Minimalistic Network Research Articles

Dynamic correlations: exact and approximate methods for mutual information.

Proteins are dynamic entities that undergo conformational changes critical for their functions. Understanding the communication pathways and information transfer within proteins is crucial for elucidating allosteric interactions in their mechanisms. This study utilizes mutual information (MI) analysis to probe dynamic allostery. Using two cases, Ubiquitin and PLpro, we have evaluated the accuracy and limitations of different approximations including the exact anisotropic and isotropic models, multivariate Gaussian model, isotropic Gaussian model, and the Gaussian Network Model (GNM) in revealing allosteric interactions. Our findings emphasize the required trajectory length for capturing accurate mutual information profiles. Long molecular dynamics trajectories, 1 ms for Ubiquitin and 100 µs for PLpro are used as benchmarks, assuming they represent the ground truth. Trajectory lengths of approximately 5 µs for Ubiquitin and 1 µs for PLpro marked the onset of convergence, while the multivariate Gaussian model accurately captured mutual information with trajectories of 5 ns for Ubiquitin and 350 ns for PLpro. However, the isotropic Gaussian model is less successful in representing the anisotropic nature of protein dynamics, particularly in the case of PLpro, highlighting its limitations. The GNM, however, provides reasonable approximations of long-range information exchange as a minimalist network model based on a single crystal structure. Overall, the optimum trajectory lengths for effective Gaussian approximations of long-time dynamic behavior depend on the inherent dynamics within the protein's topology. The GNM, by showcasing dynamics across relatively diverse time scales, can be used either as a standalone method or to gauge the adequacy of MD simulation lengths. Mutual information codes are available at https://github.com/kemaldemirtas/prc-MI.git.

Digital-twin-enabled 6G network autonomy and generative intelligence: Architecture, technologies and applications

Background: The 6G network provides on-demand services and efficient governance, which is an important capability of the 6G network in the future. Providing more flexibility, availability, and dynamicity in services and network function enablement face many challenges in the 6G network due to the system complexity. To fulfill the requirement of the new generation of a digital and intelligent network, the 6G architecture with digital twin as a new enabler technology, is expected to evolve in the network autonomy and generative intelligence properties, which could optimize and adapt the network and services themselves to a variety of scenarios and deployments. Methods: To achieve 6G network autonomy and generative intelligence, we propose an architecture based on digital twin technology. This architecture integrates the digital twin network with the minimalist network and supports single-domain autonomous and cross-domain collaboration via centralized-distributed digital twin deployment, and defines the interactions between the digital twin and the service layer as well as the physical network. Results: Based on the analysis of the architecture, we put forward the following design principles for the 6G digital twin network architecture: decoupling, interactions, endogenous AI, distribution, heterogeneity, autonomous, and closed-loop. In addition, we get the key technologies achieving collaboration efficiently between the network autonomy domain and generative intelligence domain in the distributed digital twin system. Important application directions of the 6G digital twin network architecture are also analyzed. Conclusions: In this paper, the new digital-twin-enabled 6G architecture and 6G digital twin network architecture design principles are proposed. The key technologies and important application of digital-twin-enabled 6G architecture are provided.

Consensus formation on heterogeneous networks

Reaching consensus—a macroscopic state where the system constituents display the same microscopic state—is a necessity in multiple complex socio-technical and techno-economic systems: their correct functioning ultimately depends on it. In many distributed systems—of which blockchain-based applications are a paradigmatic example—the process of consensus formation is crucial not only for the emergence of a leading majority but for the very functioning of the system. We build a minimalistic network model of consensus formation on blockchain systems for quantifying how central nodes—with respect to their average distance to others—can leverage on their position to obtain competitive advantage in the consensus process. We show that in a wide range of network topologies, the probability of forming a majority can significantly increase depending on the centrality of nodes that initiate the spreading. Further, we study the role that network topology plays on the consensus process: we show that central nodes in scale-free networks can win consensus in the network even if they broadcast states significantly later than peripheral ones.

Football is becoming more predictable; network analysis of 88 thousand matches in 11 major leagues.

In recent years, excessive monetization of football and professionalism among the players have been argued to have affected the quality of the match in different ways. On the one hand, playing football has become a high-income profession and the players are highly motivated; on the other hand, stronger teams have higher incomes and therefore afford better players leading to an even stronger appearance in tournaments that can make the game more imbalanced and hence predictable. To quantify and document this observation, in this work, we take a minimalist network science approach to measure the predictability of football over 26 years in major European leagues. We show that over time, the games in major leagues have indeed become more predictable. We provide further support for this observation by showing that inequality between teams has increased and the home-field advantage has been vanishing ubiquitously. We do not include any direct analysis on the effects of monetization on football’s predictability or therefore, lack of excitement; however, we propose several hypotheses which could be tested in future analyses.

Generation of diverse insect-like gait patterns using networks of coupled Rössler systems.

The generation of walking patterns is central to bio-inspired robotics and has been attained using methods encompassing diverse numerical as well as analog implementations. Here, we demonstrate the possibility of synthesizing viable gaits using a paradigmatic low-dimensional non-linear entity, namely, the Rössler system, as a dynamical unit. Through a minimalistic network wherein each instance is univocally associated with one leg, it is possible to readily reproduce the canonical gaits as well as generate new ones via changing the coupling scheme and the associated delays. Varying levels of irregularity can be introduced by rendering individual systems or the entire network chaotic. Moreover, through tailored mapping of the state variables to physical angles, adequate leg trajectories can be accessed directly from the coupled systems. The functionality of the resulting generator was confirmed in laboratory experiments by means of an instrumented six-legged ant-like robot. Owing to their simple form, the 18 coupled equations could be rapidly integrated on a bare-metal microcontroller, leading to the demonstration of real-time robot control navigating an arena using a brain-machine interface.

Lightning network: a second path towards centralisation of the Bitcoin economy**J-HL and KP performed the analysis. TS, CD and CJT designed the research. All authors wrote, reviewed and approved the manuscript.

The Bitcoin lightning network (BLN), a so-called ‘second layer’ payment protocol, was launched in 2018 to scale up the number of transactions between Bitcoin owners. In this paper, we analyse the structure of the BLN over a period of 18 months, ranging from 12th January 2018 to 17th July 2019, at the end of which the network has reached 8.216 users, 122.517 active channels and 2.732,5 transacted Bitcoins. Here, we consider three representations of the BLN: the daily snapshot one, the weekly snapshot one and the daily-block snapshot one. By studying the topological properties of the binary and weighted versions of the three representations above, we find that the total volume of transacted Bitcoins approximately grows as the square of the network size; however, despite the huge activity characterising the BLN, the Bitcoins distribution is very unequal: the average Gini coefficient of the node strengths (computed across the entire history of the Bitcoin lightning network) is, in fact, ≃0.88 causing the 10% (50%) of the nodes to hold the 80% (99%) of the Bitcoins at stake in the BLN (on average, across the entire period). This concentration brings up the question of which minimalist network model allows us to explain the network topological structure. Like for other economic systems, we hypothesise that local properties of nodes, like the degree, ultimately determine part of its characteristics. Therefore, we have tested the goodness of the undirected binary configuration model (UBCM) in reproducing the structural features of the BLN: the UBCM recovers the disassortative and the hierarchical character of the BLN but underestimates the centrality of nodes; this suggests that the BLN is becoming an increasingly centralised network, more and more compatible with a core-periphery structure. Further inspection of the resilience of the BLN shows that removing hubs leads to the collapse of the network into many components, an evidence suggesting that this network may be a target for the so-called split attacks.

Modular topology emerges from plasticity in a minimalistic excitable network model.

Topological features play a major role in the emergence of complex brain network dynamics underlying brain function. Specific topological properties of brain networks, such as their modular organization, have been widely studied in recent years and shown to be ubiquitous across spatial scales and species. However, the mechanisms underlying the generation and maintenance of such features are still unclear. Using a minimalistic network model with excitable nodes and discrete deterministic dynamics, we studied the effects of a local Hebbian plasticity rule on global network topology. We found that, despite the simple model set-up, the plasticity rule was able to reorganize the global network topology into a modular structure. The structural reorganization was accompanied by enhanced correlations between structural and functional connectivity, and the final network organization reflected features of the dynamical model. These findings demonstrate the potential of simple plasticity rules for structuring the topology of brain connectivity.

Navigable networks as Nash equilibria of navigation games.

Common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organized so that networks can perform their functions well. One function common to many networks is targeted transport or navigation. Here, using game theory, we show that minimalistic networks designed to maximize the navigation efficiency at minimal cost share basic structural properties with real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. We show that these skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road networks, and in a structural network of the human brain. The knowledge of these skeletons allows one to identify the minimal number of edges, by altering which one can efficiently improve or paralyse navigation in the network.

Quality of data delivery in peer-to-peer video streaming

QoS in a P2P video streaming system is evaluated in three stages: content generation, data delivery and video playback. We use jitter-free probability as the main performance metric to study Quality of Data delivery (QoD). A new model that incorporates both bandwidth and data availability of P2P network is proposed. Our model relies on a sharing factor that models data availability among all peers. We simulate on a minimalistic network to demonstrate how to apply the analytical model to design a P2P video streaming system with a very low jitter rate. Our simulation experimental results reveal that the lower bound on jitter-free probability is indeed effective to reflect the QoD of the entire system. Our model captures the impact of many design choices, including upload bandwidth limit, peer selection strategies, and video stream chunking schemes.

Response of an actin filament network model under cyclic stretching through a coarse grained Monte Carlo approach

Cells are complex, dynamic systems that actively adapt to various stimuli including mechanical alterations. Central to understanding cellular response to mechanical stimulation is the organization of the cytoskeleton and its actin filament network. In this manuscript, we present a minimalistic network Monte Carlo based approach to model actin filament organization under cyclic stretching. Utilizing a coarse-grained model, a filament network is prescribed within a two-dimensional circular space through nodal connections. When cyclically stretched, the model demonstrates that a perpendicular alignment of the filaments to the direction of stretch emerges in response to nodal repositioning to minimize net nodal forces from filament stress states. In addition, the filaments in the network rearrange and redistribute themselves to reduce the overall stress by decreasing their individual stresses. In parallel, we cyclically stretch NIH 3T3 fibroblasts and find a similar cytoskeletal response. With this work, we test the hypothesis that a first-principles mechanical model of filament assembly in a confined space is by itself capable of yielding the remodeling behavior observed experimentally. Identifying minimal mechanisms sufficient to reproduce mechanical influences on cellular structure has important implications in a diversity of fields, including biology, physics, medicine, computer science, and engineering.

A Computational Model for Understanding Stem Cell, Trophectoderm and Endoderm Lineage Determination

BackgroundRecent studies have associated the transcription factors, Oct4, Sox2 and Nanog as parts of a self-regulating network which is responsible for maintaining embryonic stem cell properties: self renewal and pluripotency. In addition, mutual antagonism between two of these and other master regulators have been shown to regulate lineage determination. In particular, an excess of Cdx2 over Oct4 determines the trophectoderm lineage whereas an excess of Gata-6 over Nanog determines differentiation into the endoderm lineage. Also, under/over-expression studies of the master regulator Oct4 have revealed that some self-renewal/pluripotency as well as differentiation genes are expressed in a biphasic manner with respect to the concentration of Oct4.Methodology/Principal FindingsWe construct a dynamical model of a minimalistic network, extracted from ChIP-on-chip and microarray data as well as literature studies. The model is based upon differential equations and makes two plausible assumptions; activation of Gata-6 by Oct4 and repression of Nanog by an Oct4–Gata-6 heterodimer. With these assumptions, the results of simulations successfully describe the biphasic behavior as well as lineage commitment. The model also predicts that reprogramming the network from a differentiated state, in particular the endoderm state, into a stem cell state, is best achieved by over-expressing Nanog, rather than by suppression of differentiation genes such as Gata-6.ConclusionsThe computational model provides a mechanistic understanding of how different lineages arise from the dynamics of the underlying regulatory network. It provides a framework to explore strategies of reprogramming a cell from a differentiated state to a stem cell state through directed perturbations. Such an approach is highly relevant to regenerative medicine since it allows for a rapid search over the host of possibilities for reprogramming to a stem cell state.

A minimalist network model for coarse-grained normal mode analysis and its application to biomolecular x-ray crystallography

In this article, we report a method for coarse-grained normal mode analysis called the minimalist network model. The main features of the method are that it can deliver accurate low-frequency modes on structures without undergoing initial energy minimization and that it also retains the details of molecular interactions. The method does not require any additional adjustable parameters after coarse graining and is computationally very fast. Tests on modeling the experimentally measured anisotropic displacement parameters in biomolecular x-ray crystallography demonstrate that the method can consistently perform better than other commonly used methods including our own one. We expect this method to be effective for applications such as structural refinement and conformational sampling.

Complex dynamics of chaperone-protein interactions under cellular stress.

We present a model of a generalizable but minimalistic network based on the properties of interactions between proteins, molecular chaperones (e.g., Hsp70, BiP) and ATP inside cells and subcellular components such as endoplasmic reticulum (ER). The dynamics of chaperone-dependent protein folding and misfolding in the cell can be modeled mathematically as a "predator-prey" problem, which can then be used to analyze the behavior of the system under conditions simulating stress (e.g., cardiac ischemia). We have tested this model under normal physiological and diseased conditions (e.g., ischemia as simulated by ATP depletion) and analyzed the effects of induction of chaperones (e.g., heat shock, tunicamycin) and inhibition of the degradative pathway (e.g., proteasome inhibition) on this model. Simulation gave the following results: (1) Under normal physiological conditions, as expected, the model predicts the stable production of correctly folded proteins. (2) A threshold of ATP levels exists below which the system tends toward increasing degrees of complex behavior. When ATP levels are just above this threshold, the system is highly vulnerable to sudden, brief drops in ATP levels such as may occur in the setting of acute ischemia: bursts of oscillations continue even when ATP levels revert to the threshold. However, if ATP levels are rapidly increased to levels considerably above the threshold, the system becomes stable again. (3) Up to 10-fold increases in chaperone levels, such as those that occur under conditions of prior heat shock or tunicamycin treatment, did not affect the behavior of the system under basal conditions, nor did it affect the tendency to complex behavior in the setting of ATP depletion. It did, however, shorten the recovery period of the system after chaotic-type oscillations were induced by acute ATP depletion. (4) Blocking the degradative pathway for misfolded proteins (e.g., proteasome inhibition) predisposes the system toward instability in the setting of ATP depletion by changing the ATP threshold at which bursts of oscillations occur. These results support the hypothesis that there are distinct thresholds for ATP, chaperones, and degradative activity, outside which cellular protein folding dynamics become unstable. They also suggest that an important mechanism by which chaperone induction protects cells from subsequent stress is by limiting the tendency to instability after an insult (e.g., acute myocardial ischemia or acute tubular injury to the kidney).