Linear Combination Of Inputs Research Articles

Mouse dLGN Receives Functional Input from a Diverse Population of Retinal Ganglion Cells with Limited Convergence

Mouse vision is based on the parallel output of more than 30 functional types of retinal ganglion cells (RGCs). Little is known about how representations of visual information change between retina and dorsolateral geniculate nucleus (dLGN) of the thalamus, the main relay between retina and cortex. Here, we functionally characterized responses of retrogradely labeled dLGN-projecting RGCs and dLGN neurons to the same set of visual stimuli. We found that many of the previously identified functional RGC types innervate dLGN, which maintained a high degree of functional diversity. Using a linear model to assess functional connectivity between RGC types and dLGN neurons, we found that responses of dLGN neurons could be predicted as linear combination of inputs from on average five RGC types, but only two of those had the strongest functional impact. Thus, mouse dLGN receives functional input from a diverse population of RGC types with limited convergence.

Gaussian Quadrature and Polynomial Approximation for One-Dimensional Ridge Functions

Many of the input-parameter-to-output-quantity-of-interest maps that arise in computational science admit a surprising low-dimensional structure, where the outputs vary primarily along a handful of directions in the high-dimensional input space. This type of structure is well modeled by a ridge function, which is a composition of a low-dimensional linear transformation with a nonlinear function. If the goal is to compute statistics of the output---e.g., as in uncertainty quantification or robust design---then one should exploit this low-dimensional structure, when present, to accelerate computations. We develop Gaussian quadrature and the associated polynomial approximation for one-dimensional ridge functions. The key elements of our method are (i) approximating the univariate density of the given linear combination of inputs by repeated convolutions and (ii) a Lanczos--Stieltjes method for constructing orthogonal polynomials and Gaussian quadrature.

Mouse dLGN Receives Input from a Diverse Population of Retinal Ganglion Cells with Limited Functional Convergence

In the mouse, the parallel output of more than 30 functional types of retinal ganglion cells (RGCs) serves as the basis for all further visual processing. Little is known about how the representation of visual information changes between the retina and the dorsolateral geniculate nucleus (dLGN) of the thalamus, the main relay station between the retina and cortex. Here, we functionally characterized responses of retrogradely labeled dLGN-projecting RGCs and dLGN neurons to the same set of visual stimuli. We found that many of the previously identified functional RGC types innervate the dLGN, which maintained a high degree of functional diversity. Using a linear model to assess functional connectivity between RGC types and dLGN neurons, we found that the responses of dLGN neurons could be predicted as a linear combination of inputs from on average five RGC types, but only two of those had the strongest functional impact. Thus, mouse dLGN receives input from a diverse population of RGCs with limited functional convergence.

Stability Analysis of a Class of MIMO Recurrent Type-2 Fuzzy Systems

This paper presents a sufficient condition for stability of a class of multiple input multiple output recurrent type-2 TSK fuzzy systems using spectrum analysis. In this class of type-2 TSK fuzzy systems, the antecedent part is interval Gaussian type-2 fuzzy sets and the consequent part is a linear combination of inputs with crisp coefficients. In the proposed method, at first a type-2 fuzzy model is built and then the stability of the model is analyzed. It should be noted that this method is suitable for strictly ascending and strictly decreasing systems. Two first-order systems and two second-order systems are simulated by type-2 and type-1 fuzzy systems. The simulation results show the effectiveness of the proposed method.

Subspace Identification of Large-Scale Interconnected Systems

We propose a decentralized subspace algorithm for the identification of large-scale, interconnected systems that are described by sparse (multi) banded state-space matrices. First, we prove that the state of a local subsystem can be approximated by a linear combination of inputs and outputs of local subsystems that are in its neighborhood. Furthermore, we prove that for interconnected systems with well-conditioned, finite-time observability Gramians (or observability matrices), the size of this neighborhood is relatively small. On the basis of these results, we develop the subspace identification algorithm that identifies the state-space model of a local subsystem from the local input-output data. Consequently, the developed algorithm is computationally feasible for interconnected systems with a large number of local subsystems. Numerical results confirm the effectiveness of the new identification algorithm.

Perfect involutory diffusion layers based on invertibility of some linear functions

One of the most important structures used in modern block ciphers is the substitution-permutation network (SPN) structure. Many block ciphers with this structure widely use Maximun Distance Separable (MDS) matrices over finite fields as their diffusion layers, for example, advanced encryption standard (AES) uses a 4-4 MDS matrix as the main part of its diffusion layer and the block cipher Khazad has an involutory 8-8 matrix. In this study, first a construction is proposed for a 4-4 linear diffusion layer that can intermix four words of arbitrary size with branch number 5. Then extend this idea for 8-8 diffusion layer using low-cost linear functions. In this construction, first, certain binary linear combinations of inputs are fed into two or three different invertible linear functions and then combined using XOR operation. In order to show the efficiency of the proposed diffusion layer, the authors exploit it in a nested SPN structure and compare its efficiency with some well-known diffusion layers such as the diffusion layer of Hierocrypt.

Nonparametric direct mapping of rainfall‐runoff relationships: An alternative approach to data analysis and modeling?

We present a new approach for the analysis and modeling of catchment rainfall‐runoff relationships that uses as predictor variables input history summary variables only. The latter are defined as linear combinations of inputs at a given number of previous time steps. This transforms the dynamic identification problem into a static one. As the identification algorithm we use regression trees, which act as a nonlinear nonparametric model. The original algorithm is adapted to account for serial correlation in variables. The new method is applied to two subcatchments of the U.S. Department of Agriculture Forest Service Andrews Experimental Forest Watershed (Oregon, United States). Simple and interpretable tree models explain more than 80% of the initial deviance of the observations in both calibration and validation. This suggests that the selected variables have a good predictive power and that further modeling attempts using them are warranted. The models show a distinct pattern of the selected explanatory variables. Applications of the method include data quality control, comparative analysis, assessment of hydrological change, and multicriterion evaluation of parametric hydrological models.

Performance of binary joint transform correlator using linear combination threshold function

A linear combination threshold function, which is defined as the linear combination of input and reference power spectra, is proposed to binarize the joint power spectrum of a joint transform correlator (JTC). The performance of binary JTC depends on the linear combination coefficients of input and reference power spectra. This relationship is investigated and an optimal linear combination threshold function is determined to get a trade-off between some of performance criteria for character recognition. The theory analysis and verification by computer simulation are described. The proposed technique is also investigated by a hybrid optoelectronic system.