Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

A Compact Tetrathiafulvalene-Benzothiadiazole Dyad and Its Highly Symmetrical Charge-Transfer Salt: Ordered Donor π-Stacks Closely Bound to Their Acceptors

A compact and planar donor–acceptor molecule 1 comprising tetrathiafulvalene (TTF) and benzothiadiazole (BTD) units has been synthesised and experimentally characterised by structural, optical, and electrochemical methods. Solution-processed and thermally evaporated thin films of 1 have also been explored as active materials in organic field-effect transistors (OFETs). For these devices, hole field-effect mobilities of μFE=(1.3±0.5)×10−3 and (2.7±0.4)×10−3 cm2 V s−1 were determined for the solution-processed and thermally evaporated thin films, respectively. An intense intramolecular charge-transfer (ICT) transition at around 495 nm dominates the optical absorption spectrum of the neutral dyad, which also shows a weak emission from its ICT state. The iodine-induced oxidation of 1 leads to a partially oxidised crystalline charge-transfer (CT) salt {(1)2I3}, and eventually also to a fully oxidised compound {1I3}⋅1/2I2. Single crystals of the former CT compound, exhibiting a highly symmetrical crystal structure, reveal a fairly good room temperature electrical conductivity of the order of 2 S cm−1. The one-dimensional spin system bears compactly bonded BTD acceptors (spatial localisation of the LUMO) along its ridge.

Consistent estimation of the fixed effects ordered logit model

The paper considers panel data methods for estimating ordered logit models with individual-specific correlated unobserved heterogeneity. We show that a popular approach is inconsistent, whereas some consistent and efficient estimators are available, including minimum distance and generalized method-of-moment estimators. A Monte Carlo study reveals the good properties of an alternative estimator that has not been considered in econometric applications before, is simple to implement and almost as efficient. An illustrative application based on data from the German Socio-Economic Panel confirms the large negative effect of unemployment on life satisfaction that has been found in the previous literature.

Identification and estimation of thresholds in the fixed effects ordered logit model

This paper proposes a new estimator for the fixed effects ordered logit model. In contrast to existing methods, the new procedure allows estimating the thresholds. The empirical relevance and simplicity of implementation is illustrated in an application on the effect of unemployment on life satisfaction.

Disentangling mental imagery and perceptual expectation

Mental imagery and perception are thought to rely on similar neural circuits, and many recent behavioral studies have attempted to demonstrate interactions between actual physical stimulation and sensory imagery in the corresponding sensory modality. However, there has been a lack of theoretical understanding of the nature of these interactions, and both interferential and facilitatory effects have been found. Facilitatory effects appear strikingly similar to those that arise due to experimental manipulations of expectation. Using a self-motion discrimination task, we try to disentangle the effects of mental imagery from those of expectation by using a hierarchical drift diffusion model to investigate both choice data and response times. Manipulations of expectation are reasonably well understood in terms of their selective influence on parameters of the drift diffusion model, and in this study, we make the first attempt to similarly characterize the effects of mental imagery. We investigate mental imagery within the computational framework of control theory and state estimation. • Mental imagery and perception are thought to rely on similar neural circuits; however, on more theoretical grounds, imagery seems to be closely related to the output of forward models (sensory predictions). • We reanalyzed data from a study of imagined self-motion. • Bayesian modeling of response times may allow us to disentangle the effects of mental imagery on behavior from other cognitive (top-down) effects, such as expectation.

Longitudinal Telomere Erosion in Lymphocyte Subsets of Patients with Atherosclerotic Peripheral Arterial Disease (PAD).

Telomere attrition has been linked to accelerate vascular ageing and seems to predispose for vascular disease. Our aim was to study the telomere length dynamics over time and in subsets of leukocytes from 15 patients with peripheral arterial disease (PAD). The mean telomere length in subsets of leukocytes of patients with PAD was in the normal range of age-related telomere length values from healthy individuals. However, we found significant higher telomere attrition for T-cells from patients with PAD over a time period of six months when compared to the controls. The higher telomere loss in T-cells of patients with PAD most likely reflects a higher cell turnover of this leukocyte subset, which is involved in the process of chronic inflammatory disease underlying vascular disease. Further studies are needed to confirm these data and to assess how far this T-cell telomere attrition will correlate to the extent of the disease.

A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

Shadow Profit Maximization and a Generalized Measure of Inefficiency

Determining the profit maximizing input-output bundle of a firm requires data on prices. This paper shows how endogenously determined shadow prices can be used in place of actual prices to obtain the optimal input-output bundle where the firm.s shadow profit is maximized. This approach amounts to an application of the Weak Axiom of Profit Maximization (WAPM) formulated by Varian (1984) based on shadow prices rather than actual prices. At these prices the shadow profit of a firm is zero. Thus, the maximum profit that could have been attained at some other input-output bundle is a measure of the inefficiency of the firm. Because the benchmark input-output bundle is always an observed bundle from the data, it can be determined without having to solve any elaborate programming problem. An empirical application to U.S. airlines data illustrates the proposed methodology.

THE RELATIONSHIP OF PRESCRIPTION RECEIPT AND EXPECTATION OF SICK-ROLE LEGITIMATION BY AMBULATORY VETERANS

This study explored the relationship of attitudes, needs, and health services utilization patterns of elderly veterans who were identified and categorized by their expectation for and receipt of sick-role legitimation. Three prescription types (new, change, renewal) were defined as the operational variables. A population of 676 ambulatory, chronically ill (average age 60 years) veterans were sent a questionnaire (74% response rate). In addition, retrospective medical and prescription record review was performed for a 45% sample of respondents. The results were analyzed using discriminant function and regression analysis. Fewer than 20% of the veterans responding expected to receive more prescriptions than were presently prescribed, whereas over 80% expected refill authorizations. Distinct attitudinal, need, and utilization patterns were identified. ^

The prevalence of periodontal disease in Mexican American vs European American elderly in three distinct socio-economic communities in San Antonio, Texas

Purpose of the Study: This study evaluated the prevalence of periodontal disease between Mexican American elderly and European American elderly residing in three socio-economically distinct neighborhoods in San Antonio, Texas. ^ Study Group: Subjects for the original protocol were participants of the Oral Health: San Antonio Longitudinal Study of Aging (OH: SALSA), which began with National Institutes of Health (NIH) funding in 1993 (M.J. Saunders, PI). The cohort in the study was the individuals who had been enrolled in Phases I and III of the San Antonio Heart Study (SAHS). This SAHS/SALSA sample is a community-based probability sample of Mexican American and European American residents from three socio-economically distinct San Antonio neighborhoods: low-income barrio, middle-income transitional, and upper-income suburban. The OH: SALSA cohort was established between July 1993 and May 1998 by sampling two subsets of the San Antonio Heart Study (SAHS) cohort. These subsets included the San Antonio Longitudinal Study of Aging (SALSA) cohort, comprised of the oldest members of the SAHS (age 65+ yrs. old), and a younger set of controls (age 35-64 yrs. old) sampled from the remainder of the SAHS cohort. ^ Methods: The study used simple descriptive statistics to describe the sociodemographic characteristics and periodontal disease indicators of the OH: SALSA participants. Means and standard deviations were used to summarize continuous measures. Proportions were used to summarize categorical measures. Simple m x n chi square statistics was used to compare ethnic differences. A multivariable ordered logit regression was used to estimate the prevalence of periodontal disease and test ethnic group and neighborhood differences in the prevalence of periodontal disease. A multivariable model adjustment for socio-economic status (income and education), gender, and age (treated as confounders) was applied. ^ Summary: In the unadjusted and adjusted model, Mexican American elderly demonstrated the greatest prevalence for periodontitis, p < 0.05. Mexican American elderly in barrio neighborhoods demonstrated the greatest prevalence for severe periodontitis, with unadjusted prevalence rates of 31.7%, 22.3%, and 22.4% for Mexican American elderly barrio, transitional, and suburban neighborhoods, respectively. Also, Mexican American elderly had adjusted prevalence rates of 29.4%, 23.7%, and 20.4% for barrio, transitional, and suburban neighborhoods, respectively. ^ Conclusion: This study indicates that the prevalence of periodontal disease is an important oral health issue among the Mexican American elderly. The results suggest that the socioeconomic status of the residential neighborhood increased the risk for severe periodontal disease among the Mexican American elderly when compared to European American elderly. A viable approach to recognizing oral health disparities in our growing population of Mexican American elderly is imperative for the provision of special care programs that will help increase the quality of care in this minority population.^

Critical aspects of substrate nanopatterning for the ordered growth of GaN nanocolumns.

Precise and reproducible surface nanopatterning is the key for a successful ordered growth of GaN nanocolumns. In this work, we point out the main technological issues related to the patterning process, mainly surface roughness and cleaning, and mask adhesion to the substrate. We found that each of these factors, process-related, has a dramatic impact on the subsequent selective growth of the columns inside the patterned holes. We compare the performance of e-beam lithography, colloidal lithography, and focused ion beam in the fabrication of hole-patterned masks for ordered columnar growth. These results are applicable to the ordered growth of nanocolumns of different materials.