Minimal Network Research Articles

A symmetric toggle switch explains the onset of random X inactivation in different mammals.

Gene-regulatory networks control establishment and maintenance of alternative gene expression states during development. A particular challenge is the acquisition of opposing states by two copies of the same gene, as it is the case in mammals for Xist at the onset of random X-chromosome inactivation (XCI). The regulatory principles that lead to stable mono-allelic expression of Xist remain unknown. Here, we uncovered the minimal Xist regulatory network, by combining mathematical modeling and experimental validation of central model predictions. We identified a symmetric toggle switch as the basis for random mono-allelic Xist up-regulation, which reproduces data from several mutant, aneuploid and polyploid murine cell lines with various Xist expression patterns. Moreover, this toggle switch explains the diversity of strategies employed by different species at the onset of XCI. In addition to providing a unifying conceptual framework to explore X-chromosome inactivation across mammals, our study sets the stage for identifying the molecular mechanisms required to initiate random XCI.

On different notions of calibrations for minimal partitions and minimal networks in ℝ2

Abstract Calibrations are a possible tool to validate the minimality of a certain candidate. They have been introduced in the context of minimal surfaces and adapted to the case of the Steiner problem in several variants. Our goal is to compare the different notions of calibrations for the Steiner problem and for planar minimal partitions that are already present in the literature. The paper is then complemented with remarks on the convexification of the problem, on nonexistence of calibrations and on calibrations in families.

Analysis of a Minimal Gene Regulatory Network for Cell Differentiation

In this letter, we provide a detailed analysis of a gene regulatory network exhibiting bistability within a certain region of parameter space. This network has been adopted in recent literature to describe cellular differentiation into two subpopulations. Biological and experimental evidence suggests that differentiation from stem cells into different tissues evolves through a cascade of similar stages characterized by differentiation into two subtypes. Each differentiation step is influenced by two mechanisms: the first one occurs within the cell and allows transition from an undifferentiated stage to a pluripotent stage where differentiation is possible and the second mechanism may be external to the cell and biases differentiation into a specific subpopulation. In this letter, we address the former mechanism for a gene circuit described by generalized Hill equations and endowed with mutual inhibitory feedback among two competing genes. The main contribution is twofold: 1) mutual inhibition is not sufficient to allow cell differentiation, but specific conditions on the generalized Hill equations’ parameters are required and 2) differentiation occurs only if the triggering gene expression level belongs to a well defined range. Theoretical analysis is complemented with numerical simulations.

Mining hidden non-redundant causal relationships in online social networks

Causal discovery is crucial to obtain a deep understanding of the actual mechanism behind the online social network, e.g., identifying the influential individuals and understanding the interaction among user behavior sequences. However, detecting causal directions and pruning causal redundancy of online social networks are still the great challenge of existing research. This paper proposed a constraint-based approach, minimal causal network (MCN), to mine hidden non-redundant causal relationships behind user behavior sequences. Under the MCN, the transfer entropy with the adaptive causal time lag is used to detect causal directions and find causal time lags, while a permutation-based significance test is proposed to prune redundant edges. Experiments on simulated data verify the effectiveness of our proposed method. We also apply our approach to real-world data from Sina Weibo and reveal some interesting discoveries.

Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations.

Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonators resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to networks having cells with 2D dynamics. Our results have direct implications for network models of firing rate type and other biological oscillatory networks (e.g, biochemical, genetic).

Fast and scalable method for distributed Boolean tensor factorization

How can we analyze tensors that are composed of 0’s and 1’s? How can we efficiently analyze such Boolean tensors with millions or even billions of entries? Boolean tensors often represent relationship, membership, or occurrences of events such as subject–relation–object tuples in knowledge base data (e.g., ‘Seoul’-‘is the capital of’-‘South Korea’). Boolean tensor factorization (BTF) is a useful tool for analyzing binary tensors to discover latent factors from them. Furthermore, BTF is known to produce more interpretable and sparser results than normal factorization methods. Although several BTF algorithms exist, they do not scale up for large-scale Boolean tensors. In this paper, we propose DBTF, a distributed method for Boolean CP (DBTF-CP) and Tucker (DBTF-TK) factorizations running on the Apache Spark framework. By distributed data generation with minimal network transfer, exploiting the characteristics of Boolean operations, and with careful partitioning, DBTF successfully tackles the high computational costs and minimizes the intermediate data. Experimental results show that DBTF-CP decomposes up to 163–323 $$\times $$ larger tensors than existing methods in 82–180 $$\times $$ less time, and DBTF-TK decomposes up to 83–163 $$\times $$ larger tensors than existing methods in 86–129 $$\times $$ less time. Furthermore, both DBTF-CP and DBTF-TK exhibit near-linear scalability in terms of tensor dimensionality, density, rank, and machines.

An Improved Multi-layer Cooperation Routing in Visual Sensor Network for Energy Minimization

Recent development on visual sensor networks (VSN) have shown the emergence of VSN as an important class of sensor-based distributed intelligent systems, with unique performance, complexity, and quality of service challenges. Furthermore, the popularity of VSN had attracted researchers and industries from many applications. Basically, VSN consists of a large number of low-power camera nodes, visual sensor networks support a great number of novel vision-based applications. The information provided by the camera nodes from a monitored site were collected data and processed in distributed and collaboratively. The use of multiple cameras in the network provides different views of the scene which enhances the reliability of the captured events. However, the cameras combined with the network's resource produce large amount of image data which require more energy consumption. Many research experts are working and publishing research papers on energy minimization in visual sensor network. However, there are no special attentions given by researchers on multi-layer cooperation routing in visual sensor network (VSN) particularly on the deficiency of forward-thinking innovation. This research proposed a new method that put forward the step and use (CO-VSN) multi-layer routing arrangement in visual sensor network. The performance of the proposed method is then compared with RASE protocol in different parameters and the result shows some meditation change in the stability of the network, increase the network life, reduce packet loss and energy drainage reduce in the VSNs. Even though, the RASE scheme used channel condition for movement of data and yet the proposed CO-VSN used cooperation and demonstrated better results.

Genome size reduction: design and analysis of a minimal metabolic network for yeast

The issue of genome minimization for a living cell has been the subject of intense study, and raises important theoretical questions and practical opportunities. We have developed an in-silico methodology, based on genome-scale models, to minimize the number of active genes encoding enzymes and transporters in a cell’s metabolic network. In the resultant minimal metabolic networks, all the remaining active genes are essential for keeping the network working to achieve the biomass value predicted by Flux Balance Analysis. We have tested our approach on a set of genome-scale metabolic models of various eukaryotic and prokaryotic organisms, but have focussed on Saccharomyces cerevisiae. The nutrient environments employed have comprised both known and automatically generated sets of nutrients and relative maximum uptake rates. The results generate more than 1000 unique minimal networks for a single condition, demonstrating the complexity of the minimization problem. We then performed a frequency analysis on the affected genes to discover patterns or similarities among the networks and the redundancy of specific pathway-related genes. In addition to this, we also evaluated the networks using a pathway-oriented robustness analysis, to see how the networks respond to random variation in the reaction fluxes. Finally, we have done a cross-species comparison of our algorithm’s results to highlight some of the homologous genes that are retained in the networks of a majority of species. Thus, our work has produced a tool for in silico genome minimization that permits the discovery of mandatory genes in the minimal metabolic networks.

Local immunodeficiency: Minimal networks and stability

Some basic aspects of the recently discovered phenomenon of local immunodeficiency (Skums et al. [1]) generated by antigenic cooperation in cross-immunoreactivity (CR) networks are investigated. We prove that local immunodeficiency (LI) that is stable under perturbations already occurs in very small networks and under general conditions on their parameters. Therefore our results are applicable not only to Hepatitis C where CR networks are known to be large (Skums et al. [1]), but also to other diseases with CR. A major necessary feature of such networks is the non-homogeneity of their topology. It is also shown that one can construct larger CR networks with stable LI by using small networks with stable LI as their building blocks. Our results imply that stable LI occurs in networks with quite general topology. In particular, the scale-free property of a CR network, assumed in Skums et al. [1], is not required.

Cluster singularity: The unfolding of clustering behavior in globally coupled Stuart-Landau oscillators.

The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate clustering dynamics in a mean-coupled ensemble of such limit-cycle oscillators. In particular, we show how clustering occurs in minimal networks and elaborate how the observed 2-cluster states crowd when increasing the number of oscillators. Using persistence, we discuss how this crowding leads to a continuous transition from balanced cluster states to synchronized solutions via the intermediate unbalanced 2-cluster states. These cascade-like transitions emerge from what we call a cluster singularity. At this codimension-2 point, the bifurcations of all 2-cluster states collapse and the stable balanced cluster state bifurcates into the synchronized solution supercritically. We confirm our results using numerical simulations and discuss how our conclusions apply to spatially extended systems.

A Simple and Flexible Computational Framework for Inferring Sources of Heterogeneity from Single-Cell Dynamics.

Single-cell time-lapse data provide the means for disentangling sources of cell-to-cell and intra-cellular variability, a key step for understanding heterogeneity in cell populations. However, single-cell analysis with dynamic models is a challenging open problem: current inference methods address only single-gene expression or neglect parameter correlations. We report on a simple, flexible, and scalable method for estimating cell-specific and population-average parameters of non-linear mixed-effects models of cellular networks, demonstrating its accuracy with a published model and dataset. We also propose sensitivity analysis for identifying which biological sub-processes quantitatively and dynamically contribute to cell-to-cell variability. Our application to endocytosis in yeast demonstrates that dynamic models of realistic size can be developed for the analysis of single-cell data and that shifting the focus from single reactions or parameters to nuanced and time-dependent contributions of sub-processes helps biological interpretation. Generality and simplicity of the approach will facilitate customized extensions for analyzing single-cell dynamics.

Analysis of limiting factors of battery assisted trolleybuses

Abstract It can be assumed that in the near future the trend of implementation of battery assisted trolleybuses in cities will grow. Battery assisted trolleybus technology combines benefits of classical trolleybus with freedom of standard bus movement. This paper deals with limiting factors of battery assisted trolleybus operation using overhead wires. During the design of minimal trolley network several limiting factors have to be considered. Limiting factors include battery capacity, ambient temperature and much more.

Large-scale directed network inference with multivariate transfer entropy and hierarchical statistical testing.

Network inference algorithms are valuable tools for the study of large-scale neuroimaging datasets. Multivariate transfer entropy is well suited for this task, being a model-free measure that captures nonlinear and lagged dependencies between time series to infer a minimal directed network model. Greedy algorithms have been proposed to efficiently deal with high-dimensional datasets while avoiding redundant inferences and capturing synergistic effects. However, multiple statistical comparisons may inflate the false positive rate and are computationally demanding, which limited the size of previous validation studies. The algorithm we present—as implemented in the IDTxl open-source software—addresses these challenges by employing hierarchical statistical tests to control the family-wise error rate and to allow for efficient parallelization. The method was validated on synthetic datasets involving random networks of increasing size (up to 100 nodes), for both linear and nonlinear dynamics. The performance increased with the length of the time series, reaching consistently high precision, recall, and specificity (>98% on average) for 10,000 time samples. Varying the statistical significance threshold showed a more favorable precision-recall trade-off for longer time series. Both the network size and the sample size are one order of magnitude larger than previously demonstrated, showing feasibility for typical EEG and magnetoencephalography experiments.

The minimal gap-junction network among melanophores and xanthophores required for stripe pattern formation in zebrafish.

Connexin 39.4 (Cx39.4) and connexin 41.8 (Cx41.8), two gap-junction proteins expressed in both melanophores and xanthophores, are crucial for the intercellular communication among pigment cells that is necessary for generating the stripe pigment pattern of zebrafish. We have previously characterized the gap-junction properties of Cx39.4 and Cx41.8, but how these proteins contribute to stripe formation remains unclear; this is because distinct types of connexins potentially form heteromeric gap junctions, which precludes accurate elucidation of individual connexin functions in vivo Here, by arranging Cx39.4 and Cx41.8 expression in pigment cells, we have identified the simplest gap-junction network required for stripe generation: Cx39.4 expression in melanophores is required but expression in xanthophores is not necessary for stripe patterning, whereas Cx41.8 expression in xanthophores is sufficient for the patterning, and Cx41.8 expression in melanophores might stabilize the stripes. Moreover, patch-clamp recordings revealed that Cx39.4 gap junctions exhibit spermidine-dependent rectification property. Our results suggest that Cx39.4 facilitates the crucial cell-cell interactions between melanophores and xanthophores that mediate a unidirectional activation-signal transfer from xanthophores to melanophores, which is essential for melanophore survival.

On the Interaction between Small Decay, Agent Heterogeneity and Diameter of Minimal Strict Nash Networks in Two-way Flow Model: A Note

On the Interaction between Small Decay, Agent Heterogeneity and Diameter of Minimal Strict Nash Networks in Two-way Flow Model: A Note

Optimal Network Reconfiguration of the Distribution Network for Minimization of Power Loss and Voltage Deviation using NSGA-II Algorithm

Optimal Network Reconfiguration of the Distribution Network for Minimization of Power Loss and Voltage Deviation using NSGA-II Algorithm

Symmetries in the time-averaged dynamics of networks: Reducing unnecessary complexity through minimal network models.

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path length, clustering coefficient, centrality measures, etc. Another important feature is the presence of network symmetries. In particular, the effect of these symmetries has been studied in the context of network synchronization, where they have been used to predict the emergence and stability of cluster synchronous states. Here, we provide theoretical, numerical, and experimental evidence that network symmetries play a role in a substantially broader class of dynamical models on networks, including epidemics, game theory, communication, and coupled excitable systems; namely, we see that in all these models, nodes that are related by a symmetry relation show the same time-averaged dynamical properties. This discovery leads us to propose reduction techniques for exact, yet minimal, simulation of complex networks dynamics, which we show are effective in order to optimize the use of computational resources, such as computation time and memory.

О ТОЧНОСТИ ПОСТРОЕНИЯ ПЛАНОВО-ВЫСОТНОЙ ГЕОДЕЗИЧЕСКОЙ РАЗБИВОЧНОЙ ОСНОВЫ НАЗЕМНЫМИ МЕТОДАМИ

The article gives comparative analysis of the creating horizontal and vertical geodetic control network for the purposes of research and building. It is recommended to create geodetic network on the territory up to 1–2 sq km by means of linear-angular measurements with the accuracy of urban fourth-order traverse. After centering the total station and the reflector with an error not more than 1 mm, the minimal network side is 140 m. The precalculation of geodetic control network accuracy with the given confidence level can be performed in CredoDAT. Creation of vertical and horizontal geodetic network should go simultaneously – by means of reciprocal trigonometric leveling of III–IV order accuracy. The height of the total station with use of specific tape measurer Leica can be measured with error of up to 1 mm. The requirements of the acting set of rules «Geodetic works in construction» are not always substantiated and require careful attitude.

A Neural Network-Based ECG Classification Processor With Exploitation of Heartbeat Similarity

This paper presents a neural network based processor with improved computation efficiency, which aims at multiclass heartbeat recognition in wearable devices. A lightweight classification algorithm that integrates both bi-directional long short-term memory (BLSTM) and convolutional neural networks (CNN) is proposed to deliver high accuracy with minimal network scale. To reduce energy consumption of the classification algorithm, the similarity between consecutive heartbeats is exploited to achieve a high degree of computation reuse in hardware architecture. In addition, neural network compression techniques are adopted in the procedure of inference to save hardware resources. Synthesized in the SMIC 40LL CMOS process, the prototype design has a total area of 1.40 mm 2 with 186.2 kB of static random-access memory (SRAM) capacity. Based on the simulation, this processor achieves an average energy efficiency of 3.52 GOPS/mW under 1.1 V supply at 100 MHz frequency. Compared with the design without computation reuse, the proposed processor provides a speedup by 2.58x and an energy dissipation reduction by 61.27% per classification. This work is a valuable exploration of neural network based design for long-term arrhythmia monitoring in daily life.

Bidirectional constraint satisfaction in rational strategic decision making

We describe the properties of a constraint satisfaction network that is able to reason and decide rationally in strategic games. We use the structure of Bidirectional Associative Memory (BAM), a minimal two-layer recurrent neural network, and assume that network layers represent self and other strategies, whereas connection weights encode best responses. We apply BAM to finite-strategy two-player games, and show that network activation in the long run is restricted to the set of rationalizable strategies. The network is not guaranteed to reach a stable activation state, but any pure strategy profile that constitutes a stable state in the network must be a pure strategy Nash equilibrium. We illustrate the properties of the network using the traveler’s dilemma, the rock–paper–scissors game, and coordination games. The network’s behavior also depends on starting activation states, and we show how biases in these starting states can resolve equilibrium selection problems. Strategic decision making is a key part of complex social behavior, and our results illustrate how bidirectional constraint satisfaction networks can perform rational computations in this domain.