A measure for the angle between projections based on the extent of correlation between corresponding central sections

A pre-condition for the ab initio assignment of Euler angles to a set of projections from an asymmetric object is that at least three of the available projections correspond to rotations about different axes. For symmetric objects this condition may be relaxed. There are some applications of single-particle electron microscopy, such as the reconstruction of filamentous macromolecular assemblies, where all available projections more-or-less correspond to rotations about a common rotation axis making it difficult to satisfy this condition. Here, a method has been developed to overcome this problem, based on the fact that the correlation between two central sections of the Fourier transform of a compact object will not be limited to an infinitesimal central line but will have a finite extent, which is related to the angle between the corresponding projections. Projections from model filaments, with different degrees of rotational symmetry about the long axis, have been used to test the methodology. The results show that angle determination is robust down to signal-to-noise ratios as low as 2 and that, in general, the error decreases as the degree of symmetry increases. The method has been used to assign angles to a set of negatively stained muscle thick filament projections to obtain an initial 3D reconstruction. The main features of the projections are seen to be faithfully reproduced in the reprojections from the reconstruction. A real-space adaptation of this method is also discussed.     

Frequency modulation within electrocardiograms during ventricular fibrillation

Periods of reentrant activation and effective refractory periods are correlated with dominant frequency or reciprocal of cycle periods during ventricular fibrillation (VF). In the present study, we used an analysis technique based on Wigner transforms to quantify time-varying dominant frequencies in electrocardiograms (ECGs) during VF. We estimated dominant frequencies within orthogonal ECGs recorded in 10 dogs during trials of 10 s of VF and in 9 dogs during trials of 30 s of VF. In four additional dogs, we compared dominant frequencies during 10 s of VF before and after administration of amiodarone. Our results showed the following. 1) There was substantial frequency variation or modulation within the ECGs during 10 and 30 s of VF, the average variation being +/-15% from the mean frequency. Amiodarone decreased mean frequencies (P < 0.05) as expected; however, amiodarone also decreased the variation in frequencies (P < 0.05). 2) During 30 s of VF, the dominant frequencies increased continuously from 7.3 to 8.1 Hz (P < 0.05). The increase in frequency was almost linear with a rate of 0.022 Hz/s (r(2) = 0.93, P < 0.0005). 3) Modulation of frequencies during the first and the last one-half of 30 s of VF was not different. Average (in time) mean frequencies and modulation of frequencies were similar in all three ECGs. 4) Although the averages were similar, during any VF episode, dominant frequencies in ECGs recorded from different locations on the body surface were similar to each other at some times and markedly different from each other at other times. We conclude that during VF, 1) frequencies in ECGs vary considerably and continuously, and amiodarone decreases this variation; 2) mean frequencies increase linearly during first 30 s; 3) the variability in frequency does not change during 30 s; and 4) at any given time, the frequencies within spatially different body surface ECGs can be either similar or markedly different.     

Blood pressure power within frequency range approximately 0.4 Hz in rat conforms to self-similar scaling following spinal cord transection

This study quantified the effect of interrupting the descending input to the sympathetic preganglionic neurons on the dynamic behavior of arterial blood pressure (BP) in the unanesthetized rat. BP was recorded for approximately 4-h intervals in six rats in the neurally intact state and in the same animals after complete spinal cord transection (SCT) between T(4) and T(5). In the intact state, power within the frequency range of 0.35-0.45 Hz was 1.53 +/- 0.38 mmHg(2)/Hz (mean +/- SD by fast Fourier transform). One week after SCT, power within this range decreased significantly (P < 0.05) to 0.43 +/- 0.62 mmHg(2)/Hz. To test for self-similarity before and after SCT, we analyzed data using a wavelet (i.e., functionally, a digital bandpass filter) tuned to be maximally sensitive to fluctuations with periods of approximately 2, 4, 8, 16, 32, or 64 s. In the control state, all fluctuations with periods of >/=4 s conformed to a "self-similar" (i.e., fractal) distribution. In marked contrast, the oscillations with a period of approximately 2 s (i.e., approximately 0.4 Hz) were significantly set apart from those at lower frequencies. One day and seven days after the complete SCT, however, the BP fluctuations at approximately 0.4 Hz now also conformed to the same self-similar behavior characteristic of the lower frequencies. We conclude that 1) an intact sympathetic nervous system endows that portion of the power spectrum centered around approximately 0.4 Hz with properties (e.g., a periodicity) that differ significantly from the self-similar behavior that characterizes the lower frequencies and 2) even within the relatively high frequency range at 0.4 Hz self-similarity is the "default" condition after sympathetic influences have been eliminated.     

Full-state tracking control of a mobile robot using neural networks

In this paper a nonholonomic mobile robot with completely unknown dynamics is discussed. A mathematical model has been considered and an efficient neural network is developed, which ensures guaranteed tracking performance leading to stability of the system. The neural network assumes a single layer structure, by taking advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot dynamic parameters. No assumptions relating to the boundedness is placed on the unmodeled disturbances. It is capable of generating real-time smooth and continuous velocity control signals that drive the mobile robot to follow the desired trajectories. The proposed approach resolves speed jump problem existing in some previous tracking controllers. Further, this neural network does not require offline training procedures. Lyapunov theory has been used to prove system stability. The practicality and effectiveness of the proposed tracking controller are demonstrated by simulation and comparison results.     

Inferring a system model of subcellular topoisomerase II beta localization dynamics

Measuring the mobility of proteins in living cells has become critical to many studies in cell biology and forms the basis for discussion on sub-cellular dynamics. Increasingly localization networks are being put together into compartment models to represent the exchange of molecules, represented mathematically as ordinary differential equations (ODE). The set-up is based on published literature, the "knowledge" of the investigator and 3D visualization of the data. Here we demonstrate this method on the example of a simple distribution model of the molecule Topoisomerase II beta (Topo II beta), nuclear protein that modifies DNA topology. It is found in high concentration in the nucleolus and diffuse in the nucleoplasm, demonstrating a non-membranous inhomogeneity in its distribution. We expand on the simple model by adding additional components to fit fluorescence recovery after photobleaching (FRAP) experiments for protein (GFP) labeled Topo II beta to measure its mobility. This model is then validated by comparing it with alternative scenarios and shown to have predictive power.     

The simultaneous recurrent neural network for addressing the scaling problem in static optimization.

A trainable recurrent neural network, Simultaneous Recurrent Neural network, is proposed to address the scaling problem faced by neural network algorithms in static optimization. The proposed algorithm derives its computational power to address the scaling problem through its ability to "learn" compared to existing recurrent neural algorithms, which are not trainable. Recurrent backpropagation algorithm is employed to train the recurrent, relaxation-based neural network in order to associate fixed points of the network dynamics with locally optimal solutions of the static optimization problems. Performance of the algorithm is tested on the NP-hard Traveling Salesman Problem in the range of 100 to 600 cities. Simulation results indicate that the proposed algorithm is able to consistently locate high-quality solutions for all problem sizes tested. In other words, the proposed algorithm scales demonstrably well with the problem size with respect to quality of solutions and at the expense of increased computational cost for large problem sizes.     

Wild Ungulate Decision-Making and the Role of Tiny Refuges in Human-Dominated Landscapes

Wildlife conservation in human-dominated landscapes requires that we understand how animals, when making habitat-use decisions, obtain diverse and dynamically occurring resources while avoiding risks, induced by both natural predators and anthropogenic threats. Little is known about the underlying processes that enable wild animals to persist in densely populated human-dominated landscapes, particularly in developing countries. In a complex, semi-arid, fragmented, human-dominated agricultural landscape, we analyzed the habitat-use of blackbuck, a large herbivore endemic to the Indian sub-continent. We hypothesized that blackbuck would show flexible habitat-use behaviour and be risk averse when resource quality in the landscape is high, and less sensitive to risk otherwise. Overall, blackbuck appeared to be strongly influenced by human activity and they offset risks by using small protected patches (~3 km²) when they could afford to do so. Blackbuck habitat use varied dynamically corresponding with seasonally-changing levels of resources and risks, with protected habitats registering maximum use. The findings show that human activities can strongly influence and perhaps limit ungulate habitat-use and behaviour, but spatial heterogeneity in risk, particularly the presence of refuges, can allow ungulates to persist in landscapes with high human and livestock densities.