On the Generalization of the Random Projection Method for Problems of the Recovery of Object Signal Described by Models of Convolution Type

Introduction. In technical systems, there is a common situation when transformation input-output is described by the integral equation of convolution type. This situation accurses if the object signal is recovered by the results of remote measurements. For example, in spectrometric tasks, for an image deblurring, etc. Matrices of the discrete representation for the output signal and the kernel of convolution are known. We need to find a matrix of the discrete representation of a signal of the object. The well known approach for solving this problem includes the next steps. First, the kernel matrix has to be represented as the Kroneker product. Second, the input-output transformation has to be presented with the usage of Kroneker product matrices. Third, the matrix of the discrete representation of the object has to be found. The object signal matrix estimation obtained with the help of pseudo inverting of Kroneker decomposition matrices is unstable. The instability of the object signal estimation in the case of usage of Kroneker decomposition matrices is caused by their discrete ill posed matrix properties (condition number is big and the series of the singular numbers smoothly decrease to zero). To find solutions of discrete ill-posed problems we developed methods based on the random projection and the random projection with an averaging by the random matrices. These methods provide a stable solutions with a small computational complexity. We consider the problem of object signals recovering in the systems where an input-output transformation is described by the integral equation of a convolution. To find a solution for these problems we need to build a generalization for two-dimensional signals case of the random projection method. Purpose. To develop a stable method of the recovery of object signal for the case in which an input-output transformation is described by the integral equation of a convolution. Results and conclusions. We developed the method of a stable recovery of object signal for the case in which an input-output transformation is described by the integral equation of a convolution. The stable estimation of the object signal is provided by Kroneker decomposition of the kernel matrix of convolution, computation of random projections for Kroneker factorization matrices, and a selection of the optimal dimension of a projector matrix. The method is illustrated by its application in technical problems.

Distinct dendritic Ca2+ spike forms produce opposing input-output transformations in rat CA3 pyramidal cells

Proper integration of different inputs targeting the dendritic tree of CA3 pyramidal cells (CA3PCs) is critical for associative learning and recall. Dendritic Ca2+ spikes have been proposed to perform associative computations in other PC types by detecting conjunctive activation of different afferent input pathways, initiating afterdepolarization (ADP), and triggering burst firing. Implementation of such operations fundamentally depends on the actual biophysical properties of dendritic Ca2+ spikes; yet little is known about these properties in dendrites of CA3PCs. Using dendritic patch-clamp recordings and two-photon Ca2+ imaging in acute slices from male rats, we report that, unlike CA1PCs, distal apical trunk dendrites of CA3PCs exhibit distinct forms of dendritic Ca2+ spikes. Besides ADP-type global Ca2+ spikes, a majority of dendrites expresses a novel, fast Ca2+ spike type that is initiated locally without bAPs, can recruit additional Na+ currents, and is compartmentalized to the activated dendritic subtree. Occurrence of the different Ca2+ spike types correlates with dendritic structure, indicating morpho-functional heterogeneity among CA3PCs. Importantly, ADPs and dendritically initiated spikes produce opposing somatic output: bursts versus strictly single-action potentials, respectively. The uncovered variability of dendritic Ca2+ spikes may underlie heterogeneous input-output transformation and bursting properties of CA3PCs, and might specifically contribute to key associative and non-associative computations performed by the CA3 network.

Environmental Innovation and Green Growth in the Repair and Maintenance of Cars—Case Study

The current phase of the sustainable development of production is primarily focused on innovation and environmental products and services, and on greening the economy through the implementation of standardized tools (according to ISO). The paper presents the application of results of ongoing research through case studies under particular conditions. We have expanded our previously proposed business model as an input/output transformation system, presented in our previous research that was published at the 18th International Scientific Conference “Globalization and Its Socio-Economic Consequences” in Zilina and supported by the fact that we are co-creators of STN EN ISO standards 14051:2012 (839051) and STN EN ISO 14045:2013 (839045). Here, it is supplemented by the proposal of a procedure for selecting an instrument for greening the economy according to the area of economic activities (NACE coding). The methodological principles and the proposed procedure are applied through a case study in a small car repair company.

Impact of functional synapse clusters on neuronal response selectivity

Clustering of functionally similar synapses in dendrites is thought to affect neuronal input-output transformation by triggering local nonlinearities. However, neither the in vivo impact of synaptic clusters on somatic membrane potential (sVm), nor the rules of cluster formation are elucidated. We develop a computational approach to measure the effect of functional synaptic clusters on sVm response of biophysical model CA1 and L2/3 pyramidal neurons to in vivo-like inputs. We demonstrate that small synaptic clusters appearing with random connectivity do not influence sVm. With structured connectivity, ~10–20 synapses/cluster are optimal for clustering-based tuning via state-dependent mechanisms, but larger selectivity is achieved by 2-fold potentiation of the same synapses. We further show that without nonlinear amplification of the effect of random clusters, action potential-based, global plasticity rules cannot generate functional clustering. Our results suggest that clusters likely form via local synaptic interactions, and have to be moderately large to impact sVm responses.

The olfactory bulb contributes to the adaptation of odor responses: the input-output transformation

While humans and other animals exhibit adaptation to odorants, the neural mechanisms involved in this process are incompletely understood. One possibility is that it primarily occurs as a result of the interactions between odorants and odorant receptors expressed on the olfactory sensory neurons in the olfactory epithelium. In this scenario, adaptation would arise as a peripheral phenomenon transmitted into the brain. An alternative possibility is that adaptation occurs as a result of processing in the brain. Here we asked whether the olfactory bulb, the first stage of olfactory information processing in the brain, is involved in perceptual adaptation. Multicolor imaging was used to simultaneously measure the olfactory receptor nerve terminals (input) and mitral/tufted cell apical dendrites (output) that innervate the olfactory bulb glomerular layer. Repeated odor stimulation of the same concentration resulted in a decline in the output maps, while the input remained relatively stable. The results indicate that the mammalian olfactory bulb participates in olfactory adaptation.

Impact of functional synapse clusters on neuronal response selectivity

SummaryClustering of functionally similar synapses in dendrites is thought to affect input-output transformation by inducing dendritic nonlinearities. However, neither the in vivo impact of synaptic clusters on somatic membrane potential (sVm), nor the rules of cluster formation are elucidated. We developed a computational approach to measure the effect of functional synaptic clusters on sVm response of biophysical model CA1 and L2/3 pyramidal neurons to behaviorally relevant in vivo-like inputs. Large-scale dendritic spatial inhomogeneities in synaptic tuning properties did influence sVm, but small synaptic clusters appearing randomly with unstructured connectivity did not. With structured connectivity, ~10-20 synapses per cluster was optimal for clustering-based tuning, but larger responses were achieved by 2-fold potentiation of the same synapses. We further show that without nonlinear amplification of the effect of random clusters, action potential-based, global plasticity rules can not generate functional clustering. Our results suggest that clusters likely form via local synaptic interactions, and have to be moderately large to impact sVm responses.

Input-Output Transformation Using the Feedback of Nonlinear Electrical Circuits: Algorithms and Linearization Examples

This paper addresses the problem of nonlinear electrical circuit input-output linearization. The transformation algorithms for linearization of nonlinear system through changing coordinates (local diffeomorphism) with the use of closed feedback loop together with the conditions necessary for linearization are presented. The linearization stages and the results of numerical simulations are discussed.