Nominal Logic with Equations Only

Many formal systems, particularly in computer science, may be captured by equations modulated by side conditions asserting the "freshness of names"; these can be reasoned about with Nominal Equational Logic (NEL). Like most logics of this sort NEL employs this notion of freshness as a first class logical connective. However, this can become inconvenient when attempting to translate results from standard equational logic to the nominal setting. This paper presents proof rules for a logic whose only connectives are equations, which we call Nominal Equation-only Logic (NEoL). We prove that NEoL is just as expressive as NEL. We then give a simple description of equality in the empty NEoL-theory, then extend that result to describe freshness in the empty NEL-theory.Comment: In Proceedings LFMTP 2011, arXiv:1110.668

Sequent Calculus in the Topos of Trees

Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of trees. We show that the semantics of the propositional fragment of this logic can be given by linear converse-well-founded intuitionistic Kripke frames, so this logic is a marriage of the intuitionistic modal logic KM and the intermediate logic LC. We therefore call this logic $\mathrm{KM}_{\mathrm{lin}}$. We give a sound and cut-free complete sequent calculus for $\mathrm{KM}_{\mathrm{lin}}$ via a strategy that decomposes implication into its static and irreflexive components. Our calculus provides deterministic and terminating backward proof-search, yields decidability of the logic and the coNP-completeness of its validity problem. Our calculus and decision procedure can be restricted to drop linearity and hence capture KM.Comment: Extended version, with full proof details, of a paper accepted to FoSSaCS 2015 (this version edited to fix some minor typos

Modal dependent type theory and dependent right adjoints

In recent years we have seen several new models of dependent type theory extended with some form of modal necessity operator, including nominal type theory, guarded and clocked type theory, and spatial and cohesive type theory. In this paper we study modal dependent type theory: dependent type theory with an operator satisfying (a dependent version of) the K-axiom of modal logic. We investigate both semantics and syntax. For the semantics, we introduce categories with families with a dependent right adjoint (CwDRA) and show that the examples above can be presented as such. Indeed, we show that any finite limit category with an adjunction of endofunctors gives rise to a CwDRA via the local universe construction. For the syntax, we introduce a dependently typed extension of Fitch-style modal lambda-calculus, show that it can be interpreted in any CwDRA, and build a term model. We extend the syntax and semantics with universes

Room-Temperature Distance Measurements of Immobilized Spin-Labeled Protein by DEER/PELDOR

Nitroxide spin labels are used for double electron-electron resonance (DEER) measurements of distances between sites in biomolecules. Rotation of gem-dimethyls in commonly used nitroxides causes spin echo dephasing times (Tm) to be too short to perform DEER measurements at temperatures between ∼80 and 295 K, even in immobilized samples. A spirocyclohexyl spin label has been prepared that has longer Tm between 80 and 295 K in immobilized samples than conventional labels. Two of the spirocyclohexyl labels were attached to sites on T4 lysozyme introduced by site-directed spin labeling. Interspin distances up to ∼4 nm were measured by DEER at temperatures up to 160 K in water/glycerol glasses. In a glassy trehalose matrix the Tm for the doubly labeled T4 lysozyme was long enough to measure an interspin distance of 3.2 nm at 295 K, which could not be measured for the same protein labeled with the conventional 1-oxyl-2,2,5,5-tetramethyl-3-pyrroline-3- (methyl)methanethio-sulfonate label

Room-Temperature Distance Measurements of Immobilized Spin-Labeled Protein by DEER/PELDOR

Nitroxide spin labels are used for double electron-electron resonance (DEER) measurements of distances between sites in biomolecules. Rotation of gem-dimethyls in commonly used nitroxides causes spin echo dephasing times (Tm) to be too short to perform DEER measurements at temperatures between ∼80 and 295 K, even in immobilized samples. A spirocyclohexyl spin label has been prepared that has longer Tm between 80 and 295 K in immobilized samples than conventional labels. Two of the spirocyclohexyl labels were attached to sites on T4 lysozyme introduced by site-directed spin labeling. Interspin distances up to ∼4 nm were measured by DEER at temperatures up to 160 K in water/glycerol glasses. In a glassy trehalose matrix the Tm for the doubly labeled T4 lysozyme was long enough to measure an interspin distance of 3.2 nm at 295 K, which could not be measured for the same protein labeled with the conventional 1-oxyl-2,2,5,5-tetramethyl-3-pyrroline-3- (methyl)methanethio-sulfonate label

Incidence of mild cognitive impairment in World Trade Center responders: Long-term consequences of re-experiencing the events on 9/11/2001

Objective: This study examined whether World Trade Center (WTC) exposures and chronic posttraumatic stress disorder (PTSD) were associated with incidence of mild cognitive impairment (MCI) in a longitudinal analysis of a prospective cohort study of WTC responders. Methods: Incidence of MCI was assessed in a clinical sample of WTC responders (N = 1800) who were cognitively intact at baseline assessment. Crude incidence rates were calculated and compared to population estimates using standardized incidence ratios. Multivariable analyses used Cox proportional-hazards regression. Results: Responders were 53.1 years old (SD = 7.9) at baseline. Among eligible cognitively intact responders, 255 (14.2%) developed MCI at follow-up. Incidence of MCI was higher than expected based on expectations from prior published research. Incidence was higher among those with increased PTSD symptom severity, and prolonged exposure was a risk factor in apolipoprotein-ε4 carriers. Conclusions: PTSD and prolonged WTC exposures were associated with increased incidence of MCI in WTC responders, results that may portend future high rates of dementia in WTC-exposed responders

Association between an Internet-Based Measure of Area Racism and Black Mortality

Racial disparities in health are well-documented and represent a significant public health concern in the US. Racism-related factors contribute to poorer health and higher mortality rates among Blacks compared to other racial groups. However, methods to measure racism and monitor its associations with health at the population-level have remained elusive. In this study, we investigated the utility of a previously developed Internet search-based proxy of area racism as a predictor of Black mortality rates. Area racism was the proportion of Google searches containing the “N-word” in 196 designated market areas (DMAs). Negative binomial regression models were specified taking into account individual age, sex, year of death, and Census region and adjusted to the 2000 US standard population to examine the association between area racism and Black mortality rates, which were derived from death certificates and mid-year population counts collated by the National Center for Health Statistics (2004–2009). DMAs characterized by a one standard deviation greater level of area racism were associated with an 8.2% increase in the all-cause Black mortality rate, equivalent to over 30,000 deaths annually. The magnitude of this effect was attenuated to 5.7% after adjustment for DMA-level demographic and Black socioeconomic covariates. A model controlling for the White mortality rate was used to further adjust for unmeasured confounders that influence mortality overall in a geographic area, and to examine Black-White disparities in the mortality rate. Area racism remained significantly associated with the all-cause Black mortality rate (mortality rate ratio = 1.036; 95% confidence interval = 1.015, 1.057; p = 0.001). Models further examining cause-specific Black mortality rates revealed significant associations with heart disease, cancer, and stroke. These findings are congruent with studies documenting the deleterious impact of racism on health among Blacks. Our study contributes to evidence that racism shapes patterns in mortality and generates racial disparities in health

Comparison of [(11)C]choline positron emission tomography with T2- and diffusion-weighted magnetic resonance imaging for delineating malignant intraprostatic lesions

Purpose: To compare the accuracy of ¹¹C-choline (CHOL) positron emission tomography (PET) with the combination of T2-weighted (T2W) and diffusion-weighted (DW) magnetic resonance imaging (MRI) for delineating malignant intraprostatic lesions (IPLs) for guiding focal therapies and to investigate factors predicting the accuracy of CHOL-PET. Methods and Materials: This study included 21 patients who underwent CHOL-PET and T2W-/DW-MRI prior to radical prostatectomy. Two observers manually delineated IPL contours for each scan, and automatic IPL contours were generated on CHOL-PET based on varying proportions of the maximum standardized uptake value (SUV). IPLs identified on prostatectomy specimens defined the reference standard contours. The imaging-based contours were compared with the reference standard contours using Dice similarity coefficient (DSC), sensitivity and specificity. Factors that could potentially predict the DSC of the best contouring method were analyzed using linear models. Results: The best automatic contouring method, SUV60, had similar correlations (DSC 0.59) with the manual PET contours (DSC 0.52, P=0.127) and significantly better correlations than the manual MRI contours (DSC 0.37, P<0.001). The sensitivity and specificity values were 72% and 71% for SUV60; 53% and 86% for PET manual contouring; and 28% and 92% for MRI manual contouring. The tumor volume and transition zone pattern could independently predict the accuracy of CHOL-PET. Conclusions: CHOL-PET is superior to the combination of T2W- and DW-MRI for delineating IPLs. The accuracy of CHOL-PET is insufficient for gland-sparing focal therapies, 3 however may be accurate enough for focal boost therapies. The transition zone pattern is a new classification that may predict for how well CHOL-PET delineates IPLs.Joe H. Chang, Daryl Lim Joon, Ian D. Davis, Sze Ting Lee, Chee-Yan Hiew, Stephen Esler, Sylvia J. Gong, Morikatsu Wada, David Clouston, Richard O'Sullivan, Yin P. Goh, Damien Bolton, Andrew M. Scott, Vincent Kho