Enumerating Cyclic Orientations of a Graph

Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set; it is cyclic otherwise. As far as we know, only the enumeration of acyclic orientations has been addressed in the literature. In this paper, we pose the problem of efficiently enumerating all the \emph{cyclic} orientations of an undirected connected graph with $n$ vertices and $m$ edges, observing that it cannot be solved using algorithmic techniques previously employed for enumerating acyclic orientations.We show that the problem is of independent interest from both combinatorial and algorithmic points of view, and that each cyclic orientation can be listed with $\tilde{O}(m)$ delay time. Space usage is $O(m)$ with an additional setup cost of $O(n^2)$ time before the enumeration begins, or $O(mn)$ with a setup cost of $\tilde{O}(m)$ time

Financial factor influence on scaling and memory of trading volume in stock market

We study the daily trading volume volatility of 17,197 stocks in the U.S. stock markets during the period 1989--2008 and analyze the time return intervals $\tau$ between volume volatilities above a given threshold q. For different thresholds q, the probability density function P_q(\tau) scales with mean interval as P_q(\tau)=^{-1}f(\tau/) and the tails of the scaling function can be well approximated by a power-law f(x)~x^{-\gamma}. We also study the relation between the form of the distribution function P_q(\tau) and several financial factors: stock lifetime, market capitalization, volume, and trading value. We find a systematic tendency of P_q(\tau) associated with these factors, suggesting a multi-scaling feature in the volume return intervals. We analyze the conditional probability P_q(\tau|\tau_0) for $\tau$ following a certain interval \tau_0, and find that P_q(\tau|\tau_0) depends on \tau_0 such that immediately following a short/long return interval a second short/long return interval tends to occur. We also find indications that there is a long-term correlation in the daily volume volatility. We compare our results to those found earlier for price volatility.Comment: 17 pages, 6 figure

Experiences of Improving Access to Psychological Therapy Services for Perinatal Mental Health Difficulties: a Qualitative Study of Women's and Therapists' Views

BACKGROUND: Perinatal mental health difficulties are highly prevalent. In England, the Improving Access to Psychological Therapy (IAPT) programme provides evidence-based psychological treatment, predominantly in the form of brief manualized cognitive behavioural therapy (CBT), to people with mild to moderate depression or anxiety. Yet little is known about the experiences of women referred to IAPT with perinatal mental health difficulties. AIMS: The aim of this qualitative study was to investigate how women view IAPT support for perinatal mental health. We also gained the perspective of IAPT therapists. METHOD: Semi-structured interviews were conducted with twelve women who had been referred to and/or received therapy from IAPT during the perinatal period. Additionally, fourteen IAPT therapists participated in two focus groups. Thematic analysis was used. RESULTS: Key themes centred on barriers to access and the need to tailor support to (expectant) mothers. Women and therapists suggested that experiences could be improved by supporting healthcare professionals to provide women with more help with referrals, better tailoring support to the perinatal context, improving perinatal-specific training, supervision and resources, and offering a more individualized treatment environment. CONCLUSIONS: Overall, women reported positive experiences of support offered by IAPT for perinatal mental health difficulties. However, services should seek to facilitate access to support and to enable therapists to better tailor treatment

Scaling and memory of intraday volatility return intervals in stock market

We study the return interval $\tau$ between price volatilities that are above a certain threshold $q$ for 31 intraday datasets, including the Standard & Poor's 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold $q$, the probability density function $P_q(\tau)$ scales with the mean interval $\bar{\tau}$ as $P_q(\tau)={\bar{\tau}}^{-1}f(\tau/\bar{\tau})$, similar to that found in daily volatilities. Since the intraday records have significantly more data points compared to the daily records, we could probe for much higher thresholds $q$ and still obtain good statistics. We find that the scaling function $f(x)$ is consistent for all 31 intraday datasets in various time resolutions, and the function is well approximated by the stretched exponential, $f(x)\sim e^{-a x^\gamma}$, with $\gamma=0.38\pm 0.05$ and $a=3.9\pm 0.5$, which indicates the existence of correlations. We analyze the conditional probability distribution $P_q(\tau|\tau_0)$ for $\tau$ following a certain interval $\tau_0$, and find $P_q(\tau|\tau_0)$ depends on $\tau_0$, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval $$ increases with $\tau_0$, consistent with the memory found for $P_q(\tau|\tau_0)$. Moreover, we find that return interval records have long term correlations with correlation exponents similar to that of volatility records.Comment: 19 pages, 8 figure

A Universal Model of Global Civil Unrest

Civil unrest is a powerful form of collective human dynamics, which has led to major transitions of societies in modern history. The study of collective human dynamics, including collective aggression, has been the focus of much discussion in the context of modeling and identification of universal patterns of behavior. In contrast, the possibility that civil unrest activities, across countries and over long time periods, are governed by universal mechanisms has not been explored. Here, we analyze records of civil unrest of 170 countries during the period 1919-2008. We demonstrate that the distributions of the number of unrest events per year are robustly reproduced by a nonlinear, spatially extended dynamical model, which reflects the spread of civil disorder between geographic regions connected through social and communication networks. The results also expose the similarity between global social instability and the dynamics of natural hazards and epidemics.Comment: 8 pages, 3 figure

Clusters and Fluctuations at Mean-Field Critical Points and Spinodals

We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different than the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken.Comment: 5 pages, 1 figur

Interfacial separation between elastic solids with randomly rough surfaces: comparison between theory and numerical techniques

We study the distribution of interfacial separations P(u) at the contact region between two elastic solids with randomly rough surfaces. An analytical expression is derived for P(u) using Persson's theory of contact mechanics, and is compared to numerical solutions obtained using (a) a half-space method based on the Boussinesq equation, (b) a Green's function molecular dynamics technique and (c) smart-block classical molecular dynamics. Overall, we find good agreement between all the different approaches.Comment: 25 pages, 12 figure

Contact mechanics: contact area and interfacial separation from small contact to full contact

We present a molecular dynamics study of the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. The numerical calculations mainly focus on the contact area and the interfacial separation from small contact (low load) to full contact (high load). For small load the contact area varies linearly with the load and the interfacial separation depends logarithmically on the load. For high load the contact area approaches the nominal contact area (i.e., complete contact), and the interfacial separation approaches zero. The numerical results have been compared with analytical theory and experimental results. They are in good agreement with each other. The present findings may be very important for soft solids, e.g., rubber, or for very smooth surfaces, where complete contact can be reached at moderate high loads without plastic deformation of the solids.Comment: 15 pages, 23 figure

Factors affecting ammonium uptake in streams - an inter-biome perspective

The Lotic Intersite Nitrogen experiment (LINX) was a coordinated study of the relationships between North American biomes and factors governing ammonium uptake in streams. Our objective was to relate inter-biome variability of ammonium uptake to physical, chemical and biological processes. 2. Data were collected from 11 streams ranging from arctic to tropical and from desert to rainforest. Measurements at each site included physical, hydraulic and chemical characteristics, biological parameters, whole-stream metabolism and ammonium uptake. Ammonium uptake was measured by injection of \u275~-ammonium and downstream measurements of 15N-ammonium concentration. 3. We found no general, statistically significant relationships that explained the variability in ammonium uptake among sites. However, this approach does not account for the multiple mechanisms of ammonium uptake in streams. When we estimated biological demand for inorganic nitrogen based on our measurements of in-stream metabolism, we found good correspondence between calculated nitrogen demand and measured assimilative nitrogen uptake. 4. Nitrogen uptake varied little among sites, reflecting metabolic compensation in streams in a variety of distinctly different biomes (autotrophic production is high where allochthonous inputs are relatively low and vice versa). 5. Both autotrophic and heterotrophic metabolism require nitrogen and these biotic processes dominate inorganic nitrogen retention in streams. Factors that affect the relative balance of autotrophic and heterotrophic metabolism indirectly control inorganic nitrogen uptake