Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities

Traditionally, it is assumed that the population size of cities in a country follows a Pareto distribution. This assumption is typically supported by nding evidence of Zipf's Law. Recent studies question this nding, highlighting that, while the Pareto distribution may t reasonably well when the data is truncated at the upper tail, i.e. for the largest cities of a country, the log-normal distribution may apply when all cities are considered. Moreover, conclusions may be sensitive to the choice of a particular truncation threshold, a yet overlooked issue in the literature. In this paper, then, we reassess the city size distribution in relation to its sensitivity to the choice of truncation point. In particular, we look at US Census data and apply a recursive-truncation approach to estimate Zipf's Law and a non-parametric alternative test where we consider each possible truncation point of the distribution of all cities. Results con rm the sensitivity of results to the truncation point. Moreover, repeating the analysis over simulated data con rms the di culty of distinguishing a Pareto tail from the tail of a log-normal and, in turn, identifying the city size distribution as a false or a weak Pareto law.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

An Empirical Examination of the R&D Boundaries of the Firm - A Problem-Solving Perspective

We consider, both theoretically and empirically, how different organization modes are aligned to govern the efficient solving of technological problems. The data set is a sample from the Chinese consumer electronics industry. Following mainly the problem solving perspective (PSP) within the knowledge based view (KBV), we develop and test several PSP and KBV hypotheses, in conjunction with competing transaction cost economics (TCE) alternatives, in an examination of the determinants of the R&D organization mode. The results show that a firm’s existing knowledge base is the single most important explanatory variable. Problem complexity and decomposability are also found to be important, consistent with the theoretical predictions of the PSP, but it is suggested that these two dimensions need to be treated as separate variables. TCE hypotheses also receive some support, but the estimation results seem more supportive of the PSP and the KBV than the TCE.

Symmetry for a Dirichlet-Neumann problem arising in water waves

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Pathological gambling and gender

Background and Aims: Gender differences have been reported among pathological gamblers populations. These differences concern variables such as type of gambling (men are more likely engaged in ''strategic gambling'' whereas women prefer ''non-strategic'' gambling), evolution of the gambling problem (faster progression for women) and suicidal behaviours (more attempted suicide by women). The aim of the present study is to investigate the relationship between gender and clinical status in a Swiss sample of treatment seeking pathological gamblers. Method: Prospective descriptive study of 260 new outpatients entering treatment between October 1999 and October 2007 at the Center for Excessive Gambling Studies, Lausanne, Switzerland. Data are issued from standardised medical records. Gender differences were examined (Chi-squares and ANOVAs) on interval between first gambling behaviours and first specialized treatment, interval between pathological gambling onset and first specialized treatment, purpose of consulting, type of gambling (« strategic gambling » vs « nonstrategic gambling ») and suicidality. Results and Discussion: In line with international findings, gender differences were observed on type of gambling, suicidality and interval between pathological gambling onset and first specialized treatment. A tendency emerged on interval between first gambling behaviours and first specialized treatment. As a new finding, we observed a difference on the purpose of consulting, with emotional crisis more reported by women whereas men are more likely to report familial crisis. Gender seems to be relevant in the context of pathological gambling and should be integrated in prevention and clinical strategies.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Predictors of early hospital readmission after acute pulmonary embolism.

BACKGROUND: Risk factors for early mortality after pulmonary embolism (PE) are widely known. However, it is uncertain which factors are associated with early readmission after PE. We sought to identify predictors of readmission after an admission for PE. METHODS: We studied 14 426 patient discharges with a primary diagnosis of PE from 186 acute care hospitals in Pennsylvania from January 1, 2000, to November 30, 2002. The outcome was readmission within 30 days of presentation for PE. We used a discrete proportional odds model to study the association between time to readmission and patient factors (age, sex, race, insurance, discharge status, and severity of illness), thrombolysis, and hospital characteristics (region, teaching status, and number of beds). RESULTS: Overall, 2064 patient discharges (14.3%) resulted in a readmission within 30 days of presentation for PE. The most common reasons for readmission were venous thromboembolism (21.9%), cancer (10.8%), pneumonia (5.2%), and bleeding (5.0%). In multivariable analysis, African American race (odds ratio [OR], 1.19; 95% confidence interval [CI], 1.02-1.38), Medicaid insurance (OR, 1.54; 95% CI, 1.31-1.81), discharge home with supplemental care (OR, 1.40; 95% CI, 1.27-1.54), leaving the hospital against medical advice (OR, 2.84; 95% CI, 1.80-4.48), and severity of illness were independently associated with readmission; readmission also varied by hospital region. CONCLUSIONS: Early readmission after PE is common. African American race, Medicaid insurance, severity of illness, discharge status, and hospital region are significantly associated with readmission. The high readmission rates for venous thromboembolism and bleeding suggest that readmission may be linked to suboptimal quality of care in the management of PE.

Plasma Level of Mmp-9 as Predictive Factor for Response and Progression Free Survival in Patients Treated with Bevacizumab (Bev) and Pegylated Liposomal Doxorubicin (Pld): Sakk 24/06

Background: There is currently no identified marker predicting benefit from Bev in patients with breast cancer (pts). We monitored prospectively 6 angiogenesis-related factors in the blood of advanced stage pts treated with a combination of Bev and PLD in a phase II trial of the Swiss Group for Clinical Cancer Research, SAKK.Methods: Pts received PLD (20 mg/m2) and Bev (10 mg/kg) every 2 weeks for a maximum of 12 administrations, followed by Bev monotherapy until progression or severe toxicity. Blood samples were collected at baseline, during treatment and at treatment discontinuation. Enzyme-linked immunosorbent assays (Quantikine, R&DSystems and Reliatech) were used to measure vascular endothelial growth factor (VEGF), placental growth factor (PlGF), matrix metalloproteinase 9 (MMP-9) and soluble VEGF receptors -1, -2 and -3. The natural log-transformed (ln) data for each factor was analyzed by analysis of variance (ANOVA) model to investigate differences between the mean values of the subgroups of interest (where a = 0.05), based on the best tumor response by RECIST.Results: 132 samples were collected in 41 pts. The mean of baseline ln MMP-9 levels was significantly lower in pts with tumor progression than those with tumor response (p=0.0202, log fold change=0.8786) or disease control (p=0.0035, log fold change=0.8427). Higher MMP-9 level was a significant predictor of superior progression free survival (PFS): p=0.0417, hazard ratio=0.574, 95% CI=0.336-0.979. In a multivariate cox proportional hazards model, containing performance status, disease free interval, number of tumor sites, visceral involvement and prior adjuvant chemotherapy, using stepwise regression baseline MMP-9 was still a statistically 117P Table 1. SOLTI-0701* AC01B07* NU07B1* SOR+CAP N=20 PL+CAP N=33 SOR+ GEM/CAP N=23 PL+ GEM/CAP N=27 SOR+PAC N=48 PL+PAC N=46 Baseline characteristics Age, median (range), y 49 (32-72) 53 (30-78 54 (32-69) 57 (31-82) 50 (27-80) 52 (23-74) AJCC stage, n (%) IIIB/IIIC 3 (15) 6 (18) 0 (0) 3 (11) 8 (17) 9 (20) IV 17 (85) 27 (82) 23 (100) 24 (89) 40 (83) 37 (80) Metastatic site, n (%) Non-visceral 3 (15) 6 (18) 7 (30) 6 (22) 9 (19) 17 (37) Visceral 17 (85) 27 (82) 16 (70) 21 (78) 39 (81) 29 (63) Prior metastatic chemo, n (%) 8 (40) 15 (45) 21 (91) 25 (93) - - Efficacy PFS, median, mo 4.3 2.5 3.1 2.6 5.6 5.5 HR (95% CI)_ 0.60 (0.31, 1.14) 0.57 (0.30, 1.09) 0.86 (0.50, 1.45) 1-sided P value_ 0.055 0.044 0.281 Overall survival, median, mo 17.5 16.1 Pending 14.7 18.2 HR (95% CI)_ 0.98 (0.50, 1.89) 1.11 (0.64, 1.94) 1-sided P value_ 0.476 0.352 Safety N=20 N=33 N=22 N=27 N=46 N=46 Tx-emergent Grade 3/4, n (%) 15 (75) 16 (48) 20 (91) 17 (63) 36 (78) 16 (35) Grade 3§ hand-foot skin reaction/ syndrome 8 (40) 5 (15) 8 (36) 0 (0) 14 (30) 2 (4) *Efficacy results based on intent-to-treat population and safety results based on safety population (pts who received study drug[s]); _Cox regression within each subgroup; _log-rank test within each subgroup; §maximum toxicity grade for hand-foot skin reaction/syndrome; AJCC, American Joint Committee on Cancer mittedabstractsª The Author 2011. Published by Oxford University Press on behalf of the European Society for Medical Oncology. All rights reserved. For permissions, please email: journals.permissions@oup.com Downloaded from annonc.oxfordjournals.org at Bibliotheque Cantonale et Universitaire on June 6, 2011 significant factor (p=0.0266). The results of the other measured factors were presented elsewhere.Conclusions: Higher levels of MMP-9 could predict tumor response and superior PFSin pts treated with a combination of Bev and PLD. These exploratory results justify further investigations of MMP-9 in pts treated with Bev combinations in order to assess its role as a prognostic and predictive factor.Disclosure: K. Zaman: Participation in advisory board of Roche; partial sponsoring ofthe study by Roche (the main sponsor was the Swiss Federation against Cancer (Oncosuisse)). B. Thu¨rlimann: stock of Roche; Research grants from Roche. R. vonMoos: Participant of Advisory Board and Speaker honoraria

Cutting edge: apoptosis of superantigen-activated T cells occurs preferentially after a discrete number of cell divisions in vivo.

Staphylococcal enterotoxins are bacterial products that display superantigen activity in vitro as well as in vivo. For instance, staphylococcal enterotoxin B (SEB) polyclonally activates T cells that bear the Vbeta8 gene segment of the TCR. SEB-activated T cells undergo a burst of proliferation that is followed by apoptosis. Using an in vivo adaptation of a fluorescent cell division monitoring technique, we show here that SEB-activated T cells divide asynchronously, and that apoptosis of superantigen-activated T cells is preferentially restricted to cells which have undergone a discrete number of cell divisions. Collectively, our data suggest that superantigen-activated T cells are programmed to undergo a fixed number of cell divisions before undergoing apoptosis. A delayed death program may provide a mechanistic compromise between effector functions and homeostasis of activated T cells.

Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

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Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.