A nilpotent IP polynomial multiple recurrence theorem

We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

Singularity results for functional equations driven by linear fractional transformations

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.Comment: 14 pages, Title changed, to appear in Journal of Theoretical Probabilit

Covering Partial Cubes with Zones

A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of a hypercube in which the graph can be embedded. We consider the problem of covering the vertices of a partial cube with the minimum number of zones. The problem admits several special cases, among which are the problem of covering the cells of a line arrangement with a minimum number of lines, and the problem of finding a minimum-size fibre in a bipartite poset. For several such special cases, we give upper and lower bounds on the minimum size of a covering by zones. We also consider the computational complexity of those problems, and establish some hardness results

The triangle map: a model of quantum chaos

We study an area preserving parabolic map which emerges from the Poincar\' e map of a billiard particle inside an elongated triangle. We provide numerical evidence that the motion is ergodic and mixing. Moreover, when considered on the cylinder, the motion appear to follow a gaussian diffusive process.Comment: 4 pages in RevTeX with 4 figures (in 6 eps-files

Recurrence and algorithmic information

In this paper we initiate a somewhat detailed investigation of the relationships between quantitative recurrence indicators and algorithmic complexity of orbits in weakly chaotic dynamical systems. We mainly focus on examples.Comment: 26 pages, no figure

Quenched Averages for self-avoiding walks and polygons on deterministic fractals

We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W_n(S), and rooted self-avoiding polygons P_n(S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P_n(S), and W_n(S) for an arbitrary point S on the lattice. These are used to compute the averages $, ,$ and $<log W_n(S)>$ over different positions of S. We find that the connectivity constant $\mu$, and the radius of gyration exponent $\nu$ are the same for the annealed and quenched averages. However, $~ n log \mu + (\alpha_q -2) log n$, and $~ n log \mu + (\gamma_q -1)log n$, where the exponents $\alpha_q$ and $\gamma_q$ take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives $\alpha_q \simeq 0.72837 \pm 0.00001$; and $\gamma_q \simeq 1.37501 \pm 0.00003$, to be compared with the annealed values $\alpha_a = 0.73421$ and $\gamma_a = 1.37522$.Comment: 17 pages, 10 figures, submitted to Journal of Statistical Physic

Equilibrium states of the pressure function for products of matrices

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to \R$ be the pressure function of $\{M_i\}_{i=1}^\ell$. We show that for each $q>0$, there are at most $d$ ergodic $q$-equilibrium states of $P$, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

A cancer rainbow mouse for visualizing the functional genomics of oncogenic clonal expansion.

Field cancerization is a premalignant process marked by clones of oncogenic mutations spreading through the epithelium. The timescales of intestinal field cancerization can be variable and the mechanisms driving the rapid spread of oncogenic clones are unknown. Here we use a Cancer rainbow (Crainbow) modelling system for fluorescently barcoding somatic mutations and directly visualizing the clonal expansion and spread of oncogenes. Crainbow shows that mutations of ß-catenin (Ctnnb1) within the intestinal stem cell results in widespread expansion of oncogenes during perinatal development but not in adults. In contrast, mutations that extrinsically disrupt the stem cell microenvironment can spread in adult intestine without delay. We observe the rapid spread of premalignant clones in Crainbow mice expressing oncogenic Rspondin-3 (RSPO3), which occurs by increasing crypt fission and inhibiting crypt fixation. Crainbow modelling provides insight into how somatic mutations rapidly spread and a plausible mechanism for predetermining the intratumor heterogeneity found in colon cancers

“Swapping” Families: Serial Parenting and Economic Support for Children

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71408/1/j.1741-3737.2000.00111.x.pd

Conflito trabalho-família, auto eficácia parental e estilos parentais percebidos em pais e mães da cidade de Talca no Chile

The relationship between levels of work-family conflict, parental self-efficacy and perceived parenting styles in a group of 43 school children and both working parents is analyzed, controlling for socio-demographic variables. Also, gender differences are identified in the variables and the relationship between them in relation to the number of children. Three instruments were applied to the sample for measuring the referred variables. A significant and negative relationship is observed between levels of work-family conflict and parental self-efficacy (r = -0.484, P <0.001). The authoritarian parenting style has greater association with self-efficacy (r = 0.301, P = 0.005). A significant and negative relationship between self-efficacy and number of children (r = -0.257, P = 0.017) is reported. Finally, it is concluded that women have greater work-family conflict than men.Se analiza la relación existente entre los niveles de conflicto trabajo-familia, autoeficacia parental y estilos parentales percibidos en un grupo de 43 niños estudiantes y ambos padres trabajadores, controlando las variables sociodemográficas. Así mismo, se identifican las diferencias por género en las variables, y la relación que existe entre ellas con respecto al número de hijos. A la muestra le fueron aplicados tres instrumentos de medición de las variables referidas. Se observa una relación significativa y negativa entre los niveles de conflicto trabajo-familia y la autoeficacia parental (r= -0,484; p<0,001). El estilo parental autoritario presenta mayor asociación con autoeficacia (r=0,301; p=0,005). Se reporta una relación significativa y negativa entre autoeficacia y número de hijos (r=-0,257; p=0,017). Finalmente se reporta que las mujeres presentan mayor conflicto trabajo-familia que los hombres.Analisa-se a relação existente entre os níveis de conflito trabalho-família, auto eficácia parental e estilos parentais percebidos em um grupo de 43 crianças estudantes de pais trabalhadores, controlando as variáveis sociodemográficas. Assim mesmo, identificam-se as diferenças por gênero nas variáveis, e a relação que existe entre elas com respeito ao número de filhos. Foram aplicados à mostra três instrumentos de medição das variáveis referidas. Observa-se uma relação significativa e negativa entre os níveis de conflito trabalho-família e a auto eficácia parental (r= -0,484; p<0,001). O estilo parental autoritário apresenta maior associação com autoeficácia (r=0,301; p=0,005). Reporta-se uma relação significativa e negativa entre autoeficácia e número de filhos (r=-0,257; p=0,017). Finalmente reporta-se que as mulheres apresentam maior conflito trabalho-família que os homens