On dominant contractions and a generalization of the zero-two law

Zaharopol proved the following result: let T,S:L^1(X,{\cf},\m)\to L^1(X,{\cf},\m) be two positive contractions such that $T\leq S$. If $\|S-T\|<1$ then $\|S^n-T^n\|<1$ for all n\in\bn. In the present paper we generalize this result to multi-parameter contractions acting on $L^1$. As an application of that result we prove a generalization of the "zero-two" law.Comment: 10 page

Thermodynamic and dynamic anomalies for a three dimensional isotropic core-softened potential

Using molecular dynamics simulations and integral equations (Rogers-Young, Percus-Yevick and hypernetted chain closures) we investigate the thermodynamic of particles interacting with continuous core-softened intermolecular potential. Dynamic properties are also analyzed by the simulations. We show that, for a chosen shape of the potential, the density, at constant pressure, has a maximum for a certain temperature. The line of temperatures of maximum density (TMD) was determined in the pressure-temperature phase diagram. Similarly the diffusion constant at a constant temperature, $D$, has a maximum at a density $\rho_{max}$ and a minimum at a density $\rho_{min}<\rho_{max}$. In the pressure-temperature phase-diagram the line of extrema in diffusivity is outside of TMD line. Although in this interparticle potential lacks directionality, this is the same behavior observed in SPC/E water.Comment: 16 page

Evolution of collision numbers for a chaotic gas dynamics

We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different pairs of particles grow as functions of time. We observe that these numbers can be represented as a time-integral of a function on the phase space. Assuming the results of the ergodic theory apply, we describe the evolution of the numbers by an effective Langevin dynamics. We use the facts that hold for these dynamics with probability one, in order to establish properties of a single trajectory of the system. We find that for any triplet of particles there will be an infinite sequence of moments of time, when the numbers of collisions of all three different pairs of the triplet will be equal. Moreover, any value of difference of collision numbers of pairs in the triplet will repeat indefinitely. On the other hand, for larger number of pairs there is but a finite number of repetitions. Thus the ergodic theory produces a limitation on the dynamics.Comment: 4 pages, published versio

Sharp error terms for return time statistics under mixing conditions

We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by T(A) the time elapsed until the process spells the finite string A and by S(A) the number of consecutive repetitions of A. We prove that, if the length of the string grows unbondedly, (1) the distribution of T(A), when the process starts with A, is well aproximated by a certain mixture of the point measure at the origin and an exponential law, and (2) S(A) is approximately geometrically distributed. We provide sharp error terms for each of these approximations. The errors we obtain are point-wise and allow to get also approximations for all the moments of T(A) and S(A). To obtain (1) we assume that the process is phi-mixing while to obtain (2) we assume the convergence of certain contidional probabilities

Enhanced bioremediation of subsurface contamination: Enzyme recruitment and redesign

Subsurface systems containing radionuclide, heavy metal, and organic wastes must be carefully attended to avoid further impacts to the environment or exposures to human populations. It is appropriate, therefore, to invest in basic research to develop the requisite tools and methods for addressing complex cleanup problems. The rational modification of subsurface microoganisms by enzyme recruitment and enzyme design, in concert with engineered systems for delivery of microorganisms and nutrients to the contaminated zone, are potentially useful tools in the spectrum of approaches that will be required for successful remediation of deep subsurface contamination

Scale-free networks as preasymptotic regimes of superlinear preferential attachment

We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing network models that perfectly match the structure of some real scale-free networks, such as the Internet. We obtain an analytic solution, supported by extensive simulations, for the degree distribution in superlinearly growing networks with arbitrary average degree, and confirm that in the true thermodynamic limit these networks are indeed degenerate, i.e., almost all nodes have low degrees. We then show that superlinear growth has vast preasymptotic regimes whose depths depend both on the average degree in the network and on how superlinear the preference kernel is. We demonstrate that a superlinearly growing network model can reproduce, in its preasymptotic regime, the structure of a real network, if the model captures some sufficiently strong structural constraints -- rich-club connectivity, for example. These findings suggest that real scale-free networks of finite size may exist in preasymptotic regimes of network evolution processes that lead to degenerate network formations in the thermodynamic limit

Supporting parent-child conversations in a history museum

BACKGROUND: Museums can serve as rich resources for families to learn about the social world through engagement with exhibits and parent-child conversation about exhibits. AIMS: This study examined ways of engaging parents and child about two related exhibits at a cultural and history museum. Sample participants consisted of families visiting the Animal Antics and the Gone Potty exhibits at the British Museum. METHODS: Whilst visiting two exhibits at the British Museum, 30 families were assigned to use a backpack of activities, 13 were assigned to a booklet of activities, and 15 were assigned to visit the exhibits without props (control condition). RESULTS: Compared to the families in the control condition, the interventions increased the amount of time parents and children engaged together with the exhibit. Additionally, recordings of the conversations revealed that adults asked more questions related to the exhibits when assigned to the two intervention conditions compared to the control group. Children engaged in more historical talk when using the booklets than in the other two conditions. CONCLUSIONS: The findings suggest that providing support with either booklets or activities for children at exhibits may prove beneficial to parent-child conversations and engagement with museum exhibits

How do you define recovery? A qualitative study of patients with eating disorders, their parents, and clinicians

ObjectiveRecovery from an eating disorder (ED) may be defined differently by different stakeholders. We set out to understand the definition of ED recovery from the perspective of patients, their parents, and clinicians.MethodWe recruited patients with EDs (n = 24, ages 12–23 years) representing different diagnoses (anorexia nervosa n = 17, bulimia nervosa n = 4, binge‐ED n = 2, avoidant/restrictive food intake disorder n = 1), along with their parents (n = 20), dietitians (n = 11), therapists (n = 14), and primary care providers (n = 9) from three sites: Boston Children’s Hospital, University of Michigan C. S. Mott Children’s Hospital, and Penn State Hershey Children’s Hospital. In‐depth, semi‐structured, qualitative interviews explored participants’ definitions of recovery. Interviews were analyzed using inductive data‐driven thematic analysis. Statistical analyses followed to examine the distribution within each theme by respondent type.ResultsQualitative analysis resulted in the emergence of four overarching themes of ED recovery: (a) psychological well‐being, (b) eating‐related behaviors/attitudes, (c) physical markers, and (d) self‐acceptance of body image. Endorsement of themes two and four did not significantly differ between patients, parents, and clinicians. Clinicians were significantly more likely to endorse theme one (χ2 = 9.90, df = 2, p = .007, φc = 0.356) and theme three (χ2 = 6.42, df = 2, p = .04, φc = 0.287) than patients and parents.DiscussionOur study demonstrates overwhelming support for psychological markers as indicators of ED recovery by all three groups. Clinicians should remain open to additional markers of recovery such as body acceptance and eating‐related behaviors/emotions that may be of critical importance to patients and their caregivers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156211/2/eat23294_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156211/1/eat23294.pd

Shuffling cards, factoring numbers, and the quantum baker's map

It is pointed out that an exactly solvable permutation operator, viewed as the quantization of cyclic shifts, is useful in constructing a basis in which to study the quantum baker's map, a paradigm system of quantum chaos. In the basis of this operator the eigenfunctions of the quantum baker's map are compressed by factors of around five or more. We show explicitly its connection to an operator that is closely related to the usual quantum baker's map. This permutation operator has interesting connections to the art of shuffling cards as well as to the quantum factoring algorithm of Shor via the quantum order finding one. Hence we point out that this well-known quantum algorithm makes crucial use of a quantum chaotic operator, or at least one that is close to the quantization of the left-shift, a closeness that we also explore quantitatively.Comment: 12 pgs. Substantially elaborated version, including a new route to the quantum bakers map. To appear in J. Phys.