Local Snapshot Research Articles

Fine-Grained Benchmarking and Targeted Optimization: Enabling Green IoT-Oriented Blockchain in the 6G Era

For 6G-empowered IoT, blockchain is widely regarded as a fundamental technique for addressing the security and privacy issues. Nonetheless, the current blockchains suffer from several flaws, especially the low performance and scalability. They seriously hinder the blockchain deployments in 6G-empowered IoT with high concurrency and complexity. To address this problem, we need to better understand blockchains and try to optimize them. However, we still lack a standard tool for comprehensively benchmarking the IoT-oriented blockchains in 6G era. As to blockchain optimization, the current general-purpose strategies can hardly hold efficiency all the time due to the heterogeneity of 6G-empowered IoT. In this paper, we present a novel pipeline for facilitating the green IoT-oriented blockchains in 6G era, called “fine-grained benchmarking + targeted optimization". Specifically, we first design a benchmarking framework which realizes the whole workflow of data acquisition, log parsing, and metric visualization, offering quantitative blockchain performance reports. Moreover, our framework provides ten metrics divided into four dimensions, leading blockchain benchmarking to the fine-grained level. Based on the acquired insights, we further present the concept of targeted optimization, i.e., directly designing optimization strategies based on the metrics that perform poorly in benchmarking. To better illustrate this pipeline, we take IOTA, the most potential IoT-oriented blockchain in 6G era, as a case study. We observe two defects of IOTA, i.e., low power efficiency and slow ledger synchronization. Following our pipeline, we design two targeted optimization mechanisms, namely Proof-of-Resource Efficiency and Dynamic Local Snapshot Protocol. Extensive experiments demonstrate that our pipeline can maximize the optimization efficiency, successfully addressing the issues hindering IOTA. Last but not least, we emphasize that the proposed pipeline can also be applied by other IoT-oriented blockchains in the 6G era.

Mixed Generalized Multiscale Finite Element Method for flow problem in thin domains

In this paper, we construct a class of Mixed Generalized Multiscale Finite Element Methods for the approximation on a coarse grid for an elliptic problem in thin two-dimensional domains. We consider the elliptic equation with homogeneous boundary conditions on the domain walls. For reference solution of the problem, we use a Mixed Finite Element Method on a fine grid that resolves complex geometry on the grid level. To construct a lower dimensional model, we use the Mixed Generalized Multiscale Finite Element Method, which is based on some multiscale basis functions for velocity fields. The construction of the basis functions is based on the local snapshot space that takes all possible flows on the interface between coarse cells into account. In order to reduce the size of the snapshot space and obtain the multiscale approximation, we solve a local spectral problem to identify dominant modes in the snapshot space. We present a convergence analysis of the presented multiscale method. Numerical results are presented for two-dimensional problems in three testing geometries along with the errors associated to different numbers of the multiscale basis functions used for the velocity field. Numerical investigations are conducted for problems with homogeneous and heterogeneous properties respectively.

English Language Teaching in Turkey in the 1960s: Plus ça change…?

The 1960s have witnessed a series of developments that paved the way to the tremendous growth and expansion in English Language Teaching (ELT) around the world. The purpose of this article is to portray a local snapshot of ELT in Turkey, both as an activity and a profession, in light of the global trends and developments. More specifically, the article opens with a broader look at the role and status of English in the country during this period. It is followed by examining what it meant to teach and be a teacher of English at the time. The discussion ends with establishing a set of connections to the current state of ELT in the local context. Finally, it is argued that the specific problems of ELT (e.g., lack of quality in pre-/in-service teacher education, recruitment methods and practices, physical conditions and infrastructure, teachers’ language proficiency, insufficient competency in developing/adapting instructional materials, inconsistency in terms of instructional practices, and lack of sustainable mentoring and appraisal practices) remain somewhat stable since the 1960s.

Seasonal Coronaviruses and Other Neglected Respiratory Viruses: A Global Perspective and a Local Snapshot.

Respiratory viral infections are the leading cause of morbidity and mortality in the world; however, there are several groups of viruses that are insufficiently routinely sought for, and can thus be considered neglected from a diagnostic and clinical standpoint. Timely detection of seasonality of certain respiratory viruses (e.g., enveloped viruses such as seasonal coronaviruses) in the local context can aid substantially in targeted and cost-effective utilization of viral diagnostic approaches. For the other, non-enveloped and year-round viruses (i.e., rhinovirus, adenovirus, and bocavirus), a continuous virological diagnosis needs to be implemented in clinical laboratories to more effectively address the aetiology of respiratory infections, and assess the overall impact of these viruses on disease burden. While the coronavirus disease 2019 (COVID-19) pandemic is still actively unfolding, we aimed to emphasize the persistent role of seasonal coronaviruses, rhinoviruses, adenoviruses and bocaviruses in the aetiology of respiratory infections. Consequently, this paper concentrates on the burden and epidemiological trends of aforementioned viral groups on a global level, but also provides a snapshot of their prevalence patterns in Croatia in order to underscore the potential implications of viral seasonality. An overall global prevalence in respiratory tract infections was found to be between 0.5 and 18.4% for seasonal coronaviruses, between 13 and 59% for rhinoviruses, between 1 and 36% for human adenoviruses, and between 1 and 56.8% for human bocaviruses. A Croatian dataset on patients with respiratory tract infection and younger than 18 years of age has revealed a fairly high prevalence of rhinoviruses (33.4%), with much lower prevalence of adenoviruses (15.6%), seasonal coronaviruses (7.1%), and bocaviruses (5.3%). These insights represent a relevant discussion point in the context of the COVID-19 pandemic where the testing of non-SARS-CoV-2 viruses has been limited in many settings, making the monitoring of disease burden associated with other respiratory viruses rather difficult.

Adaptive generalized multiscale approximation of a mixed finite element method with velocity elimination

In this paper, we propose offline and online adaptive enrichment algorithms for the generalized multiscale approximation of a mixed finite element method with velocity elimination to solve the subsurface flow problem in high-contrast and heterogeneous porous media. In the offline adaptive method, we first derive an a-posteriori error indicator based on one weighted L2-norm of the local residual operator, where the weighted L2-norm is related to the pressure fields of the local snapshot space. Then we enrich the multiscale space by increasing the number of offline basis functions iteratively on coarse elements where the error indicator takes large values. While in the online adaptive method, we add online basis functions on selected coarse elements based on another weighted L2-norm of the local residual operator to enrich the multiscale space, here the weighted L2-norm is associated with the velocity fields of the local snapshot space. Online basis functions are constructed in the online stage depending on the solution of the previous iteration and some optimal estimates. We give theoretical analyses for the convergences of these two adaptive methods, which show that sufficient initial basis functions (belong to the offline space) lead to faster convergence rates. A series of numerical examples are provided to highlight the performances of both these two adaptive methods and also validate the theoretical analyses. Both offline and online adaptive methods are effective that can reduce the relative error substantially. In addition, the online adaptive method generally performs better than the offline adaptive method as online basis functions contain important global information such as distant effects that cannot be captured by offline basis functions. The numerical results also show that with a suitable initial multiscale space that includes all offline basis functions corresponding to relative smaller eigenvalues of each local spectral decomposition in the offline stage, the convergence rate of the online enrichment is independent of the permeability contrast.

Generalized multiscale approximation of a multipoint flux mixed finite element method for Darcy–Forchheimer model

In this paper, we propose a multiscale method for the Darcy–Forchheimer model in highly heterogeneous porous media. The problem is solved in the framework of generalized multiscale finite element method (GMsFEM) combined with a multipoint flux mixed finite element (MFMFE) method. We consider a MFMFE method that utilizes the lowest order Brezzi–Douglas–Marini (BDM1) mixed finite element spaces for the approximation of velocity and pressure. The symmetric trapezoidal quadrature rule is employed for the integral of bilinear forms related to velocity variables so that the local velocity elimination is allowed which leads to a cell-centered system for pressure. We construct the multiscale space for pressure and solve the problem on the coarse grid following the GMsFEM framework. In the offline stage, we construct local snapshot spaces and perform spectral decompositions to get the offline space with a smaller dimension. In the online stage, we use Newton iterative algorithm to solve the nonlinear problem and obtain the offline solution, which reduces the number of iterations greatly compared to the standard Picard iterative algorithm. Based on the offline basis functions and the offline solution, we calculate online basis functions on each coarse element to enrich the multiscale space iteratively. The online basis functions contain the important global information and are effective to reduce relative errors substantially. Numerical examples are provided to highlight the performance of the proposed multiscale method.

Mixed GMsFEM for linear poroelasticity problems in heterogeneous porous media

Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome this computational challenge, various multiscale methods are developed. In this paper, we consider a class of linear poroelasticity problems in high contrast heterogeneous porous media, and develop a mixed generalized multiscale finite element method (GMsFEM) to obtain a fast computational method. Our aim is to develop a multiscale method that is robust with respect to the heterogeneities and contrast of the media, and gives a mass conservative fluid velocity field. We will construct decoupled multiscale basis functions for the elastic displacement as well as fluid velocity. Our multiscale basis functions are local. The construction is based on some suitable choices of local snapshot spaces and local spectral decomposition, with the goal of extracting dominant modes of the solutions. For the pressure, we will use piecewise constant approximation. We will present several numerical examples to illustrate the performance of our method. Our results indicate that the proposed method is able to give accurate numerical solutions with a small degree of freedoms.

A third-party replication service for dynamic hidden databases

Much data on the web is available in hidden databases. Users browse their contents by sending search queries to form-based interfaces or APIs. Yet, hidden databases just return the top-k result entries and limit the number of queries per time interval. Such access restrictions constrict those tasks that require many/specific queries or need to access many/all data entries. For a temporary solution, an unrestricted local snapshot can be created by crawling the hidden database. Yet, keeping the snapshot permanently consistent is challenging due to the access restrictions of its origin. In this paper, we propose a replication approach providing permanent unrestricted access to the local copy of a hidden database with dynamic changes. To this end, we present an algorithm to effectively crawl hidden databases that outperforms the state of the art. Furthermore, we propose a new way to continuously control the consistency of the replicated database in an efficient manner. We also introduce the cloud-based architecture of a replication service for hidden databases. We show the effectiveness of the approach through a variety of reproducible experimental evaluations.

A hybridizable discontinuous Galerkin Generalized Multiscale Finite element method for highly heterogeneous linear elasticity problems

In this paper, we consider a multiscale hybridizable discontinuous Galerkin (HDG) for heterogeneous linear elasticity problem in a mixed formulation. Within the framework of HDG, the entire problem can be decomposed into a global problem defined in coarse interfaces and several local problems in coarse elements. Our goal here is to propose a multiscale basis space defined in the coarse interface. We will employ local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods (GMsFEM). Numerical experiments on highly heterogeneous material and nearly incompressible material are provided to verify the efficiency of the proposed method.

Generalized multiscale multicontinuum model for fractured vuggy carbonate reservoirs

Simulating flow in a highly heterogeneous reservoir with multiscale characteristics is computationally demanding. To tackle this problem, we propose a numerical scheme based on the Generalized Multiscale Finite Element Method (GMsFEM) and a triple-continuum model. The aim is to obtain a more efficient numerical approach that can explicitly represent the interactions among different continua. To enhance the applicability of our proposed model, we combine the Discrete Fracture Model (DFM) to model the local effects of discrete fractures. In the proposed model, the GMsFEM, as an advanced model reduction technique, enables capturing the multiscale flow dynamics. This is accomplished by systematically generating an approximation space through solving a series of local snapshot and spectral problems. The resulting eigenfunctions can pass the local features to the global level when acting as basis functions in the global coarse problems. Our goal in this paper is to further improve the accuracy of flow simulation in complicated reservoirs especially for the case when multiple discrete fractures located in single coarse neighborhood. Several numerical experiments are conducted to confirm the success of our proposed method, and a rigorous convergence proof is also given.

Multiscale hybridizable discontinuous Galerkin method for elliptic problems in perforated domains

We propose a multiscale hybridizable discontinuous Galerkin method in perforated domains. Perforations may have various shapes and sizes. Following Generalized Multiscale Finite Element method, local snapshot spaces are constructed by solving local spectral problems. Then multiscale finite element spaces for numerical traces are built on the coarse edges within the framework of hybridizable discontinuous Galerkin method. Some representative examples are presented to investigate numerical performance of the proposed method.

Generalized multiscale finite element methods for space–time heterogeneous parabolic equations

In this paper, we consider local multiscale model reduction for problems with multiple scales in space and time. We developed our approaches within the framework of the Generalized Multiscale Finite Element Method (GMsFEM) using space–time coarse cells. The main idea of GMsFEM is to construct a local snapshot space and a local spectral decomposition in the snapshot space. Previous research in developing multiscale spaces within GMsFEM focused on constructing multiscale spaces and relevant ingredients in space only. In this paper, our main objective is to develop a multiscale model reduction framework within GMsFEM that uses space–time coarse cells. We construct space–time snapshot and offline spaces. We compute these snapshot solutions by solving local problems. A complete snapshot space will use all possible boundary conditions; however, this can be very expensive. We propose using randomized boundary conditions and oversampling (cf. Calo et al., 2016). We construct the local spectral decomposition based on our analysis, as presented in the paper. We present numerical results to confirm our theoretical findings and to show that using our proposed approaches, we can obtain an accurate solution with low dimensional coarse spaces. We discuss using online basis functions constructed in the online stage and using the residual information. Online basis functions use global information via the residual and provide fast convergence to the exact solution provided a sufficient number of offline basis functions. We present numerical studies for our proposed online procedures. We remark that the proposed method is a significant extension compared to existing methods, which use coarse cells in space only because of (1) the parabolic nature of cell solutions, (2) extra degrees of freedom associated with space–time cells, and (3) local boundary conditions in space–time cells.

An Enriched Multiscale Mortar Space for High Contrast Flow Problems

Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the standard mortar spaces are not robust, and some enrichments are necessary in order to obtain an efficient and robust mortar space. In this paper, we consider a class of flow problems in high contrast heterogeneous media, and develop a systematic approach to obtain an enriched multiscale mortar space. Our approach is based on the constructions of local multiscale basis functions. The multiscale basis functions are constructed from local problems by following the framework of the Generalized Multiscale Finite Element Method (GMsFEM). In particular, we first create a local snapshot space. Then we select the dominated modes within the snapshot space using an appropriate Proper Orthogonal Decomposition (POD) technique. These multiscale basis functions show better accuracy than polynomial basis for multiscale problems. Using the proposed multiscale mortar space, we will construct a multiscale finite element method to solve the flow problem on a coarse grid and a preconditioning technique for the fine scale discretization of the flow problem. In particular, we develop a multiscale mortar mixed finite element method using the mortar space. In addition, we will design a two-level additive preconditioner and a two-level hybrid preconditioner based on the proposed mortar space for the iterative method applied to the fine scale discretization of the flow problem. We present several numerical examples to demonstrate the efficiency and robustness of our proposed mortar space with respect to both the coarse multiscale solver and the preconditioners.

A conservative local multiscale model reduction technique for Stokes flows in heterogeneous perforated domains

In this paper, we present a new multiscale model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the fact that the solution contains many multiscale features and requires a very fine mesh to resolve all details. In order to efficiently compute the solutions, some model reductions are necessary. To obtain a reduced model, we apply the generalized multiscale finite element approach, which is a framework allowing systematic construction of reduced models. Based on this general framework, we will first construct a local snapshot space, which contains many possible multiscale features of the solution. Using the snapshot space and a local spectral problem, we identify dominant modes in the snapshot space and use them as the multiscale basis functions. Our basis functions are constructed locally with non-overlapping supports, which enhances the sparsity of the resulting linear system. In order to enforce the mass conservation, we propose a hybridized technique, and uses a Lagrange multiplier to achieve mass conservation. We will mathematically analyze the stability and the convergence of the proposed method. In addition, we will present some numerical examples to show the performance of the scheme. We show that, with a few basis functions per coarse region, one can obtain a solution with excellent accuracy.

Mixed GMsFEM for the simulation of waves in highly heterogeneous media

Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of simulating waves at a much lower cost. Our method is based on a mixed Galerkin type method with carefully designed basis functions that can capture various scales in the solution. The basis functions are constructed based on some local snapshot spaces and local spectral problems defined on them. The spectral problems give a natural ordering of the basis functions in the snapshot space and allow systematically enrichment of basis functions. In addition, by using a staggered coarse mesh, our method is energy conserving and has block diagonal mass matrix, which are desirable properties for wave propagation. We will prove that our method has spectral convergence, and present numerical results to show the performance of the method.

Mixed GMsFEM for second order elliptic problem in perforated domains

We consider a class of second order elliptic problems in perforated domains with homogeneous Neumann boundary condition. It is well-known that numerically solving these problems require a very fine computational mesh, and some model reduction techniques are therefore necessary. We will develop a new model reduction technique based on the generalized multiscale finite element method (GMsFEM). The GMsFEM has been applied successfully to second order elliptic problems in perforated domains with Dirichlet boundary conditions Chung et al. (2015). However, due to the use of multiscale partition of unity functions, the same method cannot be applied to the case with Neumann boundary conditions. The aim of this paper is to develop a new mixed GMsFEM, based on a piecewise constant approximation for pressure and a multiscale approximation for velocity, giving a mass conservative method. The method can handle the Neumann boundary condition naturally. The multiscale basis functions for velocity are constructed by some carefully chosen local snapshot spaces and local spectral decompositions. The spectral convergence of the method is analyzed. Moreover, by using some local error indicators, the basis functions can be added locally and adaptively. We also consider an online procedure for the construction of new basis functions in the online stage in order to capture the distant effects. We will present some numerical examples to show the performance of the method.

Structural and practical identifiability analysis of S‐system

In the field of systems biology, biological reaction networks are usually modelled by ordinary differential equations. A sub-class, the S-systems representation, is a widely used form of modelling. Existing S-systems identification techniques assume that the system itself is always structurally identifiable. However, due to practical limitations, biological reaction networks are often only partially measured. In addition, the captured data only covers a limited trajectory, therefore data can only be considered as a local snapshot of the system responses with respect to the complete set of state trajectories over the entire state space. Hence the estimated model can only reflect partial system dynamics and may not be unique. To improve the identification quality, the structural and practical identifiablility of S-system are studied. The S-system is shown to be identifiable under a set of assumptions. Then, an application on yeast fermentation pathway was conducted. Two case studies were chosen; where the first case is based on a larger state trajectories and the second case is based on a smaller one. By expanding the dataset which span a relatively larger state space, the uncertainty of the estimated system can be reduced. The results indicated that initial concentration is related to the practical identifiablity.

Sparse Generalized Multiscale Finite Element Methods and their applications

In a number of previous papers, local (coarse grid) multiscale model reduction techniques are developed using a Generalized Multiscale Finite Element Method. In these approaches, multiscale basis functions are constructed using local snapshot spaces, where a snapshot space is a large space that represents the solution behavior in a coarse block. In a number of applications (e.g., those discussed in the paper), one may have a sparsity in the snapshot space for an appropriate choice of a snapshot space. More precisely, the solution may only involve a portion of the snapshot space. In this case, one can use sparsity techniques to identify multiscale basis functions. In this paper, we consider two such sparse local multiscale model reduction approaches. In the first approach (which is used for parameter-dependent multiscale PDEs), we use local minimization techniques, such as sparse POD, to identify multiscale basis functions, which are sparse in the snapshot space. These minimization techniques use l1 minimization to find local multiscale basis functions, which are further used for finding the solution. In the second approach (which is used for the Helmholtz equation), we directly apply l1 minimization techniques to solve the underlying PDEs. This approach is more expensive as it involves a large snapshot space; however, in this example, we cannot identify a local minimization principle, such as local generalized SVD. All our numerical results assume the sparsity and we discuss this assumption for the snapshot spaces. Moreover, we discuss the computational savings provided by our approach. The sparse solution allows a fast evaluation of stiffness matrices and downscaling the solution to the fine grid since the reduced dimensional solution representation is sparse in terms of local snapshot vectors. Numerical results are presented, which show the convergence of the proposed method and the sparsity of the solution.

A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

Abstract We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.

Flexible Symmetrical Global-Snapshot Algorithms for Large-Scale Distributed Systems

Most existing global-snapshot algorithms in distributed systems use control messages to coordinate the construction of a global snapshot among all processes. Since these algorithms typically assume the underlying logical overlay topology is fully connected, the number of control messages exchanged among the whole processes is proportional to the square of number of processes, resulting in higher possibility of network congestion. Hence, such algorithms are neither efficient nor scalable for a large-scale distributed system composed of a huge number of processes. Recently, some efforts have been presented to significantly reduce the number of control messages, but doing so incurs higher response time instead. In this paper, we propose an efficient global-snapshot algorithm able to let every process finish its local snapshot in a given number of rounds. Particularly, such an algorithm allows a tradeoff between the response time and the message complexity. Moreover, our global-snapshot algorithm is symmetrical in the sense that identical steps are executed by every process. This means that our algorithm is able to achieve better workload balance and less network congestion. Most importantly, based on our framework, we demonstrate that the minimum number of control messages required by a symmetrical global-snapshot algorithm is Ω(N log N), where N is the number of processes. Finally, we also assume non-FIFO channels.