Algebra and the Complexity of Digraph CSPs: a Survey

We present a brief survey of some of the key results on the interplay between algebraic and graph-theoretic methods in the study of the complexity of digraph-based constraint satisfaction problems

The complexity of the list homomorphism problem for graphs

We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is first-order definable; descriptive complexity equivalents are given as well via Datalog and its fragments. Our algebraic characterisations match important conjectures in the study of constraint satisfaction problems.Comment: 12 pages, STACS 201

Dismantlability, connectedness, and mixing in relational structures

The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, and elsewhere. Its structural and algorithmic properties have demonstrated to play a crucial role in many of those applications. For instance, in the decision CSPs, structural properties of the relational structures involved---like, for example, dismantlability---and their logical characterizations have been instrumental for determining the complexity and other properties of the problem. Topological properties of the solution set such as connectedness are related to the hardness of CSPs over random structures. Additionally, in approximate counting and statistical physics, where CSPs emerge in the form of spin systems, mixing properties and the uniqueness of Gibbs measures have been heavily exploited for approximating partition functions and free energy. In spite of the great diversity of those features, there are some eerie similarities between them. These were observed and made more precise in the case of graph homomorphisms by Brightwell and Winkler, who showed that dismantlability of the target graph, connectedness of the set of homomorphisms, and good mixing properties of the corresponding spin system are all equivalent. In this paper we go a step further and demonstrate similar connections for arbitrary CSPs. This requires much deeper understanding of dismantling and the structure of the solution space in the case of relational structures, and new refined concepts of mixing introduced by Brice\~no. In addition, we develop properties related to the study of valid extensions of a given partially defined homomorphism, an approach that turns out to be novel even in the graph case. We also add to the mix the combinatorial property of finite duality and its logic counterpart, FO-definability, studied by Larose, Loten, and Tardif.Comment: 27 pages, full version of the paper accepted to ICALP 201

Skalans betydelse vid utformning av stadsrum

When one experiences a place, it is a complex composition of both social and spatial factors. One of these spatial elements, is scale, which is influenced both by the room size and its proportions. This paper aims to explore both large and small scale concepts and thus increase the understanding of how scale directly and indirectly affects the experiences and uses of urban space. First, is a theoretical discussion of scale in relation to aesthetics and the differences between real scale and perceived scale. Next, is an analysis of spatial perception using examples from two existing sites. One, which is understood to have been planned in a large scale and one which is understood to have been planned in a small scale. When preparing this paper, the focus quickly became the importance of scale as it relates to street spaces. The perception of a street usually takes place while in motion, which forces it to be perceived in sections. Depending on the design, these sections can create an experience of the street space that could be large, small or diverse. The key to creating interesting environments is to find the right balance between variation in scale and richness in details

Correlates of coronary artery calcification prevalence and severity in patients with heterozygous familial hypercholesterolemia

Background Determinants of coronary artery calcification (CAC) prevalence and severity in heterozygous familial hypercholesterolemia (HeFH) remain understudied. The objective of this cross-sectional study was to investigate correlates of CAC in patients with HeFH. Methods A CAC score was calculated by a noncontrast computed tomography scan in women (n = 68) and men (n = 78) with genetically defined HeFH. We classified CAC prevalence and severity using 3 categories: CAC score = 0 Agatston Unit (AU), CAC score = 1-100 AU, and CAC score > 100 AU. Information on potential correlates of CAC including familial and personal health history, cardiovascular risk factors, lipid-lowering medication, and lifestyle habits was collected. Results A total of 95 patients had prevalent CAC. Independent correlates of CAC prevalence and severity included age (odds ratio [OR] per 10 years: 5.06, 95% confidence interval [CI]: 3.19, 7.93, P < 0.0001), family history of premature cardiovascular disease (OR: 3.88, 95% CI: 1.71, 8.81, P = 0.001), male sex (OR: 3.40, 95% CI: 1.49, 7.78, P = 0.004), statin use (OR: 15.5, 95% CI: 1.89, 126, P = 0.01), diet quality assessed with the Alternative Healthy Eating Index score (OR per 1 standard deviation: 0.59, 95% CI: 0.39, 0.90, P = 0.01), ever smoking (OR: 3.06, 95% CI: 1.20, 7.81, P = 0.02), receptor-negative genotype (OR: 3.17, 95% CI: 1.16, 8.66, P = 0.02), lipoprotein(a) year-score (OR per 1 standard deviation of log-transformed year-score: 1.53, 95% CI: 0.99, 2.36, P = 0.05). Conclusions In individuals with HeFH, age, family history of premature cardiovascular disease, sex, statin use, diet quality, smoking status, the LDLR genotype, and lipoprotein(a) concentrations were independently associated with CAC prevalence and severity.Contexte Les déterminants de la prévalence et de la sévérité de la calcification des artères coronaires (CAC) dans l'hypercholestérolémie familiale hétérozygote (HFHe) demeurent peu étudiés. L’objectif de cette étude transversale était d'identifier les corrélats de la CAC chez des patients atteints d’HFHe. Méthodologie Un score calcique coronarien (SCC) a été calculé par un examen de tomodensitométrie sans contraste chez des femmes (n = 68) et des hommes (n = 78) avec HFHe génétiquement définie. Nous avons classé la prévalence et la gravité de la CAC en trois catégories : SCC = 0 unité d’Agatston (UA), SCC = 1 à 100 UA et SCC > 100 UA. Des renseignements ont été recueillis sur des corrélats potentiels de la CAC, dont les antécédents médicaux familiaux et personnels, les facteurs de risque cardiovasculaire, les médicaments hypolipidémiants et les habitudes de vie. Résultats Au total, 95 patients présentaient une CAC. Les corrélats indépendants de la prévalence et de la gravité de la CAC comprenaient l’âge (rapport de cotes [RC] par tranche de 10 ans : 5,06; intervalle de confiance [IC] à 95 % : 3,19 à 7,93; p < 0,0001), des antécédents familiaux de maladie cardiovasculaire précoce (RC : 3,88; IC à 95 % : 1,71 à 8,81; p = 0,001), le sexe masculin (RC : 3,40; IC à 95 % : 1,49 à 7,78; p = 0,004), l’emploi de statines (RC : 15,5; IC à 95 % : 1,89 à 126; p = 0,01), la qualité du régime alimentaire évaluée selon le score AHEI (Alternative Healthy Eating Index) (RC par écart-type : 0,59; IC à 95 % : 0,39 à 0,90; p = 0,01), le tabagisme (RC : 3,06; IC à 95 % : 1,20 à 7,81; p = 0,02), le génotype récepteur-négatif (RC : 3,17; IC à 95 % : 1,16 à 8,66; p = 0,02) et le score lipoprotéine(a)-année (RC par écart-type du score-année transformé en logarithme : 1,53; IC à 95 % : 0,99 à 2,36; p = 0,05). Conclusions Chez les personnes atteintes d’HFHe, l’âge, les antécédents familiaux de maladie cardiovasculaire précoce, le sexe, l’emploi de statines, la qualité du régime alimentaire, le statut de tabagisme, le génotype du LDLR et les concentrations de lipoprotéine(a) ont été associés de façon indépendante à la prévalence et à la gravité de la CAC

Impact of plasma Lp-PLA2 activity on the progression of aortic stenosis : the PROGRESSA study.

Objectives : The purpose of this prospective study was to examine the relationship between plasma lipoprotein–associated phospholipase A2 (Lp-PLA2) activity and the progression rate of aortic stenosis (AS). Background : We recently reported that Lp-PLA2 is highly expressed in stenotic aortic valves where it may contribute to the mineralization of valvular interstitial cells. Methods : Patients with AS were prospectively recruited in the PROGRESSA (Metabolic Determinants of the Progression of Aortic Stenosis) study. AS progression rate was assessed by annualized increase in peak aortic jet velocity (Vpeak), mean gradient (MG), and aortic valve area index (AVAi). Circulating Lp-PLA2 activity was measured and dichotomized based on the median value. Results : Of 183 patients included in this subanalysis of the PROGRESSA study, 70% were men and the mean age was 66 ± 13 years. Over the 2.5 ± 1.4 years of follow up, the AS progression rate tended to be higher in patients with high versus low Lp-PLA2 activity (annualized Vpeak = 0.17 ± 0.23 m/s vs. 0.12 ± 0.18 m/s; p = 0.14). There was a significant interaction (p < 0.05) between baseline AS severity and Lp-PLA2 activity with respect to impact on AS progression rate. In patients with mild AS (i.e., Vpeak <3 m/s; n = 123), increased Lp-PLA2 activity was associated with a significantly faster AS progression rate (Vpeak 0.16 ± 0.18 m/s vs. 0.09 ± 0.14 m/s; p = 0.01) but not in patients with moderate or severe AS (p = 0.99). After adjustment for other risk factors, increased Lp-PLA2 activity remained independently associated with faster AS progression rate (p = 0.005) in the former subset. Conclusions : There was no significant association between plasma Lp-PLA2 activity or mass and stenosis progression in the whole cohort. However, increased Lp-PLA2 activity was associated with a faster stenosis progression rate in the subset of patients with mild AS. These findings provide an impetus for the elaboration of a randomized trial targeting Lp-PLA2 activity in patients with early stages of calcific aortic valve disease