Mutualistic networks, such as plant–pollinator networks, have attracted increasing attention in the ecological literature in the last decades, not only because of their fascinating natural history, but also because mutualistic interactions have been shown to play a key role in the maintenance of biodiversity. Although inter-specific competition has long been known to be a crucial driver of species coexistence as well, there is a lack of theory investigating the interplay between the structures of competitive and mutualistic networks when jointly considered. Here, we develop an analytical framework to study the structural stability — the range of conditions under which all species coexist stably, i.e. where the community is both feasible and stable — of ecological communities in which both mutualistic interactions between plants and pollinators and competitive interactions among plants and among pollinators are present. Using the structure of 50 real networks for mutualistic interactions, combined with analytical and numerical analyses, we show that the structure of the competitive network radically alters the necessary conditions for species coexistence in these communities. Our mathematical framework also allows to accurately characterize the structural stability of these systems. Moreover, we introduce a new metric that accurately links the network structures of competitive and mutualistic interactions to species coexistence. Our results highlight the joint role of the structures of different interaction types to understand the stability of ecological communities and facilitate the analysis of similar natural and artificial systems in which mutualism and competition coexist.@en

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest control). Often the worst strategy for the leader is to adopt a constant aggressive strategy (e.g. overfishing in fisheries management or maximum tolerable dose in cancer treatment). Taking into account the ecological dynamics typically leads to better outcomes for the leader and corresponds to the Nash equilibria in game-theoretic terms. However, the leader's most profitable strategy is to anticipate and steer the eco-evolutionary dynamics, leading to the Stackelberg equilibrium of the game. We show how our results have the potential to help in fields where humans try to bring an evolutionary system into the desired outcome, such as, among others, fisheries management, pest management and cancer treatment. Finally, we discuss limitations and opportunities for applying SEGs to improve the management of evolving biological systems. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

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This paper develops and analyzes a Markov chain model for the treatment of cancer. Cancer therapy is modeled as the patient's Markov Decision Problem, with the objective of maximizing the patient's discounted expected quality of life years. Patients make decisions on the duration of therapy based on the progression of the disease as well as their own preferences. We obtain a powerful analytic decision tool through which patients may select their preferred treatment strategy. We illustrate the tradeoffs patients in a numerical example and calculate the value lost to a cohort in suboptimal strategies. In a second model patients may make choices to include drug holidays. By delaying therapy, the patient temporarily forgoes the gains of therapy in order to delay its side effects. We obtain an analytic tool that allows numerical approximations of the optimal times of delay.

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Fish populations subject to heavy exploitation are expected to evolve over time smaller average body sizes. We introduce Stackelberg evolutionary game theory to show how fisheries management should be adjusted to mitigate the potential negative effects of such evolutionary changes. We present the game of a fisheries manager versus a fish population, where the former adjusts the harvesting rate and the net size to maximize profit, while the latter responds by evolving the size at maturation to maximize the fitness. We analyze three strategies: i) ecologically enlightened (leading to a Nash equilibrium in game-theoretic terms); ii) evolutionarily enlightened (leading to a Stackelberg equilibrium) and iii) domestication (leading to team optimum) and the corresponding outcomes for both the fisheries manager and the fish. Domestication results in the largest size for the fish and the highest profit for the manager. With the Nash approach the manager tends to adopt a high harvesting rate and a small net size that eventually leads to smaller fish. With the Stackelberg approach the manager selects a bigger net size and scales back the harvesting rate, which lead to a bigger fish size and a higher profit. Overall, our results encourage managers to take the fish evolutionary dynamics into account. Moreover, we advocate for the use of Stackelberg evolutionary game theory as a tool for providing insights into the eco-evolutionary consequences of exploiting evolving resources.

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The power system is one of the most complicated man-made non-linear systems which plays an important role for human being since it was first made in the 19th century. In the past decade, the integration of renewable power sources such as wind energy and solar energy has increased rapidly due to their sustainability. However, these energy sources are weather dependent which cannot be controlled or even predicted precisely. A challenge brought by this transition to renewable power generation is the uncertain fluctuations that negatively affects the stability of the power system, which leads to the important problem: how to improve by control the stability of the system such that it remains stable when subjected to considerable fluctuations in the energy supply? Hence, research is needed into the stability metrics of the non-linear power system and control strategies for the stability improvement. In this chapter, we describe the linear and non-linear stability analysis of power systems and summarize the corresponding control strategies for stability improvement.@en

The linear relation between Kemeny's constant, a graph metric directly linked with random walks, and the effective graph resistance in a regular graph has been an incentive to calculate Kemeny's constant for various networks. In this paper we consider complete bipartite graphs, (generalized) windmill graphs and tree networks with large diameter and give exact expressions of Kemeny's constant. For non-regular graphs we propose two approximations for Kemeny's constant by adding to the effective graph resistance term a linear term related to the degree heterogeneity in the graph. These approximations are exact for complete bipartite graphs, but show some discrepancies for generalized windmill and tree graphs. However, we show that a recently obtained upper-bound for Kemeny's constant in Wang et al. (2017) based on the pseudo inverse Laplacian gives the exact value of Kemeny's constant for generalized windmill graphs. Finally, we have evaluated Kemeny's constant, its two approximations and its upper bound, for 243 real-world networks. This evaluation reveals that the upper bound is tight, with average relative error of only 0.73%. In most cases the upper bound clearly outperforms the other two approximations.

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In the classical susceptible-infected-susceptible (SIS) model, a disease or infection spreads over a given, mostly fixed graph. However, in many real complex networks, the topology of the underlying graph can change due to the influence of the dynamical process. In this paper, besides the spreading process, the network adaptively changes its topology based on the states of the nodes in the network. An entire class of link-breaking and link-creation mechanisms, which we name Generalized Adaptive SIS (G-ASIS), is presented and analyzed. For each instance of G-ASIS using the complete graph as initial network, the relation between the epidemic threshold and the effective link-breaking rate is determined to be linear, constant, or unknown. Additionally, we show that there exist link-breaking and link-creation mechanisms for which the metastable state does not exist. We confirm our theoretical results with several numerical simulations.

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In this paper, we focus on option pricing models based on time-fractional diffusion with generalized Hilfer-Prabhakar derivative. It is demonstrated how the option is priced for fractional cases of European vanilla option pricing models. Series representations of the pricing formulas and the risk-neutral parameter under the time-fractional diffusion are also derived.

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We study generalized diffusion-wave equation in which the second order time derivative is replaced by an integro-differential operator. It yields time fractional and distributed order time fractional diffusion-wave equations as particular cases. We consider different memory kernels of the integro-differential operator, derive corresponding fundamental solutions, specify the conditions of their non-negativity and calculate the mean squared displacement for all cases. In particular, we introduce and study generalized diffusion-wave equations with a regularized Prabhakar derivative of single and distributed orders. The equations considered can be used for modeling the broad spectrum of anomalous diffusion processes and various transitions between different diffusion regimes.

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This paper presents a parameter estimation method to determine the linear behavior of an object constructed of thin plates. Based on the magnetostatic field equations, an integral equation is derived that fully determines the induced magnetization, whenever the spatial magnetic susceptibility distribution is known. This forward problem is used as an underlying physical model for the parameter estimation method. Using near-field magnetic measurements around a thin plate, the parameter estimation yields a distribution of the magnetic susceptibility. Furthermore, a sensitivity analysis is performed to understand the behavior of this parameter estimation method.

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In machine vision typical heuristic methods to extract parameterized objects out of raw data points are the Hough transform and RANSAC. Bayesian models carry the promise to optimally extract such parameterized objects given a correct definition of the model and the type of noise at hand. A category of solvers for Bayesian models are Markov chain Monte Carlo methods. Naive implementations of MCMC methods suffer from slow convergence in machine vision due to the complexity of the parameter space. Towards this blocked Gibbs and split-merge samplers have been developed that assign multiple data points to clusters at once. In this paper we introduce a new split-merge sampler, the triadic split-merge sampler, that perform steps between two and three randomly chosen clusters. This has two advantages. First, it reduces the asymmetry between the split and merge steps. Second, it is able to propose a new cluster that is composed out of data points from two different clusters. Both advantages speed up convergence which we demonstrate on a line extraction problem. We show that the triadic split-merge sampler outperforms the conventional split-merge sampler. Although this new MCMC sampler is demonstrated in this machine vision context, its application extend to the very general domain of statistical inference.@en

The traditional secondary frequency control of power systems restores nominal frequency by steering Area Control Errors (ACEs) to zero. Existing methods are a form of integral control with the characteristic that large control gain coefficients introduce an overshoot and small ones result in a slow convergence to a steady state. In order to deal with the large frequency deviation problem, which is the main concern of the power system integrated with a large number of renewable energy, a faster convergence is critical. In this paper, we propose a secondary frequency control method named Power-Imbalance Allocation Control (PIAC) to restore the nominal frequency with a minimized control cost, in which a coordinator estimates the power imbalance and dispatches the control inputs to the controllers after solving an economic power dispatch problem. The power imbalance estimation converges exponentially in PIAC, both overshoots and large frequency deviations are avoided. In addition, when PIAC is implemented in a multi-area controlled network, the controllers of an area are independent of the disturbance of the neighbor areas, which allows an asynchronous control in the multi-area network. A Lyapunov stability analysis shows that PIAC is locally asymptotically stable and simulation results illustrate that it effectively eliminates the drawback of the traditional integral control based methods.

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Synchronization is essential for the proper functioning of power grids, we investigate the synchronous states
and their stability for cyclic power grids. We calculate the number of stable equilibria and investigate both the linear and nonlinear stability of the synchronous state. The linear stability analysis shows that the stability of the state, determined by the smallest nonzero eigenvalue, is inversely proportional to the size of the network. We use the energy barrier to measure the nonlinear stability and calculate it by comparing the potential energy of the type-1 saddles with that of the stable synchronous
state. We find that the energy barrier depends on the network size ($N$) in a more complicated fashion compared to the linear stability. In particular, when the generators and consumers are evenly distributed in an alternating way, the energy barrier decreases to a constant when $N$ approaches infinity.
For a heterogeneous distribution of generators and consumers, the energy barrier decreases with $N$. The more heterogeneous the distribution is, the stronger the energy barrier depends on $N$. Finally, we find that by comparing situations with equal line loads in
cyclic and tree networks, tree networks exhibit reduced stability. This difference disappears in the limit of $N\to\infty$. This finding corroborates previous results reported in the literature and suggests that cyclic (sub)networks may be applied to enhance power
transfer while maintaining stable synchronous operation.@en

Kemeny's constant and its relation to the effective graph resistance has been established for regular graphs by Palacios et al. [1]. Based on the Moore–Penrose pseudo-inverse of the Laplacian matrix, we derive a new closed-form formula and deduce upper and lower bounds for the Kemeny constant. Furthermore, we generalize the relation between the Kemeny constant and the effective graph resistance for a general connected, undirected graph.

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Line detection is a fundamental problem in the world of computer vision. Many sophisticated methods have been proposed for performing inference over multiple lines; however, they are quite ad-hoc. Our fully Bayesian model extends a linear Bayesian regression model to an infinite mixture model and uses a Dirichlet Process as a prior. Gibbs sampling over non-unique parameters as well as over clusters is performed to fit lines of a fixed length, a variety of orientations, and a variable number of data points. Bayesian inference over data is optimal given a model and noise definition. Initial computer experiments show promising results with respect to clustering performance indicators such as the Rand Index, the Adjusted Rand Index, the Mirvin metric, and the Hubert metric. In future work, this ematical foundation can be used to extend the algorithms to inference over multiple line segments and multiple volumetric objects.

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To balance the power supply and demand with optimized control cost and nominal synchronized frequency, we propose a secondary frequency control approach, named Power-Imbalance Allocation Control (PIAC), for power systems with lossless networks, consisting of synchronous machines, frequency dependent power sources and passive loads. With Proportional-Integral control, the power imbalance is estimated by a coordinator with aggregated frequency deviations and the control inputs are optimally allocated to the controllers after solving an economic power dispatch problem on-line. The advantage of the approach is that the estimated power imbalance converges to the actual power imbalance exponentially with neither overshoot of control inputs nor unnecessary oscillations of the frequency. In addition, the convergence speed only depends on a control coefficient which is independent of any other parameters of the power systems and of the economic power dispatch problem.@en

In computer vision there are many sophisticated methods to perform inference over multiple lines, however they are quite ad-hoc. In this paper a fully Bayesian approach is used to fit multiple lines to a point cloud simultaneously. Our model extends a linear Bayesian regression model to an infinite mixture model and
uses a Dirichlet process as a prior for the partition. We perform Gibbs sampling over non-unique parameters as well as over clusters to fit lines of a fixed length, a variety of orientations, and a variable number of data points. The performance is measured using the Rand Index, the Adjusted Rand Index, and two other clustering performance indicators. This paper is mainly meant to demonstrate that general Bayesian methods can be used for line estimation. Bayesian methods, namely, given a model and noise, perform optimal inference over the data. Moreover, rather than only demonstrating the concept as such, the first results are promising with respect to the described clustering performance indicators. Further research is required to extend the method
to inference over multiple line segments and multiple volumetric objects that will need to be built on the mathematical foundation that has been laid down in this paper.@en

In computer and robotic vision point clouds from depth sensors have to be processed to form higher-level concepts such as lines, planes, and objects. Bayesian methods formulate precisely prior knowledge with respect to the noise and likelihood of points given a line, plane, or object. Nonparametric methods also formulate a prior with respect to the number of those lines, planes, or objects. Recently, a nonparametric Bayesian method has been proposed to perform optimal inference simultaneously over line fitting and the number of lines. In this paper we propose a nonparametric Bayesian method for segment fitting. Segments are lines of finite length. This requires 1.) a prior for line segment lengths: the symmetric Pareto distribution, 2.) a sampling method that handles nonconjugacy: an auxiliary variable MCMC method. Results are measured according to clustering performance indicators, such as the Rand Index, the Adjusted Rand Index, and the Hubert metric. Surprisingly, the performance of segment recognition is worse than that of line recognition. The paper therefore concludes with recommendations towards improving Bayesian segment recognition in future wo@en