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 PLOS ONE , 2012, DOI: 10.1371/journal.pone.0029793 Abstract: Emitted biosonar clicks and auditory evoked potential (AEP) responses triggered by the clicks were synchronously recorded during echolocation in an Atlantic bottlenose dolphin (Tursiops truncatus) trained to wear suction-cup EEG electrodes and to detect targets by echolocation. Three targets with target strengths of ？34, ？28, and ？22 dB were used at distances of 2 to 6.5 m for each target. The AEP responses were sorted according to the corresponding emitted click source levels in 5-dB bins and averaged within each bin to extract biosonar click-related AEPs from noise. The AEP amplitudes were measured peak-to-peak and plotted as a function of click source levels for each target type, distance, and target-present or target-absent condition. Hearing sensation levels of the biosonar clicks were evaluated by comparing the functions of the biosonar click-related AEP amplitude-versus-click source level to a function of external (in free field) click-related AEP amplitude-versus-click sound pressure level. The results indicated that the dolphin's hearing sensation levels to her own biosonar clicks were equal to that of external clicks with sound pressure levels 16 to 36 dB lower than the biosonar click source levels, varying with target type, distance, and condition. These data may be assumed to indicate that the bottlenose dolphin possesses effective protection mechanisms to isolate the self-produced intense biosonar beam from the animal's ears during echolocation.
 Mathematics , 2006, DOI: 10.1007/s00006-006-0016-5 Abstract: We establish the basis of a discrete function theory starting with a Fischer decomposition for difference Dirac operators. Discrete versions of homogeneous polynomials, Euler and Gamma operators are obtained. As a consequence we obtain a Fischer decomposition for the discrete Laplacian.
 Journal of Biomedical Science and Engineering (JBiSE) , 2010, DOI: 10.4236/jbise.2010.32025 Abstract: The aim of this article is to develop an automatic algorithm for the classification of non stationary signals. The application context is to classify uterine electromyogram (EMG) events to prevent the onset of preterm birth. The idea is to discriminate between the events by allocating them to the physiological classes: contractions, foetus motions, Alvarez or Long Duration Low Frequency waves. Our method is based on the Wavelet Packet (WP) decomposition and the choice of a best basis for classification purpose. Before classification, there is a need to detect events in the recorded signals. The discrimination criterion is based on the calculation of the ratio between intra-class variance and total variance (sum of the intra-class and inter-class variances), calculated directly from the coefficients of the selected WP. We evaluated the performance of the algorithm on real signals by using the classification methods Neural Networks (NN) and Support Vector Machines (SVM). Subband energies of the best selected WP are used as effective features. The determined best basis is applicable to a wide range of uterine EMG signals from large range of patients. In most cases, more than 85% of events are well classified whatever the term of gestation.
 中国物理 B , 2010, Abstract: In this paper, the ensemble empirical mode decomposition ({EEMD}) is applied to analyse accelerometer signals collected during human normal walking. First, the self-adaptive feature of {EEMD} is utilised to decompose the accelerometer signals, thus sifting out several intrinsic mode functions {(IMFs}) at disparate scales. Then, gait series can be extracted through peak detection from the eigen {\rm IMF} that best represents gait rhythmicity. Compared with the method based on the empirical mode decomposition ({EMD}), the {EEMD}-based method has following advantages: it remarkably improves the detection rate of peak values hidden in the original accelerometer signal, even when the signal is severely contaminated by the intermittent noises; this method effectively prevents the phenomenon of mode mixing found in the process of {EMD}. And a reasonable selection of parameters for the stop-filtering criteria can improve the calculation speed of the {EEMD}-based method. Meanwhile, the endpoint effect can be suppressed by using the {auto regressive and moving average} model to extend a short-time series in dual directions. The results suggest that {EEMD} is a powerful tool for extraction of gait rhythmicity and it also provides valuable clues for extracting eigen rhythm of other physiological signals.
 物理学报 , 2007, Abstract: Animals such as dolphin and bat feature powerful biological sonar structure. The research on the mechanism and principle of signal processing performed by neural system will provide a novel viewpoint for signal processing. In this paper, a biological neural loop is established to handle Doppler signal based on neural coding theory of ordered space. From simulation, the system loop achieves fast operation and high resolution. Furthermore, Doppler signals of continuously-changing frequency can be properly coped with as well. The network structure for handling Doppler signals may take many forms. However, the structure proposed in the paper is possibly the simplest one, for it comprises only one or two neuron(s), ensuring rapid processing and high resolution.
 Radioengineering , 2008, Abstract: The papers deals with a modeling of a Time- Difference of Arrival system for a subscriber station localization, based on the 802.11 standard wireless network. In the case of severe multipath effects the standard TDOA estimation methods, based on correlation of signals, received by conveniently displaced receiving stations show large errors. Thus, a new algorithm is proposed using received signals decomposition to a set of delayed replicas. This represents a linear estimation of reflected signals amplitudes. The described method leads to a better estimation of time differences of the signals, propagating on the direct paths between the emitter and the receiving stations.
 Mathematics , 2015, Abstract: We introduce a class of strongly \'{e}tale difference algebras, whose role in the study of difference equations is analogous to the role of \'{e}tale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's decomposition theorem and we present applications to difference algebraic groups and the compatibility problem.
 Mathematics , 2013, Abstract: This paper presents a theoretical and numerical investigation of the following practical question: Should the time difference quotients of the snapshots be used to generate the proper orthogonal decomposition basis functions? The answer to this question is important, since some published numerical studies use the time difference quotients, whereas other numerical studies do not. The criterion used in this paper to answer this question is the rate of convergence of the error of the reduced order model with respect to the number of proper orthogonal decomposition basis functions. Two cases are considered: the no_DQ case, in which the snapshot difference quotients are not used, and the DQ case, in which the snapshot difference quotients are used. The error estimates suggest that the convergence rates in the $C^0(L^2)$-norm and in the $C^0(H^1)$-norm are optimal for the DQ case, but suboptimal for the no_DQ case. The convergence rates in the $L^2(H^1)$-norm are optimal for both the DQ case and the no_DQ case. Numerical tests are conducted on the heat equation and on the Burgers equation. The numerical results support the conclusions drawn from the theoretical error estimates. Overall, the theoretical and numerical results strongly suggest that, in order to achieve optimal pointwise in time rates of convergence with respect to the number of proper orthogonal decomposition basis functions, one should use the snapshot difference quotients.
 Mathematics , 2015, Abstract: The concept of $t$-difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of $t$-hooks. It is well-known that the hook lengths of multiples of $t$ can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes modulo $t$.
 PLOS Biology , 2012, DOI: 10.1371/journal.pbio.1001150 Abstract: Active-sensing systems abound in nature, but little is known about systematic strategies that are used by these systems to scan the environment. Here, we addressed this question by studying echolocating bats, animals that have the ability to point their biosonar beam to a confined region of space. We trained Egyptian fruit bats to land on a target, under conditions of varying levels of environmental complexity, and measured their echolocation and flight behavior. The bats modulated the intensity of their biosonar emissions, and the spatial region they sampled, in a task-dependant manner. We report here that Egyptian fruit bats selectively change the emission intensity and the angle between the beam axes of sequentially emitted clicks, according to the distance to the target, and depending on the level of environmental complexity. In so doing, they effectively adjusted the spatial sector sampled by a pair of clicks—the “field-of-view.” We suggest that the exact point within the beam that is directed towards an object (e.g., the beam's peak, maximal slope, etc.) is influenced by three competing task demands: detection, localization, and angular scanning—where the third factor is modulated by field-of-view. Our results suggest that lingual echolocation (based on tongue clicks) is in fact much more sophisticated than previously believed. They also reveal a new parameter under active control in animal sonar—the angle between consecutive beams. Our findings suggest that acoustic scanning of space by mammals is highly flexible and modulated much more selectively than previously recognized.
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