Number of distinct sites visited by N random walkers on a Euclidean lattice

The evaluation of the average number S_N(t) of distinct sites visited up to time t by N independent random walkers all starting from the same origin on an Euclidean lattice is addressed. We find that, for the nontrivial time regime and for large N, S_N(t) \approx \hat S_N(t) (1-\Delta), where \hat S_N(t) is the volume of a hypersphere of radius (4Dt \ln N)^{1/2}, \Delta={1/2}\sum_{n=1}^\infty \ln^{-n} N \sum_{m=0}^n s_m^{(n)} \ln^{m} \ln N, d is the dimension of the lattice, and the coefficients s_m^{(n)} depend on the dimension and time. The first three terms of these series are calculated explicitly and the resulting expressions are compared with other approximations and with simulation results for dimensions 1, 2, and 3. Some implications of these results on the geometry of the set of visited sites are discussed.Comment: 15 pages (RevTex), 4 figures (eps); to appear in Phys. Rev.

Survival probability and order statistics of diffusion on disordered media

We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem we assume that, for short times, the survival probability (the probability that a single random walker is not absorbed by a hyperspherical surface during some time interval) decays for disordered media in the same way as for Euclidean and some class of deterministic fractal lattices. This conjecture is checked by simulation on the incipient percolation aggregate embedded in two dimensions. Arbitrary moments of t_{j,N} are expressed in terms of an asymptotic series in powers of 1/ln N which is formally identical to those found for Euclidean and (some class of) deterministic fractal lattices. The agreement of the asymptotic expressions with simulation results for the two-dimensional percolation aggregate is good when the boundary is defined in terms of the chemical distance. The agreement worsens slightly when the Euclidean distance is used.Comment: 8 pages including 9 figure

Family Health Development in Life Course Research: A Scoping Review of Family Functioning Measures

BACKGROUND AND OBJECTIVES: Our objective is to identify common family functioning measurement tools and assess their compatibility with family-health development and life-course perspectives. METHODS: Data sources include PubMed, ERIC, CINAHL, Families and Societies Worldwide, PsychInfo, Web of Science, PsychNet, and Health and Psychosocial Instruments. Title and abstract screening and full-text review of articles were conducted by multiple reviewers based on prespecified inclusion criteria. Data extraction focused on features of identified measurements tools, including: (1) name (2) domains of family functioning measured, (3) established psychometric properties, and (4) original context of psychometric evaluation (eg, details about the study sample). RESULTS: Of the 50 measurement tools identified, 94% measured organizational patterns (eg, flexibility, connectedness, or resources), 46% measured belief systems (eg, making meaning of adversity, or positive outlook), and 54% measured communication processes (eg, open emotional sharing, or collaborative problem-solving). CONCLUSIONS: Existing measures of family functioning can aid life-course researchers in understanding family processes as contexts for health and well-being. There also remain opportunities to refine or develop measures of family functioning more compatible with a life-course perspective that assess family processes (1) at various life stages; (2) with various backgrounds, identities, structures, and experiences; and (3) embedded in or impacted by various contexts that may facilitate or hinder family functioning

Induced QCD and Hidden Local ZN Symmetry

We show that a lattice model for induced lattice QCD which was recently proposed by Kazakov and Migdal has a $Z_N$ gauge symmetry which, in the strong coupling phase, results in a local confinement where only color singlets are allowed to propagate along links and all Wilson loops for non-singlets average to zero. We argue that, if this model is to give QCD in its continuum limit, it must have a phase transition. We give arguments to support presence of such a phase transition

Some exact results for the trapping of subdiffusive particles in one dimension

We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided random distribution of static absorbing traps with concentration c. The survival probability Phi(t) that the random walker is not trapped by time t is obtained exactly in both versions of the problem through a fractional diffusion approach. Comparison with simulation results is madeComment: 15 pages, 2 figure

Carbon Nanotubes as Nanoelectromechanical Systems

We theoretically study the interplay between electrical and mechanical properties of suspended, doubly clamped carbon nanotubes in which charging effects dominate. In this geometry, the capacitance between the nanotube and the gate(s) depends on the distance between them. This dependence modifies the usual Coulomb models and we show that it needs to be incorporated to capture the physics of the problem correctly. We find that the tube position changes in discrete steps every time an electron tunnels onto it. Edges of Coulomb diamonds acquire a (small) curvature. We also show that bistability in the tube position occurs and that tunneling of an electron onto the tube drastically modifies the quantized eigenmodes of the tube. Experimental verification of these predictions is possible in suspended tubes of sub-micron length.Comment: 8 pages, 5 eps figures included. Major changes; new material adde

No Association Between Screening for Hepatocellular Carcinoma and Reduced Cancer-Related Mortality in Patients With Cirrhosis

Background & Aims: Screening patients with cirrhosis for hepatocellular carcinoma (HCC) has been recommended. We conducted a matched case–control study within the US Veterans Affairs (VA) health care system to determine whether screening by abdominal ultrasonography (USS) and/or by measuring serum level of α-fetoprotein (AFP) was associated with decreased cancer-related mortality in patients with cirrhosis. Methods: We defined cases (n = 238) as patients with cirrhosis who died of HCC from January 1, 2013 through August 31, 2015 and had been in VA care with a diagnosis of cirrhosis for at least 4 years before the diagnosis of HCC. We matched each case to 1 control (n = 238), defined as a patient with cirrhosis who did not die of HCC and had been in VA care for at least 4 years before the date of the matched case's HCC diagnosis. Controls were matched to cases by year of cirrhosis diagnosis, race and ethnicity, age, sex, etiology of cirrhosis, Model for End-Stage Liver Disease score, and VA medical center. We identified all USS and serum AFP tests performed within 4 years before the date of HCC diagnosis in cases or the equivalent index date in controls and determined by chart extraction (blinded to case or control status) whether these tests were performed for screening. Results: There were no significant differences between cases and controls in the proportions of patients who underwent screening USS (52.9% vs 54.2%), screening measurement of serum AFP (74.8% vs 73.5%), screening USS or measurement of serum AFP (81.1% vs 79.4%), or screening USS and measurement of serum AFP (46.6% vs 48.3%) within 4 years before the index date, with or without adjusting for potential confounders. There also was no difference in receipt of these screening tests within 1, 2, or 3 years before the index date. Conclusions: In a matched case–control study of the VA health care system, we found that screening patients with cirrhosis for HCC by USS, measurement of serum AFP, either test, or both tests was not associated with decreased HCC-related mortality. We encourage additional case–control studies to evaluate the efficacy of screening for HCC in other health care systems, in which available records are sufficiently detailed to enable identification of the indication for USS and AFP tests

Reply

Reply. We are grateful for the interest others have shown in our paper, which allowed us to clarify critical aspects of the case-control study design and the nature of our study population

Branching Fractions for D0 -> K+K- and D0 -> pi+pi-, and a Search for CP Violation in D0 Decays

Using the large hadroproduced charm sample collected in experiment E791 at Fermilab, we have measured ratios of branching fractions for the two-body singly-Cabibbo-suppressed charged decays of the D0: (D0 -> KK)/(D0 -> Kpi) = 0.109 +- 0.003 +- 0.003, (D0 -> pipi)/(D0 -> Kpi) = 0.040 +- 0.002 +- 0.003, and (D0 -> KK)/(D0 -> pipi) = 2.75 +- 0.15 +- 0.16. We have looked for differences in the decay rates of D0 and D0bar to the CP eigenstates K+K- and pi+pi-, and have measured the CP asymmetry parameters A_CP(K+K-) = -0.010 +- 0.049 +- 0.012 and A_CP(pi+pi-) = -0.049 +- 0.078 +- 0.030, both consistent with zero.Comment: 10 Postscript pages, including 2 figures. Submitted to Phys. Lett.