A sharp threshold for minimum bounded-depth and bounded-diameter spanning trees and Steiner trees in random networks

In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to zeta(3)=1/1^3+1/2^3+1/3^3+... as n goes to infinity. We consider spanning trees constrained to have depth bounded by k from a specified root. We prove that if k > log_2 log n+omega(1), where omega(1) is any function going to infinity with n, then the minimum bounded-depth spanning tree still has weight tending to zeta(3) as n -> infinity, and that if k < log_2 log n, then the weight is doubly-exponentially large in log_2 log n - k. It is NP-hard to find the minimum bounded-depth spanning tree, but when k < log_2 log n - omega(1), a simple greedy algorithm is asymptotically optimal, and when k > log_2 log n+omega(1), an algorithm which makes small changes to the minimum (unbounded depth) spanning tree is asymptotically optimal. We prove similar results for minimum bounded-depth Steiner trees, where the tree must connect a specified set of m vertices, and may or may not include other vertices. In particular, when m = const * n, if k > log_2 log n+omega(1), the minimum bounded-depth Steiner tree on the complete graph has asymptotically the same weight as the minimum Steiner tree, and if 1 <= k <= log_2 log n-omega(1), the weight tends to (1-2^{-k}) sqrt{8m/n} [sqrt{2mn}/2^k]^{1/(2^k-1)} in both expectation and probability. The same results hold for minimum bounded-diameter Steiner trees when the diameter bound is 2k; when the diameter bound is increased from 2k to 2k+1, the minimum Steiner tree weight is reduced by a factor of 2^{1/(2^k-1)}.Comment: 30 pages, v2 has minor revision

THE MYSTERY OF MONOGAMY

This paper examines why developed countries are monogamous while rich men throughout history have tended to practice polygyny (multiple wives). Wealth inequality naturally produces multiple wives for rich men in a standard model of the marriage market. This paper argues that the sources of inequality, not just the level of inequality, determine the equilibrium degree of monogamy or polygamy. In particular, when inequality is determined more by disparities in human capital versus non-labor income (such as land, capital, corruption), the outcome is more monogamous. This explains why developed countries, where human capital is the main source of income and inequality, are monogamous while less-developed economies tend to be polygynous. The results are driven by the larger inequality in the value of women in the marriage market in modern economies. When the value of human capital increases, rich men increasingly value quality women who can help them raise quality children more efficiently. As a result, high quality women are valued much more than low quality women, which makes polygyny less affordable for rich men. In this manner, we show that male inequality generates polygyny, but female inequality reduces it. Using data from Cote d'Ivoire, we provide evidence for all the main implications of the model. In particular, we control for a man's total income and show that polygyny increases with non-labor income but decreases with labor income and education. These patterns are strong even within social groups where norms regarding polygyny are likely to be constant.Marriage, Monogamy, Polygyny, Human Capital, Inequality, J12, J24, O10, O40, Labor and Human Capital,

Relativistic Photon Mediated Shocks

A system of equations governing the structure of a steady, relativistic radiation dominated shock is derived, starting from the general form of the transfer equation obeyed by the photon distribution function. Closure is obtained by truncating the system of moment equations at some order. The anisotropy of the photon distribution function inside the shock is shown to increase with increasing shock velocity, approaching nearly perfect beaming at upstream Lorentz factors $\Gamma_{-}>>1$. Solutions of the shock equations are presented for some range of upstream conditions. These solutions are shown to converge as the truncation order is increased.Comment: 5 pages, a shorter version will appear in PR

Blunted Cystine–Glutamate Antiporter Function in the Nucleus Accumbens Promotes Cocaine-induced Drug Seeking

Repeated cocaine alters glutamate neurotransmission, in part, by reducing cystine–glutamate exchange via system xc−, which maintains glutamate levels and receptor stimulation in the extrasynaptic compartment. In the present study, we undertook two approaches to determine the significance of plasticity involving system xc−. First, we examined whether the cysteine prodrug N-acetylcysteine attenuates cocaine-primed reinstatement by targeting system xc−. Rats were trained to self-administer cocaine (1 mg/kg/200 μl, i.v.) under extended access conditions (6 h/day). After extinction training, cocaine (10 mg/kg, i.p.) primed reinstatement was assessed in rats pretreated with N-acetylcysteine (0–60 mg/kg, i.p.) in the presence or absence of the system xc− inhibitor (S)-4-carboxyphenylglycine (CPG; 0.5 μM; infused into the nucleus accumbens). N-acetylcysteine attenuated cocaine-primed reinstatement, and this effect was reversed by co-administration of CPG. Secondly, we examined whether reduced system xc− activity is necessary for cocaine-primed reinstatement. To do this, we administered N-acetylcysteine (0 or 90 mg/kg, i.p.) prior to 12 daily self-administration sessions (1 mg/kg/200 μl, i.v.; 6 h/day) since this procedure has previously been shown to prevent reduced activity of system xc−. On the reinstatement test day, we then acutely impaired system xc− in some of the rats by infusing CPG (0.5 μM) into the nucleus accumbens. Rats that had received N-acetylcysteine prior to daily self-administration sessions exhibited diminished cocaine-primed reinstatement; this effect was reversed by infusing the cystine–glutamate exchange inhibitor CPG into the nucleus accumbens. Collectively these data establish system xc− in the nucleus accumbens as a key mechanism contributing to cocaine-primed reinstatement

Effective patient–clinician interaction to improve treatment outcomes for patients with psychosis: a mixed-methods design

BACKGROUND:At least 100,000 patients with schizophrenia receive care from community mental health teams (CMHTs) in England. These patients have regular meetings with clinicians, who assess them, engage them in treatment and co-ordinate care. As these routine meetings are not commonly guided by research evidence, a new intervention, DIALOG, was previously designed to structure consultations. Using a hand-held computer, clinicians asked patients to rate their satisfaction with eight life domains and three treatment aspects, and to indicate whether or not additional help was needed in each area, with responses being graphically displayed and compared with previous ratings. In a European multicentre trial, the intervention improved patients’ quality of life over a 1-year period. The current programme builds on this research by further developing DIALOG in the UK. RESEARCH QUESTIONS:(1) How can the practical procedure of the intervention be improved, including the software used and the design of the user interface? (2) How can elements of resource-oriented interventions be incorporated into a clinician manual and training programme for a new, more extensive ‘DIALOG+’ intervention? (3) How effective and cost-effective is the new DIALOG+ intervention in improving treatment outcomes for patients with schizophrenia or a related disorder? (4) What are the views of patients and clinicians regarding the new DIALOG+ intervention? METHODS:We produced new software on a tablet computer for CMHTs in the NHS, informed by analysis of videos of DIALOG sessions from the original trial and six focus groups with 18 patients with psychosis. We developed the new ‘DIALOG+’ intervention in consultation with experts, incorporating principles of solution-focused therapy when responding to patients’ ratings and specifying the procedure in a manual and training programme for clinicians. We conducted an exploratory cluster randomised controlled trial with 49 clinicians and 179 patients with psychosis in East London NHS Foundation Trust, comparing DIALOG+ with an active control. Clinicians working as care co-ordinators in CMHTs (along with their patients) were cluster randomised 1 : 1 to either DIALOG+ or treatment as usual plus an active control, to prevent contamination. Intervention and control were to be administered monthly for 6 months, with data collected at baseline and at 3, 6 and 12 months following randomisation. The primary outcome was subjective quality of life as measured on the Manchester Short Assessment of Quality of Life; secondary outcomes were also measured. We also established the cost-effectiveness of the DIALOG intervention using data from the Client Service Receipt Inventory, which records patients’ retrospective reports of using health- and social-care services, including hospital services, outpatient services and medication, in the 3 months prior to each time point. Data were supplemented by the clinical notes in patients’ medical records to improve accuracy. We conducted an exploratory thematic analysis of 16 video-recorded DIALOG+ sessions and measured adherence in these videos using a specially developed adherence scale. We conducted focus groups with patients (n = 19) and clinicians (n = 19) about their experiences of the intervention, and conducted thematic analyses. We disseminated the findings and made the application (app), manual and training freely available, as well as producing a protocol for a definitive trial. RESULTS:Patients receiving the new intervention showed more favourable quality of life in the DIALOG+ group after 3 months (effect size: Cohen’s d = 0.34), after 6 months (Cohen’s d = 0.29) and after 12 months (Cohen’s d = 0.34). An analysis of video-recorded DIALOG+ sessions showed inconsistent implementation, with adherence to the intervention being a little over half of the possible score. Patients and clinicians from the DIALOG+ arm of the trial reported many positive experiences with the intervention, including better self-expression and improved efficiency of meetings. Difficulties reported with the intervention were addressed by further refining the DIALOG+ manual and training. Cost-effectiveness analyses found a 72% likelihood that the intervention both improved outcomes and saved costs. LIMITATIONS:The research was conducted solely in urban east London, meaning that the results may not be broadly generalisable to other settings. CONCLUSIONS:(1) Although services might consider adopting DIALOG+ based on the existing evidence, a definitive trial appears warranted; (2) applying DIALOG+ to patient groups with other mental disorders may be considered, and to groups with physical health problems; (3) a more flexible use with variable intervals might help to make the intervention even more acceptable and effective; (4) more process evaluation is required to identify what mechanisms precisely are involved in the improvements seen in the intervention group in the trial; and (5) what appears to make DIALOG+ effective is that it is not a separate treatment and not a technology that is administered by a specialist; rather, it changes and utilises the existing therapeutic relationship between patients and clinicians in CMHTs to initiate positive change, helping the patients to improve their quality of life. FUTURE RESEARCH:Future studies should include a definitive trial on DIALOG+ and test the effectiveness of the intervention with other populations, such as people with depression. TRIAL REGISTRATION:Current Controlled Trials ISRCTN34757603. FUNDING:The National Institute for Health Research Programme Grants for Applied Research programme

Repeated \u3cem\u3eN\u3c/em\u3e-Acetylcysteine Administration Alters Plasticity-Dependent Effects of Cocaine

Cocaine produces a persistent reduction in cystine–glutamate exchange via system xc− in the nucleus accumbens that may contribute to pathological glutamate signaling linked to addiction. System xc− influences glutamate neurotransmission by maintaining basal, extracellular glutamate in the nucleus accumbens, which, in turn, shapes synaptic activity by stimulating group II metabotropic glutamate autoreceptors. In the present study, we tested the hypothesis that a long-term reduction in system xc− activity is part of the plasticity produced by repeated cocaine that results in the establishment of compulsive drug seeking. To test this, the cysteine prodrug N-acetylcysteine was administered before daily cocaine to determine the impact of increased cystine–glutamate exchange on the development of plasticity-dependent cocaine seeking. Although N-acetylcysteine administered before cocaine did not alter the acute effects of cocaine on self-administration or locomotor activity, it prevented behaviors produced by repeated cocaine including escalation of drug intake, behavioral sensitization, and cocaine-primed reinstatement. Because sensitization or reinstatement was not evident even 2–3 weeks after the last injection of N-acetylcysteine, we examined whether N-acetylcysteine administered before daily cocaine also prevented the persistent reduction in system xc− activity produced by repeated cocaine. Interestingly, N-acetylcysteine pretreatment prevented cocaine-induced changes in [35S]cystine transport via system xc−, basal glutamate, and cocaine-evoked glutamate in the nucleus accumbens when assessed at least 3 weeks after the last N-acetylcysteine pretreatment. These findings indicate that N-acetylcysteine selectively alters plasticity-dependent behaviors and that normal system xc− activity prevents pathological changes in extracellular glutamate that may be necessary for compulsive drug seeking

Does high inequality attract high skilled immigrants?

This study examines how the sources and levels of income inequality affect how a country attracts and retains high skilled workers. With parameter values that yield realistic levels of emigration, our model shows that emigration rates increase with education when the returns to education are higher abroad. However, the relationship between unobservable skills (‘residual wages’) and emigration can display an inverse U-shaped pattern, if unobservable skills are composed of both ‘general’ and ‘country-specific’ skills. Using data on Israeli emigrants before they decide to emigrate, we find strong empirical evidence in support of the model's predictions