Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Local Utility Functions and Local Probability Transformations

This note shows that, under appropriate conditions, preferences may be locally approximated by the linear utility or risk-neutral preference functional associated with a local probability transformation.

Dynamical local models for segmentation and prediction of financial time series

In the analysis and prediction of many real-world time series, the assumption of stationarity is not valid. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We introduce a new model which combines a dynamic switching (controlled by a hidden Markov model) and a non-linear dynamical system. We show how to train this hybrid model in a maximum likelihood approach and evaluate its performance on both synthetic and financial data.

Hierarchical GTM: Constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 19-dimensional data sets.

Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

Mach edges: local features predicted by 3rd derivative spatial filtering

Edges are key points of information in visual scenes. One important class of models supposes that edges correspond to the steepest parts of the luminance profile, implying that they can be found as peaks and troughs in the response of a gradient (1st derivative) filter, or as zero-crossings in the 2nd derivative (ZCs). We tested those ideas using a stimulus that has no local peaks of gradient and no ZCs, at any scale. The stimulus profile is analogous to the Mach ramp, but it is the luminance gradient (not the absolute luminance) that increases as a linear ramp between two plateaux; the luminance profile is a blurred triangle-wave. For all image-blurs tested, observers marked edges at or close to the corner points in the gradient profile, even though these were not gradient maxima. These Mach edges correspond to peaks and troughs in the 3rd derivative. Thus Mach edges are inconsistent with many standard edge-detection schemes, but are nicely predicted by a recent model that finds edge points with a 2-stage sequence of 1st then 2nd derivative operators, each followed by a half-wave rectifier.

Constructing localized non-linear projection manifolds in a principled way:hierarchical generative topographic mapping

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis (Bishop98a) in several directions: 1. We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. 2. We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. 3. Using tools from differential geometry we derive expressions for local directionalcurvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model.We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set andapply our system to two more complex 12- and 19-dimensional data sets.

Understanding change in the public sector:a local authority case study

Increasingly managers in the public sector are being required to manage change, but many of the models of change which are available to them have been developed from private sector experience. There is a need to understand more about how the change process unfolds in the public sector. A case study of change in one local authority over the period 1974-87 is provided. The events surrounding housing decentralisation and the introduction of community development are considered in detail. To understand these events a twofold model of change is proposed: a short wave model which explains a change project or event; and a long wave model which considers how these projects or events might be linked together to provide a picture of an organisation over a longer period. The short wave model identifies multiple triggers of change and signals the importance of mediators in recognising these triggers. The extent to which new ideas are implemented and the pace of their adoption is influenced by the balance of power within the organisation and the political tactics which are used. Broad phases in the change process can be identified, but there is not a simple linear passage through these. The long wave model considers the way in which continuity and change feed off one another. It suggests that periods of relative stability may be interspersed with more radical transformations as the dominant paradigm guiding the organisation shifts. However, such paradigmatic shifts in local government may be less obvious than in the private sector due to the diverse nature of the former.

An Interactive Method of Linear Mixed Integer Multicriteria Optimization

The paper describes a learning-oriented interactive method for solving linear mixed integer problems of multicriteria optimization. The method increases the possibilities of the decision maker (DM) to describe his/her local preferences and at the same time it overcomes some computational difficulties, especially in problems of large dimension. The method is realized in an experimental decision support system for finding the solution of linear mixed integer multicriteria optimization problems.

Weak Convergence to the Tangent Process of the Linear Multifractional Stable Motion

2000 Mathematics Subject Classification: 60G18, 60E07

Scalable harmonization of complex networks with local controllers

Computational and communication complexities call for distributed, robust, and adaptive control. This paper proposes a promising way of bottom-up design of distributed control in which simple controllers are responsible for individual nodes. The overall behavior of the network can be achieved by interconnecting such controlled loops in cascade control for example and by enabling the individual nodes to share information about data with their neighbors without aiming at unattainable global solution. The problem is addressed by employing a fully probabilistic design, which can cope with inherent uncertainties, that can be implemented adaptively and which provide a systematic rich way to information sharing. This paper elaborates the overall solution, applies it to linear-Gaussian case, and provides simulation results.

Towards probabilistic synchronization of local controllers

The traditional use of global and centralised control methods, fails for large, complex, noisy and highly connected systems, which typify many real world industrial and commercial systems. This paper provides an efficient bottom up design of distributed control in which many simple components communicate and cooperate to achieve a joint system goal. Each component acts individually so as to maximise personal utility whilst obtaining probabilistic information on the global system merely through local message-passing. This leads to an implied scalable and collective control strategy for complex dynamical systems, without the problems of global centralised control. Robustness is addressed by employing a fully probabilistic design, which can cope with inherent uncertainties, can be implemented adaptively and opens a systematic rich way to information sharing. This paper opens the foreseen direction and inspects the proposed design on a linearised version of coupled map lattice with spatiotemporal chaos. A version close to linear quadratic design gives an initial insight into possible behaviours of such networks.

Development of local homeland security networks in the state of Florida: A social network analysis approach

How do local homeland security organizations respond to catastrophic events such as hurricanes and acts of terrorism? Among the most important aspects of this response are these organizations ability to adapt to the uncertain nature of these "focusing events" (Birkland 1997). They are often behind the curve, seeing response as a linear process, when in fact it is a complex, multifaceted process that requires understanding the interactions between the fiscal pressures facing local governments, the institutional pressures of working within a new regulatory framework and the political pressures of bringing together different levels of government with different perspectives and agendas. ^ This dissertation has focused on tracing the factors affecting the individuals and institutions planning, preparing, responding and recovering from natural and man-made disasters. Using social network analysis, my study analyzes the interactions between the individuals and institutions that respond to these "focusing events." In practice, it is the combination of budgetary, institutional, and political pressures or constraints interacting with each other which resembles a Complex Adaptive System (CAS). ^ To investigate this system, my study evaluates the evolution of two separate sets of organizations composed of first responders (Fire Chiefs, Emergency Management Coordinators) and community volunteers organized in the state of Florida over the last fifteen years. Using a social network analysis approach, my dissertation analyzes the interactions between Citizen Corps Councils (CCCs) and Community Emergency Response Teams (CERTs) in the state of Florida from 1996–2011. It is the pattern of interconnections that occur over time that are the focus of this study. ^ The social network analysis revealed an increase in the amount and density of connections between these organizations over the last fifteen years. The analysis also exposed the underlying patterns in these connections; that as the networks became more complex they also became more decentralized though not in any uniform manner. The present study brings to light a story of how communities have adapted to the ever changing circumstances that are sine qua non of natural and man-made disasters.^

The impact of Round II Urban Empowerment Zones on local communities

In the United States, the federal Empowerment Zone (EZ) program aimed to create and retain business investment in poor communities and to encourage local hiring through the use of special tax credits, relaxed regulations, social service grants, and other incentives. My dissertation explores whether the Round II Urban EZs had a beneficial impact on local communities and what factors influenced the implementation and performance of the EZs, using three modes of inquiry. First, linear regression models investigate whether the federal revitalization program had a statistically significant impact on the creation of new businesses and jobs in Round II Urban EZ communities. Second, location quotient and shift-share analysis are used to reveal the industry clusters in three EZ communities that experienced positive business and job growth. Third, qualitative analysis is employed to explore factors that influenced the implementation and performance of EZs in general, and in particular, Miami-Dade County, Florida. The results show an EZ's presence failed to have a significant influence on local business and job growth. In communities that experienced a beneficial impact from EZs, there has been a pattern of decline in manufacturing companies and increase in service-driven firms. The case study suggests that institutional factors, such as governance structure, leadership, administrative capacity, and community participation have affected the effectiveness of the program's implementation and performance.