Adaptive and phase transition behavior in performance of discrete multi-articular actions by degenerate neurobiological systems

The identification of attractors is one of the key tasks in studies of neurobiological coordination from a dynamical systems perspective, with a considerable body of literature resulting from this task. However, with regards to typical movement models investigated, the overwhelming majority of actions studied previously belong to the class of continuous, rhythmical movements. In contrast, very few studies have investigated coordination of discrete movements, particularly multi-articular discrete movements. In the present study, we investigated phase transition behavior in a basketball throwing task where participants were instructed to shoot at the basket from different distances. Adopting the ubiquitous scaling paradigm, throwing distance was manipulated as a candidate control parameter. Using a cluster analysis approach, clear phase transitions between different movement patterns were observed in performance of only two of eight participants. The remaining participants used a single movement pattern and varied it according to throwing distance, thereby exhibiting hysteresis effects. Results suggested that, in movement models involving many biomechanical degrees of freedom in degenerate systems, greater movement variation across individuals is available for exploitation. This observation stands in contrast to movement variation typically observed in studies using more constrained bi-manual movement models. This degenerate system behavior provides new insights and poses fresh challenges to the dynamical systems theoretical approach, requiring further research beyond conventional movement models.

Output feedback control of discrete-time systems in networked environments

This correspondence paper addresses the problem of output feedback stabilization of control systems in networked environments with quality-of-service (QoS) constraints. The problem is investigated in discrete-time state space using Lyapunov’s stability theory and the linear inequality matrix technique. A new discrete-time modeling approach is developed to describe a networked control system (NCS) with parameter uncertainties and nonideal network QoS. It integrates a network-induced delay, packet dropout, and other network behaviors into a unified framework. With this modeling, an improved stability condition, which is dependent on the lower and upper bounds of the equivalent network-induced delay, is established for the NCS with norm-bounded parameter uncertainties. It is further extended for the output feedback stabilization of the NCS with nonideal QoS. Numerical examples are given to demonstrate the main results of the theoretical development.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

Discrete phase-locked loop systems and spreadsheets

This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behaviour interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behviour of systems with different types of non-linear characteristic.

Optimal allocation of a cross-connection and sectionalizers in distribution systems

In this paper, the placement of sectionalizers, as well as, a cross-connection is optimally determined so that the objective function is minimized. The objective function employed in this paper consists of two main parts, the switch cost and the reliability cost. The switch cost is composed of the cost of sectionalizers and cross-connection and the reliability cost is assumed to be proportional to a reliability index, SAIDI. To optimize the allocation of sectionalizers and cross-connection problem realistically, the cost related to each element is considered as discrete. In consequence of binary variables for the availability of sectionalizers, the problem is extremely discrete. Therefore, the probability of local minimum risk is high and a heuristic-based optimization method is needed. A Discrete Particle Swarm Optimization (DPSO) is employed in this paper to deal with this discrete problem. Finally, a testing distribution system is used to validate the proposed method.

Performing with grid music systems

Grid music systems provide discrete geometric methods for simplified music-making by providing spatialised input to construct patterned music on a 2D matrix layout. While they are conceptually simple, grid systems may be layered to enable complex and satisfying musical results. Grid music systems have been applied to a range of systems from small portable devices up to larger systems. In this paper we will discuss the use of grid music systems in general and present an overview of the HarmonyGrid system we have developed as a new interactive performance system. We discuss a range of issues related to the design and use of larger-scale grid- based interactive performance systems such as the HarmonyGrid.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Improved algebraic cryptanalysis of QUAD, Bivium and Trivium via graph partitioning on equation systems

We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting certain vertices on the graph, the variable-sharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations would be separated into smaller systems of near-equal sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimum-weight vertex separators. The techniques of finding these vertex partitions are discussed, and experiments are performed to evaluate its practicality for general graphs and systems of polynomial equations. Applications of this approach in algebraic cryptanalysis on symmetric ciphers are presented: For the QUAD family of stream ciphers, we show how a malicious party can manufacture conforming systems that can be easily broken. For the stream ciphers Bivium and Trivium, we nachieve significant speedups in algebraic attacks against them, mainly in a partial key guess scenario. In each of these cases, the systems of polynomial equations involved are well-suited to our graph partitioning method. These results may open a new avenue for evaluating the security of symmetric ciphers against algebraic attacks.

Strengthening and formally verifying privacy in identity management systems

In a digital world, users’ Personally Identifiable Information (PII) is normally managed with a system called an Identity Management System (IMS). There are many types of IMSs. There are situations when two or more IMSs need to communicate with each other (such as when a service provider needs to obtain some identity information about a user from a trusted identity provider). There could be interoperability issues when communicating parties use different types of IMS. To facilitate interoperability between different IMSs, an Identity Meta System (IMetS) is normally used. An IMetS can, at least theoretically, join various types of IMSs to make them interoperable and give users the illusion that they are interacting with just one IMS. However, due to the complexity of an IMS, attempting to join various types of IMSs is a technically challenging task, let alone assessing how well an IMetS manages to integrate these IMSs. The first contribution of this thesis is the development of a generic IMS model called the Layered Identity Infrastructure Model (LIIM). Using this model, we develop a set of properties that an ideal IMetS should provide. This idealized form is then used as a benchmark to evaluate existing IMetSs. Different types of IMS provide varying levels of privacy protection support. Unfortunately, as observed by Jøsang et al (2007), there is insufficient privacy protection in many of the existing IMSs. In this thesis, we study and extend a type of privacy enhancing technology known as an Anonymous Credential System (ACS). In particular, we extend the ACS which is built on the cryptographic primitives proposed by Camenisch, Lysyanskaya, and Shoup. We call this system the Camenisch, Lysyanskaya, Shoup - Anonymous Credential System (CLS-ACS). The goal of CLS-ACS is to let users be as anonymous as possible. Unfortunately, CLS-ACS has problems, including (1) the concentration of power to a single entity - known as the Anonymity Revocation Manager (ARM) - who, if malicious, can trivially reveal a user’s PII (resulting in an illegal revocation of the user’s anonymity), and (2) poor performance due to the resource-intensive cryptographic operations required. The second and third contributions of this thesis are the proposal of two protocols that reduce the trust dependencies on the ARM during users’ anonymity revocation. Both protocols distribute trust from the ARM to a set of n referees (n > 1), resulting in a significant reduction of the probability of an anonymity revocation being performed illegally. The first protocol, called the User Centric Anonymity Revocation Protocol (UCARP), allows a user’s anonymity to be revoked in a user-centric manner (that is, the user is aware that his/her anonymity is about to be revoked). The second protocol, called the Anonymity Revocation Protocol with Re-encryption (ARPR), allows a user’s anonymity to be revoked by a service provider in an accountable manner (that is, there is a clear mechanism to determine which entity who can eventually learn - and possibly misuse - the identity of the user). The fourth contribution of this thesis is the proposal of a protocol called the Private Information Escrow bound to Multiple Conditions Protocol (PIEMCP). This protocol is designed to address the performance issue of CLS-ACS by applying the CLS-ACS in a federated single sign-on (FSSO) environment. Our analysis shows that PIEMCP can both reduce the amount of expensive modular exponentiation operations required and lower the risk of illegal revocation of users’ anonymity. Finally, the protocols proposed in this thesis are complex and need to be formally evaluated to ensure that their required security properties are satisfied. In this thesis, we use Coloured Petri nets (CPNs) and its corresponding state space analysis techniques. All of the protocols proposed in this thesis have been formally modeled and verified using these formal techniques. Therefore, the fifth contribution of this thesis is a demonstration of the applicability of CPN and its corresponding analysis techniques in modeling and verifying privacy enhancing protocols. To our knowledge, this is the first time that CPN has been comprehensively applied to model and verify privacy enhancing protocols. From our experience, we also propose several CPN modeling approaches, including complex cryptographic primitives (such as zero-knowledge proof protocol) modeling, attack parameterization, and others. The proposed approaches can be applied to other security protocols, not just privacy enhancing protocols.

Halogen bonding between an isoindoline nitroxide and 1,4-diiodotetrafluorobenzene: new tools and tectons for self-assembling organic spin systems

Halogen bonding has been observed for the first time between an isoindoline nitroxide and an iodoperfluorocarbon (see figure), which cocrystallize to form a discrete 2:1 supramolecular compound in which NO.⋅⋅⋅I halogen bonding is the dominant intermolecular interaction. This illustrates the potential use of halogen bonding and isoindoline nitroxide tectons for the assembly of organic spin systems...

Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Practical stability with respect to model mismatch of approximate discrete-time output feedback control

This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.