637 research outputs found
Analyzing Interference from Static Cellular Cooperation using the Nearest Neighbour Model
The problem of base station cooperation has recently been set within the
framework of Stochastic Geometry. Existing works consider that a user
dynamically chooses the set of stations that cooperate for his/her service.
However, this assumption often does not hold. Cooperation groups could be
predefined and static, with nodes connected by fixed infrastructure. To analyse
such a potential network, in this work we propose a grouping method based on
proximity. It is a variation of the so called Nearest Neighbour Model. We
restrict ourselves to the simplest case where only singles and pairs of base
stations are allowed to be formed. For this, two new point processes are
defined from the dependent thinning of a Poisson Point Process, one for the
singles and one for the pairs. Structural characteristics for the two are
provided, including their density, Voronoi surface, nearest neighbour, empty
space and J-function. We further make use of these results to analyse their
interference fields and give explicit formulas to their expected value and
their Laplace transform. The results constitute a novel toolbox towards the
performance evaluation of networks with static cooperation.Comment: 10 pages, 6 figures, 12 total subfigures, WIOPT-SPASWIN 201
Cooperative success in epithelial public goods games
Cancer cells obtain mutations which rely on the production of diffusible
growth factors to confer a fitness benefit. These mutations can be considered
cooperative, and studied as public goods games within the framework of
evolutionary game theory. The population structure, benefit function and update
rule all influence the evolutionary success of cooperators. We model the
evolution of cooperation in epithelial cells using the Voronoi tessellation
model. Unlike traditional evolutionary graph theory, this allows us to
implement global updating, for which birth and death events are spatially
decoupled. We compare, for a sigmoid benefit function, the conditions for
cooperation to be favoured and/or beneficial for well mixed and structured
populations. We find that when population structure is combined with global
updating, cooperation is more successful than if there were local updating or
the population were well-mixed. Interestingly, the qualitative behaviour for
the well-mixed population and the Voronoi tessellation model is remarkably
similar, but the latter case requires significantly lower incentives to ensure
cooperation.Comment: 29 Pages, 13 Figure
Evolutionary games between epithelial cells: the impact of population structure and tissue dynamics on the success of cooperation
Cooperation is usually understood as a social phenomenon. However, it also occurs on the cellular level. A number of key mutations associated with malignancy can be considered cooperative, as they rely on the production of diffusible growth factors to confer a fitness benefit. Evolutionary game theory provides a framework for modelling the evolutionary dynamics of these cooperative mutations. This thesis uses evolutionary game theory to examine the evolutionary dynamics of cooperation within epithelial cells, which are the origin point of most cancers. In particular, we consider how the structure and dynamics of an epithelium affect cooperative success. We use the Voronoi tessellation model to represent an epithelium. This allows us much greater flexibility, compared to evolutionary graph theory models, to explore realistic dynamics for population updating. Initially, we consider a model where death and division are spatially decoupled. We analyse pairwise social dilemma games, focussing on the additive prisoner’s dilemma, and multiplayer public goods games. We calculate fixation probabilities, and conditions for cooperative success, by simulation, as well as deriving quasi-analytic results. Comparing with results for graph structured populations with spatially coupled birth and death, or well-mixed populations, we find that in general cooperation is promoted by local game play, but global competition for offspring. We then introduce a more realistic model of population updating, whereby death and division are spatially coupled as a consequence of contact inhibition. The strength of this coupling is positively correlated with the strength of contact inhibition. However, the extent to which strong spatial coupling inhibits cooperation depends on mechanical properties of the tissue
Certified Reinforcement Learning with Logic Guidance
This paper proposes the first model-free Reinforcement Learning (RL)
framework to synthesise policies for unknown, and continuous-state Markov
Decision Processes (MDPs), such that a given linear temporal property is
satisfied. We convert the given property into a Limit Deterministic Buchi
Automaton (LDBA), namely a finite-state machine expressing the property.
Exploiting the structure of the LDBA, we shape a synchronous reward function
on-the-fly, so that an RL algorithm can synthesise a policy resulting in traces
that probabilistically satisfy the linear temporal property. This probability
(certificate) is also calculated in parallel with policy learning when the
state space of the MDP is finite: as such, the RL algorithm produces a policy
that is certified with respect to the property. Under the assumption of finite
state space, theoretical guarantees are provided on the convergence of the RL
algorithm to an optimal policy, maximising the above probability. We also show
that our method produces ''best available'' control policies when the logical
property cannot be satisfied. In the general case of a continuous state space,
we propose a neural network architecture for RL and we empirically show that
the algorithm finds satisfying policies, if there exist such policies. The
performance of the proposed framework is evaluated via a set of numerical
examples and benchmarks, where we observe an improvement of one order of
magnitude in the number of iterations required for the policy synthesis,
compared to existing approaches whenever available.Comment: This article draws from arXiv:1801.08099, arXiv:1809.0782
Information Diffusion on Social Networks
In this thesis we model the diffusion of information on social networks. A game
played on a specific type of graph generator, the iterated local transitivity
model, is examined. We study how the dynamics of the game change as the
graph grows, and the relationship between properties of the game on a graph
initially and properties of the game later in the graph’s development. We
show that, given certain conditions, for the iterated local transitivity model
it is possible to predict the existence of a Nash equilibrium at any point in
the graph’s growth. We give sufficient conditions for the existence of Nash
Equilibria on star graphs, cliques and trees. We give some results on potential
games on the iterated local transitivity model.
Chapter 2 provides an introduction to graph properties, and describes various
early graph models. Chapter 3 describes some models for online social
networks, and introduces the iterated local transitivity model which we use
later in the thesis. In Chapter 4 various models for games played on networks
are examined. We study a model for competitive information diffusion on
star graphs, cliques and trees, and we provide conditions for the existence of
Nash Equilibria on these. This model for competitive information diffusion is
studied in detail for the iterated local transitivity model in Chapter 5. We
discuss potential games in Chapter 6 and their existence on the iterated local
transitivity model. We conclude with some suggestions on how to extend and
develop upon the work done in this thesis
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