There is uncertainty in various domains, requiring a robust understanding and quantification in order to make informed decisions. This article presents a comprehensive discussion of uncertainty quantification (UQ) in dynamical systems. Beginning with an overview, we examine the multifaceted nature of uncertainty and the challenges in its modeling and analysis. Identifying key sources that shape uncertainty is essential for accurate quantification. Whether models are deterministic or stochastic, statistical inference remains crucial for robust modeling and decision-making in UQ. This article introduces a state-of-the-art classification of UQ methods, comprising two fundamental categories: 1) forward propagation techniques and 2) backward propagation techniques, each designed to address specific challenges in UQ. By equipping readers with essential tools for managing uncertainty, this article aims to broaden the application of UQ across engineering, physics, technology, and healthcare.

BACKGROUND: Network analysis is a powerful tool for studying gene regulation and identifying biological processes associated with gene function. However, constructing gene co-expression networks can be a challenging task, particularly when dealing with a large number of missing values. RESULTS: We introduce GeCoNet-Tool, an integrated gene co-expression network construction and analysis tool. The tool comprises two main parts: network construction and network analysis. In the network construction part, GeCoNet-Tool offers users various options for processing gene co-expression data derived from diverse technologies. The output of the tool is an edge list with the option of weights associated with each link. In network analysis part, the user can produce a table that includes several network properties such as communities, cores, and centrality measures. With GeCoNet-Tool, users can explore and gain insights into the complex interactions between genes.

BACKGROUND: Gene co-expression networks (GCNs) can be used to determine gene regulation and attribute gene function to biological processes. Different high throughput technologies, including one and two-channel microarrays and RNA-sequencing, allow evaluating thousands of gene expression data simultaneously, but these methodologies provide results that cannot be directly compared. Thus, it is complex to analyze co-expression relations between genes, especially when there are missing values arising for experimental reasons. Networks are a helpful tool for studying gene co-expression, where nodes represent genes and edges represent co-expression of pairs of genes. RESULTS: transcriptome from 257 unique studies obtained with different methodologies and experimental designs. We introduce the sliding threshold approach to select node pairs with high Pearson correlation coefficients. The resulting network, which we name AgGCN1.0, is robust to random removal of conditions and has similar characteristics to small-world and scale-free networks. Analysis of network sub-graphs revealed that the core is largely comprised of genes that encode components of the mitochondrial respiratory chain and the ribosome, while different communities are enriched for genes involved in distinct biological processes. CONCLUSION: Analysis of the network reveals that both the architecture of the core sub-network and the network communities are based on gene function, supporting the power of the proposed method for GCN construction. Application of network science methodology reveals that the overall network structure is driven to maximize the integration of essential cellular functions, possibly allowing the flexibility to add novel functions.

West Nile virus (WNV)-a mosquito-borne arbovirus-entered the USA through New York City in 1999 and spread to the contiguous USA within three years while transitioning from epidemic outbreaks to endemic transmission. The virus is transmitted by vector competent mosquitoes and maintained in the avian populations. WNV spatial distribution is mainly determined by the movement of residential and migratory avian populations. We developed an individual-level heterogeneous network framework across the USA with the goal of understanding the long-range spatial distribution of WNV. To this end, we proposed three distance dispersal kernels model: 1) exponential-short-range dispersal, 2) power-law-long-range dispersal in all directions, and 3) power-law biased by flyway direction -long-range dispersal only along established migratory routes. To select the appropriate dispersal kernel we used the human case data and adopted a model selection framework based on approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC). From estimated parameters, we find that the power-law biased by flyway direction kernel is the best kernel to fit WNV human case data, supporting the hypothesis of long-range WNV transmission is mainly along the migratory bird flyways. Through extensive simulation from 2014 to 2016, we proposed and tested hypothetical mitigation strategies and found that mosquito population reduction in the infected states and neighboring states is potentially cost-effective.

In this paper, we analyze dynamic switching networks, wherein the networks switch arbitrarily among a set of topologies. For this class of dynamic networks, we derive an epidemic threshold, considering the susceptible-infected-susceptible epidemic model. First, an epidemic probabilistic model is developed assuming independence between states of nodes. We identify the conditions under which the epidemic dies out by linearizing the underlying dynamical system and analyzing its asymptotic stability around the origin. The concept of joint spectral radius is then used to derive the epidemic threshold, which is later validated using several networks (Watts-Strogatz, Barabasi-Albert, MIT reality mining graphs, Regular, and Gilbert). A simplified version of the epidemic threshold is proposed for undirected networks. Moreover, in the case of static networks, the derived epidemic threshold is shown to match conventional analytical results. Then, analytical results for the epidemic threshold of dynamic networks are proved to be applicable to periodic networks. For dynamic regular networks, we demonstrate that the epidemic threshold is identical to the epidemic threshold for static regular networks. An upper bound for the epidemic spread probability in dynamic Gilbert networks is also derived and verified using simulation.

Several applications within a shipboard system involve the integration of physical systems (e.g., power systems) and cyber computing platforms such as command and control, communications, and sensing networks, and require real-time quality of service (QoS) guarantees. In this paper, the distribution of total (end-to-end) delay associated with fault diagnosis and reconfiguration of shipboard power system (SPS) is investigated from a cyber-physical systems (CPS) perspective. Specifically, a cross-layer end-to-end delay analysis framework is introduced for SPS reconfiguration. The proposed framework stochastically models the heterogeneity of actions of various subsystems involved in the reconfiguration tasks viz., generation of fault information by sensor nodes associated to the power system, processing of actions at control center to resolve fault locations and reconfiguration, and flow of information through communication network to perform necessary actions. The proposed framework then combines appropriately the output delay distributions from each subsystem to: 1) analytically predict the distribution of end-to-end delay in SPS reconfiguration after the occurrence of faults and 2) analyze and design real-time reconfiguration solutions for shipboard CPS, that meet total delay requirements. Simulations using various topological scenarios demonstrate that the proposed analytical framework closely predict the total delay associated with SPS reconfiguration.

Mean-field deterministic epidemic models have been successful in uncovering several important dynamic properties of stochastic epidemic spreading processes over complex networks. In particular, individual-based epidemic models isolate the impact of the network topology on spreading dynamics. In this paper, the existing models are generalized to develop a class of models that includes the spreading process in multilayer complex networks. We provide a detailed description of the stochastic process at the agent level where the agents interact through different layers, each represented by a graph. The set of differential equations that describes the time evolution of the state occupancy probabilities has an exponentially growing state-space size in terms of the number of the agents. Based on a mean-field type approximation, we developed a set of nonlinear differential equations that has linearly growing state-space size. We find that the latter system, referred to as the generalized epidemic mean-field (GEMF) model, has a simple structure characterized by the elements of the adjacency matrices of the network layers and the Laplacian matrices of the transition rate graphs. Finally, we present several examples of epidemic models, including spreading of virus and information in computer networks and spreading of multiple pathogens in a host population .

The KAD network is one of the largest distributed hash tables utilized by the popular P2P file-sharing systems: aMule and eMule. However, its lookup performance is recognized as inefficient. In this work, based on the fact that peers publish and retrieve information with the help of their routing t

In this paper, we describe a multi-objective approach to determine an effective mitigation strategy during an outbreak of foot and mouth disease in cattle. The goal of the approach is to minimize the total number of infections. In addition, the direct costs must also be minimized as a secondary objective. The animals culled and vaccinations may also be minimized, as long as the number of infections is not compromised. Thus a three-tier hierarchy of objectives exists. A framework that considers objective hierarchies during a multi-objective optimization algorithm is suggested. Results show that this produces better results than a conventional multi-objective optimization approach.

The task of routing in epidemic networks faces certain difficulties involving minimizing the delivery delay with a reduced consumption of resources. Every node has severe power constraints and the network is also susceptible to temporary but random failure of nodes. In the previous work, the parameter of mobility has been considered a constant for a certain setting. In our setting, we consider a varying parameter of mobility. In this framework, we determine the optimal mobility pattern and a forwarding policy that a network should follow in order to meet the trade-off between delivery delay and power consumption. In addition, the mobility pattern should be such that it can be practically incorporated. In this paper, we formulate an optimization problem which is solved by using the principles of dynamic programming. The resultant strategy, OFACT optimal forwarding algorithm with controlled transmission range, has been studied through extensive simulations. The performance of OFACT has been compared with a few existing strategies. Our results show that this optimization problem has a global solution.

Prior research efforts on cognitive radio networks have mainly focused on effective sensing of primary users to determine the availability of a spectrum band for opportunistic use. However, when multiple secondary users compete for a limited amount of spectrum, quality of service (QoS) for these users could degrade due to interference. In this paper, we present an integrated modeling and forecasting framework characterizing spectrum use by secondary users in a cognitive radio network (CRN). In our proposed method, each secondary user in a CRN, first enters a learning and modeling phase where it attempts to estimate the traffic parameters of other secondary users. Following this phase, the secondary user actively participates in opportunistic spectrum use. Assuming a continuous time Markov chain model for secondary user activity, we develop a Kalman filter based approach for estimating the number of secondary users. This estimate is in turn used to predict the number of secondary users in a future time instant. Experimental results show that our proposed forecasting technique provides a good upper bound prediction for the number of secondary users.

High bandwidth one-to-many applications emerging in IP over WDM optical networks demand multicast support at WDM layer so that data signals would be efficiently duplicated inside network without O/E/O conversion. Multicast trees in an optical layer can be built with light-trees which use light-splitting technique. Most of recent studies have been focused to efficiently build and configure light-trees without existing unicast or multicast traffic into consideration. In this paper we consider the dynamic and optimal design problem of multicast configuration for realistic and constrained WDM networks. In such a network, both unicast and multicast are supported, and WDM switches have limited number of wavelengths and light splitting capability. On the other hand, the amount of bandwidth per wavelength is abundant. Using subwavelength sharing among traffic demands of unicast and multicast, we build a hybrid virtual topology which exploits both existing light-trees and light- paths. By optimizing WDM resources in addition to resource sharing with existing unicast and multicast demands, we truly maximize the WDM layer capability and efficiently support more multicast traffic demands. We validate the efficiency of our approach with extensive simulations.

Forecasting of network traffic plays a very important role in many domains such as congestion control, adaptive applications, network management and traffic engineering. A good traffic model should have the ability to capture prominent traffic characteristics, such as long-range dependence (LRD), self-similarity and heavy-tailed distributions. In this paper, we propose a non-linear time series model, Generalized AutoRegressive Conditional Heteroskedasticity (GARCH), with innovation process generalized to the class of heavy-tailed distributions. Our model is fitted on real data and our results confirms the goodness of fit of our model. We then evaluate a forecasting scheme based on our model. Comparative study with other generic models shows that our model have a better prediction accuracy. In addition, the parameter estimation is less complex than the other models used so far in modeling Internet traffic data.

This paper deals with IP traffic engineering (TE) for multipath selection in MPLS networks. A centralized and a distributed routing algorithms are proposed, which aggregate IP flows entering the MPLS domain, and optimally partition them among virtual flows that are forwarded on multiple paths according to their quality of service (QoS) requirements. The virtual-flow multipath routing problem is formulated as a multicommodity network flow (MCNF) problem, and is solved by implementing on-line the Dantzig-Wolfe decomposition method, which is proven to converge to the optimal solution through an iterative procedure that divides the complex optimization problem into a tractable subproblem. The proposed multipath algorithms are shown to outperform single-path routing solutions by means of extensive simulation experiments.

The combined use of the differentiated services (DiffServ) and multiprotocol label switching (MPLS) technologies is envisioned to provide guaranteed quality of service (QoS) for multimedia traffic in IP networks, while effectively using network resources. These networks need to be managed adaptively to cope with the changing network conditions and provide satisfactory QoS. An efficient strategy is to map the traffic from different DiffServ classes of service on separate label switched paths (LSPs), which leads to distinct layers of MPLS networks corresponding to each DiffServ class. In this paper, three aspects of the management of such a layered MPLS network are discussed. In particular, an optimal technique for the setup of LSPs, capacity allocation of the LSPs and LSP routing are presented. The presented techniques are based on measurement of the network state to adapt the network configuration to changing traffic conditions.

Emerging applications demand strict quality of service from the network. To meet these demands, a suitable path with enough resources needs to be selected. The paper focuses on the path computation in an MPLS network for a traffic flow, based on distance, bandwidth and delay constraints. The goal of the paper is to find a feasible path that minimizes the cost incurred. The cost is attributed to bandwidth carriage, and switching and signaling efforts in the network for the requested connection.

In this paper, a new policy is introduced to determine and adapt the generalized multiprotocol label switching (GMPLS) network topology based on the current traffic load. The objective of the new policy is to minimize the costs involving bandwidth, switching and signaling. The new policy is based on a threshold criterion. The policy is split into two levels, the first deals with the MPLS network and the second with the lightpath level. The two thresholds depends on the cost coefficients and the number of the intermediate hops. Our policy also performs a filtering control to avoid oscillations which occur due to highly variable traffic. The proposed policy has been evaluated by simulation and numerical results, which show its effectiveness and the achieved performance improvement.

An approach to dimensioning DiffServ/MPLS networks taking into account the per-class bandwidth reservation and fault tolerance cushion weights is proposed. Our dimensioning algorithm is based on Lagrange relaxation and it uses a bandwidth constraint model in order to provide per-class bandwidth reservation, and link costs which translate to backup LSP cushion weights. We propose an optimization formulation for our policy and also a polynomial time heuristic capable of approximating the optimal results. Besides a-priori dimensioning, a modified version of our dimensioning policy can also be run weekly/monthly in order to redimension LSPs according to the stored traffic history. Both the proposed heuristics have polynomial complexity and provides bounds on the value of the optimal objective function, which can be used to evaluate the accuracy of the results.

In this work DIMRO, an efficient algorithm to build source specific multicast trees, is presented. DIMRO aims at achieving a high traffic balance in the network in order to avoid bandwidth bottlenecks and consequent network partitions, one of the main causes for low network performance. To do so, it computes multicast trees by dynamically selecting the least loaded available paths, obtaining an optimal distribution of network resources. Strictly integrated with the DiffServ Quality of Service (QoS) approach, the proposed multirate native multicast algorithm maps the QoS service requested by receivers into the proper DiffServ class, so as to respect the expected QoS requirements. The results are a better leverage of the network bandwidth resources, an improved QoS perceived by multicast group members, and time and resource saving due to its low computational complexity, as shown through extensive C++ based simulation campaign.

In this paper, a new optimal policy is introduced to determine and adapt the generalized multiprotocol label switching (GMPLS) network topology based on the current traffic load. The integrated traffic engineering paradigm provides mechanisms for dynamic addition of physical capacity to optical networks. In the absence of such mechanisms, the rejection of incoming requests will be higher. The objective of the proposed policy is to minimize the costs involving bandwidth, switching and signaling. The policy is derived by utilizing the Markov decision process theory. The new policy is split into two levels: the MPLS network level and the optical network level. In addition to the optimal policy, a sub-optimal policy and a threshold-based policy are also proposed which are less computationally intensive but have comparable performance to the optimal policy. The proposed policies have been evaluated by simulation and compared to some heuristics. Numerical results, which show their effectiveness and the achieved performance improvement, are presented.

The preemption policy currently in use in MPLS-enabled commercial routers selects LSPs for preemption based only on their priority and holding time. This can lead to waste of resources and excessive number of rerouting decisions. In this paper, a new preemption policy is proposed and complemented with an adaptive scheme that aims to minimize rerouting. The new policy combines the three main preemption optimization criteria: number of LSPs to be preempted, priority of the LSPs, and preempted bandwidth. Weights can be configured to stress the desired criteria. The new policy is complemented by an adaptive scheme that selects lower priority LSPs that can afford to have their rate reduced. The selected LSPs will fairly reduce their rate in order to accommodate the new high-priority LSP setup request. Performance comparisons of a nonpreemptive approach, a policy currently in use by commercial routers, and our policies are also investigated.

We present a method for an on-line traffic optimal estimation on a communication link. The proposed filtering procedure is based on a traffic model consisting of a birth-and-death process, elaborates the current noisy measurements from the link and minimizes the estimation error conditional variance. Performance of the method is tested by considering both simulated and real data. This result is of interest with reference to a possible procedure for bandwidth allocation in the framework of bandwidth brokers. The bandwidth allocation is necessary to provide quality of service guarantees to users and requires, as a preliminary step, on-line traffic estimation.

In this paper, a method for enhancing current QoS routing methods by means of QoS protection is presented. In an MPLS network, the segments (links) to be protected are predefined and an LSP request involves, apart from establishing a working path, creating a specific type of backup path (local, reverse or global). Different QoS parameters, such as network load balancing, resource optimization and minimization of LSP request rejection should be considered. QoS protection is defined as a function of QoS parameters, such as packet loss, restoration time, and resource optimization. A framework to add QoS protection to many of the current QoS routing algorithms is introduced. A backup decision module to select the most suitable protection method is formulated and different case studies are analyzed.

The explosive growth of the Internet has induced a need for developing tools to understand the composition and dynamics of the Internet traffic. Measurements of the various characteristics of a network provide insight into the state and performance of the network whether it is behaving as expected and whether changes in the network have improved or degraded its performance. Available bandwidth on the links of a network is an important metric which can predict the performance of the network. In this paper, an estimation algorithm for the available bandwidth on a link is presented. The algorithm estimates the available bandwidth and tells the duration for which the estimate is valid with a high degree of confidence. The algorithm dynamically changes the number of past samples that an used for prediction and also the duration for which the prediction holds.

A new algorithm for dynamic routing of LSPs is proposed. While off-line algorithms are not suitable due to the necessary a priori knowledge of future LSP setup requests, our proposed algorithm, SPeCRA (stochastic performance comparison routing algorithm), does not assume any specific stochastic traffic model and does not require any knowledge of future demands. Both features are a must for the new Internet traffic. In order to analyze SPeCRA's performance, we compare the ISP rejection ratios of SPeCRA and MIRA (Kar, K. et al., IEEE J. on Selected Areas in Commun., vol.18, no.12, p.2566-79, 2000). SPeCRA is easy to implement. It can be implemented using only simple shortest-hop or shortest-cost algorithms, which are interesting solutions for vendors, and not as computationally heavy as other routing algorithms.

In this paper, a new preemption policy is proposed and complemented with an adaptive scheme that aims to minimize rerouting. The preemption policy combines the three main optimization criteria: number of LSP to be preempted, priority of LSP to be preempted, and amount of bandwidth to be preempted. The preemption policy is complemented by an adaptive scheme that selects LSP with lower priority and reduces their rate in order to accommodate the new high-priority LSP setup request. Heuristics for both preemption and adaptive preemption policies are derived. Simulation results show the heuristics' accuracy. Performance comparisons of a non-preemptive approach, our preemption policy, the adaptive rate policy, and the policy in use by commercial routers are included.

The point-to-multipoint routing problem is studied for an asynchronous transfer mode (ATM) network that uses virtual paths (VPs). ATM networks with asymmetric and symmetric VPs are considered, and the performance factors studied are bandwidth and establishment and switching costs. A VP with intermediate exit, where a node that performs VP switching can copy the switched packets for the local destination, is proposed and studied. Mathematical formulations of multicast routing problems are presented, and heuristics for finding a low cost multicast routing tree, based on the transshipment simplex algorithm, are developed.>