Prime and semiprime inner functions

Abstract This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

Equality of P-partition Generating Functions

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

Quantitative 1H-magnetic resonance spectroscopy of human brain: Influence of composition and parameterization of the basis set in linear combination model-fitting

Localized short-echo-time (1)H-MR spectra of human brain contain contributions of many low-molecular-weight metabolites and baseline contributions of macromolecules. Two approaches to model such spectra are compared and the data acquisition sequence, optimized for reproducibility, is presented. Modeling relies on prior knowledge constraints and linear combination of metabolite spectra. Investigated was what can be gained by basis parameterization, i.e., description of basis spectra as sums of parametric lineshapes. Effects of basis composition and addition of experimentally measured macromolecular baselines were investigated also. Both fitting methods yielded quantitatively similar values, model deviations, error estimates, and reproducibility in the evaluation of 64 spectra of human gray and white matter from 40 subjects. Major advantages of parameterized basis functions are the possibilities to evaluate fitting parameters separately, to treat subgroup spectra as independent moieties, and to incorporate deviations from straightforward metabolite models. It was found that most of the 22 basis metabolites used may provide meaningful data when comparing patient cohorts. In individual spectra, sums of closely related metabolites are often more meaningful. Inclusion of a macromolecular basis component leads to relatively small, but significantly different tissue content for most metabolites. It provides a means to quantitate baseline contributions that may contain crucial clinical information.

Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Π1-equivalent to KP

We introduce a version of operational set theory, OST−, without a choice operation, which has a machinery for Δ0Δ0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke–Platek set theory KPKP with infinity are pairwise Π1Π1 equivalent. We also show analogous assertions for subtheories with ∈-induction restricted in various ways and for supertheories extended by powerset, beta, limit and Mahlo operations. Whereas the upper bound is given by a refinement of inductive definition in KPKP, the lower bound is by a combination, in a specific way, of realisability, (intuitionistic) forcing and negative interpretations. Thus, despite interpretability between classical theories, we make “a detour via intuitionistic theories”. The combined interpretation, seen as a model construction in the sense of Visser's miniature model theory, is a new way of construction for classical theories and could be said the third kind of model construction ever used which is non-trivial on the logical connective level, after generic extension à la Cohen and Krivine's classical realisability model.

Measurement of inclusive jet charged-particle fragmentation functions in Pb+Pb collisions at √sNN = 2.76 TeV with the ATLAS detector

Measurements of charged-particle fragmentation functions of jets produced in ultra-relativistic nuclear collisions can provide insight into the modification of parton showers in the hot, dense medium created in the collisions. ATLAS has measured jets in √sNN=2.76 TeV Pb+Pb collisions at the LHC using a data set recorded in 2011 with an integrated luminosity of 0.14 nb−1. Jets were reconstructed using the anti-kt algorithm with distance parameter values R = 0.2, 0.3, and 0.4. Distributions of charged-particle transverse momentum and longitudinal momentum fraction are reported for seven bins in collision centrality for R=0.4 jets with pjetT>100 GeV. Commensurate minimum pT values are used for the other radii. Ratios of fragment distributions in each centrality bin to those measured in the most peripheral bin are presented. These ratios show a reduction of fragment yield in central collisions relative to peripheral collisions at intermediate z values, 0.04≲z≲0.2 and an enhancement in fragment yield for z≲0.04. A smaller, less significant enhancement is observed at large z and large pT in central collisions.

Advance P. Chem. Problems (I) Populations, Partition Functions, Particle in Box, Harmonic Oscillators, Angular Momentum and Rigid Rotor

This is a set of P. Chem. problems posed at slightly higher than the normal text book level, for students who are continuing in the study of this subject.

Nuclear functions of dynein light chain 1 in hormone action

It is widely accepted that the process of breast cancer tumorigenesis involves estrogen receptor-alpha (ER)-regulated stimulatory pathways, which feed into survival, cell cycle progression and proliferative response. Recent data from Kumar laboratory indicate that dynein light chain 1 (DLC1) plays a role in survival, motility and invasiveness, all of which are required for a successful tumorigenesis process. In the present research, we have discovered a mechanistic bidirectional regulatory link between the DLC1 and ER. We found that DLC1 facilitates ligand-induced ER transactivation involving the recruitment of the DLC1-ER complex to ER-target genes. To gain insights into the mechanism by which DLC1 regulates the ER pathway, we set out to identify novel DLC1-interacting proteins. Among other proteins, we identified KIBRA and Ciz1 as two novel DLC1-interacting proteins. We found that the KIBRA-DLC1 complex is recruited to ER-responsive promoters, and that KIBRA-DLC1 interaction is needed for the recruitment of ER to its targets as well as for ER's transactivation function. Finally, we found that KIBRA utilizes its histone H3interacting glutamic acid-rich region to regulate the transactivation activity of ER. During the course of this work, we also discovered that DLC1 interacts with Cdk2 and Ciz1, and such interactions play a direct accelerating role in the G1-S transition of breast cancer cells. While delineating the role of Ciz1 in hormone-responsive cancer cells, we found that Ciz1 is an estrogen-responsive gene, and acts as a co-regulator of ER. Accordingly, Ciz1 overexpression in breast cancer cells conferred estrogen hypersensitivity, promoted the growth-rate, anchorage-independency and tumorigenic properties. Collectively, findings made during the course of the present dissertation research introduced two new molecular players in the action of ER in breast cancer cells, with a particular focus on cell cycle progression and ER-chromatin target regulation. In addition, findings presented here provide novel mechanistic insight about the contribution of DLC1 and its interacting proteins in amplifying the hormone action and promoting the process of breast cancer tumorigenesis. ^

GENOME-WIDE PROFILING UNVEILS CRITICIAL FUNCTIONS OF p53 IN HUMAN EMBRYONIC STEM CELLS

Embryonic stem cells (ESCs) possess two unique characteristics: infinite self-renewal and the potential to differentiate into almost every cell type (pluripotency). Recently, global expression analyses of metastatic breast and lung cancers revealed an ESC-like expression program or signature, specifically for cancers that are mutant for p53 function. Surprisingly, although p53 is widely recognized as the guardian of the genome, due to its roles in cell cycle checkpoints, programmed cell death or senescence, relatively little is known about p53 functions in normal cells, especially in ESCs. My hypothesis is that p53 has specific transcription regulatory functions in human ESCs (hESCs) that a) oppose pluripotency and b) protect the stem cell genome in response to DNA damage and stress signaling. In mouse ESCs, these roles are believed to coincide, as p53 promotes differentiation in response to DNA damage, but this is unexplored in hESCs. To determine the biological roles of p53, specifically in hESCs, we mapped genome-wide chromatin interactions of p53 by chromatin immunoprecipitation and massively parallel tag sequencing (ChIP-Seq), and did so under three VIdifferent conditions of hESC status: pluripotency, differentiation-initiated and DNA-damage-induced. ChIP-Seq showed that p53 is enriched at distinct, induction-specific gene loci during each of these different conditions. Microarray gene expression analysis and functional annotation of the distinct p53-target genes revealed that p53 regulates specific genes encoding developmental regulators, which are expressed in differentiation-initiated but not DNA- damaged hESCs. We further discovered that, in response to differentiation signaling, p53 binds regions of chromatin that are repressed but also poised for rapid activation by core pluripotency factors OCT4 and NANOG in pluripotent hESCs. In response to DNA damage, genes associated with migration and motility are targeted by p53; whereas, the prime targets of p53 in control of cell death are conserved for p53 regulation in both differentiation and DNA damage. Our genome-wide profiling and bioinformatics analyses show that p53 occupies a special set of developmental regulatory genes during early differentiation of hESCs and functions in an induction-specific manner. In conclusion, our research unveiled previously unknown functions of p53 in ESC biology, which augments our understanding of one of the most deregulated proteins in human cancers.

A new set of relativistic screening constants for the screened hydrogenic model

AnewRelativisticScreenedHydrogenicModel has been developed to calculate atomic data needed to compute the optical and thermodynamic properties of high energy density plasmas. The model is based on anewset of universal screeningconstants, including nlj-splitting that has been obtained by fitting to a large database of ionization potentials and excitation energies. This database was built with energies compiled from the National Institute of Standards and Technology (NIST) database of experimental atomic energy levels, and energies calculated with the Flexible Atomic Code (FAC). The screeningconstants have been computed up to the 5p3/2 subshell using a Genetic Algorithm technique with an objective function designed to minimize both the relative error and the maximum error. To select the best set of screeningconstants some additional physical criteria has been applied, which are based on the reproduction of the filling order of the shells and on obtaining the best ground state configuration. A statistical error analysis has been performed to test the model, which indicated that approximately 88% of the data lie within a ±10% error interval. We validate the model by comparing the results with ionization energies, transition energies, and wave functions computed using sophisticated self-consistent codes and experimental data.

Efficient top-down set-sharing analysis using cliques

Abstract. We study the problem of efficient, scalable set-sharing analysis of logic programs. We use the idea of representing sharing information as a pair of abstract substitutions, one of which is a worst-case sharing representation called a clique set, which was previously proposed for the case of inferring pair-sharing. We use the clique-set representation for (1) inferring actual set-sharing information, and (2) analysis within a top-down framework. In particular, we define the new abstract functions required by standard top-down analyses, both for sharing alone and also for the case of including freeness in addition to sharing. We use cliques both as an alternative representation and as widening, defining several widening operators. Our experimental evaluation supports the conclusión that, for inferring set-sharing, as it was the case for inferring pair-sharing, precisión losses are limited, while useful efficieney gains are obtained. We also derive useful conclusions regarding the interactions between thresholds, precisión, efficieney and cost of widening. At the limit, the clique-set representation allowed analyzing some programs that exceeded memory capacity using classical sharing representations.

A study of set-sharing analysis via cliques

We study the problem of efñcient, scalable set-sharing analysis of logic programs. We use the idea of representing sharing information as a pair of abstract substitutions, one of which is a worst-case sharing representation called a clique set, which was previously proposed for the case of inferring pair-sharing. We use the clique-set representation for (1) inferring actual set-sharing information, and (2) analysis within a topdown framework. In particular, we define the abstract functions required by standard top-down analyses, both for sharing alone and also for the case of including freeness in addition to sharing. Our experimental evaluation supports the conclusión that, for inferring set-sharing, as it was the case for inferring pair-sharing, precisión losses are limited, while useful efñciency gains are obtained. At the limit, the clique-set representation allowed analyzing some programs that exceeded memory capacity using classical sharing representations.

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

Cooperative functions of the reaper and head involution defective genes in the programmed cell death of Drosophila central nervous system midline cells

In Drosophila, the chromosomal region 75C1–2 contains at least three genes, reaper (rpr), head involution defective (hid), and grim, that have important functions in the activation of programmed cell death. To better understand how cells are killed by these genes, we have utilized a well defined set of embryonic central nervous system midline cells that normally exhibit a specific pattern of glial cell death. In this study we show that both rpr and hid are expressed in dying midline cells and that the normal pattern of midline cell death requires the function of multiple genes in the 75C1–2 interval. We also utilized the P[UAS]/P[Gal4] system to target expression of rpr and hid to midline cells. Targeted expression of rpr or hid alone was not sufficient to induce ectopic midline cell death. However, expression of both rpr and hid together rapidly induced ectopic midline cell death that resulted in axon scaffold defects characteristic of mutants with abnormal midline cell development. Midline-targeted expression of the baculovirus p35 protein, a caspase inhibitor, blocked both normal and ectopic rpr- and hid-induced cell death. Taken together, our results suggest that rpr and hid are expressed together and cooperate to induce programmed cell death during development of the central nervous system midline.

SET1, A Yeast Member of the Trithorax Family, Functions in Transcriptional Silencing and Diverse Cellular Processes

The trithorax gene family contains members implicated in the control of transcription, development, chromosome structure, and human leukemia. A feature shared by some family members, and by other proteins that function in chromatin-mediated transcriptional regulation, is the presence of a 130- to 140-amino acid motif dubbed the SET or Tromo domain. Here we present analysis of SET1, a yeast member of the trithorax gene family that was identified by sequence inspection to encode a 1080-amino acid protein with a C-terminal SET domain. In addition to its SET domain, which is 40–50% identical to those previously characterized, SET1 also shares dispersed but significant similarity to Drosophila and human trithorax homologues. To understand SET1 function(s), we created a null mutant. Mutant strains, although viable, are defective in transcriptional silencing of the silent mating-type loci and telomeres. The telomeric silencing defect is rescued not only by full-length episomal SET1 but also by the conserved SET domain of SET1. set1 mutant strains display other phenotypes including morphological abnormalities, stationary phase defects, and growth and sporulation defects. Candidate genes that may interact with SET1 include those with functions in transcription, growth, and cell cycle control. These data suggest that yeast SET1, like its SET domain counterparts in other organisms, functions in diverse biological processes including transcription and chromatin structure.