scholarly journals Network Enhancement: a general method to denoise weighted biological networks

2018 ◽  
Author(s):  
Bo Wang ◽  
Armin Pourshafeie ◽  
Marinka Zitnik ◽  
Junjie Zhu ◽  
Carlos D. Bustamante ◽  
...  

Networks are ubiquitous in biology where they encode connectivity patterns at all scales of organization, from molecular to the biome. However, biological networks are noisy due to the limitations of technology used to generate them as well as inherent variation within samples. The presence of high levels of noise can hamper discovery of patterns and dynamics encapsulated by these networks. Here we propose Network Enhancement (NE), a novel method for improving the signal-to-noise ratio of undirected, weighted networks, and thereby improving the performance of downstream analysis. NE applies a novel operator that induces sparsity and leverages higher-order network structures to remove weak edges and enhance real connections. This iterative approach has a closed-form solution at convergence with desirable performance properties. We demonstrate the effectiveness of NE in denoising biological networks for several challenging yet important problems. Our experiments show that NE improves gene function prediction by denoising interaction networks from 22 human tissues. Further, we use NE to interpret noisy Hi-C contact maps from the human genome and demonstrate its utility across varying degrees of data quality. Finally, when applied to fine-grained species identification, NE outperforms alternative approaches by a significant margin. Taken together, our results indicate that NE is widely applicable for denoising weighted biological networks, especially when they contain high levels of noise.

Author(s):  
A. Stassopoulou ◽  
M. Petrou

We present in this paper a novel method for eliciting the conditional probability matrices needed for a Bayesian network with the help of a neural network. We demonstrate how we can obtain a correspondence between the two networks by deriving a closed-form solution so that the outputs of the two networks are similar in the least square error sense, not only when determining the discriminant function, but for the full range of their outputs. For this purpose we take into consideration the probability density functions of the independent variables of the problem when we compute the least square error approximation. Our methodoloy is demonstrated with the help of some real data concerning the problem of risk of desertification assessment for some burned forests in Attica, Greece where the parameters of the Bayesian network constructed for this task are successfully estimated given a neural network trained with a set of data.


2020 ◽  
Vol 641 ◽  
pp. A67
Author(s):  
F. Sureau ◽  
A. Lechat ◽  
J.-L. Starck

The deconvolution of large survey images with millions of galaxies requires developing a new generation of methods that can take a space-variant point spread function into account. These methods have also to be accurate and fast. We investigate how deep learning might be used to perform this task. We employed a U-net deep neural network architecture to learn parameters that were adapted for galaxy image processing in a supervised setting and studied two deconvolution strategies. The first approach is a post-processing of a mere Tikhonov deconvolution with closed-form solution, and the second approach is an iterative deconvolution framework based on the alternating direction method of multipliers (ADMM). Our numerical results based on GREAT3 simulations with realistic galaxy images and point spread functions show that our two approaches outperform standard techniques that are based on convex optimization, whether assessed in galaxy image reconstruction or shape recovery. The approach based on a Tikhonov deconvolution leads to the most accurate results, except for ellipticity errors at high signal-to-noise ratio. The ADMM approach performs slightly better in this case. Considering that the Tikhonov approach is also more computation-time efficient in processing a large number of galaxies, we recommend this approach in this scenario.


2001 ◽  
Vol 11 (04) ◽  
pp. 349-359 ◽  
Author(s):  
UDANTHA R. ABEYRATNE ◽  
G. ZHANG ◽  
P. SARATCHANDRAN

We address the problem of estimating biopotential sources within the brain, based on EEG signals observed on the scalp. This problem, known as the inverse problem of electrophysiology, has no closed-form solution, and requires iterative techniques such as the Levenberg – Marquardt (LM) algorithm. Considering the nonlinear nature of the inverse problem, and the low signal to noise ratio inherent in EEG signals, a backpropagation neural network (BPN) has been recently proposed as a solution. The technique has not been properly compared with classical techniques such as the LM method, or with more recent neural network techniques such as the Radial Basis Function (RBF) network. In this paper, we provide improved strategies based on BPN and consider RBF networks in solving the inverse problem. We compare the performances of BPN, RBF and a hybrid technique with that of the classical LM method.


1998 ◽  
Vol 18 (12) ◽  
pp. 1365-1377 ◽  
Author(s):  
Keith S. St. Lawrence ◽  
Ting-Yim Lee

Using the adiabatic approximation, which assumes that the tracer concentration in parenchymal tissue changes slowly relative to that in capillaries, we derived a time-domain, closed-form solution of the tissue homogeneity model. This solution, which is called the adiabatic solution, is similar in form to those of two-compartment models, Owing to its simplicity, the adiabatic solution can be used in CBF experiments in which kinetic data with only limited time resolution or signal-to-noise ratio, or both, are obtained. Using computer simulations, we investigated the accuracy and the precision of the parameters in the adiabatic solution for values that reflect 2H-labeled water (D2O) clearance from the brain (see Part II). It was determined that of the three model parameters, (1) the vascular volume ( Vi), (2) the product of extraction fraction and blood flow ( EF), and (3) the clearance rate constant ( kadb), only the last one could be determined accurately, and therefore CBF must be determined from this parameter only. From the error analysis of the adiabatic solution, it was concluded that for the D2O clearance experiments described in Part II, the coefficient of variation of CBF was approximately 7% in gray matter and 22% in white matter.


2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Zhiwen Hu ◽  
Zhenhua Xu

The problem of optimal power constrained distributed detection over a noisy multiaccess channel (MAC) is addressed. Under local power constraints, we define the transformation function for sensor to realize the mapping from local decision to transmitted waveform. The deflection coefficient maximization (DCM) is used to optimize the performance of power constrained fusion system. Using optimality conditions, we derive the closed-form solution to the considered problem. Monte Carlo simulations are carried out to evaluate the performance of the proposed new method. Simulation results show that the proposed method could significantly improve the detection performance of the fusion system with low signal-to-noise ratio (SNR). We also show that the proposed new method has a robust detection performance for broad SNR region.


2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Keyun Liao ◽  
Sai Zhao ◽  
Yusi Long ◽  
Gaofei Huang ◽  
Dong Tang

This paper considers the distributed beamforming design for a simultaneous wireless information and power transfer (SWIPT) in two-way relay network, which consists of two sources, K relay nodes and one energy harvesting (EH) node. For such a network, assuming perfect channel state information (CSI) is available, and we study two different beamforming design schemes. As the first scheme, we design the beamformer through minimization of the average mean squared error (MSE) subject to the total transmit power constraint at the relays and the energy harvesting constraint at the EH receiver. Due to the intractable expression of the objective function, an upper bound of MSE is derived via the approximation of the signal-to-noise ratio (SNR). Based on the minimization of this upper bound, this problem can be turned into a convex feasibility semidefinite programming (SDP) and, therefore, can be efficiently solved using interior point method. To reduce the computational complexity, a suboptimal beamforming scheme is proposed in the second scheme, for which the optimization problem could be recast to the form of the Rayleigh–Ritz ratio and a closed-form solution is obtained. Numerical results are provided and analyzed to demonstrate the efficiency of our proposed beamforming schemes.


2015 ◽  
Vol 743 ◽  
pp. 792-795
Author(s):  
Z.H. Xu ◽  
J.Y. Li ◽  
J. Wang

In this paper, we consider the problem of local power constrained coherent distributed detection over fading multi-access channel (MAC). The deflection coefficient maximization (DCM) is used to optimize the performance of fusion system under local power constraint of sensors. We use the statistical information of channel gain to obtain the deflection coefficient of the detection statistics at the fusion center. We derive the closed-form solution to the considered optimization problem. Monte-Carlo simulations are carried out to verify the performance of the proposed method. Simulation results show that the proposed method could significantly improve the detection performance of the fusion system under local power constraint and low signal-to-noise ratio (SNR).


1980 ◽  
Vol 12 (9) ◽  
pp. 983-1000 ◽  
Author(s):  
P A Phiri

This paper presents a range of methods for computing the equilibrium configuration of shopping facility sizes. First, the presently available range of quasi-balancing factor methods is considered and built into a theoretical framework in which further algorithms may be defined. Then the use of the gradient method is considered, which is a general method of solution of nonlinear equations. Last, it is shown that a special case exists in which a closed form solution may be obtained.


In this paper, closed form solution of outage and bit error rate (BER) is evaluated for the purpose of performance analysis of the amplify and forward relaying scheme under the asymmetric fading environment. In this dual hop system, we have used Rayleigh fading along source S to relay R and Mixture Gamma fading along relay R to destination D. First, we have derived closed form solution of outage and then we have used this derived expression for getting closed form solution of bit error rate (BER) for different kinds of modulation. Since Mixture Gamma fading channel represents many fading channels as its special case, so proposed closed form solution of outage and bit error rate may be used for analysis of outage and bit error rate under various fading scenarios. Specifically, in this paper, for analysis of outage and bit error rate (BER), we have taken Nakagami-m fading as a particular case of Mixture Gamma fading and analyzed the performance of proposed system after observing effect of fading severity factor and signal to noise ratio (SNR) on outage probability and bit error rate (BER)


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