Number squeezed and fragmented states of strongly interacting bosons in a double well

We present a systematic study of the phenomena of number squeezing and fragmentation for a repulsive Bose-Einstein condensate (BEC) in a three dimensional double well potential over a range of interaction strengths and barrier heights, including geometries that exhibit appreciable overlap in the one-body wavefunctions localized in the left and right wells. We compute the properties of the condensate with numerically exact, full dimensional path integral ground state (PIGS) Quantum Monte Carlo simulations and compare with results obtained from using two- and eight-mode truncated basis models. The truncated basis models are found to agree with the numerically exact PIGS simulations for weak interactions, but fail to correctly predict the amount of number squeezing and fragmentation exhibited by the PIGS simulations for strong interactions. We find that both number squeezing and fragmentation of the BEC show non-monotonic behavior at large values of interaction strength a. The number squeezing shows a universal scaling with the product of number of particles and interaction strength (Na) but no such universal behavior is found for fragmentation. Detailed analysis shows that the introduction of repulsive interactions not only suppresses number fluctuations to enhance number squeezing, but can also enhance delocalization across wells and tunneling between wells, each of which may suppress number squeezing. This results in a dynamical competition whose resolution shows a complex dependence on all three physical parameters defining the system: interaction strength, number of particles, and barrier height.Comment: 33 pages, 21 figures. Submitted for publication in Physical Review

Partitioning of gene expression among zebrafsh photoreceptor subtypes

Abstract Vertebrate photoreceptors are categorized into two broad classes, rods and cones, responsible for dim- and bright-light vision, respectively. While many molecular features that distinguish rods and cones are known, gene expression differences among cone subtypes remain poorly understood. Teleost fishes are renowned for the diversity of their photoreceptor systems. Here, we used single-cell RNA-seq to profile adult photoreceptors in zebrafish, a teleost. We found that in addition to the four canonical zebrafish cone types, there exist subpopulations of green and red cones (previously shown to be located in the ventral retina) that express red-shifted opsin paralogs (opn1mw4 or opn1lw1) as well as a unique combination of cone phototransduction genes. Furthermore, the expression of many paralogous phototransduction genes is partitioned among cone subtypes, analogous to the partitioning of the phototransduction paralogs between rods and cones seen across vertebrates. The partitioned cone-gene pairs arose via the teleost-specific whole-genome duplication or later clade-specific gene duplications. We also discovered that cone subtypes express distinct transcriptional regulators, including many factors not previously implicated in photoreceptor development or differentiation. Overall, our work suggests that partitioning of paralogous gene expression via the action of differentially expressed transcriptional regulators enables diversification of cone subtypes in teleosts

Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem

Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly crystalline photoreceptor patterns of some fish and reptiles. Birds are highly visual animals with five different cone photoreceptor subtypes, yet their photoreceptor patterns are not perfectly regular. By analyzing the chicken cone photoreceptor system consisting of five different cell types using a variety of sensitive microstructural descriptors, we find that the disordered photoreceptor patterns are ``hyperuniform'' (exhibiting vanishing infinite-wavelength density fluctuations), a property that had heretofore been identified in a unique subset of physical systems, but had never been observed in any living organism. Remarkably, the photoreceptor patterns of both the total population and the individual cell types are simultaneously hyperuniform. We term such patterns ``multi-hyperuniform'' because multiple distinct subsets of the overall point pattern are themselves hyperuniform. We have devised a unique multiscale cell packing model in two dimensions that suggests that photoreceptor types interact with both short- and long-ranged repulsive forces and that the resultant competition between the types gives rise to the aforementioned singular spatial features characterizing the system, including multi-hyperuniformity.Comment: 31 pages, 12 figure

A Hybrid Photoreceptor Expressing Both Rod and Cone Genes in a Mouse Model of Enhanced S-Cone Syndrome

Rod and cone photoreceptors subserve vision under dim and bright light conditions, respectively. The differences in their function are thought to stem from their different gene expression patterns, morphologies, and synaptic connectivities. In this study, we have examined the photoreceptor cells of the retinal degeneration 7 (rd7) mutant mouse, a model for the human enhanced S-cone syndrome (ESCS). This mutant carries a spontaneous deletion in the mouse ortholog of NR2E3, an orphan nuclear receptor transcription factor mutated in ESCS. Employing microarray and in situ hybridization analysis we have found that the rd7 retina contains a modestly increased number of S-opsin–expressing cells that ultrastructurally appear to be normal cones. Strikingly, the majority of the photoreceptors in the rd7 retina represent a morphologically hybrid cell type that expresses both rod- and cone-specific genes. In addition, in situ hybridization screening of genes shown to be up-regulated in the rd7 mutant retina by microarray identified ten new cone-specific or cone-enriched genes with a wide range of biochemical functions, including two genes specifically involved in glucose/glycogen metabolism. We suggest that the abnormal electroretinograms, slow retinal degeneration, and retinal dysmorphology seen in humans with ESCS may, in part, be attributable to the aberrant function of a hybrid photoreceptor cell type similar to that identified in this study. The functional diversity of the novel cone-specific genes identified here indicates molecular differences between rods and cones extending far beyond those previously discovered

Retinal horizontal cells lacking Rb1 sustain persistent DNA damage and survive as polyploid giant cells

The retinoblastoma tumor susceptibility gene, Rb1, is a key regulator of the cell cycle, and mutations in this gene have been found in many human cancers. Prior studies showed that retina-specific knockout of Rb1 in the mouse results in the formation of abnormally large horizontal cells, but the development, fate, and genomic status of these cells remain unknown. In this study, we conditionally inactivate Rb1 in early retinal progenitors and show that the loss of Rb1 leads to the rapid degeneration of most retinal cells except horizontal cells, which persist as giant cells with aberrant centrosome content, DNA damage, and polyploidy/aneuploidy. We observed inappropriate cell cycle entry of Rb1-deficient horizontal cells during the first postnatal weeks, which dropped off abruptly by P30. Despite extensive DNA damage in Rb1-deficient horizontal cells, these cells can still enter mitosis. Adult Rb1-deficient horizontal cells display elevated DNA content (5N–34N) that varied continuously, suggesting the presence of aneuploidy. We also found evidence of supernumerary and disoriented centrosomes in a rare population of mitotic cells in the mutant retinas. Overall our data demonstrate that horizontal cells are a remarkably robust cell type and can survive for months despite extensive DNA damage and elevated genome content

The Importance of Network Topology in Local Contribution Games

We consider a model of content contribution in peer-to-peer networks with linear quadratic payoffs and very general interaction patterns. We find that Nash equilibria of this game always exist; moreover, they are computable by solving a linear complementarity problem. The equilibrium is unique when goods are strategic complements or weak substitutes and contributions are proportional to a network centrality measure called the Bonacich index. In the case of public goods, the equilibrium is non-unique and characterized by k-order maximal independent sets. The structure of optimal networks is always star-like when the game exhibits strict or weak complements. Under public good scenarios, while star-like networks remain optimal in the best case, they also yield the worst-performing equilibria. We also discuss a network-based policy for improving the equilibrium performance of networks by the exclusion of a single player.Engineering and Applied Science