Adaptive matched field processing in an uncertain propagation environment

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution January 1992Adaptive array processing algorithms have achieved widespread use because they are very effective at rejecting unwanted signals (i.e., controlling sidelobe levels) and in general have very good resolution (i.e., have narrow mainlobes). However, many adaptive high-resolution array processing algorithms suffer a significant degradation in performance in the presence of environmental mismatch. This sensitivity to environmental mismatch is of particular concern in problems such as long-range acoustic array processing in the ocean where the array processor's knowledge of the propagation characteristics of the ocean is imperfect. An Adaptive Minmax Matched Field Processor has been developed which combines adaptive matched field processing and minmax approximation techniques to achieve the effective interference rejection characteristic of adaptive processors while limiting the sensitivity of the processor to environmental mismatch. The derivation of the algorithm is carried out within the framework of minmax signal processing. The optimal array weights are those which minimize the maximum conditional mean squared estimation error at the output of a linear weight-and-sum beamformer. The error is conditioned on the propagation characteristics of the environment and the maximum is evaluated over the range of environmental conditions in which the processor is expected to operate. The theorems developed using this framework characterize the solutions to the minmax array weight problem, and relate the optimal minmax array weights to the solution to a particular type of Wiener filtering problem. This relationship makes possible the development of an efficient algorithm for calculating the optimal minmax array weights and the associated estimate of the signal power emitted by a source at the array focal point. An important feature of this algorithm is that it is guarenteed to converge to an exact solution for the array weights and estimated signal power in a finite number of iterations. The Adaptive Minmax Matched Field Processor can also be interpreted as a two-stage Minimum Variance Distortionless Response (MVDR) Matched Field Processor. The first stage of this processor generates an estimate of the replica vector of the signal emitted by a source at the array focal point, and the second stage is a traditional MVDR Matched Field Processor implemented using the estimate of the signal replica vector. Computer simulations using several environmental models and types of environmental uncertainty have shown that the resolution and interference rejection capability of the Adaptive Minmax Matched Field Processor is close to that of a traditional MVDR Matched Field Processor which has perfect knowledge of the characteristics of the propagation environment and far exceeds that of the Bartlett Matched Field Processor. In addition, the simulations show that the Adaptive Minmax Matched Field Processor is able to maintain it's accuracy, resolution and interference rejection capability when it's knowledge of the environment is only approximate, and is therefore much less sensitive to environmental mismatch than is the traditional MVDR Matched Field Processor.The National Science Foundation, the General Electric Foundation, the Office of Naval Research, the Defense Advanced Research Projects Agency, and the Woods Hole Oceanographic Institution

van der Waals density functionals built upon the electron-gas tradition: Facing the challenge of competing interactions

The theoretical description of sparse matter attracts much interest, in particular for those ground-state properties that can be described by density functional theory (DFT). One proposed approach, the van der Waals density functional (vdW-DF) method, rests on strong physical foundations and offers simple yet accurate and robust functionals. A very recent functional within this method called vdW-DF-cx [K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412] stands out in its attempt to use an exchange energy derived from the same plasmon-based theory from which the nonlocal correlation energy was derived. Encouraged by its good performance for solids, layered materials, and aromatic molecules, we apply it to several systems that are characterized by competing interactions. These include the ferroelectric response in PbTiO$_3$, the adsorption of small molecules within metal-organic frameworks (MOFs), the graphite/diamond phase transition, and the adsorption of an aromatic-molecule on the Ag(111) surface. Our results indicate that vdW-DF-cx is overall well suited to tackle these challenging systems. In addition to being a competitive density functional for sparse matter, the vdW-DF-cx construction presents a more robust general purpose functional that could be applied to a range of materials problems with a variety of competing interactions

Tests of the random phase approximation for transition strengths

We investigate the reliability of transition strengths computed in the random-phase approximation (RPA), comparing with exact results from diagonalization in full $0\hbar\omega$ shell-model spaces. The RPA and shell-model results are in reasonable agreement for most transitions; however some very low-lying collective transitions, such as isoscalar quadrupole, are in serious disagreement. We suggest the failure lies with incomplete restoration of broken symmetries in the RPA. Furthermore we prove, analytically and numerically, that standard statements regarding the energy-weighted sum rule in the RPA do not hold if an exact symmetry is broken.Comment: 11 pages, 7 figures; Appendix added with new proof regarding violation of energy-weighted sum rul

Scalar ground-state observables in the random phase approximation

We calculate the ground-state expectation value of scalar observables in the matrix formulation of the random phase approximation (RPA). Our expression, derived using the quasiboson approximation, is a straightforward generalization of the RPA correlation energy. We test the reliability of our expression by comparing against full diagonalization in 0 h-bar omega shell-model spaces. In general the RPA values are an improvement over mean-field (Hartree-Fock) results, but are not always consistent with shell-model results. We also consider exact symmetries broken in the mean-field state and whether or not they are restored in RPA.Comment: 7 pages, 3 figure

An associative memory of Hodgkin-Huxley neuron networks with Willshaw-type synaptic couplings

An associative memory has been discussed of neural networks consisting of spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which memorize P patterns in their synaptic weights. In addition to excitatory synapses whose strengths are modified after the Willshaw-type learning rule with the 0/1 code for quiescent/active states, the network includes uniform inhibitory synapses which are introduced to reduce cross-talk noises. Our simulations of the HH neuron network for the noise-free state have shown to yield a fairly good performance with the storage capacity of $\alpha_c = P_{\rm max}/N \sim 0.4 - 2.4$ for the low neuron activity of $f \sim 0.04-0.10$. This storage capacity of our temporal-code network is comparable to that of the rate-code model with the Willshaw-type synapses. Our HH neuron network is realized not to be vulnerable to the distribution of time delays in couplings. The variability of interspace interval (ISI) of output spike trains in the process of retrieving stored patterns is also discussed.Comment: 15 pages, 3 figures, changed Titl

Through-skull fluorescence imaging of the brain in a new near-infrared window

To date, brain imaging has largely relied on X-ray computed tomography and magnetic resonance angiography with limited spatial resolution and long scanning times. Fluorescence-based brain imaging in the visible and traditional near-infrared regions (400–900 nm) is an alternative but currently requires craniotomy, cranial windows and skull thinning techniques, and the penetration depth is limited to 1–2 mm due to light scattering. Here, we report through-scalp and through-skull fluorescence imaging of mouse cerebral vasculature without craniotomy utilizing the intrinsic photoluminescence of single-walled carbon nanotubes in the 1.3–1.4 micrometre near-infrared window. Reduced photon scattering in this spectral region allows fluorescence imaging reaching a depth of >2 mm in mouse brain with sub-10 micrometre resolution. An imaging rate of ~5.3 frames/s allows for dynamic recording of blood perfusion in the cerebral vessels with sufficient temporal resolution, providing real-time assessment of blood flow anomaly in a mouse middle cerebral artery occlusion stroke model