Seizure warning algorithm based on optimization and nonlinear dynamics

There is growing evidence that temporal lobe seizures are preceded by a preictal transition, characterized by a gradual dynamical change from asymptomatic interictal state to seizure. We herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing EEG signals. Such, the algorithm constitutes a seizure warning system. The algorithm estimates STL_max, a measure of the order or disorder of the signal, of EEG signals recorded from individual electrode sites. The optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures. Specifically, a quadratically constrained quadratic 0-1 programming problem is formulated to identify critical electrode sites. The automated seizure warning algorithm was tested in continuous, long-term EEG recordings obtained from 5 patients with temporal lobe epilepsy. For individual patient, we use the first half of seizures to train the parameter settings, which is evaluated by ROC (Receiver Operating Characteristic) curve analysis. With the best parameter setting, the algorithm applied to all cases predicted an average of 91.7% of seizures with an average false prediction rate of 0.196 per hour. These results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes.Mathematics Subject Classification (1991):20E28, 20G40, 20C20     

Electroencephalogram (EEG) time series classification: Applications in epilepsy

Epilepsy is among the most common brain disorders. Approximately 25–30% of epilepsy patients remain unresponsive to anti-epileptic drug treatment, which is the standard therapy for epilepsy. In this study, we apply optimization-based data mining techniques to classify the brain's normal and epilepsy activity using intracranial electroencephalogram (EEG), which is a tool for evaluating the physiological state of the brain. A statistical cross validation and support vector machines were implemented to classify the brain's normal and abnormal activities. The results of this study indicate that it may be possible to design and develop efficient seizure warning algorithms for diagnostic and therapeutic purposes. Research was partially supported by the Rutgers Research Council grant-202018, the NSF grants DBI-980821, CCF-0546574, IIS-0611998, and NIH grant R01-NS-39687-01A1.     

Entropy and the First Law of Thermodynamics

Plancks work on the Second Law of Thermodynamics in combination with a simple thermodynamic approach developed by Blinder show that the concept of entropy is introduced from the First and not the Second Law of Thermodynamics. In particular, it is proved that the First Law of Thermodynamics leads directly to the following statement: For every system of whatever complexity there exists an extensive function of state S defined from dS = q_rev/T, where q_rev is the infinitesimal quantity of heat exchanged reversibly between the system and the surroundings and T is the absolute temperature of the system. Thus, for reversible adiabatic processes we readily have from the First Law that dS = 0. Therefore, the Second Law should be properly reformulated, restricted to the inequality dS 0 for irreversible processes only.     

Synthesis of N-acyl-2-pyrrolidinones from the corresponding N-acyl-GABA derivatives

In this work, the synthesis of 1-(pyridine-3-carbonyl)pyrrolidin-2-one ( 1a ) and 1-(2-propyl-1-pentanoyl)pyrrolidin-2-one ( 1b ) by cyclization of the corresponding GABA derivatives, is reported. Two different methods are developed. For the synthesis of 1a , the parent molecule 4-[(pyridine-3-carbonyl)-amino]butanoic acid ( 2a ) is treated first with thionyl chloride and then with triethylamine. The second derivative, 1b , is produced by an intramolecular dehydration of 4-(2-propylpentanoylamino)butanoic acid ( 2b ) using an acid catalyst.     

Quantitative analysis of small pharmaceutical drugs using a high repetition rate laser matrix-assisted laser/desorption ionization source

In this work, a high repetition rate laser matrix-assisted laser desorption/ionization (MALDI) source is studied on a quadrupole-time-of-flight (QqTOF) and a triple quadrupole (QqQ) mass spectrometer for rapid quantification of small pharmaceutical drugs. The high repetition rate laser allows an up to 100-fold higher pulse frequency as compared with regular MALDI lasers, resulting in much larger sample throughput and number of accumulated spectra. This increases the reproducibility of signal intensities considerably, with average values being around 5% relative standard deviation after taking into account the area ratio of the analyte to an internal standard. Experiments were conducted in MS/MS mode to circumvent the large chemical background due to MALDI matrix ions in the low mass range. The dynamic range of calibration curves on the QqTOF mass spectrometer extended over at least two orders of magnitude, whereas on the QqQ it extended over at least three orders of magnitude. Detection limits ranged from 60-400 pg/microL on the QqTOF and from 6-70 pg/microL on the QqQ for a series of benzodiazepines. The benzodiazepine content of commercial pill formulations was quantified, and less than 5% error was obtained between the present method and the manufacturer's certified values. Furthermore, a high sample throughput was achieved with this method, so that a single MALDI spot could be quantitatively scanned in as little as 15 s, and an entire 96-well MALDI plate in 24 min.     

A Mesh Adaptive Basin Hopping Method for the Design of Circular Antenna Arrays

The design of circular antenna arrays is a challenging optimization problem, which requires ad-hoc methods to fulfill the engineering requirements. In this work, we introduce the Mesh Adaptive Basin Hopping algorithm to tackle such problem effectively; the experimental results show that the new approach proposed outperforms the state-of-the-art methods, both in terms of quality of the solutions and computational efficiency.     

Optimization and data mining in medicine

Mathematical theory of optimization has found many applications in the area of medicine over the last few decades. Several data analysis and decision making problems in medicine can be formulated using optimization and data mining techniques. The significance of the mathematical models is greatly realized in the recent years owing to the growing technological capabilities and the large amounts of data available. In this paper, we attempt to give a brief overview of some of the most interesting applications of mathematical programming and data mining in medicine. In the overview, we include applications like radiation therapy treatment, microarray data analysis, and computational neuroscience.     

Routing-efficient CDS construction in Disk-Containment Graphs

In wireless networks, Connected Dominating Sets (CDSs) are widely used as virtual backbones for communications. On one hand, reducing the backbone size will reduce the maintenance overhead. So how to minimize the CDS size is a critical issue. On the other hand, when evaluating the performance of a wireless network, the hop distance between two communication nodes, which reflect the energy consumption and response delay, is of great importance. Hence how to minimize the routing cost is also a key problem for constructing the network virtual backbone. In this paper, we study the problem of constructing applicable CDS in wireless networks in terms of size and routing cost. We formulate a wireless network as a Disk-Containment Graph (DCG), which is a generalization of the Unit-Disk Graph (UDG), and we develop an efficient algorithm to construct CDS in such kind of graphs. The algorithm contains two parts and is flexible to balance the performance between the two metrics. We also analyze the algorithm theoretically. It is shown that our algorithm has provable performance in minimizing the CDS size and reducing the communication distance for routing.