Minimum Neighborhood Research Articles

Experimental Results for and Theoretical Analysis of a Self-Organizing Global Coordinate System for Ad Hoc Sensor Networks

We present an algorithm for achieving robust and reasonably accurate localization in a randomly placed wireless sensor network, without the use of global control, globally-accessible beacon signals, or accurate estimates of inter-sensor distances. We present theoretical analysis, simulation results and recent experimental results. The theoretical analysis shows that there is a critical minimum average neighborhood size of 15 for good accuracy, and simulation results show that position accuracy to within 20% of the local radio range can be achieved, even with upto 10% variation in the radio ranges.

The photometric behaviour of SU Dra, 1955–2000

A multicolour photometric data basis is compiled for SU Dra from 356 Johnson UBV and 228 UBV(RI)C observations reported in this paper, in addition to 483 BV , 289 UBV ,a nd 85UBVRI ob- servations found in the literature. Mean period, period change (4:40:14) 10 10 day/day, and phase noise are derived from the V light curves by a variational procedure minimizing the length of the folded light curve (string length minimization, SLM). From variation of string length in the neighbourhood of minimum, observational error of photometry, observed amplitude, number of observations formulae are derived for the error of period and phase noise by statistical and analytical considerations. Secondary periodic variations are excluded to a few mmag level, indication of amplitude variation (Blazhko-eect) has not been found, however, systematic segrega- tion of light curve segments is reported from dierent epochs in the descending branch before the brightness rise. Mean light and colour curves are derived from photometry and they are compared with those from integration of spectrophotometric observations. The period change is interpreted in terms of mixing events in the stellar interior.

On quasifactorability in graphs

Given a graph G and two functions f and g:V(G)→ Z + with f(v)⩾g(v) for each v∈V(G), a (g,f)-quasifactor in G is a subgraph Q of G such that for each vertex v in V(Q), g(v)⩽d Q(v)⩽f(v) ; in the particular case when ∀v∈V(Q), f(v)=g(v)=k∈ N , we say that Q is a k-quasifactor. A subset S of vertices of G is said (g,f)-quasifactorable in G if there exists some (g,f)-quasifactor that contains all the vertices of S. In this paper, we give several results on the 2-quasifactorability of a vertex subset which are related to minimum degree, degree sum, independence number and neighborhood union conditions.

Phase Structures in the Micromaser Photon Statistics

Abstract In the photon number distribution p(θ,k) of the micromaser, distinct structures are formed by the ridges connecting the peaks in the θ-k space. We refer to these structures as phases. By a simple condition we can distinguish between "semiclassical" and "quantum" regimes of operation near and far above threshold, respectively. In the semiclassical regime, the equations of state of the phases θ= θ(k) are monotonous and coincide with the steady state solutions of the semiclassical theory. They reflect typical features of the micromaser dynamics. The transition jumps, e. g., between the phases decrease with increasing pumping parameter θ, signifying the onset of the Jaynes-Cummings collapse. On increasing 9 further, the phases first disintegrate and then restructure into new kinds of phases in the quantum regime. The equations of state are no longer monotonous. Large single peaks, the quantum island states (QIS), develop in the neighborhoods of minima. The system undergoes oscillations between two kinds of quantum island states, QIS- and QIS+ , as a function of θ. The disintegration and transformation of phases recur periodically as θ is varied, and the phases in the semiclassical region are followed by consecutive phase structures in the quantum regime. The subsequent collapses and revivals of phases are directly connected to the Jaynes-Cummings collapse and revival. The observation of these phase structures and the accompanying QIS is experimentally feasible.

Automatic 1-D waveform inversion of marine seismic refraction data

SUMMARY Full waveform synthetic seismograms are now used as standard in the interpretation of marine refraction data, but only with a laborious trial-and-error fitting procedure. We show how the matching of observed waveforms with WKBJ synthetic seismograms can be efficiently and automatically performed for 1-D earth models. Automation of the inversion is difficult because of the multi-modal, irregular form of the misfit of data and synthetics. A sequence of three steps is required for a complete inversion: location of the deepest valley of the misfit function, descent to the global minimum, and description of the neighbourhood of the minimum for error analysis. The first step is accomplished with a Monte Carlo search through a very large model space defined by poor prior knowledge of velocities and gradients of the solution. Weak traveltime constraints are used to eliminate poorly fitting models from waveform calculations. A comparison of the traveltime and waveform misfits of the Monte Carlo models clearly illustrates that waveforms are providing more information than traveltimes alone. Bayesian statistics are used to construct marginal probability distributions and the covariance matrix, which give a rough preliminary error analysis. In the second step, damped least-squares linearized inversion makes small adjustments to the best-fitting Monte Carlo model as it descends to the global minimum. Finally the immediate neighbourhood of the global minimum is explored with constrained least-squares inversion. Realistic error bounds on each parameter are defined from the resulting slices through the misfit function. These bounds are much narrower than traveltime inversion provides. Correlations between parameters are obtained from the covariance matrix constructed from models examined during this error analysis. The inversion methods are illustrated on the FF2 refraction data set of the Scripps Institution of Oceanography. The Monte Carlo search successfully locates the valley of the global minimum as well as a nearby secondary minimum. The error analysis puts realistic error bounds on the detailed inversion of this data set by Spudich & Orcutt.

A novel method of hypocentre location

Summary. The determination of earthquake locations requires a good velocity model for the region of interest, appropriate statistics for the residuals encountered and an efficient, stable inversion algorithm. A direct nonlinear inversion scheme has been constructed which can use any velocity model for which travel times can be calculated from an arbitrary source position to the receivers in the seismic network. The procedure is based on the minimization of a misfit function depending on the residuals between observed and calculated arrival times. Different statistics, e.g. Gaussian and Jeffreys distributions, can be accommodated by the choice of misfit function. The algorithm is based on a directed grid search which narrows down the range of possible origin times whilst carrying out a spatial search in the neighbourhood of the current minimum of the misfit function. No numerical differentiation of travel times is required, and convergence is rapid, stable and tolerant of occasional large errors in reading observed travel times. A useful product of the method is that the misfit function values are available in the neighbourhood of the minimum, so that a fully nonlinear treatment of the statistical confidence regions for a particular location can be made. A prerequisite for the use of the algorithm is the delineation of bounds on the four hypocentral parameters. Epicentral bounds are constructed using a variant of the ‘arrival order’ technique, and rapid scanning in depth and origin time over this region yields useful bounds on these parameters. The new nonlinear algorithm is illustrated by application to the SE Australian seismic network, for an event in the most active seismic zone. Two different velocity models are used with both Gaussian and Jeffreys statistics and good convergence for the algorithm is achieved despite significant nonlinearity in the behaviour. The Jeffreys statistics are more tolerant of large residuals and are to be preferred when the requisite velocity model is not too well known.

Invariant strings and pattern-recognizing properties of one-dimensional cellular automata

A cellular automaton is a discrete dynamical system whose evolution is governed by a deterministic rule involving local interactions. It is shown that given an arbitrary string of values and an arbitrary neighborhood size (representing the range of interaction), a simple procedure can be used to find the rules of that neighborhood size under which the string is invariant. The set of nearestneighbor rules for which invariant strings exist is completely specified, as is the set of strings invariant under each such rule. For any automaton rule, an associated “filtering” rule is defined for which the only attractors are spatial sequences consisting of concatenations of invariant strings. A result is provided defining the rule of minimum neighborhood size for which an arbitrarily chosen string is the unique invariant string. The applications of filtering rules to pattern recognition problems are discussed.

Improvements in isolated word recognition

For isolated word recognition, possibilities for improving the recognition accuracy are investigated for a given feature extraction, which is based on a short term spectrum analysis by means of band-pass filtering. A number of preprocessing steps are discussed, which are to be applied prior to time alignment via dynamic programming. These preprocessing steps include normalization of short term spectra with respect to the long term spectrum, amplitude normalization and spectral channel contour smoothing. For nonlinear time alignment, a method based on spectral change is investigated, alone and in combination with dynamic programming. The resulting distance measure is incorporated into pattern recognition schemes according to the minimum distance and nearest neighbor principles. The different processing steps are evaluated in a speaker dependent mode of operation separately for two vocabularies: the ten German digits and twelve major German airport city names. In comparison with the use of standard mean normalization of short term spectra and dynamic programming, the aforementioned techniques allow for a performance improvement in terms of error rate reduction by a factor of 3-5, while at the same time offering savings in computing time and reference memory requirements by a factor of 10 and 3, respectively.

The use of first and second derivatives in optical model parameter searches

This paper compares the efficiencies of standard minimization procedures in carrying out nuclear optical-model fits. It is shown that first-order perturbation theory permits computation of the gradient of x 2 more than five times as fast as is possible by difference methods. A linear approximation to the second-derivative matrix in terms of first derivatives of residuals is found to be very accurate in the neighborhood of minima; it provides a way of introducing second-derivative information that is significantly superior to the use of variable-metric algorithms. The resulting restricted-step Gauss-Newton procedures are shown to be about five times as fast as direct-search methods. The use of the methods of pseudo-inverses to “freeze” linear combinations of parameters poorly determined by the data is discussed.

Interpretation of H? contrast profiles of chromospheric fine structures

Recent observations of the Hα contrast profiles of identifiable chromospheric fine structures are interpreted in terms of an empirical model. It is shown that the parameters inferred from an application of Beckers' ‘cloud’ model are unreliable, and the problem of line asymmetries is re-examined. Quantitative models for the Hα chromosphere near the limb suggest that the ‘dark band’ phenomenon is due to low opacity in the neighbourhood of the temperature minimum, while the peculiar appearance of mottle contrast profiles near the limb is explained in terms of foreground absorption.

Cellular automata complexity trade-offs

The general theory of cellular automata is investigated with special attention to structural complexity. In particular, simulation of cellular automata by cellular automata is used to make explicit trade-off relationships between neighborhood size and state-set cardinality. A minimum neighborhood template with d + 1 elements is established for the class of d -dimensional cellular automata. The minimum state set for this class is shown to be the binary state set. The temporal costs, if any, of structural complexity trade-offs are also studied. It is demonstrated that any linear time cost can be eliminated and, in fact, a speed-up by arbitrary positive integer factor k can be attained at an increased structural cost.