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

Well-posedness of Hydrodynamics on the Moving Elastic Surface

The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the dynamic equations of the two-dimensional fluid, and the incompressible equation, all of which operate within a curved geometry. In this paper, we prove the local existence and uniqueness of the solution to the reduced elastic surface model by reformulating the model into a new system in the isothermal coordinates. One major difficulty is that of constructing an appropriate iterative scheme such that the limit system is consistent with the original system.Comment: The introduction is rewritte

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

The Timing of School Transitions and Early Adolescent Problem Behavior

This longitudinal study investigates whether rural adolescents who transition to a new school in sixth grade have higher levels of risky behavior than adolescents who transition in seventh grade. Our findings indicate that later school transitions had little effect on problem behavior between sixth and ninth grades. Cross-sectional analyses found a small number of temporary effects of transition timing on problem behavior: Spending an additional year in elementary school was associated with higher levels of deviant behavior in the Fall of Grade 6 and higher levels of antisocial peer associations in Grade 8. However, transition effects were not consistent across waves and latent growth curve models found no effects of transition timing on the trajectory of problem behavior. We discuss policy implications and compare our findings with other research on transition timing

Associations between reasons to attend and late high school dropout

This study addressed (1) whether there were unique profiles of student self-reported reasons for attending school among 10th graders, (2) whether these profiles were differentially associated with late high-school dropout, and (3) whether parent characteristics differed across profiles. Using data from the Educational Longitudinal Study of 2002 (N= 15,362), five latent classes were found. The first class (49%) reported intrinsic, identified/introjected, and external motivations for attending school. The second class (32%) attended for identified/introjected and external reasons, while the third class (11%) reported intrinsic and identified/introjected reasons. The final two classes reported only identified/introjected (5%) or external (4%) motivations. Individuals in the identified/introjected and external classes were at greatest risk of dropping out between 10th and 12th grade. A host of parenting characteristics differed across class, with students in the intrinsic-identified/introjected-external class displaying the most favorable pattern of results. Implications for dropout prevention and academic promotion programs are discussed

Engineered nonlinear lattices

We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term a quasilattice, which interpolates between a lattice system and a continuous system.Peer ReviewedPostprint (published version

Directly converted astrocytes retain the ageing features of the donor fibroblasts and elucidate the astrocytic contribution to human CNS health and disease

Astrocytes are highly specialised cells, responsible for CNS homeostasis and neuronal activity. Lack of human in vitro systems able to recapitulate the functional changes affecting astrocytes during ageing represents a major limitation to studying mechanisms and potential therapies aiming to preserve neuronal health. Here, we show that induced astrocytes from fibroblasts donors in their childhood or adulthood display age‐related transcriptional differences and functionally diverge in a spectrum of age‐associated features, such as altered nuclear compartmentalisation, nucleocytoplasmic shuttling properties, oxidative stress response and DNA damage response. Remarkably, we also show an age‐related differential response of induced neural progenitor cells derived astrocytes (iNPC‐As) in their ability to support neurons in co‐culture upon pro‐inflammatory stimuli. These results show that iNPC‐As are a renewable, readily available resource of human glia that retain the age‐related features of the donor fibroblasts, making them a unique and valuable model to interrogate human astrocyte function over time in human CNS health and disease

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types