One-dimensional wave equations defined by fractal Laplacians

We study one-dimensional wave equations defined by a class of fractal Laplacians. These Laplacians are defined by fractal measures generated by iterated function systems with overlaps, such as the well-known infinite Bernoulli convolution associated with the golden ratio and the 3-fold convolution of the Cantor measure. The iterated function systems defining these measures do not satisfy the post-critically finite condition or the open set condition. By using second-order self-similar identities introduced by Strichartz et al., we discretize the equations and use the finite element and central difference methods to obtain numerical approximations to the weak solutions. We prove that the numerical solutions converge to the weak solution, and obtain estimates for the rate of convergence

Earliest-deadline-first service in heavy-traffic acyclic networks

This paper presents a heavy traffic analysis of the behavior of multi-class acyclic queueing networks in which the customers have deadlines. We assume the queueing system consists of J stations, and there are K different customer classes. Customers from each class arrive to the network according to independent renewal processes. The customers from each class are assigned a random deadline drawn from a deadline distribution associated with that class and they move from station to station according to a fixed acyclic route. The customers at a given node are processed according to the earliest-deadline-first (EDF) queue discipline. At any time, the customers of each type at each node have a lead time, the time until their deadline lapses. We model these lead times as a random counting measure on the real line. Under heavy traffic conditions and suitable scaling, it is proved that the measure-valued lead-time process converges to a deterministic function of the workload process

Tissue-specific Expression of Distinct Spectrin and Ankyrin Transcripts in Erythroid and Nonerythroid Cells

cDNA probes for three components of the erythroid membrane skeleton, α spectrin, β spectrin, and ankyrin, were obtained by using monospecific antibodies to screen a λgt11 expression vector library containing cDNA prepared from chicken erythroid poly(A)^+ RNA. Each cDNA appears to hybridize to one gene type in the chicken genome. Qualitatively distinct RNA species in myogenic and erythroid cells are detected for β spectrin and ankyrin, while α spectrin exists as a single species of transcript in all tissues examined. This tissue-specific expression of RNAs is regulated quantitatively during myogenesis in vitro, since all three accumulate only upon myoblast fusion. Furthermore, RNAs for two of the three genes do not accumulate to detectable levels in chicken embryo fibroblasts, demonstrating that their accumulation can be noncoordinate. These observations suggest that independent gene regulation and tissue-specific production of heterogeneous transcripts from the β spectrin and ankyrin genes underlie the formation of distinct membrane skeletons in erythroid and muscle cells

Onset of Odorant Receptor Gene Expression during Olfactory Sensory Neuron Regeneration

AbstractIndividual olfactory sensory neurons are thought to express only one odorant receptor gene from a repertoire of hundreds to thousands of genes. How do these sensory neurons choose just one specific odorant receptor to express during their differentiation? As an initial attempt toward understanding the process of odorant receptor gene regulation, we studied when odorant receptor expression is activated during sensory neuron regeneration. We find that receptor gene expression is activated in postmitotic neurons and can occur in the absence of the olfactory bulb. These results suggest that receptor expression is restricted to the terminal stages of olfactory neuron differentiation, and sensory neurons do not simply inherit the odorant receptor that is already expressed in mitotic precursor cells. Our results also support a model in which odorant receptor gene expression occurs independent of the olfactory bulb

The repertoire of olfactory C family G protein-coupled receptors in zebrafish: candidate chemosensory receptors for amino acids

BACKGROUND: Vertebrate odorant receptors comprise at least three types of G protein-coupled receptors (GPCRs): the OR, V1R, and V2R/V2R-like receptors, the latter group belonging to the C family of GPCRs. These receptor families are thought to receive chemosensory information from a wide spectrum of odorant and pheromonal cues that influence critical animal behaviors such as feeding, reproduction and other social interactions. RESULTS: Using genome database mining and other informatics approaches, we identified and characterized the repertoire of 54 intact "V2R-like" olfactory C family GPCRs in the zebrafish. Phylogenetic analysis – which also included a set of 34 C family GPCRs from fugu – places the fish olfactory receptors in three major groups, which are related to but clearly distinct from other C family GPCRs, including the calcium sensing receptor, metabotropic glutamate receptors, GABA-B receptor, T1R taste receptors, and the major group of V2R vomeronasal receptor families. Interestingly, an analysis of sequence conservation and selective pressure in the zebrafish receptors revealed the retention of a conserved sequence motif previously shown to be required for ligand binding in other amino acid receptors. CONCLUSION: Based on our findings, we propose that the repertoire of zebrafish olfactory C family GPCRs has evolved to allow the detection and discrimination of a spectrum of amino acid and/or amino acid-based compounds, which are potent olfactory cues in fish. Furthermore, as the major groups of fish receptors and mammalian V2R receptors appear to have diverged significantly from a common ancestral gene(s), these receptors likely mediate chemosensation of different classes of chemical structures by their respective organisms

The odorant receptor repertoire of teleost fish

BACKGROUND: Vertebrate odorant receptors comprise three types of G protein-coupled receptors: the OR, V1R and V2R receptors. The OR superfamily contains over 1,000 genes in some mammalian species, representing the largest gene superfamily in the mammalian genome. RESULTS: To facilitate an informed analysis of OR gene phylogeny, we identified the complete set of 143 OR genes in the zebrafish genome, as well as the OR repertoires in two pufferfish species, fugu (44 genes) and tetraodon (42 genes). Although the genomes analyzed here contain fewer genes than in mammalian species, the teleost OR genes can be grouped into a larger number of major clades, representing greater overall OR diversity in the fish. CONCLUSION: Based on the phylogeny of fish and mammalian repertoires, we propose a model for OR gene evolution in which different ancestral OR genes or gene families were selectively lost or expanded in different vertebrate lineages. In addition, our calculations of the ratios of non-synonymous to synonymous codon substitutions among more recently expanding OR subgroups in zebrafish implicate residues that may be involved in odorant binding

Slingshot: cell lineage and pseudotime inference for single-cell transcriptomics.

BackgroundSingle-cell transcriptomics allows researchers to investigate complex communities of heterogeneous cells. It can be applied to stem cells and their descendants in order to chart the progression from multipotent progenitors to fully differentiated cells. While a variety of statistical and computational methods have been proposed for inferring cell lineages, the problem of accurately characterizing multiple branching lineages remains difficult to solve.ResultsWe introduce Slingshot, a novel method for inferring cell lineages and pseudotimes from single-cell gene expression data. In previously published datasets, Slingshot correctly identifies the biological signal for one to three branching trajectories. Additionally, our simulation study shows that Slingshot infers more accurate pseudotimes than other leading methods.ConclusionsSlingshot is a uniquely robust and flexible tool which combines the highly stable techniques necessary for noisy single-cell data with the ability to identify multiple trajectories. Accurate lineage inference is a critical step in the identification of dynamic temporal gene expression