Critical Subnetwork Research Articles

Explainable Multimodal Graph Isomorphism Network for Interpreting Sex Differences in Adolescent Neurodevelopment

Explainable Multimodal Graph Isomorphism Network for Interpreting Sex Differences in Adolescent Neurodevelopment

Development of an educational method to rethink and learn oncological brain surgery in an "a la carte" connectome-based perspective.

Understanding the structural connectivity of white matter tracts (WMT) and their related functions is a prerequisite to implementing an "a la carte" "connectomic approach" to glioma surgery. However, accessible resources facilitating such an approach are lacking. Here we present an educational method that is readily accessible, simple, and reproducible that enables the visualization of WMTs on individual patient images via an atlas-based approach. Our method uses the patient's own magnetic resonance imaging (MRI) images and consists of three main steps: data conversion, normalization, and visualization; these are accomplished using accessible software packages and WMT atlases. We implement our method on three common cases encountered in glioma surgery: a right supplementary motor area tumor, a left insular tumor, and a left temporal tumor. Using patient-specific perioperative MRIs with open-sourced and co-registered atlas-derived WMTs, we highlight the critical subnetworks requiring specific surgical monitoring identified intraoperatively using direct electrostimulation mapping with cognitive monitoring. The aim of this didactic method is to provide the neurosurgical oncology community with an accessible and ready-to-use educational tool, enabling neurosurgeons to improve their knowledge of WMTs and to better learn their oncologic cases, especially in glioma surgery using awake mapping. Taking no more than 3-5min per patient and irrespective of their resource settings, we believe that this method will enable junior surgeons to develop an intuition, and a robust 3-dimensional imagery of WMT by regularly applying it to their cases both before and after surgery to develop an "a la carte" connectome-based perspective to glioma surgery.

Mechanism of Action of a Chinese Herbal Compound Containing Quercetin, Luteolin, and Kaempferol in the Treatment of Vitiligo Based on Network Pharmacology and Experimental Verification.

This study aimed to explore the mechanisms of Baishi tablets (BSTs) in the treatment of vitiligo through network pharmacology-based identification and experimental validation. In brief, the compounds and related targets of BST were extracted from the TCMSP database, and disease information was obtained from the OMIM, GeneCards, PharmGkb, TTD, and DrugBank databases. A Venn diagram was generated to visualize the common targets of BST and vitiligo. GO and KEGG analyses were performed to explore the potential biological processes and signaling pathways. The PPI network and core gene subnetwork were constructed using STRING and Cytoscape software. In addition, the measurement of apoptosis in PIG1 cells and intracellular reactive oxygen species were measured using quercetin (QU), luteolin (LU), and kaempferol (KA) to protect melanocytes from oxidative stress. A total of 55 compounds with 236 targets and 1205 vitiligo-related genes were obtained from the TCMSP database. GO and KEGG analyses were performed to explore the potential biological processes and signaling pathways, revealing that BST may cure vitiligo by influencing the biological processes of cellular oxidative stress and related signaling pathways. A critical subnetwork was obtained with 13 core genes by analyzing the PPI network, which includes HMOX1, CXCL8, CCL2, IL6, MAPK8, CASP3, PTGS2, AKT1, IL1B, MYC, TP53, IFNG, and IL2. Furthermore, a molecular docking analysis was conducted to simulate the combination of compounds and gene proteins, reflecting that QU, LU, and KA can strongly bind the core genes. Through a series of experimental validations, we found that QU, LU, and KA could attenuate H2O2-induced apoptosis in melanocytes. Further evidence revealed that QU, LU, and KA could enhance the scavenging of intracellular reactive oxygen species (ROS). Based on the results of network pharmacology analysis and experimental verification, QA, LU, and KA can be utilized to protect PIG1 cells by inhibiting oxidative stress and reducing the intracellular level of ROS. This may explain the underlying mechanism of BST therapy and provide a novel strategy for the treatment of vitiligo.

An Integrated Risk Management Framework for Global Supply Chains

In this study, a risk management framework is developed to support risk management decisions in global supply chains. The proposed framework covers all phases of risk management, namely, risk identification, risk miti-gation and control. In the risk identification phase of the framework, the supply chain is decomposed into either material-level or product-level sub-networks according to the decision maker’s preference. Afterwards, the most crit-ical sub-network is modelled to evaluate different risk mitigation strategies. In particular, a combination of redun-dancy and flexibility strategies is considered for risk mitigation. These strategies are evaluated by simulation models in terms of their effectiveness and efficiency. While inventory holding cost is used as efficiency measure, effective-ness of the strategies is measured by premium freight ratio. The proposed framework provides a comprehensive and reliable decision support since it covers all phases of risk management and relies on quantitative data, and statistical analysis in risk modelling. Moreover, it is flexible as it can be easily adapted to any change in supply chain environ-ment and strategy. In order to show the applicability of the framework, a practical demonstration is presented for a European automotive company. The results indicate that the proposed framework improves the supply chain perfor-mance in terms of efficiency and effectiveness.

Task‐aware swapping for efficient DNN inference on DRAM‐constrained edge systems

Object detection at the edge side is a common task in various environments. The deployment of convolutional neural networks in intelligent edge systems is very challenging because of the highly constrained main-memory space. This study aims at operating neural networks with a reduced memory requirement. The basic idea is that tasks of the same type would involve the same critical subnetwork. We propose identifying the critical network connections by considering the importance of channels. During runtime, the proposed method detects the task types and timely swaps the model parameters of the critical subnetworks from the external storage into dynamic random access memory (DRAM). Compared with conventional network pruning, the proposed approach further reduced the DRAM requirement by 34.6% while maintaining a high inference accuracy.

Transcriptional landscape of circulating platelets from patients with COVID-19 reveals key subnetworks and regulators underlying SARS-CoV-2 infection: implications for immunothrombosis

BackgroundThrombosis and coagulopathy are pervasive pathological features of coronavirus disease 2019 (COVID-19), and thrombotic complications are a sign of severe COVID-19 disease and are associated with multiple organ failure and increased mortality. Platelets are essential cells that regulate hemostasis, thrombus formation and inflammation; however, the mechanism underlying the interaction between platelets and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remains unclear.ResultsThe present study performed RNA sequencing on the RNA isolated from platelets obtained from 10 COVID-19 patients and eight healthy donors, and discovered that SARS-CoV-2 not only significantly altered the coding and non-coding transcriptional landscape, but also altered the function of the platelets, promoted thrombus formation and affected energy metabolism of platelets. Integrative network biology analysis identified four key subnetworks and 16 risk regulators underlying SARS-CoV-2 infection, involved in coronavirus disease-COVID-19, platelet activation and immune response pathways. Furthermore, four risk genes (upstream binding transcription factor, RNA polymerase II, I and III subunit L, Y-box binding protein 1 and yippee like 2) were found to be associated with COVID-19 severity. Finally, a significant alteration in the von Willebrand factor/glycoprotein Ib-IX-V axis was revealed to be strongly associated with platelet aggregation and immunothrombosis.ConclusionsThe transcriptional landscape and the identification of critical subnetworks and risk genes of platelets provided novel insights into the molecular mechanisms of immunothrombosis in COVID-19 progression, which may pave the way for the development of novel therapeutic strategies for preventing COVID-19-associated thrombosis and improving the clinical outcome of COVID-19 patients.

A network pharmacology approach to explore active compounds and pharmacological mechanisms of a patented Chinese herbal medicine in the treatment of endometriosis.

ObjectiveEndometriosis is a common benign disease in women of reproductive age. Qu’s formula (QUF) is a patented Chinese herbal medicine for treating endometriosis that has been proven to be effective in treating and preventing the recurrence of endometriosis. This study is aimed to discover its molecular mechanism and to explore the potential drug targets.MethodsA QUF target and endometriosis-related gene set was identified by the Traditional Chinese Medicine Systems Pharmacology (TCMSP) and Bioinformatics Analysis Tool for Molecular Mechanism of Traditional Chinese Medicine (BATMAN-TCM) databases and five disease-gene databases. Gene ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses were performed, and a protein–protein interaction (PPI) network was established to discover the potential mechanism. MalaCards was searched for targets and signaling pathways related to endometriosis, and the search results were also used to identify the key factors in QUF. Molecular docking was performed to visualize the interactions between the effective molecules and proteins encoded by critical genes. Cell experiments and molecular dynamics (MD) simulations were used to further validate the therapeutic effects of the active compounds in QUF on endometriosis.ResultsA compound-target network with 117 nodes (94 genes and 23 active compounds) and 224 edges was generated. The results of GO and KEGG analyses indicated that QUF could act by regulating the immune response, apoptosis and proliferation, oxidative stress, and angiogenesis. VEGFA, CXCL8, CCL2, IL1B and PTGS2 were selected for molecular docking analysis from two critical subnetworks with high correlation scores in MalaCards, and the active compounds of QUF had binding potential and high affinity for them. The mRNA expression levels of CCL2, IL1B and PTGS2 significantly decreased after treatment with quercetin. MD simulations showed that the combinations of quercetin and these proteins were relatively stable.ConclusionThe network pharmacological strategy integrates molecular docking to unravel the molecular mechanism by which QUF protects against endometriosis. Our findings not only confirm the clinical effectiveness of QUF but also provide a foundation for further experimental study.

Investigating EEG-based functional connectivity patterns for multimodal emotion recognition

Objective. Previous studies on emotion recognition from electroencephalography (EEG) mainly rely on single-channel-based feature extraction methods, which ignore the functional connectivity between brain regions. Hence, in this paper, we propose a novel emotion-relevant critical subnetwork selection algorithm and investigate three EEG functional connectivity network features: strength, clustering coefficient, and eigenvector centrality. Approach. After constructing the brain networks by the correlations between pairs of EEG signals, we calculated critical subnetworks through the average of brain network matrices with the same emotion label to eliminate the weak associations. Then, three network features were conveyed to a multimodal emotion recognition model using deep canonical correlation analysis along with eye movement features. The discrimination ability of the EEG connectivity features in emotion recognition is evaluated on three public datasets: SEED, SEED-V, and DEAP. Main results. The experimental results reveal that the strength feature outperforms the state-of-the-art features based on single-channel analysis. The classification accuracies of multimodal emotion recognition are on the SEED dataset, on the SEED-V dataset, and and for arousal and valence on the DEAP dataset, respectively, which all achieved the best performance. In addition, the brain networks constructed with 18 channels achieve comparable performance with that of the 62-channel network and enable easier setups in real scenarios. Significance. The EEG functional connectivity networks combined with emotion-relevant critical subnetworks selection algorithm we proposed is a successful exploration to excavate the information between channels.

The possible mechanism of Hippophae fructus oil applied in tympanic membrane repair identified based on network pharmacology and molecular docking.

ObjectiveThis study aimed to explore the mechanisms of Hippophae fructus oil (HFO) in the treatment of tympanic membrane (TM) perforation through network pharmacology‐based identification.MethodsThe compounds and related targets of HFO were extracted from the TCMSP database, and disease information was obtained from the OMIM, GeneCards, PharmGkb, TTD, and DrugBank databases. A Venn diagram was generated to show the common targets of HFO and TM, and GO and KEGG analyses were performed to explore the potential biological processes and signaling pathways. The PPI network and core gene subnetwork were constructed using the STRING database and Cytoscape software. A molecular docking analysis was also conducted to simulate the combination of compounds and gene proteins.ResultsA total of 33 compounds and their related targets were obtained from the TCMSP database. After screening the 393 TM‐related targets, 21 compounds and 22 gene proteins were selected to establish the network diagram. GO and KEGG enrichment analyses revealed that HFO may promote TM healing by influencing cellular oxidative stress and related signaling pathways. A critical subnetwork was obtained by analyzing the PPI network with nine core genes: CASP3, MMP2, IL1B, TP53, EGFR, CXCL8, ESR1, PTGS2, and IL6. In addition, a molecular docking analysis revealed that quercetin strongly binds the core proteins.ConclusionAccording to the analysis, HFO can be utilized to repair perforations by influencing cellular oxidative stress. Quercetin is one of the active compounds that potentially plays an important role in TM regeneration by influencing 17 gene proteins.

Bioinformatics analysis of differentially expressed genes and pathways in the development of cervical cancer

BackgroundThis study aimed to explore and identify key genes and signaling pathways that contribute to the progression of cervical cancer to improve prognosis.MethodsThree gene expression profiles (GSE63514, GSE64217 and GSE138080) were screened and downloaded from the Gene Expression Omnibus database (GEO). Differentially expressed genes (DEGs) were screened using the GEO2R and Venn diagram tools. Then, Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analyses were performed. Gene set enrichment analysis (GSEA) was performed to analyze the three gene expression profiles. Moreover, a protein–protein interaction (PPI) network of the DEGs was constructed, and functional enrichment analysis was performed. On this basis, hub genes from critical PPI subnetworks were explored with Cytoscape software. The expression of these genes in tumors was verified, and survival analysis of potential prognostic genes from critical subnetworks was conducted. Functional annotation, multiple gene comparison and dimensionality reduction in candidate genes indicated the clinical significance of potential targets.ResultsA total of 476 DEGs were screened: 253 upregulated genes and 223 downregulated genes. DEGs were enriched in 22 biological processes, 16 cellular components and 9 molecular functions in precancerous lesions and cervical cancer. DEGs were mainly enriched in 10 KEGG pathways. Through intersection analysis and data mining, 3 key KEGG pathways and related core genes were revealed by GSEA. Moreover, a PPI network of 476 DEGs was constructed, hub genes from 12 critical subnetworks were explored, and a total of 14 potential molecular targets were obtained.ConclusionsThese findings promote the understanding of the molecular mechanism of and clinically related molecular targets for cervical cancer.

Interpret Neural Networks by Extracting Critical Subnetworks.

In recent years, deep neural networks have achieved excellent performance in many fields of artificial intelligence. The requirements for the interpretability and robustness of neural networks are also increasing. In this paper, we propose to understand the functional mechanism of neural networks by extracting critical subnetworks. Specifically, we denote the critical subnetworks as a group of important channels across layers such that if they were suppressed to zeros, the final test performance would deteriorate severely. This novel perspective can not only reveal the layerwise semantic behavior within the model but also present more accurate visual explanations appearing in the data through attribution methods. Moreover, we propose two adversarial example detection methods based on the properties of sample-specific and class-specific subnetworks, which provides the possibility for increasing the model robustness.

Abstract 2456: NetZen: A comprehensive network-based pathway and target discovery platform

Abstract BACKGROUND: Success in precision medicine depends on the ability to accurately and rapidly identify master regulators of critical gene subnetworks. To achieve this goal requires a seamless computational target discovery platform that integrates global network visualization with identification of master regulatory subnetworks (MRS) and their key influencers. METHODS: We have created NetZen - a computer cluster-capable computational suite allowing for 1) robust network generation with million edges; 2) network-based MRS identification; 3) hierarchical analysis with automated annotations; and 4) whole-network 3D visualization of all 20,000 genes. To identify cancer MRS, we applied NetZen to expression datasets of tumors and normal tissues, tumor-initiating cells (TICs), non-TIC cancer cells, and normal stem and non-stem cells from TCGA, GEO and internal sources. For validation, we introduced these subnetworks in normal cells to recapitulate TIC phenotypes in vivo or disrupted them in patients-derived TICs and mouse xenografts (PDX). To identify MRS of mortality, we applied NetZen to survival data in TCGA. RESULTS: Networks of 28 human cancers were generated, integrating transcriptomics, microRNAs, proteomics, and clinical data. For cancers with TIC datasets, we identified TIC-specific MRS with clear-cut hierarchy controlling immune surveillance, EMT and developmental functions. Interestingly, in some cancers, the immune subnetwork including immune checkpoints was entirely encompassed in the developmental subnetwork. We present representative validation on glioblastoma TIC (GIC) MRS with features common in other cancers’ TICs. Exogenous introduction of this subnetwork in normal astrocytes forced them to become GICs and form tumors in mice. Disrupting this subnetwork in 10 independent PDXs profoundly blunted tumor growth and prolonged survival. Lastly, we present detailed MRS of mortality analysis of multiple cancer types and identify common pathways directly influencing outcomes. DISCUSSION: NetZen provides a complete solution to big data analysis by effortlessly processing million-edge hierarchical networks with biological insights through automated annotations. The findings that the immune and developmental subnetworks were intimately linked suggest that immune escape by TICs is intrinsic of cellular transformation rather than a product of selection. Lastly, detailed network hierarchy provides a logical roadmap for cancer therapeutic development. Citation Format: Son Le, Alberto Riva, Changwang Deng, David D. Tran. NetZen: A comprehensive network-based pathway and target discovery platform [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 2456.

Two citation-based indicators to measure latent referential value of papers

Traditional bibliometric indicators aim at helping academic administrators or research investors measure the influence of publications. These indicators focus on how to quantify and compare the scientific output of researchers. However, little attention has been paid to the aspect that bibliometric indicators can also be used to help scientists find valuable referential papers. In this paper, we propose three points to characterize valuable referential papers: first, valuable referential papers always are high-quality research; second, valuable referential papers are closely related to a considerable quantity of recent papers; third, valuable referential papers lead to hotspots which attract papers to follow successively. We extract the critical subnetwork from the original citation network which only reserves the significant nodes and edges that meet the three preceding points. Then we present two indicators on the basis of the critical subnetwork. The experimental results demonstrate that papers recommended by our indicators are relatively new and our indicators have greater Spearman's rank correlation coefficients with the future citation count compared with other bibliometric indicators like the raw citation count.

INTRA-OPERATIVE MAPPING OF NEURAL NETWORKS DURING AWAKE CRANIOTOMY FOR RESECTION OF BRAIN TUMORS: WORK IN PROGRESS

BACKGROUND: Direct cortical stimulation (DCS) is considered the gold-standard for identification of functional brain regions during awake craniotomy for tumor resection. This technique allows maximal resection while preserving neurological function and quality of life. To date, no intra-operative methodology for mapping neural networks, which are crucial for adequate neurological functions, has been described. We describe the feasibility of a novel intra-operative technique, aiming to map critical language sub-networks using simultaneous, multi-site cortical stimulations. METHODS: 15 eligible patients who underwent awake craniotomy for removal of tumors involving language areas participated in this study. Following standard DCS using a bipolar Ojemann stimulator, a strip electrode was placed on “silent” cortex (where DCS has not elicited any language dysfunction). Functional testing was continued while applying simultaneous two to three-site bipolar stimulation via two pairs of adjacent contacts and Ojemann stimulator. Dysfunction was documented when occurred consistently during stimulation. RESULTS: 12 of the 15 patients (80%) experienced language dysfunction following standard single-site stimulation. Two-site simultaneous stimulations (neither causing dysfunction by itself) were associated with additive language dysfunction in 10 of the 15 patients. Three-site stimulations caused additive language dysfunction in 8 patients, as compared to the single- and two- site stimulations. Language dysfunctions caused by multifocal stimulation varied among patients and tumor locations and included primary production and comprehension dysfunctions (i.e. speech arrest and word-deafness, respectively); as well as secondary language dysfunctions such as phonological and semantic paraphasias. Importantly, using multifocal stimulations we identified eloquent regions in patients who did not experience any dysfunction using the standard DCS (two patients). Functional regions identified were spared during surgery. In none of the patients a new neurological deficit was observed following surgery, and in six patients who experienced dysfunction caused by multifocal stimulation, post-operative language function has improved. CONCLUSIONS: In this preliminary study we show that multi-site intra-operative stimulations enables identification of additional functional nodes and sub-networks which are more refined and cannot be mapped with standard single site stimulations. Using such technique may allow for preservation of neural networks and further enhance functional preservation in patients who undergo surgery for brain tumors. SECONDARY CATEGORY: n/a.

The effect of smoking on DNA methylation of peripheral blood mononuclear cells from African American women

BackgroundRegular smoking is associated with a wide variety of syndromes with prominent inflammatory components such as cancer, obesity and type 2 diabetes. Heavy regular smoking is also associated with changes in the DNA methylation of peripheral mononuclear cells. However, in younger smokers, inflammatory epigenetic findings are largely absent which suggests the inflammatory response(s) to smoking may be dose dependent. To help understand whether peripheral mononuclear cells have a role in mediating these responses in older smokers with higher cumulative smoke exposure, we examined genome-wide DNA methylation in a group of well characterized adult African American subjects informative for smoking, as well as serum C-reactive protein (CRP) and interleukin-6 receptor (IL6R) levels. In addition, complementary bioinformatic analyses were conducted to delineate possible pathways affected by long-term smoking.ResultsGenome-wide DNA methylation analysis with respect to smoking status yielded 910 significant loci after Benjamini-Hochberg correction. In particular, two loci from the AHRR gene (cg05575921 and cg23576855) and one locus from the GPR15 gene (cg19859270) were identified as highly significantly differentially methylated between smokers and non-smokers. The bioinformatic analyses showed that long-term chronic smoking is associated with altered promoter DNA methylation of genes coding for proteins mapping to critical sub-networks moderating inflammation, immune function, and coagulation.ConclusionsWe conclude that chronic regular smoking is associated with changes in peripheral mononuclear cell methylation signature which perturb inflammatory and immune function pathways and may contribute to increased vulnerability for complex illnesses with inflammatory components.

Abstract PR8: Network modeling of epithelial-to-mesenchymal transition in liver cancer metastasis

Abstract Hepatocellular carcinoma (HCC) is the third most common cause of cancer death in the world and its incidence is rising in the United States. Over 90% of cancer deaths occur due to tumor metastasis. Epithelial-to-mesenchymal transition (EMT) is a developmental process hijacked by cancer cells to leave the primary tumor site and establish distant metastases. Cells undergoing EMT lose cell-cell adhesion properties and change cell morphology in order to migrate into the blood stream. Loss of expression of E-cadherin, a cell adhesion protein, is considered the hallmark of EMT, and molecular analyses have revealed complex signaling pathways regulating E-cadherin expression. The hepatocyte growth factor (HGF)/C-met receptor axis is a major EMT inducer and is dysregulated in 40% of HCC. TGF-beta signaling, another important EMT inducer, is dysregulated in 20% of HCC. To systematically understand signaling components that regulate HCC metastasis, we constructed an EMT network (74 nodes, 143 edges) by integrating the signaling pathways involved in developmental EMT and known dysregulations in metastatic HCC. This network was subsequently translated into a predictive, discrete, dynamic model. Using HGF and TGF-beta1 as our EMT inducers and E-cadherin expression as our EMT marker, we reveal that the EMT process, although robust, appears to be targetable through inhibition of a small subset of critical (EMT “driver”) nodes. Our model suggests the following: 1) A critical eight-node transcriptional network that is downstream of major growth signals is necessary for EMT induction. 2) Cross-talk with TGF-beta and Notch signaling pathways exists and coordinated inhibition of both pathways will inhibit HGF-induced EMT. 3) Of the 135 nodes that did not block EMT transmission (termed “passenger” nodes), when combined with other EMT “passengers,” 11 combination knockouts were able to inhibit transmission of the EMT signal. 5) Analysis of the states in the basin of attraction of the “EMT negative” steady states has revealed a critical subnetwork (a strongly connected component of the larger EMT network) for EMT transmission. Initial testing has revealed that Snail1 inhibition blocks TGF-Beta1 induced EMT. Further predictions for nodes that inhibit EMT are currently being tested with a novel in vitro EMT screen. These results reveal network modeling as an important tool for identifying critical mediators in biological processes. Furthermore, we propose network modeling as a tool for rational drug targeting of disease pathways, specifically in liver cancer metastasis. This proffered talk is also presented as Poster A12. Citation Format: Steven N. Steinway, Hien Dang, Wei Ding, Carl B. Rountree, Reka Albert. Network modeling of epithelial-to-mesenchymal transition in liver cancer metastasis [abstract]. In: Proceedings of the AACR Special Conference on Chemical Systems Biology: Assembling and Interrogating Computational Models of the Cancer Cell by Chemical Perturbations; 2012 Jun 27-30; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2012;72(13 Suppl):Abstract nr PR8.

Structure and conductivity of clusters generated by variable-range hopping percolation

An important class of models for variable-range hopping (VRH) transport processes of electrons in highly disordered systems is based on percolation arguments. In these models the so-called critical path analysis (CPA) is combined with percolation arguments based on standard percolation models. Despite the increased computer power in the last decade there have been little attempts to validate the applicability of standard percolation theory on VRH problems. We have performed systematic numerical calculations on the structure and conductivity of VRH percolation clusters in two dimensions. It is shown by analyzing the mass of the clusters and the correlation length that VRH percolation clusters indeed behave as standard percolation clusters. The main difference between VRH percolation and standard percolation seems to be the existence of a temperature dependent effective lattice constant. Conductivity calculations on VRH clusters have been performed that support the central idea behind CPA models. Furthermore, these calculations confirm the existence of critical subnetworks.

Effect of the variance of pore size distribution on the transport properties of heterogeneous networks

The goal of this paper is to evaluate the effect of the variance of pore size distribution on the transport properties of rocks. Several heterogeneous network realizations with very broad, uniform, or log uniform pore size distributions were constructed. A series of networks were then derived deterministically from these initial networks by repeatedly applying a shrinking operator to the pores of the original realizations. This operator was devised in such a way as to maintain the mean pore size constant while changing the variance of the pore size distribution, therefore allowing its effect on the transport properties to be isolated. We thus assessed the validity of several permeability models from the literature as a function of the variance of the pore size distribution. We found that the product of the permeability by the electrical formation factor was proportional to the square of the critical radius as proposed in the Katz‐Thompson model [Katz and Thompson, 1986]. However, we observed that the dramatic flow localization occurring at high pore size variance was not restricted to the backbone of the critical subnetwork (or critical path) as assumed in the Katz‐Thompson model. We propose that a better justification of the relation mentioned above arises from the underlying percolation problem of the viscous‐inertial transition observed in harmonic flow as a function of frequency. In addition, we appraised the stochastic Bernabé‐Revil model [Bernabé and Revil, 1995]. We found that this model was more and more difficult to implement as the pore size variance was increased. A possible interpretation could be that at high levels of pore‐scale heterogeneity, very large pore size fluctuations occur and the flow pattern is so strongly and determimstically related to these extreme fluctuations that a stochastic description becomes inadequate.

Size effects in electrical behavior of high-T/sub c/ thin-film bridges

The size effects in electrical characteristics of polycrystalline YBa/sub 2/Cu/sub 3/O/sub 7-x/ thin-film bridges were studied in the temperature range 4-300 K. It is shown that at T>T/sub c/ the decrease of bridge widths w from 200 to 10 mu m leads to an increase of resistance R/sub Square Operator / of several times and to a change in R/sub Square Operator / (T) behavior from a metallic type to an activation type. At T<T/sub c/ the R/sub Square Operator / (w) values exponentially increased from the width w was decreased under some definite size L/sub 0/. At T<T/sub c/ the index alpha in the temperature dependence of critical current I/sub c/(T) approximately (T/sub c/-T)/sup alpha / changed from 3 to 1 if bridge width was decreased. Experimental data are discussed within the framework of the model which takes into account large-scale percolation processes in the system of different intergrain Josephson junctions, where characteristic length L/sub 0/ of critical subnetwork is much larger than the grain size.

The transient photoconductivity of inhomogeneous amorphous semiconductors

Abstract In inhomogeneous amorphous semiconductors the energy of the lowest extended electronic states, which is called the local mobility edge, can be a function of position. As a result, charge carriers formed initially at an arbitrary point in the material will tend to move towards regions in which the local mobility edge has its lowest energy. An analysis is presented of the transient photocurrent inhomogenous amorphous semiconductors. Model systems consisting of two distinct media are analysed in detail by means of the multi-state continuous-time random-walk method, and general formulae are derived for the transient photocurrent appropriate to various types of medium. These results indicate that, in many cases, the transient photoconductivity is determined mainly by the properties of the critical subnetwork, along which the energy of the local mobility edge does not exceed its percolation value by more than kBT.