Network Formulation Research Articles

Comparison of material models for anterior cruciate ligament in tension: from poroelastic to a novel fibril-reinforced nonlinear composite model

Computational models of the knee joint are useful for evaluating stresses and strains within the joint tissues. However, the outcome of those models is sensitive to the material model and material properties chosen for ligaments, the collagen reinforced tissues connecting bone to bone. The purpose of this study was to investigate different compositionally motivated material models and further to develop a model that can accurately reproduce experimentally measured stress-relaxation data of bovine anterior cruciate ligament (ACL).Tensile testing samples were extracted from ACLs of bovine knee joints (N = 10) and subjected to a three-step stress-relaxation test at the toe region. Data from the experiments was averaged and one average finite element model was generated to replicate the experiment. Poroelastic and different fibril-reinforced poro(visco)elastic material models were applied, and their material parameters were optimized to reproduce the experimental force-time response.Material models with only fluid flow mediated relaxation were not able to capture the stress-relaxation behavior (R2 = 0.806, 0.803 and 0.938). The inclusion of the viscoelasticity of the fibrillar network improved the model prediction (R2 = 0.978 and 0.976), but the complex stress-relaxation behavior was best captured by a poroelastic model with a nonlinear two-relaxation-time strain-recruited viscoelastic fibrillar network (R2 = 0.997).The results suggest that in order to replicate the multi-step stress-relaxation behavior of ACL in tension, the fibrillar network formulation should include the complex nonlinear viscoelastic phenomena.

Specification and Estimation of Network Formation and Network Interaction Models with the Exponential Probability Distribution

In this paper, we model network formation and network interactions under a unified framework. The key feature of our model is to allow individuals to respond to incentives that stem from interaction benefits of certain activities when they choose friends (network links), while capturing homophily in terms of unobserved characteristic variables in network formation and activities. There are two advantages of this modeling approach: first, one can evaluate whether incentives from certain interactions are important factors for friendship formation or not. Second, in addition to homophily effects in terms of unobserved characteristics, inclusion of incentive effects in the network formulation also corrects possible friendship selection bias on activity outcomes under network interactions. A theoretical foundation of this unified model is based on a sub-game perfect equilibrium of a two-stage game. A tractable Bayesian MCMC approach is proposed for the estimation of the model, and we demonstrate its finite sample performance in a simulation study. We apply the model to study empirically American high school students' friendship networks from the Add Health dataset. We consider two activity variables, GPA and smoking frequency, and find a significant incentive effect from GPA, but not from smoking, on friendship formation. These results suggest that the benefit of interactions in academic learning is an important factor for friendship formation, whereas the interaction benefit of smoking is not. On the other hand, from the perspective of network interactions, both GPA and smoking frequency are subject to significant positive interaction (peer) effects.

On dispersion of stress state and variability in fractured media: effect of fracture scattering

The presence and distribution of fractures in a fractured rock play a vital role in its stress state and variability. Understanding the stress condition is also one of the most important aspects of rock mechanics and geomechanical studies. In this study, we attempted to determine the influence of fracture distribution and interaction between fractures on the dispersion of stress perturbation by employing a discrete fracture network formulation. To do so, at first, a discrete fracture network was generated using a stochastic approach. Then, under technical stress loading conditions, in two different scenarios, the stress field was computed by a finite difference software. Finally, obtained stress data were analyzed using tensor-based formulations. The results showed that stress perturbation and stress dispersion (which was evaluated using effective variance) were affected by the fracture distribution in two different fracture network models, including the typical and conditional fracture network. The values of effective variance in conditional fracture networks (where there is no connection between the fractures and the fractures have no interaction with each other and are scattered in different parts of the model) is higher than the typical model. This is due to the reason that in the typical model, because of the connection, interaction, and intersection between fractures, the model is a more consolidated fracture network system. Therefore, less dispersion occurs in the stress distribution.

Tailoring composite materials for nonlinear viscoelastic properties using artificial neural networks

Polymer matrix composites exhibit nonlinear viscoelastic behavior over a wide range of temperatures and loading frequencies, which requires an elaborate experimental characterization campaign. Methods are now available to accelerate the characterization process and recover elastic modulus from storage modulus ( E′). However, these methods are limited to the linear viscoelastic region and need to be expanded to nonlinear viscoelastic problems to enable materials design. The present work aims to build a general machine learning based architecture to accelerate the characterization and materials design process for nonlinear viscoelastic materials using the E′ results. To expand outside the linear viscoelastic region, general relations of viscoelasticity are first developed so the master relation of E′ considering nonlinear viscoelasticity can be transformed to time domain relaxation function. The transform starts with building the master relation by optimizing the artificial neural network (ANN) formulation using Kriging model and genetic algorithm. Then the master relation is transformed to a relaxation function, which can be used to predict the stress response with a given strain history and to further extract the elastic modulus. The transform is tested on high density polyethylene matrix syntactic foams and the accuracy is found by comparing the predicted materials properties with those obtained from tensile tests. The good agreements indicate the transform can predict the elastic modulus under a wide range of temperatures and strain rates for any composition of the composite and can be used for material design problems.

Snow plow route optimization: A constraint programming approach

Many cities have to cope with annual snowfall, but are struggling to manage their snow plowing activities efficiently. Despite the fact that winter road maintenance has been a popular research subject for decades, very few papers propose scalable models that can incorporate side constraints encountered in real-life applications. In this work, we propose a Constraint Programming formulation for a Snow Plow Routing Problem (SPRP). The SPRP under consideration involves finding a set of vehicle routes to service a street network in a pre-defined service area, while accounting for various vehicle constraints and traffic restrictions. The fundamental mathematical problem underlying SPRP is the well-known Capacitated Arc Routing Problem (CARP). Common Mathematical Programming (MP) approaches for CARP are typically based on: (i) a graph transformation, thereby transforming CARP into an equivalent node routing problem, or (ii) a sparse network formulation. The CP formulation in this article is based on the former graph transformation. Using geospatial data from the city of Pittsburgh, we empirically show that our CP approach outperforms existing MP formulations for SPRP. For some of the larger instances, our CP model finds 26% shorter plowing schedules than alternative Integer Programming formulations. A test pilot held with actual vehicles proves the applicability of our approach in practice: our routes are 3–156% shorter than the routes the city of Pittsburgh generated with commercial routing software.

Integer Programming for Learning Directed Acyclic Graphs from Continuous Data.

Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the form of a mathematical programming model that can naturally incorporate a superstructure to reduce the set of possible candidate DAGs. We use a negative log-likelihood score function with both and penalties and propose a new mixed-integer quadratic program, referred to as a layered network (LN) formulation. The LN formulation is a compact model that enjoys as tight an optimal continuous relaxation value as the stronger but larger formulations under a mild condition. Computational results indicate that the proposed formulation outperforms existing mathematical formulations and scales better than available algorithms that can solve the same problem with only regularization. In particular, the LN formulation clearly outperforms existing methods in terms of computational time needed to find an optimal DAG in the presence of a sparse superstructure.

Knights Exchange Puzzle—Teaching the Efficiency of Modeling

Puzzles and games enhance the quality of teaching by creating an enjoyable, interactive, and playful atmosphere. The knight exchange is a famous, very old, and amusing game on the chessboard. This puzzle was used by the author to teach modeling in a mathematical programming course designed for graduate students. The aim was to teach the students the efficiency of the models. Accordingly, first, a binary programming formulation was developed. This formulation was, however, found to be inefficient, and tremendous time (i.e., more than four hours) and a large amount of processing memory were needed to solve the puzzle. The puzzle was subsequently formulated as a minimum cost network flow problem. The latter formulation outperformed the general binary formulation by solving the puzzle in less than a minute. The network formulation could also save the required processing memory. The results could help students to learn the value of modeling combinatorial optimization problems as network flows.

Tensor network formulation of two-dimensional gravity

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We then augment the action with a Yang-Mills term which allows us to control the lattice spacing and show how to apply the TRG to compute the free energy and look for critical behavior. Finally we perform an analytic continuation in the gravity coupling in this extended model and show that its critical behavior in a certain scaling limit depends only on the topology of the underlying lattice. We also show how the lattice gauge theory can be naturally generalized to generate the Polyakov or Liouville action for two dimensional quantum gravity.

Valuation of travel time reliability: Considering the traveler's adaptive expectation with an indifference band on daily trip duration

Abstract In this article, we focus on the valuation of travel time reliability that considers the adaptive expectation with an indifference band on daily trip duration. Owing to the learning effect of adaptive expectation, travel time variation relates to the travel time forecast bias but not to the absolute deviation of daily trip duration. Meanwhile, the indifference band toward travel time variation moderates the adaptive expectation formation in daily trip repetition. In this case, travel time reliability follows the discrete probability distribution. We use the rank-dependent utility framework to capture the value of travel time reliability (VOR), in which the probability transformation accommodates the risk attitude toward random trip duration and provides us the subjective probability weight to each potential reliability point. Numerical simulation indicates that the traveler's subjective VOR awareness associates with both learning rate and indifference band in the adaptive expectation on daily trip duration. We also set forth some policy and practice implications of this research in the traffic assignment and network formulation.

Color illusions also deceive CNNs for low-level vision tasks: Analysis and implications

The study of visual illusions has proven to be a very useful approach in vision science. In this work we start by showing that, while convolutional neural networks (CNNs) trained for low-level visual tasks in natural images may be deceived by brightness and color illusions, some network illusions can be inconsistent with the perception of humans. Next, we analyze where these similarities and differences may come from. On one hand, the proposed linear eigenanalysis explains the overall similarities: in simple CNNs trained for tasks like denoising or deblurring, the linear version of the network has center-surround receptive fields, and global transfer functions are very similar to the human achromatic and chromatic contrast sensitivity functions in human-like opponent color spaces. These similarities are consistent with the long-standing hypothesis that considers low-level visual illusions as a by-product of the optimization to natural environments. Specifically, here human-like features emerge from error minimization. On the other hand, the observed differences must be due to the behavior of the human visual system not explained by the linear approximation. However, our study also shows that more ‘flexible’ network architectures, with more layers and a higher degree of nonlinearity, may actually have a worse capability of reproducing visual illusions. This implies, in line with other works in the vision science literature, a word of caution on using CNNs to study human vision: on top of the intrinsic limitations of the L + NL formulation of artificial networks to model vision, the nonlinear behavior of flexible architectures may easily be markedly different from that of the visual system.

Enhancing Local Disaster Management Network through Developing Resilient Community in New Taipei City, Taiwan.

Large-scaled disaster events had increasingly occurred worldwide due to global and environmental change. Evidently, disaster response cannot rely merely on the public force. In the golden hour of crisis, not only the individuals should learn to react, protect themselves, and try to help each other, but also the local school, enterprise, non-government organization (NGO), nonprofit organization (NPO), and volunteer groups should collaborate to effectively deal with disaster events. New Taipei City (NTPC), Taiwan, was aware of the need for non-public force response and therefore developed the process of enhancing local disaster management networks through promoting the resilient community since 2009. The concept of a resilient community is to build community-based capacity for mitigation, preparedness, response, and recovery in an all-hazards manner. This study organized the NTPC experience and presented the standard operation procedure (SOP) to promote the resilient community, key obstacles, maintenance mechanism, and the successful formulation of the local disaster management network. The performance of the promotion was evaluated through a questionnaire survey and found that participants affirmed the positive effect of building community capacity through the entire process. In general, the resilient community as the center of the local disaster management work is shown promising to holistically bridge the inner/outer resources and systematically respond to disaster events.

Partial regularity of weak solutions and life-span of smooth solutions to a biological network formulation model

In this paper we study partial regularity of weak solutions to the initial boundary value problem for the system $$-\text {div}\left[ (I+\mathbf{m}\otimes \mathbf{m})\nabla p\right] =S(x), \partial _t\mathbf{m}-D^2\Delta \mathbf{m}-E^2(\mathbf{m}\cdot \nabla p)\nabla p+|\mathbf{m}|^{2(\gamma -1)}{} \mathbf{m}=0$$ , where S(x) is a given function and $$D, E, \gamma$$ are given numbers. This problem has been proposed as a PDE model for biological transportation networks. The mathematical difficulty is due to the fact that the system in the model features both a quadratic nonlinearity and a cubic nonlinearity. The regularity issue seems to have a connection to a conjecture by De Giorgi (Congetture sulla continuita delle soluzioni di equazioni lineari ellittiche autoaggiunte a coefficienti illimitati, Unpublished, 1995). We also investigate the life-span of classical solutions. Our results show that local existence of a classical solution can always be obtained and the life-span of such a solution can be extended as far away as one wishes as long as the term $$\Vert \mathbf{m}(x,0)\Vert _{\infty , \Omega }+\Vert S(x)\Vert _{\frac{2N}{3}, \Omega }$$ is made suitably small, where N is the space dimension and $$\Vert \cdot \Vert _{q,\Omega }$$ denotes the norm in $$L^q(\Omega )$$ .

Multimode Equivalent Network for Boxed Multilayer Arbitrary Planar Circuits

The multimode equivalent network (MEN) formulation has been originally developed for the efficient and accurate analysis of waveguide devices. In this article, we extend the use of the MEN to the analysis of zero-thickness, planar printed circuits in a metallic enclosure. The formulation is developed for metallic areas of arbitrary shape and includes both internal and external ports in the transverse plane to model connections to external components, and coaxial input/output ports. The boundary integral resonant mode expansion (BI-RME) method is used for the analysis of the arbitrary shape metallizations. On this basis, shielded multilayered microstrip circuits of complex geometry are analyzed in the common frame of the MEN technique. To validate the theoretical formulation, several boxed microstrip structures are analyzed, including multilayered configurations with several metallization interfaces, showing good agreement with respect to both other commercial tools, and measurements.

Carpool for Big Data: Enabling Efficient Crowd Cooperation in Data Market for Pervasive AI

Big data is the fuel for powering pervasive artificial intelligence (AI) applications. Aiming at promoting efficient cooperation in data market for big data, in this paper we propose a novel cooperative data purchase framework, by leveraging the power of the data user crowd and their intrinsic trustworthy collaboration relationships. For achieving efficient cooperative data purchase, we develop a comprehensive approach consisting of both data purchase group formation and selection. For the data purchase group formation, we partition the users into multiple data purchase groups for the purpose of budget pooling, by taking into account their data interest and budget levels, meanwhile respecting their underlying collaboration relationships and the maximum allowable group size for data sharing enforced by the data market platform. For the data purchase group selection, we construct a data purchase flow network formulation and devise a minimum cut based solution for selecting the proper set of data purchase groups to fully support their demands subject to the budget constraints. We extensively evaluate the performance of cooperative data purchase framework using both Erdos-Renyi and scale-free collaboration graphs. The numerical results demonstrate that the proposed framework can achieve superior performance, with more than ${40}\%$ and ${100}\%$ performance gain over the case without cooperation in terms of the total received payment and the number of satisfied users, respectively.

Simulation of differential-algebraic equation systems with optimization criteria embedded in Modelica

Differential-algebraic equations with embedded optimization criteria (DAEO) are a class of mathematical models for underdetermined differential-algebraic equation (DAE) systems with less algebraic equations than algebraic variables. The algebraic variables may be calculated as the solution of an embedded (non)linear program, yielding a DAEO system. An example for DAEOs is the dynamic flux balance analysis (DFBA) approach, where the formulation of metabolic reaction networks leads to an underdetermined equation system for the intracellular fluxes that are assumed to behave optimally with respect to some cell-specific optimization criterion.We present a toolbox that allows formulation of DAEOs in the object-oriented Modelica modeling language. The solution method is based on substituting the embedded optimization problem with its first-order Karush-Kuhn-Tucker conditions to obtain a nonsmooth DAE system that can be simulated by a root-finding DAE solver. One nonlinear example and two examples based on DFBA demonstrate the performance of the toolbox.

Unbalance Mitigation via Phase-Switching Device and Static Var Compensator in Low-Voltage Distribution Network

As rooftop solar PVs installed by residential customers penetrate in low voltage distribution network (LVDN), some issues, e.g. over/under voltage and unbalances, which may undermine the network's operational performance, need to be effectively addressed. To mitigate unbalances in LVDN, dynamic switching devices (PSDs) and static var compensator (SVC) are two equipment that are cost-effective and efficient. However, most existing research on operating PSDs are based on inflexible heuristic algorithms or without considering the network formulation, which may lead to strategies that violate operational requirements. Moreover, few pieces of literature have been reported on mitigating unbalances in LVDN via SVC and PSDs together. This paper, after presenting the dispatch model of SVC, formulates the decision-making process as a mixed-integer non-convex programming (MINCP) problem considering all practical operational requirements. To efficiently solve the challenging problem, the MINCP is reformulated as a mixed-integer second order-cone programming (MISOCP) problem based on either exact reformulations or accurate approximations, making it possible to employ efficient off-the-shelf solvers. Simulations based on a modified IEEE system and a practical system in Australia demonstrates the efficiency of the proposed method in mitigating unbalances in LVDN.

Tensor network formulation of the massless Schwinger model with staggered fermions

We construct a tensor network representation of the partition function for the massless Schwinger model on a two-dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using a particular implementation of the tensor renormalization group we calculate the average plaquette and topological charge density for the theory. For a range of values of the coupling constant for the topological term, $\mathrm{\ensuremath{\Theta}}$, and the gauge coupling, $\ensuremath{\beta}$, we compare with results from hybrid Monte Carlo simulations when possible and find good agreement. In order to further understand the role of fermions and topology in this model, we compare calculations of the same observables in a similar model, the Abelian Higgs model.

Semi-supervised process fault classification based on convolutional ladder network with local and global feature fusion

Effective fault classification is of great significance to isolate and eliminate faults in the smart manufacturing process, especially for chemical industry. However, incipient faults and limited labeled samples make it hard to classify faults accurately. This motivates the formulation of a semi-supervised convolutional ladder network with local and global feature fusion. In the algorithm, a convolutional ladder network is developed to capture higher-order correlations from both labeled and unlabeled samples simultaneously to overcome the problem caused by limited labeled samples, skipped connections are embedded within which to make a balance between supervised and unsupervised feature learning for further identifying faults. To improve the classification performance on incipient faults, a local and global feature fusion strategy is proposed to enhance the representation of incipient faults. Furthermore, a semi-supervised dynamic data representation strategy is introduced to jointly deal with labeled and unlabeled process samples, which enables the proposed method to handle process dynamics by characterizing temporal information of process variables. Experiments on the Tennessee Eastman process show that the proposed method is effective for process fault classification when labeled samples are limited compared to the state-of-the-art algorithms.

Glycerol as a green solvent for enhancing the formulation of dextran methacrylate and gellan-based semi-interpenetrating polymer networks

Recently, glycerol has been exploited in a number of industrial applications, thanks to its high availability, its low cost and, overall, its peculiar properties which fit well with the green chemistry principles. In this work, the ability of glycerol to solubilize high molecular weight polymers and to allow the formation of glycerol-based semi-interpenetrating polymer networks, called “gly-semi-IPNs”, has been investigated. Compared to water, glycerol deeply affects the structural properties of the biopolymers, especially with reference to their chain flexibility. Among the polysaccharides, dextran methacrylate (DexMA) and gellan gum (Ge) were selected. Glycerol solutions of both polysaccharides and their mixtures, as well as a DexMA network (obtained by cross-linking in glycerol and in the presence of a photoinitiator), were rheologically characterized to assess the role of the solvent on the chain conformation and on the mechanical properties of the networks. Interestingly, glycerol was found to deeply influence the mechanical, morphological and optical properties of the formed hydrogels, as well as to improve the cross-linking kinetic of DexMA. Furthermore, glycerol leads to more homogeneous mixtures of the two polysaccharides than those observed in aqueous buffers. As such, novel gly-semi-IPNs, with enhanced formulation and mechanical properties, were prepared and characterized.

Deep reinforcement learning for the real time control of stormwater systems

A new generation of smart stormwater systems promises to reduce the need for new construction by enhancing the performance of the existing infrastructure through real-time control. Smart stormwater systems dynamically adapt their response to individual storms by controlling distributed assets, such as valves, gates, and pumps. This paper introduces a real-time control approach based on Reinforcement Learning (RL), which has emerged as a state-of-the-art methodology for autonomous control in the artificial intelligence community. Using a Deep Neural Network, a RL-based controller learns a control strategy by interacting with the system it controls - effectively trying various control strategies until converging on those that achieve a desired objective. This paper formulates and implements a RL algorithm for the real-time control of urban stormwater systems. This algorithm trains a RL agent to control valves in a distributed stormwater system across thousands of simulated storm scenarios, seeking to achieve water level and flow set-points in the system. The algorithm is first evaluated for the control of an individual stormwater basin, after which it is adapted to the control of multiple basins in a larger watershed (4 km2). The results indicate that RL can very effectively control individual sites. Performance is highly sensitive to the reward formulation of the RL agent. Generally, more explicit guidance led to better control performance, and more rapid and stable convergence of the learning process. While the control of multiple distributed sites also shows promise in reducing flooding and peak flows, the complexity of controlling larger systems comes with a number of caveats. The RL controller’s performance is very sensitive to the formulation of the Deep Neural Network and requires a significant amount of computational resource to achieve a reasonable performance enhancement. Overall, the controlled system significantly outperforms the uncontrolled system, especially across storms of high intensity and duration. A frank discussion is provided, which should allow the benefits and drawbacks of RL to be considered when implementing it for the real-time control of stormwater systems. An open source implementation of the full simulation environment and control algorithms is also provided.