Canonical neural networks perform active inference

This work considers a class of canonical neural networks comprising rate coding models, wherein neural activity and plasticity minimise a common cost function—and plasticity is modulated with a certain delay. We show that such neural networks implicitly perform active inference and learning to minimise the risk associated with future outcomes. Mathematical analyses demonstrate that this biological optimisation can be cast as maximisation of model evidence, or equivalently minimisation of variational free energy, under the well-known form of a partially observed Markov decision process model. This equivalence indicates that the delayed modulation of Hebbian plasticity—accompanied with adaptation of firing thresholds—is a sufficient neuronal substrate to attain Bayes optimal inference and control. We corroborated this proposition using numerical analyses of maze tasks. This theory offers a universal characterisation of canonical neural networks in terms of Bayesian belief updating and provides insight into the neuronal mechanisms underlying planning and adaptive behavioural control.

New Method to Estimate Central Systolic Blood Pressure From Peripheral Pressure: A Proof of Concept and Validation Study

Objective: The non-invasive estimation of central systolic blood pressure (cSBP) is increasingly performed using new devices based on various pulse acquisition techniques and mathematical analyses. These devices are most often calibrated assuming that mean (MBP) and diastolic (DBP) BP are essentially unchanged when pressure wave travels from aorta to peripheral artery, an assumption which is evidence-based. We tested a new empirical formula for the direct central blood pressure estimation of cSBP using MBP and DBP only (DCBP = MBP2/DBP).Methods and Results: First, we performed a post-hoc analysis of our prospective invasive high-fidelity aortic pressure database (n = 139, age 49 ± 12 years, 78% men). The cSBP was 146.0 ± 31.1 mmHg. The error between aortic DCBP and cSBP was −0.9 ± 7.4 mmHg, and there was no bias across the cSBP range (82.5–204.0 mmHg). Second, we analyzed 64 patients from two studies of the literature in whom invasive high-fidelity pressures were simultaneously obtained in the aorta and brachial artery. The weighed mean error between brachial DCBP and cSBP was 1.1 mmHg. Finally, 30 intensive care unit patients equipped with fluid-filled catheter in the radial artery were prospectively studied. The cSBP (115.7 ± 18.2 mmHg) was estimated by carotid tonometry. The error between radial DCBP and cSBP was −0.4 ± 5.8 mmHg, and there was no bias across the range.Conclusion: Our study shows that cSBP could be reliably estimated from MBP and DBP only, provided BP measurement errors are minimized. DCBP may have implications for assessing cardiovascular risk associated with cSBP on large BP databases, a point that deserves further studies.

Hebbian plasticity in parallel synaptic pathways: A circuit mechanism for systems memory consolidation

Systems memory consolidation involves the transfer of memories across brain regions and the transformation of memory content. For example, declarative memories that transiently depend on the hippocampal formation are transformed into long-term memory traces in neocortical networks, and procedural memories are transformed within cortico-striatal networks. These consolidation processes are thought to rely on replay and repetition of recently acquired memories, but the cellular and network mechanisms that mediate the changes of memories are poorly understood. Here, we suggest that systems memory consolidation could arise from Hebbian plasticity in networks with parallel synaptic pathways—two ubiquitous features of neural circuits in the brain. We explore this hypothesis in the context of hippocampus-dependent memories. Using computational models and mathematical analyses, we illustrate how memories are transferred across circuits and discuss why their representations could change. The analyses suggest that Hebbian plasticity mediates consolidation by transferring a linear approximation of a previously acquired memory into a parallel pathway. Our modelling results are further in quantitative agreement with lesion studies in rodents. Moreover, a hierarchical iteration of the mechanism yields power-law forgetting—as observed in psychophysical studies in humans. The predicted circuit mechanism thus bridges spatial scales from single cells to cortical areas and time scales from milliseconds to years.

Mycorrhiza-Induced Alterations in Metabolome of Medicago lupulina Leaves during Symbiosis Development

The present study is aimed at disclosing metabolic profile alterations in the leaves of the Medicago lupulina MlS-1 line that result from high-efficiency arbuscular mycorrhiza (АМ) symbiosis formed with Rhizophagus irregularis under condition of a low phosphorus level in the substrate. A highly effective AM symbiosis was established in the period from the stooling to the shoot branching initiation stage (the efficiency in stem height exceeded 200%). Mycorrhization led to a more intensive accumulation of phosphates (glycerophosphoglycerol and inorganic phosphate) in M. lupulina leaves. Metabolic spectra were detected with GS-MS analysis. The application of complex mathematical analyses made it possible to identify the clustering of various groups of 320 metabolites and thus demonstrate the central importance of the carbohydrate and carboxylate-amino acid clusters. The results obtained indicate a delay in the metabolic development of mycorrhized plants. Thus, AM not only accelerates the transition between plant developmental stages but delays biochemical “maturation” mainly in the form of a lag of sugar accumulation in comparison with non-mycorrhized plants. Several methods of statistical modeling proved that, at least with respect to determining the metabolic status of host-plant leaves, stages of phenological development have priority over calendar age.

Turing pattern design principles and their robustness

Turing patterns have morphed from mathematical curiosities into highly desirable targets for synthetic biology. For a long time, their biological significance was sometimes disputed but there is now ample evidence for their involvement in processes ranging from skin pigmentation to digit and limb formation. While their role in developmental biology is now firmly established, their synthetic design has so far proved challenging. Here, we review recent large-scale mathematical analyses that have attempted to narrow down potential design principles. We consider different aspects of robustness of these models and outline why this perspective will be helpful in the search for synthetic Turing-patterning systems. We conclude by considering robustness in the context of developmental modelling more generally. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

Influence of Microstepping Signal Shape on Shaft Movement Precision and Torque Variation of the Stepper Motor

Stepper motors are widely used in many applications where discrete, precise movement is required. There is a variety of dedicated stepper motor controllers (sometimes referred to as “step sticks”) available on the market. Those controllers provide a number of different motor control schemes that vary by aspects like current control method, reference current shape or maximum resolution increase (microstepping). The two most widely acknowledged signal shapes are sine-cosine microstepping and quadrature microstepping. The choice of the control scheme impacts torque output, torque variation, positioning error and maximum power supply requirements. This paper presents a family of generalised microstepping signal shapes, ranging from sine-cosine microstepping to quadrature microstepping. Derivation of signal shapes as well as their mathematical analyses are provided. Those signals are then implemented on the control board. A series of experiments is performed on a test bench to analyse the influence of different signal shapes on the performance of the motor in both load and no load conditions. The comparison of the new generalized shapes influence on the motor operation to the commonly used sine-cosine and quadrature control is provided.

Design and Analysis of Mathematical Model for the Concentration of Pollution and River Water Quality

This paper mainly focuses on the recent advances in the mathematical models that provide the ability to predict the contaminant concentration levels of river water. The study represents an attempt for the researchers to study the problem of pollution, and we think that these mathematical analyses would provide better planning for water quality control. The model consists of a pair of coupled reaction Advection-diffusion equations for the pollutant and dissolved oxygen concentrations. Numerical solutions are obtained and some important inferences are drawn through simulation study. The Advection-Diffusion equation is characterized by the reaction term whenever it depends on concentration of the contaminants and in this case the original single Advection-diffusion equation will evolve to be a system of equations. It is no ticked that the higher are diffusion and reaeration coefficients, the faster is the river purity.

The problem of measuring the quantity of output in the input–output model by W. Leontief in modeling the trends in economic reproduction of nations and regions

Subject. This article deals with the problem of constructing a Leontief's input–output matrix. Objectives. The article aims to determine the rules for constructing a Leontief's input–output matrix on the basis of data on production time and quantity of product output. Methods. For the study, I used the methods of logical and mathematical analyses. Results. The article formulates the rules for constructing a Leontief's input–output matrix, taking into account differences in the time of production, quantity of output, as well as the conditions for the reproduction of the resources expended. It summarizes these rules for the J. von Neumann model. Conclusions. The proposed approach to the analysis of the material mechanism of economic reproduction defines the relationship between the quantitative and cost characteristics of the production and consumption of products and resources. This relationship opens up new opportunities for the application of input–output models to create simple and accurate algorithms for identifying and predicting the macroeconomic trends.

Data Integration in Logic-based Models of Biological Mechanisms

Discrete, logic-based models are increasingly used to describe biological mechanisms. Initially introduced to study gene regulation, these models evolved to cover various molecular mechanisms, such as signalling, transcription factor cooperativity, and even metabolic processes. The abstract nature and amenability of discrete models to robust mathematical analyses make them appropriate for addressing a wide range of complex biological problems. Recent technological breakthroughs have generated a wealth of high throughput data. Novel, literature-based representations of biological processes and emerging algorithms offer new opportunities for model construction. Here, we review up-to-date efforts to address challenging biological questions by incorporating omic data into logic-based models, and discuss critical difficulties in constructing and analysing integrative, large-scale, logic-based models of biological mechanisms.

MULTIPRODUCT MANUFACTURING WITH DELAYED DIFFERENTIATION, OUTSOURCING, EXPEDITED RATE, AND REWORK STRATEGIES

This study examines the effect of delayed differentiation, outsourcing, expedited fabrication rate, and rework strategies on optimal cycle-time decisions for a multi-item manufacturing system. Today’s manufacturing firms must simultaneously deal with externally increasing client multi-item requirements with rapid lead-time and high-quality products and internally on a limited capacity. This study is aimed at assisting manufacturers in meeting client needs in conditions of restricted-capacity and minimum total operating expenses, and adopts a delayed differentiation two-stage multiproduct manufacturing scheme to manage the end products’ commonality. The first stage produces all required common components, and the second stage fabricates individual finished goods. In both stages, we adopt the reworking of the inevitable nonconforming items produced to assure product quality. Furthermore, we implemented partial outsourcing of common parts’ batch and expedited the manufacturing rate of finished products to effectively reduce the uptimes in both stages. We explicitly developed a model to describe the characteristics of the problem. Mathematical analyses with optimization proved the cost function’s convexity and determined the cost-minimization rotation cycle policy. Finally, we numerically validated our model’s and results’ applicability and capability with a simulated example. Apart from creating a useful decision model, this study makes another important contribution to the existing literature in that its revelation of collective/individual effect of the manufacturing-relevant methods on the problem’s best-operating cycle policy and crucial performance indices helps manufacturers have better control over their operations and make effective and efficient managerial decisions.