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The learning-based super-resolution reconstruction method inputs a low-resolution image into a network, and learns a non-linear mapping relationship between low-resolution and high-resolution through the network. In this study, the multi-scale super-resolution reconstruction network is used to fuse the effective features of different scale images, and the non-linear mapping between low resolution and high resolution is studied from coarse to fine to realise the end-to-end super-resolution reconstruction task. The loss of some features of the low-resolution image will negatively affect the quality of the reconstructed image. To solve the problem of incomplete image features in low-resolution, this study adopts the multi-scale super-resolution reconstruction method based on guided image filtering. The high-resolution image reconstructed by the multi-scale super-resolution network and the real high-resolution image are merged by the guide image filter to generate a new image, and the newly generated image is used for secondary training of the multi-scale super-resolution reconstruction network. The newly generated image effectively compensates for the details and texture information lost in the low-resolution image, thereby improving the effect of the super-resolution reconstructed image.Compared with the existing super-resolution reconstruction scheme, the accuracy and speed of super-resolution reconstruction are improved.

A network consists of two interdependent parts: the network topology or graph, consisting of the links between nodes and the network dynamics, specified by some governing equations. A crucial challenge is the prediction of dynamics on networks, such as forecasting the spread of an infectious disease on a human contact network. Unfortunately, an accurate prediction of the dynamics seems hardly feasible, because the network is often complicated and unknown. In this work, given past observations of the dynamics on a fixed graph, we show the contrary: Even without knowing the network topology, we can predict the dynamics. Specifically, for a general class of deterministic governing equations, we propose a two-step prediction algorithm. First, we obtain a surrogate network by fitting past observations of every nodal state to the dynamical model. Second, we iterate the governing equations on the surrogate network to predict the dynamics. Surprisingly, even though there is no similarity between the surrogate topology and the true topology, the predictions are accurate, for a considerable prediction time horizon, for a broad range of observation times, and in the presence of a reasonable noise level. The true topology is not needed for predicting dynamics on networks, since the dynamics evolve in a subspace of astonishingly low dimension compared to the size and heterogeneity of the graph. Our results constitute a fresh perspective on the broad field of nonlinear dynamics on complex networks.

Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available. A challenging case, frequently encountered due to privacy issues in the analysis of interbank flows and Big Data, is when there is only local (node-specific) aggregate information available. For binary networks, the relevant ensemble is one where the degree (number of links) of each node is constrained to its observed value. However, for weighted networks the problem is much more complicated. While the naïve approach prescribes to constrain the strengths (total link weights) of all nodes, recent counter-intuitive results suggest that in weighted networks the degrees are often more informative than the strengths. This implies that the reconstruction of weighted networks would be significantly enhanced by the specification of both strengths and degrees, a computationally hard and bias-prone procedure. Here we solve this problem by introducing an analytical and unbiased maximum-entropy method that works in the shortest possible time and does not require the explicit generation of reconstructed samples. We consider several real-world examples and show that, while the strengths alone give poor results, the additional knowledge of the degrees yields accurately reconstructed networks. Information-theoretic criteria rigorously confirm that the degree sequence, as soon as it is non-trivial, is irreducible to the strength sequence. Our results have strong implications for the analysis of motifs and communities and whenever the reconstructed ensemble is required as a null model to detect higher-order patterns.

Petri nets are directed, weighted bipartite graphs that have successfully been applied to the systems biology of metabolic and signal transduction pathways in modeling both stochastic (discrete) and deterministic (continuous) processes. Here we exemplify how molecular mechanisms, biochemical or genetic, can be consistently respresented in the form of place/transition Petri nets. We then describe the application of Petri nets to the reconstruction of molecular and genetic networks from experimental data and their power to represent biological processes with arbitrary degree of resolution of the subprocesses at the cellular and the molecular level. Petri nets are executable formal language models that permit the unambiguous visualization of regulatory mechanisms, and they can be used to encode the results of mathematical algorithms for the reconstruction of causal interaction networks from experimental time series data.

Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system, including the implied level of systemic risk, requires detailed information about the structure of the underlying network of dependencies. However, since data about financial linkages are typically subject to confidentiality, network reconstruction techniques become necessary to infer both the presence of connections and their intensity. Recently, several 'horse races' have been conducted to compare the performance of the available financial network reconstruction methods. These comparisons were based on arbitrarily chosen metrics of similarity between the real network and its reconstructed versions. Here we establish a generalized maximum-likelihood approach to rigorously define and compare weighted reconstruction methods. Our generalization uses the maximization of a certain conditional entropy to solve the problem represented by the fact that the density-dependent constraints required to reliably reconstruct the network are typically unobserved and, therefore, cannot enter directly, as sufficient statistics, in the likelihood function. The resulting approach admits as input any reconstruction method for the purely binary topology and, conditionally on the latter, exploits the available partial information to infer link weights. We find that the most reliable method is obtained by 'dressing' the best-performing binary method with an exponential distribution of link weights having a properly density-corrected and link-specific mean value and propose two safe (i.e. unbiased in the sense of maximum conditional entropy) variants of it. While the one named CReMA is perfectly general (as a particular case, it can place optimal weights on a network if the bare topology is known), the one named CReMB is recommended both in case of full uncertainty about the network topology and if the existence of some links is certain. In these cases, the CReMB is faster and reproduces empirical networks with highest generalized likelihood among the considered competing models.

The initial genome‐scale reconstruction of the metabolic network of Escherichia coli K‐12 MG1655 was assembled in 2000. It has been updated and periodically released since then based on new and curated genomic and biochemical knowledge. An update has now been built, named i JO1366, which accounts for 1366 genes, 2251 metabolic reactions, and 1136 unique metabolites. i JO1366 was (1) updated in part using a new experimental screen of 1075 gene knockout strains, illuminating cases where alternative pathways and isozymes are yet to be discovered, (2) compared with its predecessor and to experimental data sets to confirm that it continues to make accurate phenotypic predictions of growth on different substrates and for gene knockout strains, and (3) mapped to the genomes of all available sequenced E. coli strains, including pathogens, leading to the identification of hundreds of unannotated genes in these organisms. Like its predecessors, the i JO1366 reconstruction is expected to be widely deployed for studying the systems biology of E. coli and for metabolic engineering applications.

Background Computational prediction of drug-target interactions (DTI) is vital for drug discovery. The experimental identification of interactions between drugs and target proteins is very onerous. Modern technologies have mitigated the problem, leveraging the development of new drugs. However, drug development remains extremely expensive and time consuming. Therefore, in silico DTI predictions based on machine learning can alleviate the burdensome task of drug development. Many machine learning approaches have been proposed over the years for DTI prediction. Nevertheless, prediction accuracy and efficiency are persisting problems that still need to be tackled. Here, we propose a new learning method which addresses DTI prediction as a multi-output prediction task by learning ensembles of multi-output bi-clustering trees (eBICT) on reconstructed networks. In our setting, the nodes of a DTI network (drugs and proteins) are represented by features (background information). The interactions between the nodes of a DTI network are modeled as an interaction matrix and compose the output space in our problem. The proposed approach integrates background information from both drug and target protein spaces into the same global network framework. Results We performed an empirical evaluation, comparing the proposed approach to state of the art DTI prediction methods and demonstrated the effectiveness of the proposed approach in different prediction settings. For evaluation purposes, we used several benchmark datasets that represent drug-protein networks. We show that output space reconstruction can boost the predictive performance of tree-ensemble learning methods, yielding more accurate DTI predictions. Conclusions We proposed a new DTI prediction method where bi-clustering trees are built on reconstructed networks. Building tree-ensemble learning models with output space reconstruction leads to superior prediction results, while preserving the advantages of tree-ensembles, such as scalability, interpretability and inductive setting.

With the increasing availability of genomic data, biologists aim to find more accurate descriptions of evolutionary histories influenced by secondary contact, where diverging lineages reconnect before diverging again. Such reticulate evolutionary events can be more accurately represented in phylogenetic networks than in phylogenetic trees. Since the root location of phylogenetic networks cannot be inferred from biological data under several evolutionary models, we consider semi-directed (phylogenetic) networks: partially directed graphs without a root in which the directed edges represent reticulate evolutionary events. By specifying a known outgroup, the rooted topology can be recovered from such networks. We introduce the algorithm Squirrel (Semi-directed Quarnet-based Inference to Reconstruct Level-1 Networks) which constructs a semi-directed level-1 network from a full set of quarnets (four-leaf semi-directed networks). Our method also includes a heuristic to construct such a quarnet set directly from sequence alignments. We demonstrate Squirrel’s performance through simulations and on real sequence data sets, the largest of which contains 29 aligned sequences close to 1.7 Mb long. The resulting networks are obtained on a standard laptop within a few minutes. Lastly, we prove that Squirrel is combinatorially consistent: given a full set of quarnets coming from a triangle-free semi-directed level-1 network, it is guaranteed to reconstruct the original network. Squirrel is implemented in Python, has an easy-to-use graphical user interface that takes sequence alignments or quarnets as input, and is freely available at https://github.com/nholtgrefe/squirrel.

Chronic diabetic wounds are the most common complication for diabetic patients. Due to high oxidative stress levels affecting the entire healing process, treating diabetic wounds remains a challenge. Here, we present a strategy for continuously regulating oxidative stress microenvironment by the catalyst-like magnesium-gallate metal-organic framework (Mg-GA MOF) and developing sprayable hydrogel dressing with sodium alginate/chitosan quaternary ammonium salts to treat diabetic wounds. Chitosan quaternary ammonium salts with antibacterial properties can prevent bacterial infection. The continuous release of gallic acid (GA) effectively eliminates reactive oxygen species (ROS), reduces oxidative stress, and accelerates the polarization of M1-type macrophages to M2-type, shortening the transition between inflammation and proliferative phase and maintaining redox balance. Besides, magnesium ions adjuvant therapy promotes vascular regeneration and neuronal formation by activating the expression of vascular-associated genes. Sprayable hydrogel dressings with antibacterial, antioxidant, and inflammatory regulation rapidly repair diabetic wounds by promoting neurovascular network reconstruction and accelerating re-epithelialization and collagen deposition. This study confirms the feasibility of catalyst-like MOF-contained sprayable hydrogel to regulate the microenvironment continuously and provides guidance for developing the next generation of non-drug diabetes dressings. [Display omitted] •An effective method for rapidly preparing magnesium-gallate MOF and regulating morphology and stability was developed.•A portable sprayable hydrogel dressing with antibacterial, anti-inflammatory, and antioxidant functions was constructed.•Oxidative stress level reduction and neurovascular network reconstruction are achieved in healing diabetic wounds.

Background COnstraint-Based Reconstruction and Analysis (COBRA) methods are widely used for genome-scale modeling of metabolic networks in both prokaryotes and eukaryotes. Due to the successes with metabolism, there is an increasing effort to apply COBRA methods to reconstruct and analyze integrated models of cellular processes. The COBRA Toolbox for MATLAB is a leading software package for genome-scale analysis of metabolism; however, it was not designed to elegantly capture the complexity inherent in integrated biological networks and lacks an integration framework for the multiomics data used in systems biology. The openCOBRA Project is a community effort to promote constraints-based research through the distribution of freely available software. Results Here, we describe COBRA for Python (COBRApy), a Python package that provides support for basic COBRA methods. COBRApy is designed in an object-oriented fashion that facilitates the representation of the complex biological processes of metabolism and gene expression. COBRApy does not require MATLAB to function; however, it includes an interface to the COBRA Toolbox for MATLAB to facilitate use of legacy codes. For improved performance, COBRApy includes parallel processing support for computationally intensive processes. Conclusion COBRApy is an object-oriented framework designed to meet the computational challenges associated with the next generation of stoichiometric constraint-based models and high-density omics data sets. Availability http://opencobra.sourceforge.net/