A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive condition. This last result slightly improves some earlier work by G. Barles and H. Ishii.

Ontology-Based Model of Representation of Knowledge about Language Mappings

The paper presents a short review of some systems for program transformations performed on the basis of the internal intermediate representations of these programs. Many systems try to support several languages of representation of the source texts of programs and solve the task of their translation into the internal representation. This task is still a challenge as it is effort-consuming. To reduce the effort, different systems of translator construction, ready compilers with ready grammars of outside designers are used. Though this approach saves the effort, it has its drawbacks and constraints. The paper presents the general idea of using the mapping approach to solve the task within the framework of program transformations and overcome the disadvantages of the existing systems. The paper demonstrates a fragment of the ontology model of high-level languages mappings onto the single representation and gives the example of how the description of (a fragment) a particular mapping is represented in accordance with the ontology model.

Fixed Point Theorems of Kannan Type for Cyclical Contractive Conditions

The main aim of this paper is to obtain fixed point theorems for Kannan and Zamfirescu operators in the presence of cyclical contractive condition. A method for approximation of the fixed points is also provided, for which both a priori and a posteriori error estimates are given. Our results generalize, unify and extend several important fixed points theorems in literature. In order to illustrate the efficiency of our generalizations five significant examples are also given.

Application of Subordination Principle to Log-Harmonic alpha-spirallike Mappings

MSC 2010: 30C45, 30C55

Applications of Subordination Principle to Log-Harmonic Mappings

MSC 2010: 30C45, 30C55

Approximation of Lipschitz Mappings

2000 Mathematics Subject Classification: 46B03

Codifferentiable Mappings with Applications to Vector Optimality

AMS subject classification: Primary 49J52; secondary: 26A27, 90C48, 47N10.

On the existence of right adjoints for surjective mappings between fuzzy structures0

En este trabajo los autores continúan su estudio de la caracterización de la existencia de adjunciones (conexiones de Galois isótonas) cuyo codominio no está dotado de estructura en principio. En este artículo se considera el caso difuso en el que se tiene un orden difuso R definido en un conjunto A y una aplicación sobreyectiva f:A-> B compatible respecto de dos relaciones de similaridad definidas en el dominio A y en el condominio B, respectivamente. Concretamente, el problema es encontrar un orden difuso S en B y una aplicación g:B-> A compatible también con las correspondientes similaridades definidas en A y en B, de tal forma que el par (f,g) constituya un adjunción.

Leveraging managed frameworks from modular languages

Managed execution frameworks, such as the.NET Common Language Runtime or the Java Virtual Machine, provide a rich environment for the creation of application programs. These execution environments are ideally suited for languages that depend on type-safety and the declarative control of feature access. Furthermore, such frameworks typically provide a rich collection of library primitives specialized for almost every domain of application programming. Thus, when a new language is implemented on one of these frameworks it becomes necessary to provide some kind of mapping from the new language to the libraries of the framework. The design of such mappings is challenging since the type-system of the new language may not span the domain exposed in the library application programming interfaces (APIs). The nature of these design considerations was clarified in the implementation of the Gardens Point Component Pascal (gpcp) compiler. In this paper we describe the issues, and the solutions that we settled on in this case. The problems that were solved have a wider applicability than just our example, since they arise whenever any similar language is hosted in such an environment.

The silk road project : dance and embodiment in the age of motion capture

The Silk Road Project was a practice-based research project investigating the potential of motion capture technology to inform perceptions of embodiment in dance performance. The project created a multi-disciplinary collaborative performance event using dance performance and real-time motion capture at Deakin University’s Deakin Motion Lab. Several new technological advances in producing real-time motion capture performance were produced, along with a performance event that examined the aesthetic interplay between a dancer’s movement and the precise mappings of its trajectories created by motion capture and real-time motion graphic visualisations.

Multi-objective optimisation of bijective s-boxes

In this paper we investigate the heuristic construction of bijective s-boxes that satisfy a wide range of cryptographic criteria including algebraic complexity, high nonlinearity, low autocorrelation and have none of the known weaknesses including linear structures, fixed points or linear redundancy. We demonstrate that the power mappings can be evolved (by iterated mutation operators alone) to generate bijective s-boxes with the best known tradeoffs among the considered criteria. The s-boxes found are suitable for use directly in modern encryption algorithms.

Emergent task-specific object semantics through distributed experience networks

Autonomous development of sensorimotor coordination enables a robot to adapt and change its action choices to interact with the world throughout its lifetime. The Experience Network is a structure that rapidly learns coordination between visual and haptic inputs and motor action. This paper presents methods which handle the high dimensionality of the network state-space which occurs due to the simultaneous detection of multiple sensory features. The methods provide no significant increase in the complexity of the underlying representations and also allow emergent, task-specific, semantic information to inform action selection. Experimental results show rapid learning in a real robot, beginning with no sensorimotor mappings, to a mobile robot capable of wall avoidance and target acquisition.

Identifying interests of web users for effective recommendations

Search log data is multi dimensional data consisting of number of searches of multiple users with many searched parameters. This data can be used to identify a user’s interest in an item or object being searched. Identifying highest interests of a Web user from his search log data is a complex process. Based on a user’s previous searches, most recommendation methods employ two-dimensional models to find relevant items. Such items are then recommended to a user. Two-dimensional data models, when used to mine knowledge from such multi dimensional data may not be able to give good mappings of user and his searches. The major problem with such models is that they are unable to find the latent relationships that exist between different searched dimensions. In this research work, we utilize tensors to model the various searches made by a user. Such high dimensional data model is then used to extract the relationship between various dimensions, and find the prominent searched components. To achieve this, we have used popular tensor decomposition methods like PARAFAC, Tucker and HOSVD. All experiments and evaluation is done on real datasets, which clearly show the effectiveness of tensor models in finding prominent searched components in comparison to other widely used two-dimensional data models. Such top rated searched components are then given as recommendation to users.

Ian Weir Research Architect

Dr Ian Weir's practice is driven by a passion for the Fitzgerald Bioregion, a remote, bushfire-prone landscape on the south coats of Western Australia which is renowned internationally for its biodiversity. It is here that Dr Weir collaborates with individuals and organisations from the fields of ecology, botany, bushfire science, land surveying, landscape architecture and art practice, all of whom seek to expand understandings of this remarkable landscape. This diverse practice formation is constructed to address a significant problem beyond the scope of conventional modes of architectural practice: the reconciliation of biodiversity and bushfire with human habitation, through a multimodal approach using art practice cartography and architectural intervention. The chapter articulates Dr Weir's practice through a formation diagram and depicts key works of landscape representaion taken from "Enacted Cartography" and "Lightsite", two of Dr Weir's key research themes.

Ian Weir Research Architect : website

Research background: Communicating the diverse nature of multimodal practice is inherently difficult for the design-led research academic. Websites are an effective means of displaying images and text, but for the user/viewer the act of viewing is often random and disorienting, due to the non-linear means of accessing the information. This characteristic of websites limits the medium’s efficacy in regard to presenting an overarching philosophical standpoint or theme - the key driver behind most academic research. Research Contribution: This website: http://www.ianweirarchitect.com, presents a means of reconciling this problem by presenting a deceptively simple graphic and temporal layout, which limits the opportunity for the user/viewer to become disoriented and miss the key themes and issues that binds, the otherwise divergent, research material together. Research significance: http://www.ianweirarchitect.com, is a creative work that supplements Dr Ian Weir’s exhibition “Enacted Cartography” held in August 2012 in Brisbane and in August/September 2012 in Venice, Italy for the 13th International Architecture Exhibition (Venice Architecture Biennale). Dr Weir was selected by the Australian Institute of Architects to represent innovation in architectural practice for the Institute’s Formations: New Practices in Australian Architecture, exhibition and catalogue (of the same name) held in the Australian Pavilion, The Giardini, Venice. This website is creative output that compliments Dr Weir’s other multimodal outputs including photographic artworks, cartographic maps and architectural designs.