Collapse transition of a square-lattice polymer with next nearest-neighbor interaction

We study the collapse transition of a polymer on a square lattice with both nearest-neighbor and next nearest-neighbor interactions, by calculating the exact partition function zeros up to chain length 36. The transition behavior is much more pronounced than that of the model with nearest-neighbor interactions only. The crossover exponent and the transition temperature are estimated from the scaling behavior of the first zeros with increasing chain length. The results suggest that the model is of the same universality class as the usual theta point described by the model with only nearest-neighbor interaction.Comment: 14 pages, 5 figure

Efficient CRISPR-rAAV engineering of endogenous genes to study protein function by allele-specific RNAi.

Gene knockout strategies, RNAi and rescue experiments are all employed to study mammalian gene function. However, the disadvantages of these approaches include: loss of function adaptation, reduced viability and gene overexpression that rarely matches endogenous levels. Here, we developed an endogenous gene knockdown/rescue strategy that combines RNAi selectivity with a highly efficient CRISPR directed recombinant Adeno-Associated Virus (rAAV) mediated gene targeting approach to introduce allele-specific mutations plus an allele-selective siRNA Sensitive (siSN) site that allows for studying gene mutations while maintaining endogenous expression and regulation of the gene of interest. CRISPR/Cas9 plus rAAV targeted gene-replacement and introduction of allele-specific RNAi sensitivity mutations in the CDK2 and CDK1 genes resulted in a >85% site-specific recombination of Neo-resistant clones versus ∼8% for rAAV alone. RNAi knockdown of wild type (WT) Cdk2 with siWT in heterozygotic knockin cells resulted in the mutant Cdk2 phenotype cell cycle arrest, whereas allele specific knockdown of mutant CDK2 with siSN resulted in a wild type phenotype. Together, these observations demonstrate the ability of CRISPR plus rAAV to efficiently recombine a genomic locus and tag it with a selective siRNA sequence that allows for allele-selective phenotypic assays of the gene of interest while it remains expressed and regulated under endogenous control mechanisms

Exact Partition Function Zeros of a Polymer on a Simple-Cubic Lattice

We study conformational transitions of a polymer on a simple-cubic lattice by calculating the zeros of the exact partition function, up to chain length 24. In the complex temperature plane, two loci of the partition function zeros are found for longer chains, suggesting the existence of both the coil-globule collapse transition and the melting-freezing transition. The locus corresponding to coil-globule transition clearly approaches the real axis as the chain length increases, and the transition temperature could be estimated by finite-size scaling. The form of the logarithmic correction to the scaling of the partition function zeros could also be obtained. The other locus does not show clear scaling behavior, but a supplementary analysis of the specific heat reveals a first-order-like pseudo-transition.Comment: 21 pages, 4 figure

Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers

Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number $C$ with ideal quantum geometry. While $C>1$ bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number $1$ that are intertwined through translation and rotation symmetry. The decomposed bands admit an $SU(C)$ action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the $SU(C)$ action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.Comment: 14+10 pages, 8 figure

The effect of incremental changes in phonotactic probability and neighborhood density on word learning by preschool children

This is the author's accepted manuscript. The original publication is available at http://jslhr.pubs.asha.org/article.aspx?articleid=1797302Purpose. Phonotactic probability or neighborhood density have predominately been defined using gross distinctions (i.e., low vs. high). The current studies examined the influence of finer changes in probability (Experiment 1) and density (Experiment 2) on word learning. Method. The full range of probability or density was examined by sampling five nonwords from each of four quartiles. Three- and 5-year-old children received training on nonword-nonobject pairs. Learning was measured in a picture-naming task immediately following training and 1-week after training. Results were analyzed using multi-level modeling. Results. A linear spline model best captured nonlinearities in phonotactic probability. Specifically word learning improved as probability increased in the lowest quartile, worsened as probability increased in the midlow quartile, and then remained stable and poor in the two highest quartiles. An ordinary linear model sufficiently described neighborhood density. Here, word learning improved as density increased across all quartiles. Conclusion. Given these different patterns, phonotactic probability and neighborhood density appear to influence different word learning processes. Specifically, phonotactic probability may affect recognition that a sound sequence is an acceptable word in the language and is a novel word for the child, whereas neighborhood density may influence creation of a new representation in long-term memory

Super-lattice, rhombus, square, and hexagonal standing waves in magnetically driven ferrofluid surface

Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits various patterns including a superlattice and subharmonic rhombuses as well as conventional harmonic hexagons and subharmonic squares. The superlattice arises in a bicritical situation where harmonic and subharmonic modes collide. The rhombic pattern arises due to the non-monotonic dispersion relation of a ferrofluid