Interacting motile agents : taking a mean-field approach beyond monomers and nearest-neighbor steps

We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.

Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrodinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the

Exploring lay views on physical activity and their implications for public health policy. A case study from East Belfast

It is now recognised that inactive lifestyles underpin much of the disease burden evident in the richer nations of the world. Indeed, the WHO has identified physical inactivity as a 'global public health problem' and has established minimum physical activity (PA) targets for people at different stages of the life-course. Yet, according to WHO, just under 1/3 of working age adults across the globe meet those targets and it is not at all clear how the disjunction between the recommendations of policy makers and the behaviour of ordinary people might be surmounted. Using an opportunity to examine the impact of an urban regeneration project on community residents in East Belfast (Northern Ireland) this paper examines the views of some 113 people on how to increase rates of PA in an area of multiple deprivation. The results of the analysis suggest that lay people rarely consider PA as a discrete issue, or one that centres on individuals and their motivation, but rather as one component in a complex web of concerns, processes and events that include such things as the actions of neighbours and relatives, material and political environments, vandalism, violence, and the weather. We explore and unravel the nature of those concerns using novel methods of content analysis that generate 'issue webs'. Particular attention is paid to the ways in which lay people conceptualize 'activity' and to the manner in which they point to ways of encouraging activity that are rooted in everyday life rather than in the corpocentric, agent-centred and often sport dominated strategies favoured by local policy makers. Our results support those who argue that interventions to increase rates of PA need to move beyond behavioural approaches that focus on individuals and consider the social, political and material contexts in which 'activity' occurs.

Analysis discrete function theory

There is a recent trend to describe physical phenomena without the use of infinitesimals or infinites. This has been accomplished replacing differential calculus by the finite difference theory. Discrete function theory was first introduced in l94l. This theory is concerned with a study of functions defined on a discrete set of points in the complex plane. The theory was extensively developed for functions defined on a Gaussian lattice. In 1972 a very suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0, O < q < l, m, n 5 Z} was found and discrete analytic function theory was developed. Very recently some work has been done in discrete monodiffric function theory for functions defined on H. The theory of pseudoanalytic functions is a generalisation of the theory of analytic functions. When the generator becomes the identity, ie., (l, i) the theory of pseudoanalytic functions reduces to the theory of analytic functions. Theugh the theory of pseudoanalytic functions plays an important role in analysis, no discrete theory is available in literature. This thesis is an attempt in that direction. A discrete pseudoanalytic theory is derived for functions defined on H.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

Physical activity and postural control in the elderly: Coupling between visual information and body sway

Background: Aging is characterized by a decline in the postural control performance, which is based on a coherent and stable coupling between sensory information and motor action. Therefore, changes in postural control in elderlies can be related to changes in this coupling. In addition, it has been observed that physical activity seems to improve postural control performance in elderlies. These improvements can be due to changes in the coupling between sensory information and motor action related to postural control. Objective: the purpose of this study was to verify the coupling between visual information and body sway in active and sedentary elderlies. Methods: Sixteen sedentary elderlies ( SE), 16 active elderlies ( AE) and 16 young adults ( YA) were asked to stand upright inside a moving room in two experimental conditions: ( 1) discrete movement and ( 2) continuous movement of the room. Results: In the continuous condition, the results showed that the coupling between the movement of the room and body sway was stronger and more stable for SE and AE compared to YA. In the discrete condition, SE showed larger body displacement compared to AE and YA. Conclusions: SE have more difficulty to discriminate and to integrate sensory information than AE and YA indicating that physical activity may improve sensory integration. Copyright (C) 2005 S. Karger AG, Basel.

Comparing skew Schur functions: a quasisymmetric perspective

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions sA and sB are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that sA and sB have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true. In fact, we work in terms of inequalities, showing that if the F-support of sA contains that of sB, then the row overlap partitions of A are dominated by those of B, and again conjecture that the converse also holds. Our evidence in favor of these conjectures includes their consistency with a complete determination of all F-support containment relations for F-multiplicity-free skew Schur functions. We conclude with a consideration of how some other quasisymmetric bases fit into our framework.

Applications of finite geometries to designs and codes

This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures. A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will examine several questions related to Hamada’s conjecture, including the existence of counterexamples. We will also study the applicability of certain decoding methods to known counterexamples. We begin by constructing an infinite family of counterexamples to Hamada’s conjecture. These designs are the first infinite class of counterexamples for the affine case of Hamada’s conjecture. We further demonstrate how these designs, along with the projective polarity designs of Jungnickel and Tonchev, admit majority-logic decoding schemes. The codes obtained from these polarity designs attain error-correcting performance which is, in certain cases, equal to that of the finite geometry designs from which they are derived. This further demonstrates the highly geometric structure maintained by these designs. Finite geometries also help us construct several types of quantum error-correcting codes. We use relatives of finite geometry designs to construct infinite families of q-ary quantum stabilizer codes. We also construct entanglement-assisted quantum error-correcting codes (EAQECCs) which admit a particularly efficient and effective error-correcting scheme, while also providing the first general method for constructing these quantum codes with known parameters and desirable properties. Finite geometry designs are used to give exceptional examples of these codes.

Vertical profiles of environmental parameters measured from physical, optical and imaging sensors during Tara Oceans expedition 2009-2013

The present data publication provides permanent links to original and updated versions of validated data files. The data files include properties of seawater, particulate matter and dissolved matter from physical, optical and imaging sensors mounted on a vertical sampling system (Rosette) used during the 2009-2013 tara Oceans Expedition. It comprised 2 pairs of conductivity and temperature sensors (SEABIRD components), and a complete set of WEtLabs optical sensors, including chrorophyll and CDOM fluorometers, a 25 cm transmissiometer, and a one-wavelength backscatter meter. In addition, a SATLANTIC ISUS nitrate sensor and a Hydroptic Underwater Vision Profiler (UVP) were mounted on the rosette. In the Arctic Ocean and Arctic Seas (2013), a second oxygen sensor (SBE43) and a four frequency Aquascat acoustic profiler were added. The system was powered on specific Li-Ion batteries and data were self-recorded at 24HZ. Sensors have all been factory calibrated before, during and after the four year program. Oxygen was validated using climatologies (WOA09). Nitrate and Fluorescence data were adjusted with discrete measurements from Niskin bottles mounted on the Rosette, and optical darks were performed monthly on board. A total of 839 quality checked vertical profiles were made during the tara Oceans expedition 2009-2013.