Dynamics of Three Agent Games

We study the dynamics and resulting score distribution of three-agent games where after each competition a single agent wins and scores a point. A single competition is described by a triplet of numbers $p$, $t$ and $q$ denoting the probabilities that the team with the highest, middle or lowest accumulated score wins. We study the full family of solutions in the regime, where the number of agents and competitions is large, which can be regarded as a hydrodynamic limit. Depending on the parameter values $(p,q,t)$, we find six qualitatively different asymptotic score distributions and we also provide a qualitative understanding of these results. We checked our analytical results against numerical simulations of the microscopic model and find these to be in excellent agreement. The three agent game can be regarded as a social model where a player can be favored or disfavored for advancement, based on his/her accumulated score. It is also possible to decide the outcome of a three agent game through a mini tournament of two-a gent competitions among the participating players and it turns out that the resulting possible score distributions are a subset of those obtained for the general three agent-games. We discuss how one can add a steady and democratic decline rate to the model and present a simple geometric construction that allows one to write down the corresponding score evolution equations for $n$-agent games

Dynamics of Multi-Player Games

We analyze the dynamics of competitions with a large number of players. In our model, n players compete against each other and the winner is decided based on the standings: in each competition, the mth ranked player wins. We solve for the long time limit of the distribution of the number of wins for all n and m and find three different scenarios. When the best player wins, the standings are most competitive as there is one-tier with a clear differentiation between strong and weak players. When an intermediate player wins, the standings are two-tier with equally-strong players in the top tier and clearly-separated players in the lower tier. When the worst player wins, the standings are least competitive as there is one tier in which all of the players are equal. This behavior is understood via scaling analysis of the nonlinear evolution equations.Comment: 8 pages, 8 figure

Effects of bark beetle outbreaks on forest landscape pattern in the southern rocky mountains, U.S.A.

Since the late 1990s, extensive outbreaks of native bark beetles (Curculionidae: Scolytinae) have affected coniferous forests throughout Europe and North America, driving changes in carbon storage, wildlife habitat, nutrient cycling, and water resource provisioning. Remote sensing is a cru-cial tool for quantifying the effects of these disturbances across broad landscapes. In particular, Landsat time series (LTS) are increasingly used to characterize outbreak dynamics, including the presence and severity of bark beetle-caused tree mortality, though broad-scale LTS-based maps are rarely informed by detailed field validation. Here we used spatial and temporal information from LTS products, in combination with extensive field data and Random Forest (RF) models, to develop 30-m maps of the presence (i.e., any occurrence) and severity (i.e., cumulative percent basal area mortality) of beetle-caused tree mortality 1997–2019 in subalpine forests throughout the Southern Rocky Mountains, USA. Using resultant maps, we also quantified spatial patterns of cumulative tree mortality throughout the region, an important yet poorly understood concept in beetle-affected forests. RF models using LTS products to predict presence and severity performed well, with 80.3% correctly classified (Kappa = 0.61) and R2 = 0.68 (RMSE = 17.3), respectively. We found that ≥10,256 km2 of subalpine forest area (39.5% of the study area) was affected by bark beetles and 19.3% of the study area experienced ≥70% tree mortality over the twenty-three year period. Variograms indi-cated that severity was autocorrelated at scales \u3c 250 km. Interestingly, cumulative patch-size dis-tributions showed that areas with a near-total loss of the overstory canopy (i.e., ≥90% mortality) were relatively small (\u3c0.24 km2) and isolated throughout the study area. Our findings help to in-form an understanding of the variable effects of bark beetle outbreaks across complex forested regions and provide insight into patterns of disturbance legacies, landscape connectivity, and susceptibility to future disturbance

A novel method for localising a randomly distributed wireless sensor network

Wireless sensor networks are dependent on sending and receiving signals; the system will not be capable of functioning if communication between sensors is not established. Localisation is one of the most important functions in this technology to localise nodes, events or the data source. In this study, we present a new method for outdoor randomly distributed nodes with no need for any excess devices, such as GPS devices or directional anten- nas or ultrasonic sensors. The method is based on using only the simple node component to provide the node and event position and has the ability to adapt mobility and scalability without affecting network functionality. All of the results are based on an ideal environment

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Impacts of climate change on plant diseases – opinions and trends

There has been a remarkable scientific output on the topic of how climate change is likely to affect plant diseases in the coming decades. This review addresses the need for review of this burgeoning literature by summarizing opinions of previous reviews and trends in recent studies on the impacts of climate change on plant health. Sudden Oak Death is used as an introductory case study: Californian forests could become even more susceptible to this emerging plant disease, if spring precipitations will be accompanied by warmer temperatures, although climate shifts may also affect the current synchronicity between host cambium activity and pathogen colonization rate. A summary of observed and predicted climate changes, as well as of direct effects of climate change on pathosystems, is provided. Prediction and management of climate change effects on plant health are complicated by indirect effects and the interactions with global change drivers. Uncertainty in models of plant disease development under climate change calls for a diversity of management strategies, from more participatory approaches to interdisciplinary science. Involvement of stakeholders and scientists from outside plant pathology shows the importance of trade-offs, for example in the land-sharing vs. sparing debate. Further research is needed on climate change and plant health in mountain, boreal, Mediterranean and tropical regions, with multiple climate change factors and scenarios (including our responses to it, e.g. the assisted migration of plants), in relation to endophytes, viruses and mycorrhiza, using long-term and large-scale datasets and considering various plant disease control methods