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Journal articles on the topic 'Gaussian inputs'

Author: Grafiati

Published: 6 September 2023

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1

Hartman, Eric, and James D. Keeler. "Predicting the Future: Advantages of Semilocal Units." Neural Computation 3, no. 4 (December 1991): 566–78. http://dx.doi.org/10.1162/neco.1991.3.4.566.

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In investigating gaussian radial basis function (RBF) networks for their ability to model nonlinear time series, we have found that while RBF networks are much faster than standard sigmoid unit backpropagation for low-dimensional problems, their advantages diminish in high-dimensional input spaces. This is particularly troublesome if the input space contains irrelevant variables. We suggest that this limitation is due to the localized nature of RBFs. To gain the advantages of the highly nonlocal sigmoids and the speed advantages of RBFs, we propose a particular class of semilocal activation functions that is a natural interpolation between these two families. We present evidence that networks using these gaussian bar units avoid the slow learning problem of sigmoid unit networks, and, very importantly, are more accurate than RBF networks in the presence of irrelevant inputs. On the Mackey-Glass and Coupled Lattice Map problems, the speedup over sigmoid networks is so dramatic that the difference in training time between RBF and gaussian bar networks is minor. Gaussian bar architectures that superpose composed gaussians (gaussians-of-gaussians) to approximate the unknown function have the best performance. We postulate that an interesing behavior displayed by gaussian bar functions under gradient descent dynamics, which we call automatic connection pruning, is an important factor in the success of this representation.

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2

Srivastava, Ankur, Arun K. Subramaniyan, and Liping Wang. "Analytical global sensitivity analysis with Gaussian processes." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 31, no. 3 (August 2017): 235–50. http://dx.doi.org/10.1017/s0890060417000142.

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AbstractMethods for efficient variance-based global sensitivity analysis of complex high-dimensional problems are presented and compared. Variance decomposition methods rank inputs according to Sobol indices that can be computationally expensive to evaluate. Main and interaction effect Sobol indices can be computed analytically in the Kennedy and O'Hagan framework with Gaussian processes. These methods use the high-dimensional model representation concept for variance decomposition that presents a unique model representation when inputs are uncorrelated. However, when the inputs are correlated, multiple model representations may be possible leading to ambiguous sensitivity ranking with Sobol indices. In this work, we present the effect of input correlation on sensitivity analysis and discuss the methods presented by Li and Rabitz in the context of Kennedy and O'Hagan's framework with Gaussian processes. Results are demonstrated on simulated and real problems for correlated and uncorrelated inputs and demonstrate the utility of variance decomposition methods for sensitivity analysis.

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3

Koukoulas, P., and N. Kalouptsidis. "Nonlinear system identification using Gaussian inputs." IEEE Transactions on Signal Processing 43, no. 8 (1995): 1831–41. http://dx.doi.org/10.1109/78.403342.

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4

Schwartz, Odelia, Terrence J. Sejnowski, and Peter Dayan. "Soft Mixer Assignment in a Hierarchical Generative Model of Natural Scene Statistics." Neural Computation 18, no. 11 (November 2006): 2680–718. http://dx.doi.org/10.1162/neco.2006.18.11.2680.

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Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixturemodel that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing.

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5

Wong, P. W., and R. M. Gray. "Sigma-delta modulation with i.i.d. Gaussian inputs." IEEE Transactions on Information Theory 36, no. 4 (July 1990): 784–98. http://dx.doi.org/10.1109/18.53738.

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6

Xu-Friedman, Matthew A., and Wade G. Regehr. "Dynamic-Clamp Analysis of the Effects of Convergence on Spike Timing. II. Few Synaptic Inputs." Journal of Neurophysiology 94, no. 4 (October 2005): 2526–34. http://dx.doi.org/10.1152/jn.01308.2004.

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Sensory pathways in the nervous system possess mechanisms for decreasing spike-timing variability (“jitter”), probably to increase acuity. Most studies of jitter reduction have focused on convergence of many subthreshold inputs. However, many neurons receive only a few active inputs at any given time, and jitter reduction under these conditions is not well understood. We examined this issue using dynamic-clamp recordings in slices from mouse auditory brain stem. Significant jitter reduction was possible with as few as two inputs, provided the inputs had several features. First, jitter reduction was greatest and most reliable for supra-threshold inputs. Second, significant jitter reduction occurred when the distribution of input times had a rapid onset, i.e., for alpha- but not for Gaussian-distributed inputs. Third, jitter reduction was compromised unless late inputs were suppressed by the refractory period of the cell. These results contrast with the finding in the previous paper in which many subthreshold inputs contribute to jitter reduction, whether alpha- or Gaussian-distributed. In addition, convergence of many subthreshold inputs could fail to elicit any postsynaptic response when the input distribution outlasted the refractory period of the cell. These significant differences indicate that each means of reducing jitter has advantages and disadvantages and may be more effective for different neurons depending on the properties of their inputs.

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7

CARD, HOWARD C. "STOCHASTIC RADIAL BASIS FUNCTIONS." International Journal of Neural Systems 11, no. 02 (April 2001): 203–10. http://dx.doi.org/10.1142/s0129065701000552.

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Stochastic signal processing can implement gaussian activation functions for radial basis function networks, using stochastic counters. The statistics of neural inputs which control the increment and decrement operations of the counter are governed by Bernoulli distributions. The transfer functions relating the input and output pulse probabilities can closely approximate gaussian activation functions which improve with the number of states in the counter. The means and variances of these gaussian approximations can be controlled by varying the output combinational logic function of the binary counter variables.

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8

Mena-Parra, J., K. Bandura, M. A. Dobbs, J. R. Shaw, and S. Siegel. "Quantization Bias for Digital Correlators." Journal of Astronomical Instrumentation 07, no. 02n03 (September 2018): 1850008. http://dx.doi.org/10.1142/s2251171718500083.

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In radio interferometry, the quantization process introduces a bias in the magnitude and phase of the measured correlations which translates into errors in the measurement of source brightness and position in the sky, affecting both the system calibration and image reconstruction. In this paper, we investigate the biasing effect of quantization in the measured correlation between complex-valued inputs with a circularly symmetric Gaussian probability density function (PDF), which is the typical case for radio astronomy applications. We start by calculating the correlation between the input and quantization error and its effect on the quantized variance, first in the case of a real-valued quantizer with a zero mean Gaussian input and then in the case of a complex-valued quantizer with a circularly symmetric Gaussian input. We demonstrate that this input-error correlation is always negative for a quantizer with an odd number of levels, while for an even number of levels, this correlation is positive in the low signal level regime. In both cases, there is an optimal interval for the input signal level for which this input-error correlation is very weak and the model of additive uncorrelated quantization noise provides a very accurate approximation. We determine the conditions under which the magnitude and phase of the measured correlation have negligible bias with respect to the unquantized values: we demonstrate that the magnitude bias is negligible only if both unquantized inputs are optimally quantized (i.e. when the uncorrelated quantization error model is valid), while the phase bias is negligible when (1) at least one of the inputs is optimally quantized, or when (2) the correlation coefficient between the unquantized inputs is small. Finally, we determine the implications of these results for radio interferometry.

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9

Xu-Friedman, Matthew A., and Wade G. Regehr. "Dynamic-Clamp Analysis of the Effects of Convergence on Spike Timing. I. Many Synaptic Inputs." Journal of Neurophysiology 94, no. 4 (October 2005): 2512–25. http://dx.doi.org/10.1152/jn.01307.2004.

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Precise action potential timing is crucial in sensory acuity and motor control. Convergence of many synaptic inputs is thought to provide a means of decreasing spike-timing variability (“jitter”), but its effectiveness has never been tested in real neurons. We used the dynamic-clamp technique in mouse auditory brain stem slices to examine how convergence controls spike timing. We tested the roles of several synaptic properties that are influenced by ongoing activity in vivo: the number of active inputs ( N), their total synaptic conductance ( Gtot), and their timing, which can resemble an alpha or a Gaussian distribution. Jitter was reduced most with large N, up to a factor of over 20. Variability in N is likely to occur in vivo, but this added little jitter. Jitter reduction also depended on the timing of inputs: alpha-distributed inputs were more effective than Gaussian-distributed inputs. Furthermore, the two distributions differed in their sensitivity to synaptic conductance: for Gaussian-distributed inputs, jitter was most reduced when Gtot was 2–3 times threshold, whereas alpha-distributed inputs showed continued jitter reduction with higher Gtot. However, very high Gtot caused the postsynaptic cell to fire multiple times, particularly when the input jitter outlasted the cell's refractory period, which interfered with jitter reduction. Gtot also greatly affected the response latency, which could influence downstream computations. Changes in Gtot are likely to arise in vivo through activity-dependent changes in synaptic strength. High rates of postsynaptic activity increased the number of synaptic inputs required to evoke a postsynaptic response. Despite this, jitter was still effectively reduced, particularly in cases when this increased threshold eliminated secondary spikes. Thus these studies provide insight into how specific features of converging inputs control spike timing.

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10

Bachoc, Francois, Fabrice Gamboa, Jean-Michel Loubes, and Nil Venet. "A Gaussian Process Regression Model for Distribution Inputs." IEEE Transactions on Information Theory 64, no. 10 (October 2018): 6620–37. http://dx.doi.org/10.1109/tit.2017.2762322.

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11

Keang-Po Ho and J. M. Kahn. "Optimal predistortion of Gaussian inputs for clipping channels." IEEE Transactions on Communications 44, no. 11 (1996): 1505–13. http://dx.doi.org/10.1109/26.544467.

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12

Ghaffari Jadidi, Maani, Jaime Valls Miro, and Gamini Dissanayake. "Warped Gaussian Processes Occupancy Mapping With Uncertain Inputs." IEEE Robotics and Automation Letters 2, no. 2 (April 2017): 680–87. http://dx.doi.org/10.1109/lra.2017.2651154.

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13

Koukoulas, P., and N. Kalouptsidis. "Mean Square Nonlinear System Identification with Gaussian Inputs." IFAC Proceedings Volumes 27, no. 8 (July 1994): 289–93. http://dx.doi.org/10.1016/s1474-6670(17)47730-5.

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14

Hu, Xiao-Li, and Han-Fu Chen. "Recursive identification for Wiener systems using Gaussian inputs." Asian Journal of Control 10, no. 3 (May 2008): 341–50. http://dx.doi.org/10.1002/asjc.27.

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15

Cambanis, Stamatis. "Random filters which preserve the stability of random inputs." Advances in Applied Probability 20, no. 2 (June 1988): 275–94. http://dx.doi.org/10.2307/1427390.

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A stationary stable random processes goes through an independently distributed random linear filter. It is shown that when the input is Gaussian or harmonizable stable, then the output is also stable provided the filter&s transfer function has non-random gain. In contrast, when the input is a non-Gaussian stable moving average, then the output is stable provided the filter&s randomness is due only to a random global sign and time shift.

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16

Cambanis, Stamatis. "Random filters which preserve the stability of random inputs." Advances in Applied Probability 20, no. 02 (June 1988): 275–94. http://dx.doi.org/10.1017/s0001867800016979.

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A stationary stable random processes goes through an independently distributed random linear filter. It is shown that when the input is Gaussian or harmonizable stable, then the output is also stable provided the filter&s transfer function has non-random gain. In contrast, when the input is a non-Gaussian stable moving average, then the output is stable provided the filter&s randomness is due only to a random global sign and time shift.

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17

Dębicki, Krzysztof, and Michel Mandjes. "Exact overflow asymptotics for queues with many Gaussian inputs." Journal of Applied Probability 40, no. 3 (September 2003): 704–20. http://dx.doi.org/10.1239/jap/1059060897.

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In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

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18

Dębicki, Krzysztof, and Michel Mandjes. "Exact overflow asymptotics for queues with many Gaussian inputs." Journal of Applied Probability 40, no. 03 (September 2003): 704–20. http://dx.doi.org/10.1017/s0021900200019653.

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In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

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19

Eshete, Sitotaw. "Observation of Gaussian quantum correlations existence of photons under linear beam splitter." Journal of Physics Communications 6, no. 2 (February 1, 2022): 025007. http://dx.doi.org/10.1088/2399-6528/ac55fa.

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Abstract In this paper, we investigate the creation of quantum correlations such as entanglement, the Gaussian quantum discord and quantum steering in a quantum system under consideration via the linear beam splitter with squeezed thermal and a single-mode Gaussian states at the inputs. This quantum system generates bright entangled output two-mode light. Specifically, the quantum entanglement can be enhanced through increasing the purity of the Gaussian state and the squeezing parameter at the input states. The quantum correlations reveal similar characteristics for each case. That means when we increase the non-classicality, purity and squeezing parameter, the quantum correlations show enhanced profile. On the other hand, upon increasing the mean thermal photon number at the input, the quantum correlations indicate inverse relation.

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20

Bershad, Neil J., Eweda Eweda, and Jose C. M. Bermudez. "Stochastic analysis of the LMS algorithm for cyclostationary colored Gaussian and non-Gaussian inputs." Digital Signal Processing 88 (May 2019): 149–59. http://dx.doi.org/10.1016/j.dsp.2019.02.011.

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21

Fan, Linhui, Bo Tang, Qiuxi Jiang, Fangzheng Liu, and Chengyou Yin. "Joint Resource Allocation for Frequency-Domain Artificial Noise Assisted Multiuser Wiretap OFDM Channels with Finite-Alphabet Inputs." Symmetry 11, no. 7 (July 2, 2019): 855. http://dx.doi.org/10.3390/sym11070855.

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The security issue on the physical layer is of significant challenge yet of paramount importance for 5G communications. In some previous works, transmit power allocation has already been studied for orthogonal frequency division multiplexing (OFDM) secure communication with Gaussian channel inputs for both a single user and multiple users. Faced with peak transmission power constraints, we adopt discrete channel inputs (e.g., equiprobable Quadrature Phase Shift Keying (QPSK) with symmetry) in a practical communication system, instead of Gaussian channel inputs. Finite-alphabet inputs impose a more significant challenge as compared with conventional Gaussian random inputs for the multiuser wiretap OFDM systems. This paper considers the joint resource allocation in frequency-domain artificial noise (AN) assisted multiuser wiretap OFDM channels with discrete channel inputs. This security problem is formulated as nonconvex sum secrecy rate optimization by jointly optimizing the subcarrier allocation, information-bearing power, and AN-bearing power. To this end, with a suboptimal subcarrier allocation scheme, we propose an efficient iterative algorithm to allocate the power between the information and the AN via the Lagrange duality method. Finally, we carry out some numerical simulations to demonstrate the performance of the proposed algorithm.

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22

Bershad, N. "Analysis of the normalized LMS algorithm with Gaussian inputs." IEEE Transactions on Acoustics, Speech, and Signal Processing 34, no. 4 (August 1986): 793–806. http://dx.doi.org/10.1109/tassp.1986.1164914.

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23

Enqvist, Martin, and Lennart Ljung. "Linear Models of Nonlinear FIR Systems with Gaussian Inputs." IFAC Proceedings Volumes 36, no. 16 (September 2003): 1873–78. http://dx.doi.org/10.1016/s1474-6670(17)35033-4.

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24

Broderick, Tamara, and Robert B. Gramacy. "Classification and Categorical Inputs with Treed Gaussian Process Models." Journal of Classification 28, no. 2 (June 17, 2011): 244–70. http://dx.doi.org/10.1007/s00357-011-9083-y.

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25

Di Paola, M., G. Falsone, and A. Pirrotta. "Stochastic response analysis of nonlinear systems under Gaussian inputs." Probabilistic Engineering Mechanics 7, no. 1 (January 1992): 15–21. http://dx.doi.org/10.1016/0266-8920(92)90004-2.

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26

Grigoriu, Mircea. "Transient response of linear systems to stationary Gaussian inputs." Probabilistic Engineering Mechanics 7, no. 3 (January 1992): 159–64. http://dx.doi.org/10.1016/0266-8920(92)90019-e.

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27

Roustant, Olivier, Espéran Padonou, Yves Deville, Aloïs Clément, Guillaume Perrin, Jean Giorla, and Henry Wynn. "Group Kernels for Gaussian Process Metamodels with Categorical Inputs." SIAM/ASA Journal on Uncertainty Quantification 8, no. 2 (January 2020): 775–806. http://dx.doi.org/10.1137/18m1209386.

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28

Kim, S. B., and E. J. Powers. "Orthogonalised frequency domain volterra model for non-gaussian inputs." IEE Proceedings F Radar and Signal Processing 140, no. 6 (1993): 402. http://dx.doi.org/10.1049/ip-f-2.1993.0059.

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29

Ermolova, N. Y., and O. Tirkkonen. "Theoretical Characterization of Memory Polynomial Models With Gaussian Inputs." IEEE Signal Processing Letters 16, no. 8 (August 2009): 651–54. http://dx.doi.org/10.1109/lsp.2009.2021328.

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30

Rosenbaum, Robert, and Krešimir Josić. "Mechanisms That Modulate the Transfer of Spiking Correlations." Neural Computation 23, no. 5 (May 2011): 1261–305. http://dx.doi.org/10.1162/neco_a_00116.

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Correlations between neuronal spike trains affect network dynamics and population coding. Overlapping afferent populations and correlations between presynaptic spike trains introduce correlations between the inputs to downstream cells. To understand network activity and population coding, it is therefore important to understand how these input correlations are transferred to output correlations.Recent studies have addressed this question in the limit of many inputs with infinitesimal postsynaptic response amplitudes, where the total input can be approximated by gaussian noise. In contrast, we address the problem of correlation transfer by representing input spike trains as point processes, with each input spike eliciting a finite postsynaptic response. This approach allows us to naturally model synaptic noise and recurrent coupling and to treat excitatory and inhibitory inputs separately.We derive several new results that provide intuitive insights into the fundamental mechanisms that modulate the transfer of spiking correlations.

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31

Dabrowska, Anita, and John Gough. "Quantum Trajectories for Squeezed Input Processes: Explicit Solutions." Open Systems & Information Dynamics 23, no. 01 (March 2016): 1650004. http://dx.doi.org/10.1142/s1230161216500049.

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We consider the quantum (trajectories) filtering equation for the case when the system is driven by Bose field inputs prepared in an arbitrary non-zero mean Gaussian state. The a posteriori evolution of the system is conditioned by the results of a single or double homodyne measurements. The system interacting with the Bose field is a single cavity mode taken initially in a Gaussian state. We show explicit solutions using the method of characteristic functions to the filtering equations exploiting the linear Gaussian nature of the problem.

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32

Wai, Kok Poh, Chai Hoon Koo, Yuk Feng Huang, and Woon Chan Chong. "Water quality index prediction with hybridized ELM and Gaussian process regression." E3S Web of Conferences 347 (2022): 04004. http://dx.doi.org/10.1051/e3sconf/202234704004.

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The Department of Environment (DOE) of Malaysia evaluates river water quality based on the water quality index (WQI), which is a single number function that considers six parameters for its determination, namely the ammonia nitrogen (AN), biochemical oxygen demand (BOD), chemical oxygen demand (COD), dissolved oxygen (DO), pH, and suspended solids (SS). The conventional WQI calculation is tedious and requires all parameter values in computing the final WQI. In this study, the extreme learning machine (ELM) and the radial basis function kernel Gaussian process regression (GPR), were enhanced with bootstrap aggregating (bagging) and adaptive boosting (AdaBoost) for the WQI prediction at the Klang River, Malaysia. The global performance indicator (GPI) was used to evaluate the models’ performance. By preparing different input combinations for the WQI prediction, the parameter importance was found in following order: DO > COD > SS > AN > BOD > pH, and all models demonstrated lower prediction accuracy with a lesser number of parameter inputs. The GPR revealed a consistent trend with higher WQI prediction accuracy than ELM. The Adaboost-ELM works better than the bagged-ELM for all input combinations, while the bagging algorithm improved the GPR prediction under certain scenarios. The bagged-GPR reported the highest GPI of 1.86 for WQI prediction using all six parameter inputs.

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Burkitt, A. N., and G. M. Clark. "Synchronization of the Neural Response to Noisy Periodic Synaptic Input." Neural Computation 13, no. 12 (December 1, 2001): 2639–72. http://dx.doi.org/10.1162/089976601317098475.

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The timing information contained in the response of a neuron to noisy periodic synaptic input is analyzed for the leaky integrate-and-fire neural model. We address the question of the relationship between the timing of the synaptic inputs and the output spikes. This requires an analysis of the interspike interval distribution of the output spikes, which is obtained in the gaussian approximation. The conditional output spike density in response to noisy periodic input is evaluated as a function of the initial phase of the inputs. This enables the phase transition matrix to be calculated, which relates the phase at which the output spike is generated to the initial phase of the inputs. The interspike interval histogram and the period histogram for the neural response to ongoing periodic input are then evaluated by using the leading eigenvector of this phase transition matrix. The synchronization index of the output spikes is found to increase sharply as the inputs become synchronized. This enhancement of synchronization is most pronounced for large numbers of inputs and lower frequencies of modulation and also for rates of input near the critical input rate. However, the mutual information between the input phase of the stimulus and the timing of output spikes is found to decrease at low input rates as the number of inputs increases. The results show close agreement with those obtained from numerical simulations for large numbers of inputs.

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34

Tan, Matthias H. Y. "Gaussian Process Modeling of Finite Element Models with Functional Inputs." SIAM/ASA Journal on Uncertainty Quantification 7, no. 4 (January 2019): 1133–61. http://dx.doi.org/10.1137/17m1112942.

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35

Zhijun Cai and Er-Wei Bai. "How Nonlinear Parametric Wiener System Identification is Under Gaussian Inputs?" IEEE Transactions on Automatic Control 57, no. 3 (March 2012): 738–42. http://dx.doi.org/10.1109/tac.2011.2166318.

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36

Liu, Yao, Xiao-Zhou Li, Ray C. C. Cheung, Sze-Chun Chan, and Hei Wong. "High-Speed Discrete Gaussian Sampler With Heterodyne Chaotic Laser Inputs." IEEE Transactions on Circuits and Systems II: Express Briefs 65, no. 6 (June 2018): 794–98. http://dx.doi.org/10.1109/tcsii.2017.2749204.

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37

Rassouli, Borzoo, and Bruno Clerckx. "On the Capacity of Vector Gaussian Channels With Bounded Inputs." IEEE Transactions on Information Theory 62, no. 12 (December 2016): 6884–903. http://dx.doi.org/10.1109/tit.2016.2615632.

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38

Bershad, N. "Behavior of the ε-normalized LMS algorithm with Gaussian inputs." IEEE Transactions on Acoustics, Speech, and Signal Processing 35, no. 5 (May 1987): 636–44. http://dx.doi.org/10.1109/tassp.1987.1165197.

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39

Amemori, Ken-ichi, and Shin Ishii. "Gaussian Process Approach to Spiking Neurons for Inhomogeneous Poisson Inputs." Neural Computation 13, no. 12 (December 1, 2001): 2763–97. http://dx.doi.org/10.1162/089976601317098529.

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This article presents a new theoretical framework to consider the dynamics of a stochastic spiking neuron model with general membrane response to input spike. We assume that the input spikes obey an inhomogeneous Poisson process. The stochastic process of the membrane potential then becomes a gaussian process. When a general type of the membrane response is assumed, the stochastic process becomes a Markov-gaussian process. We present a calculation method for the membrane potential density and the firing probability density. Our new formulation is the extension of the existing formulation based on diffusion approximation. Although the single Markov assumption of the diffusion approximation simplifies the stochastic process analysis, the calculation is inaccurate when the stochastic process involves a multiple Markov property. We find that the variation of the shape of the membrane response, which has often been ignored in existing stochastic process studies, significantly affects the firing probability. Our approach can consider the reset effect, which has been difficult to deal with by analysis based on the first passage time density.

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40

Eweda, Eweda, Neil J. Bershad, and Jose Carlos M. Bermudez. "Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian and Non-Gaussian Inputs." IEEE Transactions on Signal Processing 66, no. 18 (September 15, 2018): 4753–65. http://dx.doi.org/10.1109/tsp.2018.2860552.

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41

Zubeldia, Martin, and Michel Mandjes. "Large deviations for acyclic networks of queues with correlated Gaussian inputs." Queueing Systems 98, no. 3-4 (February 18, 2021): 333–71. http://dx.doi.org/10.1007/s11134-021-09689-9.

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AbstractWe consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive drifts, which can be correlated across different queues. The flow of work departing from each server is split deterministically and routed to its neighbors according to a fixed routing matrix, with a fraction of it leaving the network altogether. We study the exponential decay rate of the probability that the steady-state queue length at any given node in the network is above any fixed threshold, also referred to as the ‘overflow probability’. In particular, we first leverage Schilder’s sample-path large deviations theorem to obtain a general lower bound for the limit of this exponential decay rate, as the number of Gaussian processes goes to infinity. Then, we show that this lower bound is tight under additional technical conditions. Finally, we show that if the input processes to the different queues are nonnegatively correlated, non-short-range dependent fractional Brownian motions, and if the processing rates are large enough, then the asymptotic exponential decay rates of the queues coincide with the ones of isolated queues with appropriate Gaussian inputs.

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42

Cortés, J. C., J. V. Romero, M. D. Roselló, and R. J. Villanueva. "Dealing with Dependent Uncertainty in Modelling: A Comparative Study Case through the Airy Equation." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/279642.

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The consideration of uncertainty in differential equations leads to the emergent area of random differential equations. Under this approach, inputs become random variables and/or stochastic processes. Often one assumes that inputs are independent, a hypothesis that simplifies the mathematical treatment although it could not be met in applications. In this paper, we analyse, through the Airy equation, the influence of statistical dependence of inputs on the output, computing its expectation and standard deviation by Fröbenius and Polynomial Chaos methods. The results are compared with Monte Carlo sampling. The analysis is conducted by the Airy equation since, as in the deterministic scenario its solutions are highly oscillatory, it is expected that differences will be better highlighted. To illustrate our study, and motivated by the ubiquity of Gaussian random variables in numerous practical problems, we assume that inputs follow a multivariate Gaussian distribution throughout the paper. The application of Fröbenius method to solve Airy equation is based on an extension of the method to the case where inputs are dependent. The numerical results show that the existence of statistical dependence among the inputs and its magnitude entails changes on the variability of the output.

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Sakai, Hiroko M., Naka Ken-Ichi, and Michael J. Korenberg. "White-noise analysis in visual neuroscience." Visual Neuroscience 1, no. 3 (May 1988): 287–96. http://dx.doi.org/10.1017/s0952523800001942.

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AbstractIn 1827, plant biologist Robert Brown discovered what is known as Brownian motion, a class of chaos. Formal derivative of Brownian motion is Gaussian white-noise. In 1938, Norbert Wiener proposed to use the Gaussian white-noise as an input probe to identify a system by a series of orthogonal functionals known as the Wiener G-functionals.White-noise analysis is uniquely suited for studying the response dynamics of retinal neurons because (1) white-noise light stimulus is a modulation around a mean luminance, as are the natural photic inputs, and it is a highly efficient input; and (2) the analysis defines the response dynamics and can be extended to spike trains, the final output of the retina. Demonstrated here are typical examples and results from applications of white-noise analysis to a visual system.

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Deistler, M. "Linear dynamic errors-in-variables models." Journal of Applied Probability 23, A (1986): 23–39. http://dx.doi.org/10.2307/3214340.

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Linear dynamical systems where both inputs and outputs are contaminated by errors are considered. A characterization of the sets of all observationally equivalent transfer functions is given, the role of the causality assumption is investigated and conditions for identifiability in the case of Gaussian as well as non-Gaussian observations are derived.

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Deistler, M. "Linear dynamic errors-in-variables models." Journal of Applied Probability 23, A (1986): 23–39. http://dx.doi.org/10.1017/s002190020011695x.

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Linear dynamical systems where both inputs and outputs are contaminated by errors are considered. A characterization of the sets of all observationally equivalent transfer functions is given, the role of the causality assumption is investigated and conditions for identifiability in the case of Gaussian as well as non-Gaussian observations are derived.

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Emara-Shabaik, Hosam E. "Filtering of Linear Systems With Unknown Inputs." Journal of Dynamic Systems, Measurement, and Control 125, no. 3 (September 1, 2003): 482–85. http://dx.doi.org/10.1115/1.1591804.

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State estimation of linear systems under the influence of both unknown deterministic inputs as well as Gaussian noise is considered. A Kalman like filter is developed which does not require the estimation of the unknown inputs as is customarily practiced. Therefore, the developed filter has reduced computational requirements. Comparative simulation results, under the influence of various types of unknown disturbance inputs, show the merits of the developed filter with respect to a conventional Kalman filter using disturbance estimation. It is found that the developed filter enjoys several practical advantages in terms of accuracy and fast tracking of the system states.

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Demianenko, Mariia, Ekaterina Samorodova, Mikhail Sysak, Aleksandr Shiriaev, Konstantin Malanchev, Denis Derkach, and Mikhail Hushchyn. "Supernova Light Curves Approximation based on Neural Network Models." Journal of Physics: Conference Series 2438, no. 1 (February 1, 2023): 012128. http://dx.doi.org/10.1088/1742-6596/2438/1/012128.

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Abstract Photometric data-driven classification of supernovae becomes a challenge due to the appearance of real-time processing of big data in astronomy. Recent studies have demonstrated the superior quality of solutions based on various machine learning models. These models learn to classify supernova types using their light curves as inputs. Preprocessing these curves is a crucial step that significantly affects the final quality. In this talk, we study the application of multilayer perceptron (MLP), bayesian neural network (BNN), and normalizing flows (NF) to approximate observations for a single light curve. We use these approximations as inputs for supernovae classification models and demonstrate that the proposed methods outperform the state-of-the-art based on Gaussian processes applying to the Zwicky Transient Facility Bright Transient Survey light curves. MLP demonstrates similar quality as Gaussian processes and speed increase. Normalizing Flows exceeds Gaussian processes in terms of approximation quality as well.

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GIOVANNETTI, VITTORIO, LORENZO MACCONE, SAIKAT GUHA, SETH LLOYD, JEFFREY H. SHAPIRO, and BRENT J. YEN. "MINIMUM OUTPUT ENTROPY OF A GAUSSIAN BOSONIC CHANNEL." International Journal of Quantum Information 03, no. 01 (March 2005): 153–58. http://dx.doi.org/10.1142/s0219749905000657.

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The entropy at the output of a Bosonic channel is analyzed when coherent fields are randomly added to the signal. Coherent-state inputs are conjectured to provide the minimum output entropy. Supporting physical and mathematical evidence is provided.

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Chan, T. H., S. Hranilovic, and F. R. Kschischang. "Capacity-Achieving Probability Measure for Conditionally Gaussian Channels With Bounded Inputs." IEEE Transactions on Information Theory 51, no. 6 (June 2005): 2073–88. http://dx.doi.org/10.1109/tit.2005.847707.

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Gao, Wei, and Jie Chen. "Transient Analysis of Signed LMS Algorithms With Cyclostationary Colored Gaussian Inputs." IEEE Transactions on Circuits and Systems II: Express Briefs 67, no. 12 (December 2020): 3562–66. http://dx.doi.org/10.1109/tcsii.2020.2997698.

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