Nonparametric instrumental regression with non-convex constraints

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, like integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition

Multilevel Approaches and the Firm-Agglomeration Ambiguity in Economic Growth Studies

Empirical studies in spatial economics have shown that agglomeration economies may be a source of the uneven distribution of economic activities and economic growth across cities and regions. Both localization and urbanization economies are hypothesized to foster agglomeration and growth, but recent meta-analyses of this burgeoning body of empirical research show that the results are ambiguous. Recent overviews show that this ambiguity is fuelled by measurement issues and heterogeneity in terms of scale of time and space, aggregation, growth definitions, and the functional form of the models applied. Alternatively, in this paper, we argue that ambiguity may be due to a lack of research on firm-level performance in agglomerations. This research is necessary because the theories that underlie agglomeration economies are microeconomic in nature. Hierarchical or multilevel modeling, which allows micro levels and macro levels to be modeled simultaneously, is becoming an increasingly common practice in the social sciences. As illustrated by detailed Dutch data on firm-level productivity, employment growth and firm survival, we argue that these approaches are also suitable for reducing the ambiguity surrounding the agglomeration-firm performance relationship and for addressing spatial, sectoral and cross-level heterogeneity

Loop structure of the lowest Bloch band for a Bose-Einstein condensate

We investigate analytically and numerically Bloch waves for a Bose--Einstein condensate in a sinusoidal external potential. At low densities the dependence of the energy on the quasimomentum is similar to that for a single particle, but at densities greater than a critical one the lowest band becomes triple-valued near the boundary of the first Brillouin zone and develops the structure characteristic of the swallow-tail catastrophe. We comment on the experimental consequences of this behavior.Comment: 4 pages, 7 figure

Atom trapping and two-dimensional Bose-Einstein condensates in field-induced adiabatic potentials

We discuss a method to create two-dimensional traps as well as atomic shell, or bubble, states for a Bose-Einstein condensate initially prepared in a conventional magnetic trap. The scheme relies on the use of time-dependent, radio frequency-induced adiabatic potentials. These are shown to form a versatile and robust tool to generate novel trapping potentials. Our shell states take the form of thin, highly stable matter-wave bubbles and can serve as stepping-stones to prepare atoms in highly-excited trap eigenstates or to study `collapse and revival phenomena'. Their creation requires gravitational effects to be compensated by applying additional optical dipole potentials. However, in our scheme gravitation can also be exploited to provide a route to two-dimensional atom trapping. We demonstrate the loading process for such a trap and examine experimental conditions under which a 2D condensate may be prepared.Comment: 16 pages, 10 figure

Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data

In this paper we study a Tikhonov-type method for ill-posed nonlinear operator equations \gdag = F( ag) where \gdag is an integrable, non-negative function. We assume that data are drawn from a Poisson process with density t\gdag where $t>0$ may be interpreted as an exposure time. Such problems occur in many photonic imaging applications including positron emission tomography, confocal fluorescence microscopy, astronomic observations, and phase retrieval problems in optics. Our approach uses a Kullback-Leibler-type data fidelity functional and allows for general convex penalty terms. We prove convergence rates of the expectation of the reconstruction error under a variational source condition as $t\to\infty$ both for an a priori and for a Lepski{\u\i}-type parameter choice rule

Dasatinib inhibits CXCR4 signaling in chronic lymphocytic leukaemia cells and impairs migration towards CXCL12

Chemokines and their ligands play a critical role in enabling chronic lymphocytic leukaemia (CLL) cells access to protective microenvironmental niches within tissues, ultimately resulting in chemoresistance and relapse: disruption of these signaling pathways has become a novel therapeutic approach in CLL. The tyrosine kinase inhibitor dasatinib inhibits migration of several cell lines from solid-organ tumours, but effects on CLL cells have not been reported. We studied the effect of clinically achievable concentrations of dasatinib on signaling induced by the chemokine CXCL12 through its' receptor CXCR4, which is highly expressed on CLL cells. Dasatinib pre-treatment inhibited Akt and ERK phosphorylation in CLL cells upon stimulation with CXCL12. Dasatinib also significantly diminished the rapid increase in actin polymerisation observed in CLL cells following CXCL12 stimulation. Moreover, the drug significantly inhibited chemotaxis in a transwell assay, and reduced the percentage of cells able to migrate beneath a CXCL12-expressing murine stromal cell line. Dasatinib also abrogated the anti-apoptotic effect of prolonged CXCL12 stimulation on cultured CLL cells. These data suggest that dasatinib, akin to other small molecule kinase inhibitors targeting the B-cell receptor signaling pathway, may redistribute CLL cells from protective tissue niches to the peripheral blood, and support the investigation of dasatinib in combination strategies

Interaction of Stress, Lead Burden, and Age on Cognition in Older Men: The VA Normative Aging Study

BACKGROUND. Low-level exposure to lead and to chronic stress may independently influence cognition. However, the modifying potential of psychosocial stress on the neurotoxicity of lead and their combined relationship to aging-associated decline have not been fully examined. OBJECTIVES. We examined the cross-sectional interaction between stress and lead exposure on Mini-Mental State Examination (MMSE) scores among 811 participants in the Normative Aging Study, a cohort of older U.S. men. METHODS. We used two self-reported measures of stress appraisal-a self-report of stress related to their most severe problem and the Perceived Stress Scale (PSS). Indices of lead exposure were blood lead and bone (tibia and patella) lead. RESULTS. Participants with higher self-reported stress had lower MMSE scores, which were adjusted for age, education, computer experience, English as a first language, smoking, and alcohol intake. In multivariable-adjusted tests for interaction, those with higher PSS scores had a 0.57-point lower (95% confidence interval, -0.90 to 0.24) MMSE score for a 2-fold increase in blood lead than did those with lower PSS scores. In addition, the combination of high PSS scores and high blood lead categories on one or both was associated with a 0.05-0.08 reduction on the MMSE for each year of age compared with those with low PSS score and blood lead level (p < 0.05). CONCLUSIONS. Psychological stress had an independent inverse association with cognition and also modified the relationship between lead exposure and cognitive performance among older men. Furthermore, high stress and lead together modified the association between age and cognition.National Institutes of Health (R01ES07821, R01HL080674, R01HL080674-02S1, R01ES013744, ES05257-06A1, P20MD000501, P42ES05947, ES03918-02); National Center for Research Resources General Clinical Research Center (M01RR02635); Leaves of Grass Foundation; United States Department of Veterans Affair

Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of H\"older type