Piecewise Bounded Quadratic Systems in the Plane

In this paper we study the sliding mode of piecewise bounded quadratic systems in the plane given by a non-smooth vector field Z=(X,Y). Analyzing the singular, crossing and sliding sets, we get the conditions which ensure that any solution, including the sliding one, is bounded.

A Heuristic with Bounded Guarantee to Compute Diverse Paths under Shared Protection in WDM Mesh Networks

Establishing a fault-tolerant connection in a network involves computation of diverse working and protection paths. The Shared Risk Link Group (SRLG) [1] concept is used to model several types of failure conditions such as link, node, fiber conduit, etc. In this work we focus on the problem of computing optimal SRLG/link diverse paths under shared protection. Shared protection technique improves network resource utilization by allowing protection paths of multiple connections to share resources. In this work we propose an iterative heuristic for computing SRLG/link diverse paths. We present a method to calculate a quantitative measure that provides a bounded guarantee on the optimality of the diverse paths computed by the heuristic. The experimental results on computing link diverse paths show that our proposed heuristic is efficient in terms of number of iterations required (time taken) to compute diverse paths when compared to other previously proposed heuristics.

Simulation results and applications of an advection bounded scheme to practical flows

This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Noisy Oncology: applications of bounded noise transitions in modelling tumor growth

I tumori macroscopici e microscopici, dopo la loro prima fase di crescita, sono composti da un numero medio elevato di cellule. Così, in assenza di perturbazioni esterne, la loro crescita e i punti di equilibrio possono essere descritti da equazioni differenziali. Tuttavia, il tumore interagisce fortemente col macroambiente che lo circonda e di conseguenza una descrizione del tutto deterministica risulta a volte inappropriata. In questo caso si può considerare l'interazione con fluttuazioni statistiche, causate da disturbi esterni, utilizzando le equazioni differenziali stocastiche (SDE). Questo è vero in modo particolare quando si cerca di modellizzare tumori altamente immunogenici che interagiscono con il sistema immunitario, in quanto la complessità di questa interazione risulta in fenomeni di multistabilità. Così, il rumore può provocare disturbi e indurre transizioni di stato (Noise-Induced-Transitions). E' importante notare che una NIT può avere implicazioni profonde sulla vita di un paziente, dal momento che una transizione da uno stato di equilibrio piccolo, nelle dimensioni del tumore, ad uno stato di equilibrio macroscopico, nella maggior parte dei casi significa il passaggio dalla vita alla morte. Generalmente l'approccio standard è quello di modellizzare le fluttuazioni stocastiche dei parametri per mezzo di rumore gaussiano bianco o colorato. In alcuni casi però questa procedura è altamente inadeguata, a causa della illimitatezza intrinseca dei rumori gaussiani che può portare a gravi incongruenze biologiche: pertanto devono essere utilizzati dei rumori "limitati", che, tuttavia, sono molto meno studiati di quelli gaussiani. Inoltre, l'insorgenza di NIT dipende dal tipo di rumore scelto, che rivela un nuovo livello di complessità in biologia. Lo scopo di questa tesi è quello di studiare le applicazioni di due tipi diversi di "rumori limitati" nelle transizioni indotte in due casi: interazione tra tumore e sistema immunitario e chemioterapia dei tumori. Nel primo caso, abbiamo anche introdotto un nuovo modello matematico di terapia, che estende, in modo nuovo, il noto modello di Norton-Simon.

Formal planning rationality in public sector professional work: between discourse and practice

Although rational models of formal planning have been seriously criticized by strategy literature, they not only remain a widely used organizational practice in private firms, but they have increasingly been entering public, professional organizations too, as part of public sector managerial reforms. This research addresses this apparent paradox, exploring the meaning of formal planning in public sector professional work. Curiously, this is an issue that remains under-investigated in the literature: the long debate on formal planning in strategy research devoted scant attention to its diffusion in the public sector, and public sector studies have scrutinized the introduction of other management tools in professional work, but very limitedly formal planning itself. In fact, little is known on the actual meaning of formal planning in public, professional services. This research is based upon a case of adoption of formal planning tools in a public hospital. Embracing a discourse analytical lens, it examines which formal planning discourse entered professional work, to what extent, and how professionals interpret it and engage with it in their practice. The analysis uncovers dynamics of social construction of meaning where, eventually, a formal planning discourse both shapes and is shaped by professional practice. In particular, it is found that formal planning rationality largely penetrated professional work, but not to the detriment of professional values. Morevover, formal planning ‘fails’ as a tool for rational decision making, but it takes up a knowledge work and a social value in professional work, as a tool for explicitation of action courses and for dialogue between otherwise more disconnected parts of the organization.

Statistical analysis and simulation techniques in wall-bounded turbulence

The present work is devoted to the assessment of the energy fluxes physics in the space of scales and physical space of wall-turbulent flows. The generalized Kolmogorov equation will be applied to DNS data of a turbulent channel flow in order to describe the energy fluxes paths from production to dissipation in the augmented space of wall-turbulent flows. This multidimensional description will be shown to be crucial to understand the formation and sustainment of the turbulent fluctuations fed by the energy fluxes coming from the near-wall production region. An unexpected behavior of the energy fluxes comes out from this analysis consisting of spiral-like paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behavior conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence. To this aim a new relation stating the leading physical processes governing the energy transfer in wall-turbulence is suggested and shown able to capture most of the rich dynamics of the shear dominated region of the flow. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The same approach is applied for the first time to a filtered velocity field. A generalized Kolmogorov equation specialized for filtered velocity field is derived and discussed. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter length compared to the cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region lb. The systematic characterization of the resolved and subgrid physics as function of the filter scale and of the wall-distance will be shown instrumental for a correct use of LES models in the simulation of wall turbulent flows. Taking inspiration from the new relation for the energy transfer in wall turbulence, a new class of LES models will be also proposed. Finally, the generalized Kolmogorov equation specialized for filtered velocity fields will be shown to be an helpful statistical tool for the assessment of LES models and for the development of new ones. As example, some classical purely dissipative eddy viscosity models are analyzed via an a priori procedure.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Policy Contexts of Social Work in Britain: the wider implications of 'New' Labour and the 'New Legal Regime'

Several commentators have expressed disappointment with New Labour's apparent adherence to the policy frameworks of the previous Conservative administrations. The employment orientation of its welfare programmes, the contradictory nature of the social exclusion initiatives, and the continuing obsession with public sector marketisation, inspections, audits, standards and so on, have all come under critical scrutiny (c.f., Blyth 2001; Jordan 2001; Orme 2001). This paper suggests that in order to understand the socio-economic and political contexts affecting social work we need to examine the relationship between New Labour's modernisation project and its insertion within an architecture of global governance. In particular, membership of the European Union (EU), International Monetary Fund (IMF) and World Trade Organisation (WTO) set the parameters for domestic policy in important ways. Whilst much has been written about the economic dimensions of 'globalisation' in relation to social work rather less has been noted about the ways in which domestic policy agenda are driven by multilateral governance objectives. This policy dimension is important in trying to respond to various changes affecting social work as a professional activity. What is possible, what is encouraged, how things might be done, is tightly bounded by the policy frameworks governing practice and affected by those governing the lives of service users. It is unhelpful to see policy formulation in purely national terms as the UK is inserted into a network governance structure, a regulatory framework where decisions are made by many countries and organisations and agencies. Together, they are producing a 'new legal regime', characterised by a marked neo-liberal policy agenda. This paper aims to demonstrate the relationship of New Labour's modernisation programme to these new forms of legality by examining two main policy areas and the welfare implications they are enmeshed in. The first is privatisation, and the second is social policy in the European Union. Examining these areas allows a demonstration of how much of the New Labour programme can be understood as a local implementation of a transnational strategy, how parts of that strategy produce much of the social exclusion it purports to address, and how social welfare, and particularly social work, are noticeable by their absence within policy discourses of the strategy. The paper details how the privatisation programme is considered to be a crucial vehicle for the further development of a transnational political-economy, where capital accumulation has been redefined as 'welfare'. In this development, frameworks, codes and standards are central, and the final section of the paper examines how the modernisation strategy of the European Union depends upon social policy marked by an employment orientation and risk rationality, aimed at reconfiguring citizen identities.The strategy is governed through an 'open mode of coordination', in which codes, standards, benchmarks and so on play an important role. The paper considers the modernisation strategy and new legality within which it is embedded as dependent upon social policy as a technology of liberal governance, one demonstrating a new rationality in comparison to that governing post-Second World War welfare, and which aims to reconfigure institutional infrastructure and citizen identity.

“Unconformity-Bounded” Stratigraphic Units in the South Polar Layered Deposits (Promethei Lingula, Mars)

We conducted a stratigraphic analysis of the South Polar Layered Deposits (SPLDs) in Promethei Lingula (PL, Mars) based on the identification of regional unconformities at visible and radar wavelengths. According to the terrestrial classification, this approach constrains the stratigraphy of the region and remedies the ambiguous interpretation of stratigraphy through marker layers, bypassing the problem related to the morphologic and radiometric appearance of the layers. Thus, the approach does not exclude diverse classifications, but complements them, whereas other discriminant elements are doubtful or difficult/impossible to be defined. Using this approach, we defined two stratigraphic units (or synthems: PL1 and PL2) in PL, which are morphologically different and divided by a regional unconformity (AuR1). This stratigraphic architecture implies that the geological history of PL has been conditioned by periodic changes in climate, which in turn are related to orbital variations of Mars.

Bounded Seas: Island Parsing Without Shipwrecks

Imprecise manipulation of source code (semi-parsing) is useful for tasks such as robust parsing, error recovery, lexical analysis, and rapid development of parsers for data extraction. An island grammar precisely defines only a subset of a language syntax (islands), while the rest of the syntax (water) is defined imprecisely. Usually, water is defined as the negation of islands. Albeit simple, such a definition of water is naive and impedes composition of islands. When developing an island grammar, sooner or later a programmer has to create water tailored to each individual island. Such an approach is fragile, however, because water can change with any change of a grammar. It is time-consuming, because water is defined manually by a programmer and not automatically. Finally, an island surrounded by water cannot be reused because water has to be defined for every grammar individually. In this paper we propose a new technique of island parsing - bounded seas. Bounded seas are composable, robust, reusable and easy to use because island-specific water is created automatically. We integrated bounded seas into a parser combinator framework as a demonstration of their composability and reusability.

Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.