Solving ill-posed bilevel programs

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to obtain local optimal solutions for the original optimistic problem by this process. Considering the intrinsic non-convexity of bilevel programs, computing local optimal solutions is the best one can hope to get in most cases. To achieve this goal, we start by establishing an equivalence between the original optimistic problem an a certain set-valued optimization problem. Next, we develop optimality conditions for the latter problem and show that they generalize all the results currently known in the literature on optimistic bilevel optimization. Our approach is then extended to multiobjective bilevel optimization, and completely new results are derived for problems with vector-valued upper- and lower-level objective functions. Numerical implementations of the results of this paper are provided on some examples, in order to demonstrate how the original optimistic problem can be solved in practice, by means of a special set-valued optimization problem

The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

Entanglement generation outside a Schwarzschild black hole and the Hawking effect

We examine the Hawking effect by studying the asymptotic entanglement of two mutually independent two-level atoms placed at a fixed radial distance outside a Schwarzschild black hole in the framework of open quantum systems. We treat the two-atom system as an open quantum system in a bath of fluctuating quantized massless scalar fields in vacuum and calculate the concurrence, a measurement of entanglement, of the equilibrium state of the system at large times, for the Unruh, Hartle-Hawking and Boulware vacua respectively. We find, for all three vacuum cases, that the atoms turn out to be entangled even if they are initially in a separable state as long as the system is not placed right at the even horizon. Remarkably, only in the Unruh vacuum, will the asymptotic entanglement be affected by the backscattering of the thermal radiation off the space-time curvature. The effect of the back scatterings on the asymptotic entanglement cancels in the Hartle-Hawking vacuum case.Comment: 15 pages, no figures, Revte

Quantum gravitational contributions to quantum electrodynamics

Quantum electrodynamics describes the interactions of electrons and photons. Electric charge (the gauge coupling constant) is energy dependent, and there is a previous claim that charge is affected by gravity (described by general relativity) with the implication that the charge is reduced at high energies. But that claim has been very controversial with the situation inconclusive. Here I report an analysis (free from earlier controversies) demonstrating that that quantum gravity corrections to quantum electrodynamics have a quadratic energy dependence that result in the reduction of the electric charge at high energies, a result known as asymptotic freedom.Comment: To be published in Nature. 19 pages LaTeX, no figure

Histone Acetylation-Mediated Regulation of the Hippo Pathway

The Hippo pathway is a signaling cascade recently found to play a key role in tumorigenesis therefore understanding the mechanisms that regulate it should open new opportunities for cancer treatment. Available data indicate that this pathway is controlled by signals from cell-cell junctions however the potential role of nuclear regulation has not yet been described. Here we set out to verify this possibility and define putative mechanism(s) by which it might occur. By using a luciferase reporter of the Hippo pathway, we measured the effects of different nuclear targeting drugs and found that chromatin-modifying agents, and to a lesser extent certain DNA damaging drugs, strongly induced activity of the reporter. This effect was not mediated by upstream core components (i.e. Mst, Lats) of the Hippo pathway, but through enhanced levels of the Hippo transducer TAZ. Investigation of the underlying mechanism led to the finding that cancer cell exposure to histone deacetylase inhibitors induced secretion of growth factors and cytokines, which in turn activate Akt and inhibit the GSK3 beta associated protein degradation complex in drug-affected as well as in their neighboring cells. Consequently, expression of EMT genes, cell migration and resistance to therapy were induced. These processes were suppressed by using pyrvinium, a recently described small molecule activator of the GSK 3 beta associated degradation complex. Overall, these findings shed light on a previously unrecognized phenomenon by which certain anti-cancer agents may paradoxically promote tumor progression by facilitating stabilization of the Hippo transducer TAZ and inducing cancer cell migration and resistance to therapy. Pharmacological targeting of the GSK3 beta associated degradation complex may thus represent a unique approach to treat cancer. © 2013 Basu et al

Drivers of risk perceptions about the invasive non-native plant Japanese knotweed in domestic gardens

This is the final version of the article. Available from Springer Verlag via the DOI in this record.How people perceive risks posed by invasive non-native plants (INNP) can influence attitudes and consequently likely influence behavioural decisions. Although some drivers of risk perception for INNP have been identified, research has not determined those for INNP in domestic gardens. This is concerning as domestic gardens are where people most commonly encounter INNP, and where impacts can be particularly acute. Using a survey approach, this study determined the drivers of perceptions of risk of INNP in domestic gardens and which risks most concern people. Japanese knotweed Fallopia japonica, in Cornwall, UK, where it is a problematic INNP in domestic gardens, was used as a case study. Possible drivers of risk were chosen a priori based on variables previously found to be important for environmental risks. Participants perceived Japanese knotweed to be less frequent on domestic property in Cornwall if their occupation involved the housing market, if they had not had Japanese knotweed in their own garden, if they did not know of Japanese knotweed within 5 km of their home, or if they were educated to degree level. Participants who thought that the consequences of Japanese knotweed being present on domestic property could be more severe had occupations that involved the housing market, knew of Japanese knotweed within 5 km of their home, or were older. Although concern about the damage Japanese knotweed could do to the structure of a property was reported as the second highest motivation to control it by the majority of participants, the perception of threat from this risk was rated as relatively low. The results of this study have implications for policy, risk communication, and garden management decisions. For example, there is a need for policy that provides support and resources for people to manage INNP in their local area. To reduce the impact and spread of INNP we highlight the need for clear and accurate risk communication within discourse about this issue. The drivers identified in this study could be used to target awareness campaigns to limit the development of over- or under-inflated risk perceptions.This project was funded as part of the Wildlife Research Co-Operative between the University of Exeter and the Animal and Plant Health Agency

Validation of the SCID-hu Thy/Liv mouse model with four classes of licensed antiretrovirals.

BackgroundThe SCID-hu Thy/Liv mouse model of HIV-1 infection is a useful platform for the preclinical evaluation of antiviral efficacy in vivo. We performed this study to validate the model with representatives of all four classes of licensed antiretrovirals.Methodology/principal findingsEndpoint analyses for quantification of Thy/Liv implant viral load included ELISA for cell-associated p24, branched DNA assay for HIV-1 RNA, and detection of infected thymocytes by intracellular staining for Gag-p24. Antiviral protection from HIV-1-mediated thymocyte depletion was assessed by multicolor flow cytometric analysis of thymocyte subpopulations based on surface expression of CD3, CD4, and CD8. These mice can be productively infected with molecular clones of HIV-1 (e.g., the X4 clone NL4-3) as well as with primary R5 and R5X4 isolates. To determine whether results in this model are concordant with those found in humans, we performed direct comparisons of two drugs in the same class, each of which has known potency and dosing levels in humans. Here we show that second-generation antiretrovirals were, as expected, more potent than their first-generation predecessors: emtricitabine was more potent than lamivudine, efavirenz was more potent than nevirapine, and atazanavir was more potent than indinavir. After interspecies pharmacodynamic scaling, the dose ranges found to inhibit viral replication in the SCID-hu Thy/Liv mouse were similar to those used in humans. Moreover, HIV-1 replication in these mice was genetically stable; treatment of the mice with lamivudine did not result in the M184V substitution in reverse transcriptase, and the multidrug-resistant NY index case HIV-1 retained its drug-resistance substitutions.ConclusionGiven the fidelity of such comparisons, we conclude that this highly reproducible mouse model is likely to predict clinical antiviral efficacy in humans

Echocardiographic assessment of pulmonary hypertension: a guideline protocol from the British Society of Echocardiography.

Pulmonary hypertension is defined as a mean arterial pressure of ≥25 mmHg as confirmed on right heart catheterisation. Traditionally, the pulmonary arterial systolic pressure has been estimated on echo by utilising the simplified Bernoulli equation from the peak tricuspid regurgitant velocity and adding this to an estimate of right atrial pressure. Previous studies have demonstrated a correlation between this estimate of pulmonary arterial systolic pressure and that obtained from invasive measurement across a cohort of patients. However, for an individual patient significant overestimation and underestimation can occur and the levels of agreement between the two is poor. Recent guidance has suggested that echocardiographic assessment of pulmonary hypertension should be limited to determining the probability of pulmonary hypertension being present rather than estimating the pulmonary artery pressure. In those patients in whom the presence of pulmonary hypertension requires confirmation, this should be done with right heart catheterisation when indicated. This guideline protocol from the British Society of Echocardiography aims to outline a practical approach to assessing the probability of pulmonary hypertension using echocardiography and should be used in conjunction with the previously published minimum dataset for a standard transthoracic echocardiogram

Geometric phase outside a Schwarzschild black hole and the Hawking effect

We study the Hawking effect in terms of the geometric phase acquired by a two-level atom as a result of coupling to vacuum fluctuations outside a Schwarzschild black hole in a gedanken experiment. We treat the atom in interaction with a bath of fluctuating quantized massless scalar fields as an open quantum system, whose dynamics is governed by a master equation obtained by tracing over the field degrees of freedom. The nonunitary effects of this system are examined by analyzing the geometric phase for the Boulware, Unruh and Hartle-Hawking vacua respectively. We find, for all the three cases, that the geometric phase of the atom turns out to be affected by the space-time curvature which backscatters the vacuum field modes. In both the Unruh and Hartle-Hawking vacua, the geometric phase exhibits similar behaviors as if there were thermal radiation at the Hawking temperature from the black hole. So, a measurement of the change of the geometric phase as opposed to that in a flat space-time can in principle reveal the existence of the Hawking radiation.Comment: 14 pages, no figures, a typo in the References corrected, version to appear in JHEP. arXiv admin note: text overlap with arXiv:1109.033

Running Gauge Coupling in Asymptotically Safe Quantum Gravity

We investigate the non-perturbative renormalization group behavior of the gauge coupling constant using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. We find a non-zero quantum gravity correction to the standard Yang-Mills beta function which has the same sign as the gauge boson contribution. Our results fit into the picture according to which Quantum Einstein Gravity (QEG) is asymptotically safe, with a vanishing gauge coupling constant at the non-trivial fixed point.Comment: 27 page