Two-dimensional Copolymers and Multifractality: Comparing Perturbative Expansions, MC Simulations, and Exact Results

We analyze the scaling laws for a set of two different species of long flexible polymer chains joined together at one of their extremities (copolymer stars) in space dimension D=2. We use a formerly constructed field-theoretic description and compare our perturbative results for the scaling exponents with recent conjectures for exact conformal scaling dimensions derived by a conformal invariance technique in the context of D=2 quantum gravity. A simple MC simulation brings about reasonable agreement with both approaches. We analyse the remarkable multifractal properties of the spectrum of scaling exponents.Comment: 5 page

Methods for Predicting an Ordinal Response with High-Throughput Genomic Data

Multigenic diagnostic and prognostic tools can be derived for ordinal clinical outcomes using data from high-throughput genomic experiments. A challenge in this setting is that the number of predictors is much greater than the sample size, so traditional ordinal response modeling techniques must be exchanged for more specialized approaches. Existing methods perform well on some datasets, but there is room for improvement in terms of variable selection and predictive accuracy. Therefore, we extended an impressive binary response modeling technique, Feature Augmentation via Nonparametrics and Selection, to the ordinal response setting. Through simulation studies and analyses of high-throughput genomic datasets, we showed that our Ordinal FANS method is sensitive and specific when discriminating between important and unimportant features from the high-dimensional feature space and is highly competitive in terms of predictive accuracy. Discrete survival time is another example of an ordinal response. For many illnesses and chronic conditions, it is impossible to record the precise date and time of disease onset or relapse. Further, the HIPPA Privacy Rule prevents recording of protected health information which includes all elements of dates (except year), so in the absence of a “limited dataset,” date of diagnosis or date of death are not available for calculating overall survival. Thus, we developed a method that is suitable for modeling high-dimensional discrete survival time data and assessed its performance by conducting a simulation study and by predicting the discrete survival times of acute myeloid leukemia patients using a high-dimensional dataset

Methods for Predicting an Ordinal Response with High-Throughput Genomic Data

Multigenic diagnostic and prognostic tools can be derived for ordinal clinical outcomes using data from high-throughput genomic experiments. A challenge in this setting is that the number of predictors is much greater than the sample size, so traditional ordinal response modeling techniques must be exchanged for more specialized approaches. Existing methods perform well on some datasets, but there is room for improvement in terms of variable selection and predictive accuracy. Therefore, we extended an impressive binary response modeling technique, Feature Augmentation via Nonparametrics and Selection, to the ordinal response setting. Through simulation studies and analyses of high-throughput genomic datasets, we showed that our Ordinal FANS method is sensitive and specific when discriminating between important and unimportant features from the high-dimensional feature space and is highly competitive in terms of predictive accuracy. Discrete survival time is another example of an ordinal response. For many illnesses and chronic conditions, it is impossible to record the precise date and time of disease onset or relapse. Further, the HIPPA Privacy Rule prevents recording of protected health information which includes all elements of dates (except year), so in the absence of a “limited dataset,” date of diagnosis or date of death are not available for calculating overall survival. Thus, we developed a method that is suitable for modeling high-dimensional discrete survival time data and assessed its performance by conducting a simulation study and by predicting the discrete survival times of acute myeloid leukemia patients using a high-dimensional dataset

Political Orientation and the Decision to Major in Economics: Some Preliminary Observations

Studies find that students major in economics for a variety of reasons. None, however, have examined students' political orientations as a possible factor in their choice of majors. Economics, as compared to other social sciences, tends to produce conservative policy recommendations. This pilot study explores whether more conservative students are attracted to economics. Our study found that men with conservative political leanings are more likely to major in economics and that male students in economics are more conservative than female students. Political orientation, however, does not appear to be a significant factor in the choice of a major for women.

A role for the cleaved cytoplasmic domain of E-cadherin in the nucleus

Cell-cell contacts play a vital role in intracellular signaling, although the molecular mechanisms of these signaling pathways are not fully understood. E-cadherin, an important mediator of cell-cell adhesions, has been shown to be cleaved by γ-secretase. This cleavage releases a fragment of E-cadherin, E-cadherin C-terminal fragment 2 (E-cad/CTF2), into the cytosol. Here, we study the fate and function of this fragment. First, we show that coexpression of the cadherin-binding protein, p120 catenin (p120), enhances the nuclear translocation of E-cad/CTF2. By knocking down p120 with short interfering RNA, we also demonstrate that p120 is necessary for the nuclear localization of E-cad/CTF2. Furthermore, p120 enhances and is required for the specific binding of E-cad/CTF2 to DNA. Finally, we show that E-cad/CTF2 can regulate the p120-Kaiso-mediated signaling pathway in the nucleus. These data indicate a novel role for cleaved E-cadherin in the nucleus

Entropy-induced separation of star polymers in porous media

We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of $f$-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function $g(r) \sim r^{-a}$. Applying the field-theoretical renormalization group approach we show in a double expansion in $\epsilon=4-d$ and $\delta=4-a$ that there is a range of correlation strengths $\delta$ for which the disorder changes the scaling behavior of star polymers. In a second approach we calculate for fixed space dimension $d=3$ and different values of the correlation parameter $a$ the corresponding scaling exponents $\gamma_f$ that govern entropic effects. We find that $\gamma_f-1$, the deviation of $\gamma_f$ from its mean field value is amplified by the disorder once we increase $\delta$ beyond a threshold. The consequences for a solution of diluted chain and star polymers of equal molecular weight inside a porous medium are: star polymers exert a higher osmotic pressure than chain polymers and in general higher branched star polymers are expelled more strongly from the correlated porous medium. Surprisingly, polymer chains will prefer a stronger correlated medium to a less or uncorrelated medium of the same density while the opposite is the case for star polymers.Comment: 14 pages, 7 figure

Enhancing Robustness and Immunization in geographical networks

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, the strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain the explicit form of the percolation threshold $q_{c}$ for networks containing arbitrary order cycles. For 3-cycles, the dependence of $q_c$ on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with an analytical evidence.Comment: 6 pages, 8 figure

Multifractality of Brownian motion near absorbing polymers

We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi^4-field theory relating higher moments of the Laplacian field of Brownian motion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity properties which are necessarily found for multifractal scaling but unusual for power of field operators in field theory. Using a field-theoretic renormalization group approach we obtain the multifractal spectrum for absorbtion at the core of a polymer star as an asymptotic series. We evaluate these series using resummation techniques.Comment: 18 pages, revtex, 6 ps-figure

Detailed studies of non-linear magneto-optical resonances at D1 excitation of Rb-85 and Rb-87 for partially resolved hyperfine F-levels

Experimental signals of non-linear magneto-optical resonances at D1 excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The D1 transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. Great care was taken to obtain accurate experimental signals and avoid systematic errors. The experimental signals were reproduced very well at each hyperfine transition and over a wide range of laser power densities, beam diameters, and laser detunings from the exact transition frequency. The bright resonance expected at the F_g=1 --> F_e=2 transition of Rb-87 has been observed. A bright resonance was observed at the F_g=2 --> F_e=3 transition of Rb-85, but displaced from the exact position of the transition due to the influence of the nearby F_g=2 --> F_e=2 transition, which is a dark resonance whose contrast is almost two orders of magnitude larger than the contrast of the bright resonance at the F_g=2 --> F_e=3 transition. Even in this very delicate situation, the theoretical model described in detail the experimental signals at different laser detunings.Comment: 11 pages, 9 figure