nonlinear integration
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2021 ◽  
Vol 17 (11) ◽  
pp. e1009569
Author(s):  
Julia C. Gorman ◽  
Oliver L. Tufte ◽  
Anna V. R. Miller ◽  
William M. DeBello ◽  
José L. Peña ◽  
...  

Emergent response properties of sensory neurons depend on circuit connectivity and somatodendritic processing. Neurons of the barn owl’s external nucleus of the inferior colliculus (ICx) display emergence of spatial selectivity. These neurons use interaural time difference (ITD) as a cue for the horizontal direction of sound sources. ITD is detected by upstream brainstem neurons with narrow frequency tuning, resulting in spatially ambiguous responses. This spatial ambiguity is resolved by ICx neurons integrating inputs over frequency, a relevant processing in sound localization across species. Previous models have predicted that ICx neurons function as point neurons that linearly integrate inputs across frequency. However, the complex dendritic trees and spines of ICx neurons raises the question of whether this prediction is accurate. Data from in vivo intracellular recordings of ICx neurons were used to address this question. Results revealed diverse frequency integration properties, where some ICx neurons showed responses consistent with the point neuron hypothesis and others with nonlinear dendritic integration. Modeling showed that varied connectivity patterns and forms of dendritic processing may underlie observed ICx neurons’ frequency integration processing. These results corroborate the ability of neurons with complex dendritic trees to implement diverse linear and nonlinear integration of synaptic inputs, of relevance for adaptive coding and learning, and supporting a fundamental mechanism in sound localization.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Decai Tang ◽  
Zhiwei Pan ◽  
Brandon J. Bethel

Abstract Although the prediction of stock prices and analyses of their returns and risks have always played integral roles in the stock market, accurate predictions are notoriously difficult to make, and mistakes may be devastatingly costly. This study attempts to resolve this difficulty by proposing and applying a two-stage long short-term memory (LSTM) model based on multi-scale nonlinear integration that considers a diverse array of factors. Initially, variational mode decomposition (VMD) is used to decompose an employed stock index to identify the different characteristics of the stock index sequence. Then, an LSTM model based on the multi-factor nonlinear integration of overnight information is established in a second stage. Finally, the joint VMD-LSTM model is used to predict the stock index. To validate the model, the Shanghai Composite, Nikkei 225, and Hong Kong Hang Seng indices were analyzed. Experiments show that, by comparison, the prediction effect of the mixed model is better than that of a single LSTM. For example, RMSE, MAE and MAPE of the mixed model of the Shanghai Composite Index are 4.22, 4.25 and 0.2 lower than the single model respectively. The RMSE, MAE and MAPE of the mixed model of the Nikkei 225 Index are 47.74, 37.21 and 0.17 lower than the single model respectively, and the RMSE, MAE and MAPE of the mixed model of the Hong Kong Hang Seng Index are 37.88, 25.06 and 0.08 lower than the single model respectively.


eLife ◽  
2021 ◽  
Vol 10 ◽  
Author(s):  
Yang Zhou ◽  
Matthew C Rosen ◽  
Sruthi K Swaminathan ◽  
Nicolas Y Masse ◽  
Ou Zhu ◽  
...  

Comparing sequential stimuli is crucial for guiding complex behaviors. To understand mechanisms underlying sequential decisions, we compared neuronal responses in the prefrontal cortex (PFC), the lateral intraparietal (LIP), and medial intraparietal (MIP) areas in monkeys trained to decide whether sequentially presented stimuli were from matching (M) or nonmatching (NM) categories. We found that PFC leads M/NM decisions, whereas LIP and MIP appear more involved in stimulus evaluation and motor planning, respectively. Compared to LIP, PFC showed greater nonlinear integration of currently visible and remembered stimuli, which correlated with the monkeys’ M/NM decisions. Furthermore, multi-module recurrent networks trained on the same task exhibited key features of PFC and LIP encoding, including nonlinear integration in the PFC-like module, which was causally involved in the networks’ decisions. Network analysis found that nonlinear units have stronger and more widespread connections with input, output, and within-area units, indicating putative circuit-level mechanisms for sequential decisions.


2021 ◽  
Author(s):  
Mu Zhang ◽  
Cheng Cao

Abstract In order to solve the problem that it is difficult to quantitatively evaluate the interactivity between attributes in the identification process of 2-order additive fuzzy measure, this work uses the hesitant fuzzy linguistic term set (HFLTS) to describe and deal with the interactivity between attributes. Firstly, the interactivity between attributes is defined by the supermodular game theory, and a linguistic term set is then established to characterize the interactivity between attributes. Secondly, under the linguistic term set, according to the above definition, the experts employ the linguistic expressions generated by the context-free grammar to evaluate the interactivity between attributes, and the opinions of all experts are then aggregated by using the defined hesitant fuzzy linguistic weighted power average operator (HFLWPA). Thirdly, based on the standard Euclidean distance formula of the hesitant fuzzy linguistic elements (HFLEs), the hesitant fuzzy linguistic interaction degree (HFLID) between attributes is defined and calculated by constructing a piecewise function. Finally, a 2-order additive fuzzy measure identification method based on HFLID is further proposed. Based on the proposed method, using the Choquet fuzzy integral as nonlinear integration operator, a multi-attribute decision making (MADM) process is presented. Taking the credit assessment of the big data listed companies in China as an application example, the feasibility and effectiveness of the proposed method is verified by the analysis results of application example.


2020 ◽  
Author(s):  
Christopher Dorsett ◽  
Benjamin Philpot ◽  
Spencer LaVere Smith ◽  
Ikuko T. Smith

AbstractExcitatory inputs arriving at the dendrites of a neuron can engage active mechanisms that nonlinearly amplify the depolarizing currents. Interneuron-mediated inhibition can modulate this active process, in a subtype-dependent manner. For example, dendrite-targeting inhibition is hypothesized to increase the amplitude of synaptic input required to activate voltage-dependent nonlinear synaptic integration. To examine how inhibition influences active synaptic integration, we optogenetically manipulated the activity of two different subtypes of interneurons: dendrite-targeting somatostatin-expressing (SOM) and perisomatic-targeting parvalbumin-expressing (PV) interneurons. In acute slices of mouse primary visual cortex, electrical stimulation evoked nonlinear synaptic integration that depended on N-methyl-D-aspartate (NMDA) receptors. Optogenetic activation of SOM neurons in conjunction with electrical stimulation resulted in predominantly divisive inhibitory gain control, reducing the magnitude of the nonlinear response without affecting its threshold. PV activation, on the other hand, had a minimal effect on dendritic nonlinearities, resulting in a small subtractive effect. Furthermore, we found that mutual inhibition among SOM interneurons was strong and more prevalent than previously thought, while mutual inhibition among PV interneurons was minimal. These results challenge previous models of inhibitory modulation of active synaptic integration. The major effect of SOM inhibition is not a shift in threshold for activation of nonlinear integration, but rather a decrease the amplitude of the nonlinear response.


2020 ◽  
Author(s):  
Yang Zhou ◽  
Matthew Rosen ◽  
Sruthi K. Swaminathan ◽  
Nicolas Y. Masse ◽  
Oliver Zhu ◽  
...  

AbstractThe ability to compare sequential sensory inputs is crucial for solving many behavioral tasks. To understand the neuronal mechanisms underlying sequential decisions, we compared neuronal responses in the prefrontal cortex (PFC) and the lateral and medial intra-parietal (LIP and MIP) areas in monkeys trained to decide whether sequentially presented stimuli were from matching (M) or nonmatching (NM) categories. We found that PFC leads the M/NM decision process relying on nonlinear neuronal integration of sensory and mnemonic information, whereas LIP and MIP are more involved in sensory evaluation and motor planning, respectively. Furthermore, multi-module recurrent neural networks trained on the same task exhibited the key features of PFC and LIP encoding, including nonlinear integrative encoding in the PFC-like module which was crucial for M/NM decisions. Together, our results illuminate the relative functions of LIP, PFC, and MIP in sensory, cognitive and motor functions, and suggest that nonlinear integration of task-related variables in PFC is important for mediating sequential decisions.


Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
Ying Nie ◽  
He Bo ◽  
Weiqun Zhang ◽  
Haipeng Zhang

Wind energy analysis and wind speed modeling have a significant impact on wind power generation systems and have attracted significant attention from many researchers in recent decades. Based on the inherent characteristics of wind speed, such as nonlinearity and randomness, the prediction of wind speed is considered to be a challenging task. Previous studies have only considered point prediction or interval measurement of wind speed separately and have not combined these two methods for prediction and analysis. In this study, we developed a novel hybrid wind speed double prediction system comprising a point prediction module and interval prediction module to compensate for the shortcomings of existing research. Regarding point prediction in the developed double prediction system, a novel nonlinear integration method based on a backpropagation network optimized using the multiobjective evolutionary algorithm based on decomposition was successfully implemented to derive the final prediction results, which enable further improvement of the accuracy of point prediction. Based on point prediction results, we propose an interval prediction method that constructs different intervals according to the classification of different data features via fuzzy clustering, which provides reliable interval prediction results. The experimental results demonstrate that the proposed system outperforms existing methods in engineering applications and can be used as an effective technology for power system planning.


2020 ◽  
Vol 10 (4) ◽  
pp. 1550 ◽  
Author(s):  
Ping Jiang ◽  
Ying Nie

Accurate and reliable power load forecasting not only takes an important place in management and steady running of smart grid, but also has environmental benefits and economic dividends. Accurate load point forecasting can provide a guarantee for the daily operation of the power grid, and effective interval forecasting can further quantify the uncertainty of power load on this basis to provide dependable and precise load information. However, most of the previous work focuses on the deterministic point prediction of power load and rarely considers the interval prediction of power load, which makes the prediction of power load not comprehensive. In this study, a new double hybrid load forecasting system including point forecasting module and interval forecasting module is developed, which can make up for the shortcomings of incomplete analysis for the existing research. The point forecasting module adopts a nonlinear integration mechanism based on Back Propagation (BP) network optimized by Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D) to improve the accuracy of point prediction. A fuzzy clustering interval prediction method based on different data feature classification is successfully proposed which provides an effective tool for load uncertainty analysis. The experiment results show that the system not only has a good effect in accurately predicting power load, but also can analyze the uncertainty of the power load, which can be used as an effective technology of power system planning.


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