Borderline Aggregation Kinetics in ``Dry'' and ``Wet'' Environments

We investigate the kinetics of constant-kernel aggregation which is augmented by either: (a) evaporation of monomers from finite-mass clusters, or (b) continuous cluster growth -- \ie, condensation. The rate equations for these two processes are analyzed using both exact and asymptotic methods. In aggregation-evaporation, if the evaporation is mass conserving, \ie, the monomers which evaporate remain in the system and continue to be reactive, the competition between evaporation and aggregation leads to several asymptotic outcomes. For weak evaporation, the kinetics is similar to that of aggregation with no evaporation, while equilibrium is quickly reached in the opposite case. At a critical evaporation rate, the cluster mass distribution decays as $k^{-5/2}$, where $k$ is the mass, while the typical cluster mass grows with time as $t^{2/3}$. In aggregation-condensation, we consider the process with a growth rate for clusters of mass $k$, $L_k$, which is: (i) independent of $k$, (ii) proportional to $k$, and (iii) proportional to $k^\mu$, with $0<\mu<1$. In the first case, the mass distribution attains a conventional scaling form, but with the typical cluster mass growing as $t\ln t$. When $L_k\propto k$, the typical mass grows exponentially in time, while the mass distribution again scales. In the intermediate case of $L_k\propto k^\mu$, scaling generally applies, with the typical mass growing as $t^{1/(1-\mu)}$. We also give an exact solution for the linear growth model, $L_k\propto k$, in one dimension.Comment: plain TeX, 17 pages, no figures, macro file prepende

Spike pattern recognition by supervised classification in low dimensional embedding space

© The Author(s) 2016. This article is published with open access at Springerlink.com under the terms of the Creative Commons Attribution License 4.0, (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.Epileptiform discharges in interictal electroencephalography (EEG) form the mainstay of epilepsy diagnosis and localization of seizure onset. Visual analysis is rater-dependent and time consuming, especially for long-term recordings, while computerized methods can provide efficiency in reviewing long EEG recordings. This paper presents a machine learning approach for automated detection of epileptiform discharges (spikes). The proposed method first detects spike patterns by calculating similarity to a coarse shape model of a spike waveform and then refines the results by identifying subtle differences between actual spikes and false detections. Pattern classification is performed using support vector machines in a low dimensional space on which the original waveforms are embedded by locality preserving projections. The automatic detection results are compared to experts’ manual annotations (101 spikes) on a whole-night sleep EEG recording. The high sensitivity (97 %) and the low false positive rate (0.1 min−1), calculated by intra-patient cross-validation, highlight the potential of the method for automated interictal EEG assessment.Peer reviewedFinal Published versio