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Considers a problem of simple random walks to study distributions of variances. Describes watching a drunk over a period of nights, taking a number of steps per night. Explores the full probability distribution for the variance of the data string and discusses the connection of the results to the problem of data binning. (Author/NB)

We investigate the long-time properties of a dynamic, out-of-equilibrium network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents' opinions are fixed, they have a preferred degree which leads them to endlessly create and delete links. Our evolving network is shaped by homophily/heterophily, a form of social interaction by which individuals tend to establish links with others having similar/dissimilar opinions. Using Monte Carlo simulations and a detailed mean-field analysis, we investigate how the sizes of the communities and the degree of homophily/heterophily affect the network structure. In particular, we show that when the network is subject to enough heterophily, an 'overwhelming transition' occurs: individuals of the smaller community are overwhelmed by links from the larger group, and their mean degree greatly exceeds the preferred degree. This and related phenomena are characterized by the network's total and joint degree distributions, as well as the fraction of links across both communities and that of agents having fewer edges than the preferred degree. We use our mean-field theory to discuss the network's polarization when the group sizes and level of homophily vary.

We consider a dynamic network of individuals that may hold one of two different opinions in a two-party society. As a dynamical model, agents can endlessly create and delete links to satisfy a preferred degree, and the network is shaped by \emph{homophily}, a form of social interaction. Characterized by the parameter $J \in [-1,1]$, the latter plays a role similar to Ising spins: agents create links to others of the same opinion with probability $(1+J)/2$, and delete them with probability $(1-J)/2$. Using Monte Carlo simulations and mean-field theory, we focus on the network structure in the steady state. We study the effects of $J$ on degree distributions and the fraction of cross-party links. While the extreme cases of homophily or heterophily ($J= \pm 1$) are easily understood to result in complete polarization or anti-polarization, intermediate values of $J$ lead to interesting features of the network. Our model exhibits the intriguing feature of an "overwhelming transition" occurring when communities of different sizes are subject to sufficient heterophily: agents of the minority group are oversubscribed and their average degree greatly exceeds that of the majority group. In addition, we introduce an original measure of polarization which displays distinct advantages over the commonly used average edge homogeneity., Comment: The paper includes 12 pages and 9 figures

Purpose: Increasingly, women newly diagnosed with breast cancer are being offered treatment-focused genetic testing (TFGT). As the demand for TFGT increases, streamlined methods of genetic education are needed. Method(s): In this noninferiority trial, women aged <50 years with either a strong family history (FH+) or other features suggestive of a germ-line mutation (FH-) were randomized before definitive breast cancer surgery to receive TFGT education either as brief written materials (intervention group (IG)) or during a genetic counseling session at a familial cancer clinic (usual-care group (UCG)). Women completed self-report questionnaires at four time points over 12 months. Result(s): A total of 135 women were included in the analysis, all of whom opted for TFGT. Decisional conflict about TFGT choice (primary outcome) was not inferior in the IG compared with the UCG (noninferiority margin of -10; mean difference = 2.45; 95% confidence interval -2.87-7.76; P = 0.36). Costs per woman counseled in the IG were significantly lower (AUD$89) compared with the UCG (AUD$173; t(115) = 6.02; P < 0.001). Conclusion(s): A streamlined model of educating women newly diagnosed with breast cancer about TFGT seems to be a cost-effective way of delivering education while ensuring that women feel informed and supported in their decision making, thus freeing resources for other women to access TFGT.

We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in [EPL 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a susceptible voter of type $q_1$ or $q_2$, or is an inflexible zealot. At each time step, a $q_i$-susceptible voter ($i = 1,2$) consults a group of $q_i$ neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever $q_1 \neq q_2$ and is characterized by two distinct regimes of low and high density of zealotry. Here, by combining analytical and numerical methods, we investigate the non-equilibrium stationary state of the system in terms of its probability distribution, non-vanishing currents and unequal-time two-point correlation functions. We also study the switching times properties of the model by exploiting an approximate mapping onto the model of [Phys. Rev. E 92, 012803 (2015)] that satisfies the detailed balance, and also outline some properties of the model near criticality., Comment: 17 pages, 12 figures

We introduce an heterogeneous nonlinear $q$-voter model with zealots and two types of susceptible voters, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a zealot or a susceptible voter of type $q_1$ or $q_2$. While here zealots never change their opinion, a $q_i$-susceptible voter ($i=1,2$) consults a group of $q_i$ neighbors at each time step, and adopts their opinion if all group members agree. We show that this model violates the detailed balance whenever $q_1 \neq q_2$ and has surprisingly rich properties. Here, we focus on the characterization of the model's non-equilibrium stationary state (NESS) in terms of its probability distribution and currents in the distinct regimes of low and high density of zealotry. We unveil the NESS properties in each of these phases by computing the opinion distribution and the circulation of probability currents, as well as the two-point correlation functions at unequal times (formally related to a "probability angular momentum"). Our analytical calculations obtained in the realm of a linear Gaussian approximation are compared with numerical results., Comment: 6 pages, 2 figures, supplementary material and movie available at https://dx.doi.org/10.6084/m9.figshare.2060595

Background: Germline BRCA1 and BRCA2 mutation testing offered shortly after a breast cancer diagnosis to inform women's treatment choices - treatment-focused genetic testing 'TFGT' - has entered clinical practice in specialist centers and is likely to be soon commonplace in acute breast cancer management, especially for younger women. Yet the optimal way to deliver information about TFGT to younger women newly diagnosed with breast cancer is not known, particularly for those who were not suspected of having a hereditary breast cancer syndrome prior to their cancer diagnosis. Also, little is known about the behavioral and psychosocial impact or cost effectiveness of educating patients about TFGT. This trial aims to examine the impact and efficiency of two models of educating younger women newly diagnosed with breast cancer about genetic testing in order to provide evidence for a safe and effective future clinical pathway for this service.Design/methods: In this non-inferiority randomized controlled trial, 140 women newly diagnosed with breast cancer (aged less than 50 years) are being recruited from nine cancer centers in Australia. Eligible women with either a significant family history of breast and/or ovarian cancer or with other high risk features suggestive of a mutation detection rate of > 10% are invited by their surgeon prior to mastectomy or radiotherapy. After completing the first questionnaire, participants are randomized to receive either: (a) an educational pamphlet about genetic testing (intervention) or (b) a genetic counseling appointment at a family cancer center (standard care). Each participant is offered genetic testing for germline BRCA mutations. Decision-related and psychosocial outcomes are assessed over 12 months and include decisional conflict (primary outcome);uptake of bilateral mastectomy and/or risk-reducing salpingo-oophorectomy; cancer-specific- and general distress; family involvement in decision making; and decision regret. A process

A very large class of kinetic growth processes manifest oscillatory behaviour in a variety of physical quantities such as the propagation of the growing interface and the density of the resulting cluster. The authors demonstrate that these oscillations should generically display quasiperiodic behaviour. Using a formalism based on the projection method for quasicrystalline spectra, they elucidate general features such as the dominant frequency and amplitude of the oscillations. They also briefly discuss the effects of interfacial roughening on the spectra of the oscillations.

Within the solid-on-solid (SOS) approximation, we carry out a calculation of the orientational dependence of the step stiffness on a square lattice with nearest- and next-nearest-neighbor interactions. At low temperature our result reduces to a simple, transparent expression. The effect of the strongest trio (three-site, nonpairwise) interaction can easily be incorporated by modifying the interpretation of the two pairwise energies. The work is motivated by a calculation based on nearest neighbors that underestimates the stiffness by a factor of 4 in directions away from close-packed directions, and a subsequent estimate of the stiffness in the two high-symmetry directions alone that suggested that inclusion of next-nearest-neighbor attractions could fully explain the discrepancy. As in these earlier papers, the discussion focuses on Cu(001).

The critical behavior of $d$-dimensional systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial Lifshitz point where a wave-vector instability occurs in an $m$-dimensional subspace ${\mathbb R}^m$ ($m{>}1$). Field theoretic renormalization group techniques are exploited to examine the effects of terms in the Hamiltonian that break the rotational symmetry of the Euclidean group ${\mathbb E}(m)$. The framework for considering general operators of second order in $\bm{\phi}$ and fourth order in the derivatives $\partial_\alpha $ with respect to the Cartesian coordinates $x_\alpha $ of ${\mathbb R}^m$ is presented. For the specific case of systems with cubic anisotropy, the effects of having an additional term, $\sum_{\alpha=1}^m(\partial_\alpha^2\bm{\phi})^2$, are investigated in an $\epsilon$ expansion about the upper critical dimension $d^{*}(m)=4+m/2$. Its associated crossover exponent is computed to order $\epsilon^2$ and found to be positive, so that it is a \emph{relevant} perturbation on a model isotropic in ${\mathbb R}^m$., Comment: Revtex4, 11 pages, to appear in PRB; v2: some additional references and minor changes

For students familiar with equilibrium statistical mechanics, the notion of a positive specific heat, being intimately related to the idea of stability, is both intuitively reasonable and mathematically provable. However, for systems in nonequilibrium stationary states, coupled to more than one energy reservoir, a negative specific heat is entirely possible. We present a minimal system that displays this phenomenon. For a system in contact with two thermal baths at different temperatures, the (internal) energy may increase when a thermostat is turned down. In another context, a similar phenomenon is negative conductivity, where a current may increase by decreasing the drive (for example, an external electric field). The counter-intuitive behavior in both processes may be described as getting more from pushing less. The crucial ingredients for this phenomenon and the elements needed for a minimal system are also presented.

It is shown that the interface model introduced in Phys. Rev. Lett. 86, 2369 (2001) violates fundamental symmetry requirements for vanishing gravitational acceleration $g$, so that its results cannot be applied to critical properties of interfaces for $g\to 0$., Comment: A Comment on a recent Letter by J.G. Segovia-L\'opez and V. Romero-Roch\'{\i}n, Phys. Rev. Lett.86, 2369 (2001). Latex file, 1 page (revtex)

We consider critical systems, such as the percolation problem, whose symmetry permits an invariant interaction of third order in the fluctuating fields φ. In the renormalization-group approach one is naturally led to look for infrared-stable fixed points which yield ε expansions in 6−ε dimensions, with ε=3 as the physical value. Since the Gaussian fixed point becomes unstable to φ4 interactions for ε>2, it is important to check that the fixed point obtained in the ε expansion remains stable to such perturbations. We report the calculation to first order in ε of the corrections to scaling induced by (stability with respect to) φ4 interactions in a general class of such theories. The results indicate that φ4 interactions remain irrelevant in the percolation problem.

The question of a possible difference between the universality classes of fluids and Ising-like magnets is addressed by perturbation theory and the renormalization group. The most dangerous possibility is that of an φ5 addition to the usual φ4 theory. We show that no φ5 fixed point exists in the framework of an expansion around d=10/3. Further we show that to O(ε2/4), ε4≡4−d, the ordinary φ4 fixed point is stable against the perturbations that mix with φ5. Two new correction-to-scaling exponents are found. One of the exponents, Δ5, is poorly determined with a range of values from 0.5 to 1.0 compatible with the O(ε2/4) result. However, its positivity rules out a separate fluid fixed point, indicating fluid-magnet asymptotic universality. The second exponent, Δ3, can be determined exactly: Δ3=1−α−β. This implies the universal existence of a contribution to the fluid diameter scaling like the internal energy.

The exact surface tension for all angles and temperatures is given for the two-dimensional square Ising system with anisotropic nearest-neighbour interactions. Using this in the Wulff construction, droplet shapes are computed and illustrated. Letting temperature approach zero allows explicit study of the roughening transition in this model. Results are compared with those of the solid-on-solid approximation.