by GOES-3, SEASAT, and GEOSAT over the Aral Sea, the Black Sea, and the Caspian Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25x0.25 deg. grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180x180 geopotential model is used as the reference surface for the collocation procedure. The result of geoid to gravity transformation is, however, sensitive to the information content of the reference geopotential model used. For example, considerable detailed surface gravity data were incorporated into the reference model over the Black Sea, resulting in a reference model with significant information content at short wavelengths. Thus, estimation of short wavelength gravity anomalies from gridded geoid heights is generally reliable over regions such as the Black Sea, using the conventional collocation technique with local empirical covariance functions. Over regions such as the Caspian Sea, where detailed surface data are generally not incorporated into the reference model, unconventional techniques are needed to obtain reliable gravity anomalies. Based on the predicted gravity anomalies over these inland seas, speculative tectonic structures are identified and geophysical processes are inferred

Analysis of altimetry over the Aral Sea

Satellite based altimetric data taken by GEOS-3, SEASAT, and GEOSAT over the Aral Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25 by 0.25 degree grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180 by 180 geopotential model is taken as the empirical model. The collocation procedure is performed with a set of local residual empirical covariance functions. For comparison, Rapp's global covariance functions and Jordan's self-consistent theoretical covariance functions based on Jordan's formulation and on locally derived parameters are also used to grid geoid undulations and to predict gravity anomalies. The sensitivity of the collocation results to the choice of covariance functions is discussed

Characterization of the Active Site and Insight into the Binding Mode of the Anti-angiogenesis Agent Fumagillin to the Manganese(II)-Loaded Methionyl Aminopeptidase from \u3cem\u3eEscherichia coli\u3c/em\u3e

EPR spectra were recorded for methionine aminopeptidase from Escherichia coli (EcMetAP-I) samples (~2.5 mM) to which one and two equivalents of Mn(II) were added (the latter is referred to as [MnMn(EcMetAP-I)]). The spectra for each sample were indistinguishable except that the spectrum of [MnMn(EcMetAP-I)] was twice as intense. The EPR spectrum of [MnMn(EcMetAP-I)] exhibited the characteristic six-line g≈2 EPR signal of mononuclear Mn(II) with A av(55Mn)=9.3 mT (93 G) and exhibited Curie-law temperature dependence. This signal is typical of Mn(II) in a ligand sphere comprising oxygen and/or nitrogen atoms. Other features in the spectrum were observed only as the temperature was raised from that of liquid helium. The temperature dependences of these features are consistent with their assignment to excited state transitions in the S=1, 2 ... 5 non-Kramer’s doublets, due to two antiferromagnetically coupled Mn(II) ions with an S=0 ground state. This assignment is supported by the observation of a characteristic 4.5 mT hyperfine pattern, and by the presence of signals in the parallel mode consistent with a non-Kramers’ spin ladder. Upon the addition of the anti-angiogenesis agent fumagillin to [MnMn(EcMetAP-I)], very small changes were observed in the EPR spectrum. MALDI-TOF mass spectrometry indicated that fumagillin was, however, covalently coordinated to EcMetAP-I. Therefore, the inhibitory action of this anti-angiogenesis agent on EcMetAP-I appears to involve covalent binding to a polypeptide component at or near the active site rather than direct binding to the metal ions