David Colella

Characterizations of Scaling Functions: Continuous Solutions

A dilation equation is a functional equation of the form

Brain chirps: spectrographic signatures of epileptic seizures

f(t) = \sum_{k=0}^{N}c_{k}f(2t-k)

The characterization of continuous, four-coefficient scaling functions and wavelets

, and any nonzero solution of such an equation is called a scaling function. Dilation equations play an important role in several fields, including interpolating subdivision schemes and wavelet theory. This paper obtains sharp bounds for the Holder exponent of continuity of any continuous, compactly supported scaling function in terms of the joint spectral radius of two matrices determined by the coefficients

Wavelet analysis of spectrogram seizure chirps

\{c_{0},\ldots,c_{N}\}

Feature-based epileptic seizure detection and prediction from ECoG recordings

. The arguments lead directly to a characterization of all dilation equations that have continuous, compactly supported solutions.

Systems Engineering Solution for Technology Deployment to Combat Complex Threat Scenarios in the Homeland

OBJECTIVE A chirp is a brief signal within which the frequency content changes rapidly. Spectrographic chirps are found in signals produced from many biological and physical phenomena. In radar and sonar engineering, signals with chirps are used to localize direction and range to the signal source. Although characteristic frequency changes during epileptic seizures have long been observed, the correlation with chirps and chirp technology seems never to have been made. METHODS We analyzed 19404 s (1870 s of which were from 43 seizures) of intracranially (subdural and depth electrode) recorded digital EEG from 6 patients for the presence of spectral chirps. Matched filters were constructed from methods in routine use in non-medical signal processing applications. RESULTS We found that chirps are very sensitive detectors of seizures (83%), and highly specific as markers (no false positive detections). The feasibility of using spectral chirps as matched filters was demonstrated. CONCLUSIONS Chirps are highly specific and sensitive spectrographic signatures of epileptic seizure activity. In addition, chirps may serve as templates for matched filter design to detect seizures, and as such, can demonstrate localization and propagation of seizures from an epileptic focus.

Wavelet-based analysis of electroencephalogram (EEG) signals for detection and localization of epileptic seizures

Four-coefficient dilation equations are examined and results converse to a theorem of Daubechies-Lagarias are given. These results complete the characterization of those four-coefficient dilation equations having a continuous solution. >

A characterization of neural network performances based on Fokker-Planck statistical models

A redundant wavelet filtering method is used in conjunction with spectrogram computations to address a component of the problem of predicting epileptic seizure activity. It is shown that spectrograms of seizure episodes exhibit multiple chirps consistent with the relatively simple almost periodic behavior of the observed time series. Scalograms corresponding to a redundant (non-dyadic) wavelet analysis are used to provide finer information about these chirps, including their evolution in preseizure intervals. Detection of the origin of such periodicities are useful in the prediction problem.

Matrix Refinement Equations: Existence and Uniqueness

This paper discusses the observation and interpretation of chirp-like striation patterns in processed spectrograms of single channel electrocorticograms associated with epileptic patients. A pulse amplitude modulation model is presented as a possible mechanism for the appearance of the chirp-like patterns.<<ETX>>

Dilation equations and the smoothness of compactly supported wavelets

Systems engineering has been applied to the problems faced by DHS, including defending the homeland against a complex threat. An initiative currently underway by DHS S&T will use systems engineering to perform analysis against a scenario prior to the field experiment. The systems engineering analysis will help define the specific configuration, location, and Concept of Operations (CONOPs) of the system. Results from the experiment will be fed back into the systems engineering framework architecture in order to refine and tune the analysis. This will give the systems engineers a higher confidence in the analysis and recommendations in future experiments as the system is improved, new sensors are added, and the threat becomes more complex.