Searching edges in the overlap of two plane graphs

Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that enables efficient searches among the red-blue intersections along edges of one of the graphs. Our technique has a number of applications to geometric problems. This includes: (1) a solution to the batched red-blue search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an algorithm to compute the maximum vertical distance between a pair of 3D polyhedral terrains one of which is convex in O(n log n) time, where n is the total complexity of both terrains; (3) an algorithm to construct the Hausdorff Voronoi diagram of a family of point clusters in the plane in O((n+m) log^3 n) time and O(n+m) space, where n is the total number of points in all clusters and m is the number of crossings between all clusters; (4) an algorithm to construct the farthest-color Voronoi diagram of the corners of n axis-aligned rectangles in O(n log^2 n) time; (5) an algorithm to solve the stabbing circle problem for n parallel line segments in the plane in optimal O(n log n) time. All these results are new or improve on the best known algorithms.Comment: 22 pages, 6 figure

Citalopram-mediated anxiolysis and differing neurobiological responses in both sexes of a genetic model of depression

Disorders such as depression and anxiety exhibit strong sex differences in their prevalence and incidence, with women also differing from men in their response to antidepressants. Furthermore, receptors for corticotrophin releasing hormone (CRHR1) and arginine vasopressin receptor subtype 1b (AVPR1b) are known to contribute to the regulation of mood and anxiety. In the present study, we compared the anxiety profile and CRHR1 and AVPR1b expression levels in control Sprague–Dawley (SD) rats and rats of the SD-derived Flinders Sensitive Line (FSL), a genetic model of depression. Additionally, given the apparent sex differences in the therapeutic efficacy of antidepressants and because antidepressants are commonly used to treat comorbid anxiety and depressive symptoms, we assessed whether the anxiolytic effects of an antidepressant occur in a sex-dependent manner. Male and female FSL rats were treated with citalopram 10 mg/kg once daily for 14 days and were then tested in the open field and the elevated plus maze paradigms. Upon completion of the behavioural analysis, AVPR1b and CRHR1 expression levels were monitored in the hypothalamus and the prefrontal cortex (PFC) using Western blotting. According to our results, male FSL rats were more anxious than control SD rats, a difference abolished by citalopram treatment. Baseline anxiety levels were similar in female FSL and SD rats, and citalopram further reduced anxiety in female FSL rats. Importantly, whereas citalopram altered AVPR1b expression in the hypothalamus of male FSL rats, its actions on this parameter were restricted to the PFC in female FSL rats. In both sexes of FSL rats, citalopram did not alter CRHR1 expression in either the hypothalamus or PFC. Our results demonstrate that antidepressant treatment reduces anxiety levels in FSL rats of both sexes: the magnitude of treatment effect was related to the starting baseline level of anxiety and the antidepressant elicited sexually differentiated neurobiological responses in specific brain regions.This research was partly supported through a German-Greek Academic Exchange Programme (DAAD-IKYDA: D/04/42259), an IBRO studentship to N.K., and a Max Planck Society fellowship to I.S

Involved margins after lumpectomy for breast cancer: Always to be re-excised?

Background: The oncologic benefit of upfront re-excision of involved margins after breast-conserving surgery in the context of current multimodal clinical management of breast cancer is unclear. The aim of the present study was to assess the 5-years locoregional recurrence (LRR)-free and distant metastases (DM)-free survival probabilities in patients not undergoing re-excision of positive margins after lumpectomy for breast cancer. Methods: A cohort of 104 patients with positive margins not undergoing re-excision was matched by propensity score with a cohort of 2006 control patients with clear margins after breast-conserving surgery, treated between 2008 and 2018. A multivariate survival analysis was performed accounting for all variables related to LRR and DM, including adjuvant treatments. Results: After adjusting for potential confounders, avoiding to re-excise a positive margin after lumpectomy had no effect on 5-years LRR-free survival probability (HR 0.98, 95%CI 0.36-2.67, p = 0.96) or 5-years DM-free survival probability (HR 0.37, 95%CI 0.08-1.61, p = 0.18). No correlation was found between occurrence of LRR and number of involved margins (HR 1.28, 95%CI 0.10-12.4, Log-rank p = 0.83), or extension of infiltrating disease (HR 1.21, 95%CI 0.20-7.40, Log-rank p = 0.83), but a trend toward higher LRR probability was found for invasive ductal (HR 6.92, 95%CI 0.7-68.8, Log-rank p = 0.10) and invasive lobular cancer (HR 12.95, 95%CI 0.79-213.6, Log-rank p = 0.07) on positive margins. Conclusions: In the era of multimodal treatment of breast cancer and accurate strategies to reduce the probability of residual disease in the post-lumpectomy cavity, re-excision of positive margins might be omitted in selected patients with low-risk breast cancers

Acute and chronic stress differentially regulate cyclin-dependent kinase 5 in mouse brain: implications to glucocorticoid actions and major depression

Stress activates the hypothalamic–pituitary–adrenal axis, which in turn increases circulating glucocorticoid concentrations and stimulates the glucocorticoid receptor (GR). Chronically elevated glucocorticoids by repetitive exposure to stress are implicated in major depression and anxiety disorders. Cyclin-dependent kinase 5 (CDK5), a molecule essential for nervous system development, function and pathogenesis of neurodegenerative disorders, can modulate GR activity through phosphorylation. We examined potential contribution of CDK5 to stress response and pathophysiology of major depression. In mice, acute immobilized stress (AS) caused a biphasic effect on CDK5 activity, initially reducing but increasing afterwards in prefrontal cortex (PFC) and hippocampus (HIPPO), whereas chronic unpredictable stress (CS) strongly increased it in these brain areas, indicating that AS and CS differentially regulate this kinase activity in a brain region-specific fashion. GR phosphorylation contemporaneously followed the observed changes of CDK5 activity after AS, thus CDK5 may in part alter GR phosphorylation upon this stress. In the postmortem brains of subjects with major depression, CDK5 activity was elevated in Brodmann's area 25, but not in entire PFC and HIPPO. Messenger RNA expression of glucocorticoid-regulated/stress-related genes showed distinct expression profiles in several brain areas of these stressed mice or depressive subjects in which CDK5-mediated changes in GR phosphorylation may have some regulatory roles. Taken together, these results indicate that CDK5 is an integral component of stress response and major depression with regulatory means specific to different stressors, brain areas and diseases in part through changing phosphorylation of GR

Continuity of the von Neumann entropy

A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and to obtain several new conditions. The method is based on a particular approximation of the von Neumann entropy by an increasing sequence of concave continuous unitary invariant functions defined using decompositions into finite rank operators. The existence of this approximation is a corollary of a general property of the set of quantum states as a convex topological space called the strong stability property. This is considered in the first part of the paper.Comment: 42 pages, the minor changes have been made, the new applications of the continuity condition have been added. To appear in Commun. Math. Phy

Intravenous sodium nitrite in acute ST-elevation myocardial infarction: a randomized controlled trial (NIAMI).

AIM: Despite prompt revascularization of acute myocardial infarction (AMI), substantial myocardial injury may occur, in part a consequence of ischaemia reperfusion injury (IRI). There has been considerable interest in therapies that may reduce IRI. In experimental models of AMI, sodium nitrite substantially reduces IRI. In this double-blind randomized placebo controlled parallel-group trial, we investigated the effects of sodium nitrite administered immediately prior to reperfusion in patients with acute ST-elevation myocardial infarction (STEMI). METHODS AND RESULTS: A total of 229 patients presenting with acute STEMI were randomized to receive either an i.v. infusion of 70 μmol sodium nitrite (n = 118) or matching placebo (n = 111) over 5 min immediately before primary percutaneous intervention (PPCI). Patients underwent cardiac magnetic resonance imaging (CMR) at 6-8 days and at 6 months and serial blood sampling was performed over 72 h for the measurement of plasma creatine kinase (CK) and Troponin I. Myocardial infarct size (extent of late gadolinium enhancement at 6-8 days by CMR-the primary endpoint) did not differ between nitrite and placebo groups after adjustment for area at risk, diabetes status, and centre (effect size -0.7% 95% CI: -2.2%, +0.7%; P = 0.34). There were no significant differences in any of the secondary endpoints, including plasma troponin I and CK area under the curve, left ventricular volumes (LV), and ejection fraction (EF) measured at 6-8 days and at 6 months and final infarct size (FIS) measured at 6 months. CONCLUSIONS: Sodium nitrite administered intravenously immediately prior to reperfusion in patients with acute STEMI does not reduce infarct size

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur

Marine biodiversity and ecosystem function relationships: The potential for practical monitoring applications

Abstract There is an increasing demand for environmental assessments of the marine environment to include ecosystem function. However, existing schemes are predominantly based on taxonomic (i.e. structural) measures of biodiversity. Biodiversity and Ecosystem Function (BEF) relationships are suggested to provide a mechanism for converting taxonomic information into surrogates of ecosystem function. This review assesses the evidence for marine BEF relationships and their potential to be used in practical monitoring applications (i.e. operationalized). Five key requirements were identified for the practical application of BEF relationships: 1) a complete understanding of strength, direction and prevalence of marine BEF relationships, 2) an understanding of which biological components are influential within specific BEF relationships, 3) the biodiversity of the selected biological components can be measured easily, 4) the ecological mechanisms that are the most important for generating marine BEF relationships, i.e. identity effects or complementarity, are known and 5) the proportion of the overall functional variance is explained by biodiversity, and hence BEF relationships, has been established. Numerous positive and some negative BEF relationships were found within the literature, although many reproduced poorly the natural species richness, trophic structures or multiple functions of real ecosystems (requirement 1). Null relationships were also reported. The consistency of the positive and negative relationships was often low that compromised the ability to generalize BEF relationships and confident application of BEF within marine monitoring. Equally, some biological components and functions have received little or no investigation. Expert judgement was used to attribute biological components using spatial extent, presence and functional rate criteria (requirement 2). This approach highlighted the main biological components contributing the most to specific ecosystem functions, and that many of the particularly influential components were found to have received the least amount of research attention. The need for biodiversity to be measureable (requirement 3) is possible for most biological components although difficult within the functionally important microbes. Identity effects underpinned most marine BEF relationships (requirement 4). As such, processes that translated structural biodiversity measures into functional diversity were found to generate better BEF relationships. The analysis of the contribution made by biodiversity, over abiotic influences, to the total expression of a particular ecosystem function was rarely measured or considered (requirement 5). Hence it is not possible to determine the overall importance of BEF relationships within the total ecosystem functioning observed. In the few studies where abiotic factors had been considered, it was clear that these modified BEF relationships and have their own direct influence on functional rate. Based on the five requirements, the information required for immediate ‘operationalization’ of BEF relationships within marine functional monitoring is lacking. However, the concept of BEF inclusion within practical monitoring applications, supported by ecological modelling, shows promise for providing surrogate indicators of functioning

Dynamics of ghost domains in spin-glasses

We revisit the problem of how spin-glasses ``heal'' after being exposed to tortuous perturbations by the temperature/bond chaos effects in temperature/bond cycling protocols. Revised scaling arguments suggest the amplitude of the order parameter within ghost domains recovers very slowly as compared with the rate it is reduced by the strong perturbations. The parallel evolution of the order parameter and the size of the ghost domains can be examined in simulations and experiments by measurements of a memory auto-correlation function which exhibits a ``memory peak'' at the time scale of the age imprinted in the ghost domains. These expectations are confirmed by Monte Calro simulations of an Edwards-Anderson Ising spin-glass model.Comment: 17 pages, 3 figure

Local mean-field study of capillary condensation in silica aerogels

We apply local mean-field (i.e. density functional) theory to a lattice model of a fluid in contact with a dilute, disordered gel network. The gel structure is described by a diffusion-limited cluster aggregation model. We focus on the influence of porosity on both the hysteretic and the equilibrium behavior of the fluid as one varies the chemical potential at low temperature. We show that the shape of the hysteresis loop changes from smooth to rectangular as the porosity increases and that this change is associated to disorder-induced out-of-equilibrium phase transitions that differ on adsorption and on desorption. Our results provide insight in the behavior of $^4$He in silica aerogels.Comment: 19 figure