Pluricomplex Green and Lempert functions for equally weighted poles

For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_j \text{when} x \to a_j, j=1,...,N \}$. When there is only one pole, or two poles in the unit ball, it turns out to be equal to the Lempert function defined from analytic disks into $\Omega$ by $L_S (z) :=\inf \{\sum^N_{j=1}\nu_j\log|\zeta_j|: \exists \phi\in \mathcal {O}(\mathbb D,\Omega), \phi(0)=z, \phi(\zeta_j)=a_j, j=1,...,N \}$. It is known that we always have $L_S (z) \ge G_S(z)$. In the more general case where we allow weighted poles, there is a counterexample to equality due to Carlehed and Wiegerinck, with $\Omega$ equal to the bidisk. Here we exhibit a counterexample using only four distinct equally weighted poles in the bidisk. In order to do so, we first define a more general notion of Lempert function "with multiplicities", analogous to the generalized Green functions of Lelong and Rashkovskii, then we show how in some examples this can be realized as a limit of regular Lempert functions when the poles tend to each other. Finally, from an example where $L_S (z) > G_S(z)$ in the case of multiple poles, we deduce that distinct (but close enough) equally weighted poles will provide an example of the same inequality. Open questions are pointed out about the limits of Green and Lempert functions when poles tend to each other.Comment: 25 page

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Superweakly interacting dark matter from the Minimal Walking Technicolor

We study a superweakly interacting dark matter particle motivated by minimal walking technicolor theories. Our WIMP is a mixture of a sterile state and a state with the charges of a standard model fourth family neutrino. We show that the model can give the right amount of dark matter over a range of the WIMP mass and mixing angle. We compute bounds on the model parameters from the current accelerator data including the oblique corrections to the precision electroweak parameters, as well as from cryogenic experiments, Super-Kamiokande and from the IceCube experiment. We show that consistent dark matter solutions exist which satisfy all current constraints. However, almost the entire parameter range of the model lies within the the combined reach of the next generation experiments.Comment: 29 pages, 6 figure

Developing and validating an experience sampling measure of aggression:The Aggression-ES Scale

Experience sampling methodologies are likely to play an important role in advancing our understanding of momentary influences on aggression, including short-term antecedent psychological states and situations. In this study, we evaluate whether a newly developed experiencing sampling measure of aggression, the Aggression Experience Sampler (Aggression-ES), provides a valid and reliable measure of aggression in experience sampling contexts. Participants were a convenience sample of 23 young adults recruited from the local University community. Data were collected using an experience sampling smartphone application over 8 days. They were analyzed using multilevel structural equation modeling. Our results support the within- and between-person reliability and the criterion validity of the Aggression-ES. The Aggression-ES represents a good choice of measure for use in experience sampling studies of aggression. Further work in other samples will help to provide further validity evidence for the measure

Victimization, crime propensity and deviance: a multinational test of general strain theory

General Strain Theory (GST) identifies victimization as one of the strains most strongly related to crime which, like other sources of strain, is moderated by individual and social factors. Recently, Agnew (2013) extended the theorization of coping strategies by proposing that the effects of strain on deviance are conditioned by individual and social factors in combination, rather than singly, which he labelled crime propensity. Tests of the propensity hypothesis have so far yielded mixed results, highlighting the value of additional studies. Whereas previous tests have focused on single countries, either in North America or Asia, we test the propensity hypothesis using data on adolescents in 25 countries collected through the International Self-Report Delinquency Study (ISRD3; n= 57,760). A series of OLS regressions show that the relationship between victimization and delinquency/substance use is conditioned by the effects of individuals’ crime propensity, thereby supporting the recent extension to GST

Bi-directional modulation of AMPA receptor unitary conductance by synaptic activity

BACKGROUND: Knowledge of how synapses alter their efficiency of communication is central to the understanding of learning and memory. The most extensively studied forms of synaptic plasticity are long-term potentiation (LTP) and its counterpart long-term depression (LTD) of AMPA receptor-mediated synaptic transmission. In the CA1 region of the hippocampus, it has been shown that LTP often involves a rapid increase in the unitary conductance of AMPA receptor channels. However, LTP can also occur in the absence of any alteration in AMPA receptor unitary conductance. In the present study we have used whole-cell dendritic recording, failures analysis and non-stationary fluctuation analysis to investigate the mechanism of depotentiation of LTP. RESULTS: We find that when LTP involves an increase in unitary conductance, subsequent depotentiation invariably involves the return of unitary conductance to pre-LTP values. In contrast, when LTP does not involve a change in unitary conductance then depotentiation also occurs in the absence of any change in unitary conductance, indicating a reduction in the number of activated receptors as the most likely mechanism. CONCLUSIONS: These data show that unitary conductance can be bi-directionally modified by synaptic activity. Furthermore, there are at least two distinct mechanisms to restore synaptic strength from a potentiated state, which depend upon the mechanism of the previous potentiation

Numerical study of transient evolution of lifted jet flames: partially premixed flame propagation and influence of physical dimensions

Three-dimensional (3D) unsteady Reynolds-averaged Navier–Stokes simulations of a spark-ignited turbulent methane/air jet flame evolving from ignition to stabilisation are conducted for different jet velocities. A partially premixed combustion model is used involving a correlated joint probability density function and both premixed and non-premixed combustion mode contributions. The 3D simulation results for the temporal evolution of the flame's leading edge are compared with previous two-dimensional (2D) results and experimental data. The comparison shows that the final stabilised flame lift-off height is well predicted by both 2D and 3D computations. However, the transient evolution of the flame's leading edge computed from 3D simulation agrees reasonably well with experiment, whereas evident discrepancies were found in the previous 2D study. This difference suggests that the third physical dimension plays an important role during the flame transient evolution process. The flame brush's leading edge displacement speed resulting from reaction, normal and tangential diffusion processes are studied at different typical stages after ignition in order to understand the effect of the third physical dimension further. Substantial differences are found for the reaction and normal diffusion components between 2D and 3D simulations especially in the initial propagation stage. The evolution of reaction progress variable scalar gradients and its interaction with the flow and mixing field in the 3D physical space have an important effect on the flame's leading edge propagation.Z. C. acknowledges the financial supports of Cambridge Overseas Trust and China Scholarship Council.This is the author accepted manuscript. The final version is available from Taylor & Francis via https://doi.org/10.1080/13647830.2016.116123

Screening for depression in hemodialysis patients: Associations with diagnosis, treatment, and outcomes in the DOPPS

Screening for depression in hemodialysis patients: Associations with diagnosis, treatment, and outcomes in the DOPPS.BackgroundDepressive symptoms and depression are the most frequent psychologic problems reported by hemodialysis patients. We assessed the prevalence of depressive symptoms and physician-diagnosed depression, their variations by country, and associations with treatment by antidepressants among hemodialysis patients. We also assessed whether depressive symptoms were independently associated with mortality, hospitalization, and dialysis withdrawal.MethodsThe sample was represented by 9382 hemodialysis patients randomly selected from dialysis centers of 12 countries enrolled in the Dialysis Outcomes and Practice Patterns Study (DOPPS II). Depressive symptoms were assessed by the short version of the Center for Epidemiological Studies Depression Screening Index (CES-D), using ≥10 CES-D score as the cut-off value.ResultsOverall prevalence of physician-diagnosed depression was 13.9%, and percentage of CES-D score ≥10 43.0%. While the smallest prevalence of physician-diagnosed depression was observed in Japan (2.0%) and France (10.6%), the percentage of CES-D score ≥10 in these counties was similar to the whole sample. Patients on antidepressants also varied by country, 34.9% and 17.3% among those with physician-diagnosed depression and CES-D scores ≥10, respectively. In Cox models adjusted for several comorbidities, CES-D scores ≥10 were associated with significantly higher relative risks (RR) of death (RR = 1.42; 95% CI = 1.29 to 1.57), hospitalization (RR = 1.12; 95% CI = 1.03 to 1.22), and dialysis withdrawal (RR = 1.55; 95% CI = 1.29 to 1.85).ConclusionThe data suggest that depression is underdiagnosed and undertreated among hemodialysis patients. CES-D can help identify hemodialysis patients who are at higher risk of death and hospitalization. Interventions should target these patients with the goal to improve survival and reduce hospitalizations