Towards a web-based progressive handwriting recognition environment for mathematical problem solving

The emergence of pen-based mobile devices such as PDAs and tablet PCs provides a new way to input mathematical expressions to computer by using handwriting which is much more natural and efficient for entering mathematics. This paper proposes a web-based handwriting mathematics system, called WebMath, for supporting mathematical problem solving. The proposed WebMath system is based on client-server architecture. It comprises four major components: a standard web server, handwriting mathematical expression editor, computation engine and web browser with Ajax-based communicator. The handwriting mathematical expression editor adopts a progressive recognition approach for dynamic recognition of handwritten mathematical expressions. The computation engine supports mathematical functions such as algebraic simplification and factorization, and integration and differentiation. The web browser provides a user-friendly interface for accessing the system using advanced Ajax-based communication. In this paper, we describe the different components of the WebMath system and its performance analysis.

A new three phase method (SDP method) for the multi-objective vehicle routing problem with simultaneous delvery and pickup (VRPSDP)

Transportation service operators are witnessing a growing demand for bi-directional movement of goods. Given this, the following thesis considers an extension to the vehicle routing problem (VRP) known as the delivery and pickup transportation problem (DPP), where delivery and pickup demands may occupy the same route. The problem is formulated here as the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), which requires the concurrent service of the demands at the customer location. This formulation provides the greatest opportunity for cost savings for both the service provider and recipient. The aims of this research are to propose a new theoretical design to solve the multi-objective VRPSDP, provide software support for the suggested design and validate the method through a set of experiments. A new real-life based multi-objective VRPSDP is studied here, which requires the minimisation of the often conflicting objectives: operated vehicle fleet size, total routing distance and the maximum variation between route distances (workload variation). The former two objectives are commonly encountered in the domain and the latter is introduced here because it is essential for real-life routing problems. The VRPSDP is defined as a hard combinatorial optimisation problem, therefore an approximation method, Simultaneous Delivery and Pickup method (SDPmethod) is proposed to solve it. The SDPmethod consists of three phases. The first phase constructs a set of diverse partial solutions, where one is expected to form part of the near-optimal solution. The second phase determines assignment possibilities for each sub-problem. The third phase solves the sub-problems using a parallel genetic algorithm. The suggested genetic algorithm is improved by the introduction of a set of tools: genetic operator switching mechanism via diversity thresholds, accuracy analysis tool and a new fitness evaluation mechanism. This three phase method is proposed to address the shortcoming that exists in the domain, where an initial solution is built only then to be completely dismantled and redesigned in the optimisation phase. In addition, a new routing heuristic, RouteAlg, is proposed to solve the VRPSDP sub-problem, the travelling salesman problem with simultaneous delivery and pickup (TSPSDP). The experimental studies are conducted using the well known benchmark Salhi and Nagy (1999) test problems, where the SDPmethod and RouteAlg solutions are compared with the prominent works in the VRPSDP domain. The SDPmethod has demonstrated to be an effective method for solving the multi-objective VRPSDP and the RouteAlg for the TSPSDP.

Semi-supervised Gaussian process latent variable model with pairwise constraints

In machine learning, Gaussian process latent variable model (GP-LVM) has been extensively applied in the field of unsupervised dimensionality reduction. When some supervised information, e.g., pairwise constraints or labels of the data, is available, the traditional GP-LVM cannot directly utilize such supervised information to improve the performance of dimensionality reduction. In this case, it is necessary to modify the traditional GP-LVM to make it capable of handing the supervised or semi-supervised learning tasks. For this purpose, we propose a new semi-supervised GP-LVM framework under the pairwise constraints. Through transferring the pairwise constraints in the observed space to the latent space, the constrained priori information on the latent variables can be obtained. Under this constrained priori, the latent variables are optimized by the maximum a posteriori (MAP) algorithm. The effectiveness of the proposed algorithm is demonstrated with experiments on a variety of data sets. © 2010 Elsevier B.V.

Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product's demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation. The analysis of results helps supply chain managers to take right decision in different demand and service level situations.

Network lifetime maximization with cross-layer design in wireless sensor networks

This paper investigates a cross-layer design approach for minimizing energy consumption and maximizing network lifetime (NL) of a multiple-source and single-sink (MSSS) WSN with energy constraints. The optimization problem for MSSS WSN can be formulated as a mixed integer convex optimization problem with the adoption of time division multiple access (TDMA) in medium access control (MAC) layer, and it becomes a convex problem by relaxing the integer constraint on time slots. Impacts of data rate, link access and routing are jointly taken into account in the optimization problem formulation. Both linear and planar network topologies are considered for NL maximization (NLM). With linear MSSS and planar single-source and single-sink (SSSS) topologies, we successfully use Karush-Kuhn-Tucker (KKT) optimality conditions to derive analytical expressions of the optimal NL when all nodes are exhausted simultaneously. The problem for planar MSSS topology is more complicated, and a decomposition and combination (D&C) approach is proposed to compute suboptimal solutions. An analytical expression of the suboptimal NL is derived for a small scale planar network. To deal with larger scale planar network, an iterative algorithm is proposed for the D&C approach. Numerical results show that the upper-bounds of the network lifetime obtained by our proposed optimization models are tight. Important insights into the NL and benefits of cross-layer design for WSN NLM are obtained.

Investment efficiency among a cross-section of UK firms:implications for the debate on financing constraints

In this paper, we address this policy issue using a stylised methodology that relies on estimates of the cash flow sensitivity of firms’ investment, as well as a relatively new methodology that enables us to generate a (0, 1) bounded measure of investment efficiency of firms, i.e., the efficiency with which firms can convert their sales into investment, after controlling for unobserved year- and industry-specific effects. Higher investment efficiency is associated with lower financing constraint. Our results indicate that there is considerable heterogeneity in investment efficiency across firms, during a given year; the range being 0.57-0.82. However, the average investment efficiency measure is similar across years, regions and NACE 2-digit industries. We also do not find discernible patterns in the relationship between investment efficiency and firm size, both before and during the financial crisis. The results suggest that while some firms are clearly less efficient at translating their performance into investment, broad policies targeting firms of a certain size, or those within a particular industry or region, may not successfully address the problem of financing constraint in the United Kingdom. The targeting of firms with financing constraints may have to be considerably more refined, and look at not easily observable factors such as credit history/events and organisational capacity of the firms.

The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

Premium e-grocery:exploring value in logistics integrated service solutions

E-grocery is gradually becoming viable or a necessity for many families. Yet, most e-supermarkets are seen as providers of low value "staple" and bulky goods mainly. While each store has a large number of SKU available, these products are mainly necessity goods with low marginal value for hedonistic consumption. A need to acquire diverse products (e.g., organic), premium priced products (e.g., wine) for special occasions (e.g., anniversary, birthday), or products just for health related reasons (e.g., allergies, diabetes) are yet to be served via one-stop e-tailers. In this paper, we design a mathematical model that takes into account consumers' geo-demographics and multi-product sourcing capacity for creating critical mass and profit. Our mathematical model is a variant of Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), which we extend by adding intermediate locations for trucks to meet and exchange goods. We illustrate our model for the city of Istanbul using GIS maps, and discuss its various extensions as well as managerial implications.

PCB assembly line assignment:a genetic algorithm approach

Purpose – This paper sets out to study a production-planning problem for printed circuit board (PCB) assembly. A PCB assembly company may have a number of assembly lines for production of several product types in large volume. Design/methodology/approach – Pure integer linear programming models are formulated for assigning the product types to assembly lines, which is the line assignment problem, with the objective of minimizing the total production cost. In this approach, unrealistic assignment, which was suffered by previous researchers, is avoided by incorporating several constraints into the model. In this paper, a genetic algorithm is developed to solve the line assignment problem. Findings – The procedure of the genetic algorithm to the problem and a numerical example for illustrating the models are provided. It is also proved that the algorithm is effective and efficient in dealing with the problem. Originality/value – This paper studies the line assignment problem arising in a PCB manufacturing company in which the production volume is high.

A verifiable solution to the MEG inverse problem

Magnetoencephalography (MEG) is a non-invasive brain imaging technique with the potential for very high temporal and spatial resolution of neuronal activity. The main stumbling block for the technique has been that the estimation of a neuronal current distribution, based on sensor data outside the head, is an inverse problem with an infinity of possible solutions. Many inversion techniques exist, all using different a-priori assumptions in order to reduce the number of possible solutions. Although all techniques can be thoroughly tested in simulation, implicit in the simulations are the experimenter's own assumptions about realistic brain function. To date, the only way to test the validity of inversions based on real MEG data has been through direct surgical validation, or through comparison with invasive primate data. In this work, we constructed a null hypothesis that the reconstruction of neuronal activity contains no information on the distribution of the cortical grey matter. To test this, we repeatedly compared rotated sections of grey matter with a beamformer estimate of neuronal activity to generate a distribution of mutual information values. The significance of the comparison between the un-rotated anatomical information and the electrical estimate was subsequently assessed against this distribution. We found that there was significant (P < 0.05) anatomical information contained in the beamformer images across a number of frequency bands. Based on the limited data presented here, we can say that the assumptions behind the beamformer algorithm are not unreasonable for the visual-motor task investigated.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Digital communication networks incorporating mobile data terminals

The use of digital communication systems is increasing very rapidly. This is due to lower system implementation cost compared to analogue transmission and at the same time, the ease with which several types of data sources (data, digitised speech and video, etc.) can be mixed. The emergence of packet broadcast techniques as an efficient type of multiplexing, especially with the use of contention random multiple access protocols, has led to a wide-spread application of these distributed access protocols in local area networks (LANs) and a further extension of them to radio and mobile radio communication applications. In this research, a proposal for a modified version of the distributed access contention protocol which uses the packet broadcast switching technique has been achieved. The carrier sense multiple access with collision avoidance (CSMA/CA) is found to be the most appropriate protocol which has the ability to satisfy equally the operational requirements for local area networks as well as for radio and mobile radio applications. The suggested version of the protocol is designed in a way in which all desirable features of its precedents is maintained. However, all the shortcomings are eliminated and additional features have been added to strengthen its ability to work with radio and mobile radio channels. Operational performance evaluation of the protocol has been carried out for the two types of non-persistent and slotted non-persistent, through mathematical and simulation modelling of the protocol. The results obtained from the two modelling procedures validate the accuracy of both methods, which compares favourably with its precedent protocol CSMA/CD (with collision detection). A further extension of the protocol operation has been suggested to operate with multichannel systems. Two multichannel systems based on the CSMA/CA protocol for medium access are therefore proposed. These are; the dynamic multichannel system, which is based on two types of channel selection, the random choice (RC) and the idle choice (IC), and the sequential multichannel system. The latter has been proposed in order to supress the effect of the hidden terminal, which always represents a major problem with the usage of the contention random multiple access protocols with radio and mobile radio channels. Verification of their operation performance evaluation has been carried out using mathematical modelling for the dynamic system. However, simulation modelling has been chosen for the sequential system. Both systems are found to improve system operation and fault tolerance when compared to single channel operation.

The development of hard real-time systems using a formal approach

Hard real-time systems are a class of computer control systems that must react to demands of their environment by providing `correct' and timely responses. Since these systems are increasingly being used in systems with safety implications, it is crucial that they are designed and developed to operate in a correct manner. This thesis is concerned with developing formal techniques that allow the specification, verification and design of hard real-time systems. Formal techniques for hard real-time systems must be capable of capturing the system's functional and performance requirements, and previous work has proposed a number of techniques which range from the mathematically intensive to those with some mathematical content. This thesis develops formal techniques that contain both an informal and a formal component because it is considered that the informality provides ease of understanding and the formality allows precise specification and verification. Specifically, the combination of Petri nets and temporal logic is considered for the specification and verification of hard real-time systems. Approaches that combine Petri nets and temporal logic by allowing a consistent translation between each formalism are examined. Previously, such techniques have been applied to the formal analysis of concurrent systems. This thesis adapts these techniques for use in the modelling, design and formal analysis of hard real-time systems. The techniques are applied to the problem of specifying a controller for a high-speed manufacturing system. It is shown that they can be used to prove liveness and safety properties, including qualitative aspects of system performance. The problem of verifying quantitative real-time properties is addressed by developing a further technique which combines the formalisms of timed Petri nets and real-time temporal logic. A unifying feature of these techniques is the common temporal description of the Petri net. A common problem with Petri net based techniques is the complexity problems associated with generating the reachability graph. This thesis addresses this problem by using concurrency sets to generate a partial reachability graph pertaining to a particular state. These sets also allows each state to be checked for the presence of inconsistencies and hazards. The problem of designing a controller for the high-speed manufacturing system is also considered. The approach adopted mvolves the use of a model-based controller: This type of controller uses the Petri net models developed, thus preservIng the properties already proven of the controller. It. also contains a model of the physical system which is synchronised to the real application to provide timely responses. The various way of forming the synchronization between these processes is considered and the resulting nets are analysed using concurrency sets.

A projected process kriging algorithm for sensor networks with heterogeneous error characteristics

Large monitoring networks are becoming increasingly common and can generate large datasets from thousands to millions of observations in size, often with high temporal resolution. Processing large datasets using traditional geostatistical methods is prohibitively slow and in real world applications different types of sensor can be found across a monitoring network. Heterogeneities in the error characteristics of different sensors, both in terms of distribution and magnitude, presents problems for generating coherent maps. An assumption in traditional geostatistics is that observations are made directly of the underlying process being studied and that the observations are contaminated with Gaussian errors. Under this assumption, sub–optimal predictions will be obtained if the error characteristics of the sensor are effectively non–Gaussian. One method, model based geostatistics, assumes that a Gaussian process prior is imposed over the (latent) process being studied and that the sensor model forms part of the likelihood term. One problem with this type of approach is that the corresponding posterior distribution will be non–Gaussian and computationally demanding as Monte Carlo methods have to be used. An extension of a sequential, approximate Bayesian inference method enables observations with arbitrary likelihoods to be treated, in a projected process kriging framework which is less computationally intensive. The approach is illustrated using a simulated dataset with a range of sensor models and error characteristics.

A generative model for online depth fusion

We present a probabilistic, online, depth map fusion framework, whose generative model for the sensor measurement process accurately incorporates both long-range visibility constraints and a spatially varying, probabilistic outlier model. In addition, we propose an inference algorithm that updates the state variables of this model in linear time each frame. Our detailed evaluation compares our approach against several others, demonstrating and explaining the improvements that this model offers, as well as highlighting a problem with all current methods: systemic bias. © 2012 Springer-Verlag.