A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

A solution framework for scheduling a BPM with non-identical job dimensions

A Batch Processing Machine (BPM) is one which processes a number of jobs simultaneously as a batch with common beginning and ending times. Also, a BPM, once started cannot be interrupted in between (Pre-emption not allowed). This research is motivated by a BPM in steel casting industry. There are three main stages in any steel casting industry viz., pre-casting stage, casting stage and post-casting stage. A quick overview of the entire process, is shown in Figure 1. There are two BPMs : (1) Melting furnace in the pre-casting stage and (2) Heat Treatment Furnace (HTF) in the post casting stage of steel casting manufacturing process. This study focuses on scheduling the latter, namely HTF. Heat-treatment operation is one of the most important stages of steel casting industries. It determines the final properties that enable components to perform under demanding service conditions such as large mechanical load, high temperature and anti-corrosive processing. In general, different types of castings have to undergo more than one type of heat-treatment operations, where the total heat-treatment processing times change. To have a better control, castings are primarily classified into a number of job-families based on the alloy type such as low-alloy castings and high alloy castings. For technical reasons such as type of alloy, temperature level and the expected combination of heat-treatment operations, the castings from different families can not be processed together in the same batch.

A non-orthogonal cooperative multiple access (NCMA) protocol and low ML decoding complexity codes

A half-duplex constrained non-orthogonal cooperative multiple access (NCMA) protocol suitable for transmission of information from N users to a single destination in a wireless fading channel is proposed. Transmission in this protocol comprises of a broadcast phase and a cooperation phase. In the broadcast phase, each user takes turn broadcasting its data to all other users and the destination in an orthogonal fashion in time. In the cooperation phase, each user transmits a linear function of what it received from all other users as well as its own data. In contrast to the orthogonal extension of cooperative relay protocols to the cooperative multiple access channels wherein at any point of time, only one user is considered as a source and all the other users behave as relays and do not transmit their own data, the NCMA protocol relaxes the orthogonality built into the protocols and hence allows for a more spectrally efficient usage of resources. Code design criteria for achieving full diversity of N in the NCMA protocol is derived using pair wise error probability (PEP) analysis and it is shown that this can be achieved with a minimum total time duration of 2N - 1 channel uses. Explicit construction of full diversity codes is then provided for arbitrary number of users. Since the Maximum Likelihood decoding complexity grows exponentially with the number of users, the notion of g-group decodable codes is introduced for our setup and a set of necesary and sufficient conditions is also obtained.

Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

The Risk of Cancer Associated with Immunosuppressive Therapy for Skin Diseases

The possible carcinogenic risk of immunosuppressive therapies is an important issue in everyday clinical practise. Carcinogenesis is a slow multi step procedure, thus a long latency period is needed before cancer develops. PUVA therapy is used for many skin diseases including psoriasis, early stage cutaneous T cell lymphoma, atopic dermatitis, palmoplantar pustulosis and chronic eczema. There has been concern about the increased melanoma risk associated to PUVA therapy, which has previously been associated with an increased risk on non-melanoma skin cancer, especially squamous cell carcinoma. The increased risk of basal cell carcinoma (BCC) is also documented but it is modest compared to squamous cell carcinoma (SCC). This thesis evaluated melanoma and noncutaneous cancer risk associated to PUVA, and the persistence of nonmelanoma cancer risk after the cessation of PUVA treatment. Also, the influence of photochemotherapy to the development of secondary cancers in cutaneous T cell lymphoma and the role of short term cyclosporine in later cancer development in inflammatory skin diseases were evaluated. The first three studies were performed on psoriasis patients. The risk of melanoma started to increase 15 years after the first treatment with PUVA. The risk was highest among persons who had received over 250 treatments compared to those under 250 treatments. In noncutaneous cancer, the overall risk was not increased (RR=1.08,95% CI=0.93-1.24), but significant increases in risk were found in thyroid cancer, breast cancer and in central nervous system neoplasms. These cancers were not associated to PUVA. The increased risk of SCC was associated to high cumulative UVA exposure in the PUVA regimen. The patients with high risk had no substantial exposure to other carcinogens. In BCC there was a similar but more modest tendency. In the two other studies, the risk of all secondary cancers (SIR) in CTCL patients was 1.4 (95% CI=1.0-1.9). In separate sites, the risk of lung cancer, Hodgkin and non-Hodgkin lymphomas were increased. PUVA seemed not to contribute to any extent to the appearance of these cancers. The carcinogenity of short-term cyclosporine was evaluated in inflammatory skin diseases. No increased risk for any type of cancer including the skin cancers was detected. To conclude, our studies confirm the increased skin cancer risk related to PUVA treatment in psoriasis patients. In clinical practice, this has led to a close and permanent follow-up of patients treated with PUVA. In CTCL patients, PUVA treatment did not contribute to the development of secondary cancers. We could not detect any increase in the risk of cancer in patients treated with short term cyclosporine, unlike in organ transplant patients under such long-term therapy.

Parenting a child with haemophilia while living in a non-metropolitan area

The experience of living in a non-metropolitan area and parenting a child with haemophilia is relatively unknown. Using Interpretive Phenomenological Analysis (IPA), the following study explored the experiences of seven parents, from which four themes emerged: ‘bearing the brunt of diagnosis’ captures the impact of the diagnosis; ‘if you can’t help me, who can?’ reveals experiences with the health system; ‘tackling the challenge of treatment’ encompasses difficulties in adhering to the treatment regime; ‘I need you to understand’ reflects desires for others support and understanding. These themes should be considered when developing support systems and interventions for parents living in non-metropolitan areas.

Two worlds apart: Indigenous community perspectives and Non-Indigenous teacher perspectives on Australian schools

Our evaluation studies of Indigenous school reform begin from a different starting point: listening to, hearing and engaging with the commentaries, voices, narratives and analyses of Indigenous community as they discuss and recount their experiences and current encounters with Australian state schools. Here we undertake a contrastive documentation of the views of Indigenous community members, Elders, parents, education workers, and young people and, indeed, of the views of their non-Indigenous teachers and school principals. This is a dramatic picture of two distinctive cultural lifeworlds, communities and worldviews in contact, of two very different ‘constructions’ by participants of a shared, mutual experience: everyday interaction in the social field of the Australian school. Taken together, our Indigenous and non-Indigenous participants repeatedly confirmed and corroborated a key theme: that Indigenous peoples continue to be viewed and ‘treated’ through the lens and language of cultural, intellectual and moral ‘deficit’.