Hohenberg-Kohn theorem for the lowest-energy resonance of unbound systems

We show that under well-defined conditions the Hohenberg-Kohn theorem (HKT) can be extended to the lowest-energy resonance of unbound systems. Using the Gel'fand Levitan theorem, the extended version of the HKT can also be applied to systems that support a finite number of bound states. The extended version of the HKT provides an adequate framework to carry out DFT calculations of negative electron affinities.Comment: 4 pages, 3 figure

Coherent states for polynomial su(1,1) algebra and a conditionally solvable system

In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed $su(1,1)$ algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1,1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1,1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.Comment: 2 figure

Methods for lineage tracing on the organism-wide level

Determining the lineage origin of cell types is a major goal in developmental biology. Furthermore, lineage tracing is a powerful approach for understanding the origin of developmental defects as well as the origin of diseases such as cancer. There is now a variety of complementary approaches for identifying lineage relationships, ranging from direct observation of cell divisions by light microscopy to genetic labeling of cells using inducible recombinases and fluorescent reporters. A recent development, and the main topic of this review article, is the use of high-throughput sequencing data for lineage analysis. This emerging approach holds the promise of increased multiplexing capacity, allowing lineage analysis of large cell numbers up to the organism-wide level combined with simultaneous transcription profiling by single cell RNA sequencing

More on coupling coefficients for the most degenerate representations of SO(n)

We present explicit closed-form expressions for the general group-theoretical factor appearing in the alpha-topology of a high-temperature expansion of SO(n)-symmetric lattice models. This object, which is closely related to 6j-symbols for the most degenerate representation of SO(n), is discussed in detail.Comment: 9 pages including 1 table, uses IOP macros Update of Introduction and Discussion, References adde

Massively parallel single cell lineage tracing using CRISPR/Cas9 induced genetic scars

A key goal of developmental biology is to understand how a single cell transforms into a full-grown organism consisting of many different cell types. Single-cell RNAsequencing (scRNA-seq) has become a widely-used method due to its ability to identify all cell types in a tissue or organ in a systematic manner(1-3). However, a major challenge is to organize the resulting taxonomy of cell types into lineage trees revealing the developmental origin of cells. Here, we present a strategy for simultaneous lineage tracing and transcriptome profiling in thousands of single cells. By combining scRNAseq with computational analysis of lineage barcodes generated by genome editing of transgenic reporter genes, we reconstruct developmental lineage trees in zebrafish larvae and adult fish. In future analyses, LINNAEUS (LINeage tracing by Nuclease-Activated Editing of Ubiquitous Sequences) can be used as a systematic approach for identifying the lineage origin of novel cell types, or of known cell types under different conditions

Klein tunneling in carbon nanostructures: a free particle dynamics in disguise

The absence of backscattering in metallic nanotubes as well as perfect Klein tunneling in potential barriers in graphene are the prominent electronic characteristics of carbon nanostructures. We show that the phenomena can be explained by a peculiar supersymmetry generated by a first order Hamiltonian and zero order supercharge operators. Like the supersymmetry associated with second order reflectionless finite-gap systems, it relates here the low-energy behavior of the charge carriers with the free particle dynamics.Comment: 4 pages, 1 fig., typos correcte

The Use of Cognitive Ability Measures As Explanatory Variables In Regression Analysis

Cognitive ability measures are often taken as explanatory variables in regression analysis, e.g., as a factor affecting a market outcome such as an individual’s wage, or a decision such as an individual’s education acquisition. Cognitive ability is a latent construct; its true value is unobserved. Nonetheless, researchers often assume that a test score, constructed via standard psychometric practice from individuals’ responses to test items, can be safely used in regression analysis. We examine problems that can arise, and suggest that an alternative approach, a “mixed effects structural equations” (MESE) model, may be more appropriate in many circumstances

Topological methods for searching barriers and reaction paths

We present a family of algorithms for the fast determination of reaction paths and barriers in phase space and the computation of the corresponding rates. The method requires the reaction times be large compared to the microscopic time, irrespective of the origin - energetic, entropic, cooperative - of the timescale separation. It lends itself to temperature cycling as in simulated annealing and to activation-relaxation routines. The dynamics is ultimately based on supersymmetry methods used years ago to derive Morse theory. Thus, the formalism automatically incorporates all relevant topological information.Comment: 4 pages, 4 figures, RevTex

Supersymmetry of the Nonstationary Schr\"odinger equation and Time-Dependent Exactly Solvable Quantum Models

New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.Comment: Talk at the 8th International Conference "Symmetry Methods in Physics". Dubna, Russia, 28 July - 2 August, 199