Online learning in discrete hidden Markov models

We present and analyze three different online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare their performance with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of the generalization error we draw learning curves in simplified situations and compare the results. The performance for learning drifting concepts of one of the presented algorithms is analyzed and compared with the Baldi-Chauvin algorithm in the same situations. A brief discussion about learning and symmetry breaking based on our results is also presented. © 2006 American Institute of Physics.

Discrete solitons in coupled active lasing cavities

We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A new family of stable localized structures is found: these are bright and gray cavity solitons representing the connections between homogeneous and inhomogeneous states. Solitons of this type can be controlled by discrete diffraction and are stable when the bistability of homogenous states is absent. © 2012 Optical Society of America.

An edge-based matching kernel through discrete-time quantum walks

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Encouraging the intellectual craft of living research:tattoos, theory and time

This chapter contributes to the anthology on learning to research - researching to learn because it emphases a need to design curricula that enables living research, and on-going researcher development, rather than one that restricts student and staff activities, within a marketised approach towards time. In recent decades higher education (HE) has come to be valued for its contribution to the global economy. Referred to as the neo-liberal university, a strong prioritisation has been placed on meeting the needs of industry by providing a better workforce. This perspective emphasises the role of a degree in HE to secure future material affluence, rather than to study as an on-going investment in the self (Molesworth , Nixon & Scullion, 2009: 280). Students are treated primarily as consumers in this model, where through their tuition fees they purchase a product, rather than benefit from the transformative potential university education offers for the whole of life.Given that HE is now measured by the numbers of students it attracts, and later places into well-paid jobs, there is an intense pressure on time, which has led to a method where the learning experiences of students are broken down into discrete modules. Whilst this provides consistency, students can come to view research processes in a fragmented way within the modular system. Topics are presented chronologically, week-by-week and students simply complete a set of tasks to ‘have a degree’, rather than to ‘be learners’ (Molesworth , Nixon & Scullion, 2009: 277) who are living their research, in relation to their own past, present and future. The idea of living research in this context is my own adaptation of an approach suggested by C. Wright Mills (1959) in The Sociological Imagination. Mills advises that successful scholars do not split their work from the rest of their lives, but treat scholarship as a choice of how to live, as well as a choice of career. The marketised slant in HE thus creates a tension firstly, for students who are learning to research. Mills would encourage them to be creative, not instrumental, in their use of time, yet they are journeying through a system that is structured for a swift progression towards a high paid job, rather than crafted for reflexive inquiry, that transforms their understanding throughout life. Many universities are placing a strong focus on discrete skills for student employability, but I suggest that embedding the transformative skills emphasised by Mills empowers students and builds their confidence to help them make connections that aid their employability. Secondly, the marketised approach creates a problem for staff designing the curriculum, if students do not easily make links across time over their years of study and whole programmes. By researching to learn, staff can discover new methods to apply in their design of the curriculum, to help students make important and creative connections across their programmes of study.

Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

Implementing an agent-based model with a spatial visual display in discrete-event simulation software

There has been an increasing interest in the use of agent-based simulation and some discussion of the relative merits of this approach as compared to discrete-event simulation. There are differing views on whether an agent-based simulation offers capabilities that discrete-event cannot provide or whether all agent-based applications can at least in theory be undertaken using a discrete-event approach. This paper presents a simple agent-based NetLogo model and corresponding discrete-event versions implemented in the widely used ARENA software. The two versions of the discrete-event model presented use a traditional process flow approach normally adopted in discrete-event simulation software and also an agent-based approach to the model build. In addition a real-time spatial visual display facility is provided using a spreadsheet platform controlled by VBA code embedded within the ARENA model. Initial findings from this investigation are that discrete-event simulation can indeed be used to implement agent-based models and with suitable integration elements such as VBA provide the spatial displays associated with agent-based software.

Using discrete event simulation to investigate road delivery policies to UK retailers

Retail customers provide a number of significant challenges to the efficiency and effectiveness of distribution systems. These challengers include shorter delivery windows, fluctuating volumes and a wider product mix. This paper demonstrates the use of discrete-event simulation to investigate policy issues regarding the incorporation of retail customers in a road delivery network from the spoke terminal of a hub and spoke distribution system. In particular a comparison of a mixed (retail and non-retail) delivery policy with a dedicated retail delivery run is made.

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

Perturbative discrete-time multivariate fiber channel model with finite memory

We introduce a discrete-time fibre channel model that provides an accurate analytical description of signal-signal and signal-noise interference with memory defined by the interplay of nonlinearity and dispersion. Also the conditional pdf of signal distortion, which captures non-circular complex multivariate symbol interactions, is derived providing the necessary platform for the analysis of channel statistics and capacity estimations in fibre optic links.

Methods of modelling people using discrete-event simulation

Discrete-event simulation (DES) is a developed technology used to model manufacturing and service systems. However, although the importance of modelling people in a DES has been recognised, there is little guidance on how this can be achieved in practice. The results from a literature review were used in order to identify examples of the use of DES to model people. Each article was examined in order to determine the method used to model people within the simulation study. It was found that there are no common methods but a diverse range of approaches used to model human behaviour in DES. This paper provides an outline of the approaches used to model people in terms of their decision making, availability for work, task performance and arrival rate. The outcome brings together the current knowledge in this area and will be of interest to researchers considering developing a methodology for modelling people in DES and to practitioners engaged with a simulation project involving the model ling of people’s behaviour.