A General Theory of Semi-Unification

Various restrictions on the terms allowed for substitution give rise to different cases of semi-unification. Semi-unification on finite and regular terms has already been considered in the literature. We introduce a general case of semi-unification where substitutions are allowed on non-regular terms, and we prove the equivalence of this general case to a well-known undecidable data base dependency problem, thus establishing the undecidability of general semi-unification. We present a unified way of looking at the various problems of semi-unification. We give some properties that are common to all the cases of semi-unification. We also the principality property and the solution set for those problems. We prove that semi-unification on general terms has the principality property. Finally, we present a recursive inseparability result between semi-unification on regular terms and semi-unification on general terms.

A Neural Theory of Visual Search: Recursive Attention to Segmentations and Surfaces

A neural theory is proposed in which visual search is accomplished by perceptual grouping and segregation, which occurs simultaneous across the visual field, and object recognition, which is restricted to a selected region of the field. The theory offers an alternative hypothesis to recently developed variations on Feature Integration Theory (Treisman, and Sato, 1991) and Guided Search Model (Wolfe, Cave, and Franzel, 1989). A neural architecture and search algorithm is specified that quantitatively explains a wide range of psychophysical search data (Wolfe, Cave, and Franzel, 1989; Cohen, and lvry, 1991; Mordkoff, Yantis, and Egeth, 1990; Treisman, and Sato, 1991).

A Neural Theory of Attentive Visual Search: Interactions of Boundary, Surface, Spatial, and Object Representations

Visual search data are given a unified quantitative explanation by a model of how spatial maps in the parietal cortex and object recognition categories in the inferotemporal cortex deploy attentional resources as they reciprocally interact with visual representations in the prestriate cortex. The model visual representations arc organized into multiple boundary and surface representations. Visual search in the model is initiated by organizing multiple items that lie within a given boundary or surface representation into a candidate search grouping. These items arc compared with object recognition categories to test for matches or mismatches. Mismatches can trigger deeper searches and recursive selection of new groupings until a target object io identified. This search model is algorithmically specified to quantitatively simulate search data using a single set of parameters, as well as to qualitatively explain a still larger data base, including data of Aks and Enns (1992), Bravo and Blake (1990), Chellazzi, Miller, Duncan, and Desimone (1993), Egeth, Viri, and Garbart (1984), Cohen and Ivry (1991), Enno and Rensink (1990), He and Nakayarna (1992), Humphreys, Quinlan, and Riddoch (1989), Mordkoff, Yantis, and Egeth (1990), Nakayama and Silverman (1986), Treisman and Gelade (1980), Treisman and Sato (1990), Wolfe, Cave, and Franzel (1989), and Wolfe and Friedman-Hill (1992). The model hereby provides an alternative to recent variations on the Feature Integration and Guided Search models, and grounds the analysis of visual search in neural models of preattentive vision, attentive object learning and categorization, and attentive spatial localization and orientation.

Laminar Cortical Dynamics of Cognitive and Motor Working Memory, Sequence Learning and Performance: Toward a Unified Theory of How the Cerebral Cortex Works

How do the layered circuits of prefrontal and motor cortex carry out working memory storage, sequence learning, and voluntary sequential item selection and performance? A neural model called LIST PARSE is presented to explain and quantitatively simulate cognitive data about both immediate serial recall and free recall, including bowing of the serial position performance curves, error-type distributions, temporal limitations upon recall, and list length effects. The model also qualitatively explains cognitive effects related to attentional modulation, temporal grouping, variable presentation rates, phonemic similarity, presentation of non-words, word frequency/item familiarity and list strength, distracters and modality effects. In addition, the model quantitatively simulates neurophysiological data from the macaque prefrontal cortex obtained during sequential sensory-motor imitation and planned performance. The article further develops a theory concerning how the cerebral cortex works by showing how variations of the laminar circuits that have previously clarified how the visual cortex sees can also support cognitive processing of sequentially organized behaviors.

Towards a Unified Theory of Neocortex: Laminar Cortical Circuits for Vision and Cognition

A key goal of computational neuroscience is to link brain mechanisms to behavioral functions. The present article describes recent progress towards explaining how laminar neocortical circuits give rise to biological intelligence. These circuits embody two new and revolutionary computational paradigms: Complementary Computing and Laminar Computing. Circuit properties include a novel synthesis of feedforward and feedback processing, of digital and analog processing, and of pre-attentive and attentive processing. This synthesis clarifies the appeal of Bayesian approaches but has a far greater predictive range that naturally extends to self-organizing processes. Examples from vision and cognition are summarized. A LAMINART architecture unifies properties of visual development, learning, perceptual grouping, attention, and 3D vision. A key modeling theme is that the mechanisms which enable development and learning to occur in a stable way imply properties of adult behavior. It is noted how higher-order attentional constraints can influence multiple cortical regions, and how spatial and object attention work together to learn view-invariant object categories. In particular, a form-fitting spatial attentional shroud can allow an emerging view-invariant object category to remain active while multiple view categories are associated with it during sequences of saccadic eye movements. Finally, the chapter summarizes recent work on the LIST PARSE model of cognitive information processing by the laminar circuits of prefrontal cortex. LIST PARSE models the short-term storage of event sequences in working memory, their unitization through learning into sequence, or list, chunks, and their read-out in planned sequential performance that is under volitional control. LIST PARSE provides a laminar embodiment of Item and Order working memories, also called Competitive Queuing models, that have been supported by both psychophysical and neurobiological data. These examples show how variations of a common laminar cortical design can embody properties of visual and cognitive intelligence that seem, at least on the surface, to be mechanistically unrelated.

Theory of elasticity and electric polarization effects in the group-III nitrides

In this work, the properties of strained tetrahedrally bonded materials are explored theoretically, with special focus on group-III nitrides. In order to do so, a multiscale approach is taken: accurate quantitative calculations of material properties are carried out in a quantum first-principles frame, for small systems. These properties are then extrapolated and empirical methods are employed to make predictions for larger systems, such as alloys or nanostructures. We focus our attention on elasticity and electric polarization in semiconductors. These quantities serve as input for the calculation of the optoelectronic properties of these systems. Regarding the methods employed, our first-principles calculations use highly- accurate density functional theory (DFT) within both standard Kohn-Sham and generalized (hybrid functional) Kohn-Sham approaches. We have developed our own empirical methods, including valence force field (VFF) and a point-dipole model for the calculation of local polarization and local polarization potential. Our local polarization model gives insight for the first time to local fluctuations of the electric polarization at an atomistic level. At the continuum level, we have studied composition-engineering optimization of nitride nanostructures for built-in electrostatic field reduction, and have developed a highly efficient hybrid analytical-numerical staggered-grid computational implementation of continuum elasticity theory, that is used to treat larger systems, such as quantum dots.

Accommodating interruptions: a grounded theory of young people with asthma

Background: Accommodating Interruptions is a theory that emerged in the context of young people who have asthma. A background to the prevalence and management of asthma in Ireland is given to situate the theory. Ireland has the fourth highest incidence of asthma in the world, with almost one in five Irish young people having asthma. Although national and international asthma management guidelines exist it is accepted that the symptom control of asthma among the young people population is poor. Aim: The aim of this research is to investigate the lives of young people who have asthma, to allow for a deeper understanding of the issues affecting them. Methods: This research was undertaken using a Classic Grounded Theory approach. It is a systematic approach to allowing conceptual emergence from data in generating a theory that explains behaviour in resolving the participant’s main concern. The data were collected through in-depth interviews with young people aged 11-16 years who had asthma for over one year. Data were also collected from participant diaries. Constant comparative analysis, theoretical coding and memo writing were used to develop the theory. Results: The theory explains how young people resolve their main concern of being restricted, by maximizing their participation and inclusion in activities, events and relationships in spite of their asthma. They achieve this by accommodating interruptions in their lives in minimizing the effects of asthma on their everyday lives. Conclusion: The theory of accommodating interruptions explains young people’s asthma management behaviours in a new way. It allows us to understand how and why young people behave the way they do in order minimise the effect of asthma on their lives. The theory adds to the body of knowledge on young people with asthma and challenges some viewpoints regarding their behaviours.

Anticipatory vigilance: A classic grounded theory of risk reduction and management in the perioperative setting

This research aimed to investigate the main concern facing nurses in minimising risk within the perioperative setting and to generate an explanatory substantive theory of how they resolve this through anticipatory vigilance. In the context of the perioperative setting, nurses encounter challenges in minimising risks for their patients on a continuous basis. Current explanations of minimising risk in the perioperative setting offers insights into how perioperative nurses undertake their work. Currently research in minimising risk is broadly related to dealing with errors as opposed to preventing them. To date, little is known about how perioperative nurses practice and maintain safety. This study was guided by the principles of classic grounded theory as described by Glaser (1978, 1998, 2001). Data was collected through individual unstructured interviews with thirty seven perioperative nurses (with varying lengths of experiences of working in the area) and thirty three hours of non-participant observation within eight different perioperative settings in the Republic of Ireland. Data was simultaneously collected and analysed. The theory of anticipatory vigilance emerged as the pattern of behaviour through which nurse’s deal with their main concern of minimising risk in a high risk setting. Anticipatory vigilance is enacted through orchestrating, routinising and momentary adapting within a spirit of trusting relations within the substantive area of the perioperative setting. This theory of offers an explanation on how nurses resolve their main concern of minimising risk within the perioperative setting. The theory of anticipatory vigilance will be useful to nurses in providing a comprehensive framework of explanation and understanding on how nurses deal with minimising risk in the perioperative setting. The theory links perioperative nursing, risk and vigilance together. Clinical improvements through understanding and awareness of the theory of anticipatory vigilance will result in an improved quality environment, leading to safe patient outcomes.

Moral shielding: A grounded theory of integrity maintenance in multidisciplinary teams

Using a classic grounded theory methodology (CGT), this study explores the phenomenon of moral shielding within mental health multidisciplinary teams (MDTS). The study was located within three catchment areas engaged in acute mental health service practice. The main concern identified was the maintenance of a sense of personal integrity during situational binds. Through theoretical sampling thirty two practitioners, including; doctors, nurses, social workers, occupational therapists, counsellors and psychologists, where interviewed face to face. In addition, emergent concepts were identified through observation of MDTs in clinical and research practice. Following a classic grounded theory methodology, data collection and analysis occurred simultaneously. A constant comparative approach was adopted and resulted in the immergence of three sub- core categories; moral abdication, moral hinting and pseudo-compliance. Moral abdication seeks to re-position within an event in order to avoid or deflect the initial obligation to act, it is a strategy used to remove or reduce moral ownership. Moral gauging represents the monitoring of an event with the goal of judging the congruence of personal principles and commitments with that of other practitioners. This strategy is enacted in a bid to seek allies for the support of a given moral position. Pseudo-compliance represents behaviour that hides desired principles and commitments in order to shield them from challenge. This strategy portrays agreement with the dominant position within the MDT, whilst holding a contrary position. It seeks to preserve a reservoir of emotional energy required to maintain a sense of personal integrity. Practitioners who were successful in enacting moral shielding were found to not experience significant emotional distress associated with the phenomenon of moral distress; suggesting that these practitioners had found mechanisms to manage situational binds that threatened their sense of personal integrity.

Theory of the electronic and optical properties of dilute bismide alloys

Dilute bismide alloys, containing small fractions of bismuth (Bi), have recently attracted interest due to their potential for applications in a range of semiconductor devices. Experiments have revealed that dilute bismide alloys such as GaBixAs1−x, in which a small fraction x of the atoms in the III-V semiconductor GaAs are replaced by Bi, exhibit a number of unusual and unique properties. For example, the band gap energy (E g) decreases rapidly with increasing Bi composition x, by up to 90 meV per % Bi replacing As in the alloy. This band gap reduction is accompanied by a strong increase in the spin-orbit-splitting energy (ΔSO) with increasing x, and both E g and ΔSO are characterised by strong, composition-dependent bowing. The existence of a ΔSO > E g regime in the GaBixAs1−x alloy has been demonstrated for x ≳10%, a band structure condition which is promising for the development of highly efficient, temperature stable semiconductor lasers that could lead to large energy savings in future optical communication networks. In addition to their potential for specific applications, dilute bismide alloys have also attracted interest from a fundamental perspective due to their unique properties. In this thesis we develop the theory of the electronic and optical properties of dilute bismide alloys. By adopting a multi-scale approach encompassing atomistic calculations of the electronic structure using the semi-empirical tight-binding method, as well as continuum calculations based on the k•p method, we develop a fundamental understanding of this unusual class of semiconductor alloys and identify general material properties which are promising for applications in semiconductor optoelectronic and photovoltaic devices. By performing detailed supercell calculations on both ordered and disordered alloys we explicitly demonstrate that Bi atoms act as isovalent impurities when incorporated in dilute quantities in III-V (In)GaAs(P) materials, strongly perturbing the electronic structure of the valence band. We identify and quantify the causes and consequences of the unusual electronic properties of GaBixAs1−x and related alloys, and our analysis is reinforced throughout by a series of detailed comparisons to the results of experimental measurements. Our k•p models of the band structure of GaBixAs1−x and related alloys, which we derive directly from detailed atomistic calculations, are ideally suited to the study of dilute bismide-based devices. We focus in the latter part of the thesis on calculations of the electronic and optical properties of dilute bismide quantum well lasers. In addition to developing an understanding of the effects of Bi incorporation on the operational characteristics of semiconductor lasers, we also present calculations which have been used explicitly in designing and optimising the first generation of GaBixAs1−x-based devices.

A theory of buyer-seller networks

This paper introduces a new model of exchange: networks, rather than markets, of buyers and sellers. It begins with the empirically motivated premise that a buyer and seller must have a relationship, a "link," to exchange goods. Networks - buyers, sellers, and the pattern of links connecting them - are common exchange environments. This paper develops a methodology to study network structures and explains why agents may form networks. In a model that captures characteristics of a variety of industries, the paper shows that buyers and sellers, acting strategically in their own self-interests, can form the network structures that maximize overall welfare.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Modeling the evolution of regulatory elements by simultaneous detection and alignment with phylogenetic pair HMMs.

The computational detection of regulatory elements in DNA is a difficult but important problem impacting our progress in understanding the complex nature of eukaryotic gene regulation. Attempts to utilize cross-species conservation for this task have been hampered both by evolutionary changes of functional sites and poor performance of general-purpose alignment programs when applied to non-coding sequence. We describe a new and flexible framework for modeling binding site evolution in multiple related genomes, based on phylogenetic pair hidden Markov models which explicitly model the gain and loss of binding sites along a phylogeny. We demonstrate the value of this framework for both the alignment of regulatory regions and the inference of precise binding-site locations within those regions. As the underlying formalism is a stochastic, generative model, it can also be used to simulate the evolution of regulatory elements. Our implementation is scalable in terms of numbers of species and sequence lengths and can produce alignments and binding-site predictions with accuracy rivaling or exceeding current systems that specialize in only alignment or only binding-site prediction. We demonstrate the validity and power of various model components on extensive simulations of realistic sequence data and apply a specific model to study Drosophila enhancers in as many as ten related genomes and in the presence of gain and loss of binding sites. Different models and modeling assumptions can be easily specified, thus providing an invaluable tool for the exploration of biological hypotheses that can drive improvements in our understanding of the mechanisms and evolution of gene regulation.

Hannah Arendt's Theory of Political Judgment

Hannah Arendt's theory of political judgment has been an ongoing perplexity among scholars who have written on her. As a result, her theory of judgment is often treated as a suggestive but unfinished aspect of her thought. Drawing on a wider array of sources than is commonly utilized, I argue that her theory of political judgment was in fact the heart of her work. Arendt's project, in other words, centered around reestablishing the possibility of political judgment in a modern world that historically has progressively undermined it. In the dissertation, I systematically develop an account of Arendt's fundamentally political and non-sovereign notion of judgment. We discover that individual judgment is not arbitrary, and that even in the complex circumstances of the modern world there are valid structures of judgment which can be developed and dependably relied upon. The result of this work articulates a theory of practical reason which is highly compelling: it provides orientation for human agency which does not rob it of its free and spontaneous character; shows how we can improve and cultivate our political judgment; and points the way toward the profoundly intersubjective form of political philosophy Arendt ultimately hoped to develop.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.