Strongly walk-regular graphs

We study a generalization of strongly regular graphs. We call a graph strongly walk-regular if there is an $\ell >1$ such that the number of walks of length $\ell$ from a vertex to another vertex depends only on whether the two vertices are the same, adjacent, or not adjacent. We will show that a strongly walk-regular graph must be an empty graph, a complete graph, a strongly regular graph, a disjoint union of complete bipartite graphs of the same size and isolated vertices, or a regular graph with four eigenvalues. Graphs from the first three families in this list are indeed strongly $\ell$-walk-regular for all $\ell$, whereas the graphs from the fourth family are $\ell$-walk-regular for every odd $\ell$. The case of regular graphs with four eigenvalues is the most interesting (and complicated) one. Such graphs cannot be strongly $\ell$-walk-regular for even $\ell$. We will characterize the case that regular four-eigenvalue graphs are strongly $\ell$-walk-regular for every odd $\ell$, in terms of the eigenvalues. There are several examples of infinite families of such graphs. We will show that every other regular four-eigenvalue graph can be strongly $\ell$-walk-regular for at most one $\ell$. There are several examples of infinite families of such graphs that are strongly 3-walk-regular. It however remains open whether there are any graphs that are strongly $\ell$-walk-regular for only one particular $\ell$ different from 3

Dual concepts of almost distance-regularity and the spectral excess theorem

Generally speaking, `almost distance-regular' graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity, thus giving a better understanding of the properties of distance-regular graphs. More precisely, we characterize $m$-partially distance-regular graphs and $j$-punctually eigenspace distance-regular graphs by using their spectra. Our results can also be seen as a generalization of the so-called spectral excess theorem for distance-regular graphs, and they lead to a dual version of it

On almost distance-regular graphs

Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study `almost distance-regular graphs'. We use this name informally for graphs that share some regularity properties that are related to distance in the graph. For example, a known characterization of a distance-regular graph is the invariance of the number of walks of given length between vertices at a given distance, while a graph is called walk-regular if the number of closed walks of given length rooted at any given vertex is a constant. One of the concepts studied here is a generalization of both distance-regularity and walk-regularity called $m$-walk-regularity. Another studied concept is that of $m$-partial distance-regularity or, informally, distance-regularity up to distance $m$. Using eigenvalues of graphs and the predistance polynomials, we discuss and relate these and other concepts of almost distance-regularity, such as their common generalization of $(\ell,m)$-walk-regularity. We introduce the concepts of punctual distance-regularity and punctual walk-regularity as a fundament upon which almost distance-regular graphs are built. We provide examples that are mostly taken from the Foster census, a collection of symmetric cubic graphs. Two problems are posed that are related to the question of when almost distance-regular becomes whole distance-regular. We also give several characterizations of punctually distance-regular graphs that are generalizations of the spectral excess theorem

A comparison of infant and toddler feeding practices of mothers with and without histories of eating disorders

This preliminary study surveyed the feeding practices of mothers with eating disorder histories through evaluation of mothers' reported feeding styles, child diet composition and restrictive special approaches to feeding. For this non-randomised cohort study, 25 mothers with eating disorder histories and 25 mothers with no history of an eating disorder with children ages 6-36 months were selected such that the groups were similar based on child age group and child sex. Mothers were compared on self-reported feeding style using the Infant Feeding Styles Questionnaire and on child diet composition and special feeding approaches using a modified version of the Toddler Diet Questionnaire from the Women, Infants, and Children program. Mothers with eating disorder histories scored lower on the restrictive feeding style subscale than controls. No significant differences were detected between groups in child diet including the percentage of mothers who breastfed, duration of breastfeeding, age at solid food introduction, daily number of meals or snacks or daily frequency of consumption of fruits, vegetables or protein foods. Mothers with eating disorder histories were more likely to report taking a restrictive special approach to feeding such as limiting processed foods or feeding organic foods only. Although mothers with eating disorder histories may not differ greatly from control mothers in terms of child diet composition (smaller effects may not have been detected due to limited sample size), they may be more likely to take restrictive special approaches to feeding which mirror dietary rules common in individuals with eating disorders

Safety, Immunogenicity, and Protective Efficacy of Intradermal Immunization with Aseptic, Purified, Cryopreserved Plasmodium falciparum Sporozoites in Volunteers Under Chloroquine Prophylaxis

Immunization of volunteers under chloroquine prophylaxis by bites of *Plasmodium falciparum* sporozoite (PfSPZ)–infected mosquitoes induces > 90% protection against controlled human malaria infection (CHMI). We studied intradermal immunization with cryopreserved, infectious PfSPZ in volunteers taking chloroquine (PfSPZ chemoprophylaxis vaccine [CVac]). Vaccine groups 1 and 3 received 3x monthly immunizations with 7.5 x 10^4 PfSPZ. Control groups 2 and 4 received normal saline. Groups 1 and 2 underwent CHMI (#1) by mosquito bite 60 days after the third immunization. Groups 3 and 4 were boosted 168 days after the third immunization and underwent CHMI (#2) 137 days later. Vaccinees (11/20, 55%) and controls (6/10, 60%) had the same percentage of mild to moderate solicited adverse events. After CHMI #1, 8/10 vaccinees (group 1) and 5/5 controls (group 2) became parasitemic by microscopy; the two negatives were positive by quantitative real-time polymerase chain reaction (qPCR). After CHMI #2, all vaccinees in group 3 and controls in group 4 were parasitemic by qPCR. Vaccinees showed weak antibody and no detectable cellular immune responses. Intradermal immunization with up to 3 x 10^5 PfSPZ-CVac was safe, but induced only minimal immune responses and no sterile protection against Pf CHMI. INTRODUCTIO

The global atmospheric electrical circuit and climate

Evidence is emerging for physical links among clouds, global temperatures, the global atmospheric electrical circuit and cosmic ray ionisation. The global circuit extends throughout the atmosphere from the planetary surface to the lower layers of the ionosphere. Cosmic rays are the principal source of atmospheric ions away from the continental boundary layer: the ions formed permit a vertical conduction current to flow in the fair weather part of the global circuit. Through the (inverse) solar modulation of cosmic rays, the resulting columnar ionisation changes may allow the global circuit to convey a solar influence to meteorological phenomena of the lower atmosphere. Electrical effects on non-thunderstorm clouds have been proposed to occur via the ion-assisted formation of ultra-fine aerosol, which can grow to sizes able to act as cloud condensation nuclei, or through the increased ice nucleation capability of charged aerosols. Even small atmospheric electrical modulations on the aerosol size distribution can affect cloud properties and modify the radiative balance of the atmosphere, through changes communicated globally by the atmospheric electrical circuit. Despite a long history of work in related areas of geophysics, the direct and inverse relationships between the global circuit and global climate remain largely quantitatively unexplored. From reviewing atmospheric electrical measurements made over two centuries and possible paleoclimate proxies, global atmospheric electrical circuit variability should be expected on many timescale

The effects of rare SERPINA1 variants on lung function and emphysema in SPIROMICS

Rationale: The role of PI (protease inhibitor) type Z heterozygotes and additional rare variant genotypes in the gene encoding alpha-1 antitrypsin, SERPINA1 (serpin peptidase inhibitor, clade A,member 1), in determining chronic obstructive pulmonary disease risk and severity is controversial. Objectives: To comprehensively evaluate the effects of rare SERPINA1 variants on lung function and emphysema phenotypes in subjects with significant tobacco smoke exposure using deep gene resequencing and alpha-1 antitrypsin concentrations. Methods: DNA samples from 1,693 non-Hispanic white individuals, 385 African Americans, and 90 Hispanics with >20 pack-years smoking were resequenced for the identification of rare variants (allele frequency,0.05) in 16.9 kB of SERPINA1. Measurements and Main Results: White PI Z heterozygotes confirmed by sequencing (MZ; n = 74) had lower postbronchodilator FEV1 (P = 0.007), FEV1/FVC (P = 0.003), and greater computed tomography-based emphysema (P = 0.02) compared with 1,411 white individuals without PI Z, S, or additional rare variants denoted as VR. PI Z-containing compound heterozygotes (ZS/ZVR; n = 7) had lower FEV1/FVC (P = 0.02) and forced expiratory flow, midexpiratory phase (P = 0.009). Nineteen white heterozygotes for five non-S/Z coding variants associated with lower alpha-1 antitrypsin had greater computed tomography-based emphysema compared with those without rare variants. In African Americans, a 59 untranslated region insertion (rs568223361) was associated with lower alpha-1 antitrypsin and functional small airway disease (P = 0.007). Conclusions: In this integrative deep sequencing study of SERPINA1 with alpha-1 antitrypsin concentrations in a heavy smoker and chronic obstructive pulmonary disease cohort, we confirmed the effects of PI Z heterozygote and compound heterozygote genotypes. We demonstrate the cumulative effects of multiple SERPINA1 variants on alpha-1 antitrypsin deficiency, lung function, and emphysema, thus significantly increasing the frequency of SERPINA1 variation associated with respiratory disease in at-risk smokers