On the minimization of Dirichlet eigenvalues of the Laplace operator

We study the variational problem \inf \{\lambda_k(\Omega): \Omega\ \textup{open in}\ \R^m,\ |\Omega| < \infty, \ \h(\partial \Omega) \le 1 \}, where $\lambda_k(\Omega)$ is the $k$'th eigenvalue of the Dirichlet Laplacian acting in $L^2(\Omega)$, \h(\partial \Omega) is the $(m-1)$- dimensional Hausdorff measure of the boundary of $\Omega$, and $|\Omega|$ is the Lebesgue measure of $\Omega$. If $m=2$, and $k=2,3, \cdots$, then there exists a convex minimiser $\Omega_{2,k}$. If $m \ge 2$, and if $\Omega_{m,k}$ is a minimiser, then $\Omega_{m,k}^*:= \textup{int}(\overline{\Omega_{m,k}})$ is also a minimiser, and $\R^m\setminus \Omega_{m,k}^*$ is connected. Upper bounds are obtained for the number of components of $\Omega_{m,k}$. It is shown that if $m\ge 3$, and $k\le m+1$ then $\Omega_{m,k}$ has at most $4$ components. Furthermore $\Omega_{m,k}$ is connected in the following cases : (i) $m\ge 2, k=2,$ (ii) $m=3,4,5,$ and $k=3,4,$ (iii) $m=4,5,$ and $k=5,$ (iv) $m=5$ and $k=6$. Finally, upper bounds on the number of components are obtained for minimisers for other constraints such as the Lebesgue measure and the torsional rigidity.Comment: 16 page

6-Mercaptopurine, still valuable for the palliative treatment of acute myeloid leukaemia

Although 6-mercaptopurine (6-MP) is frequently used in the treatment of acute myeloid leukaemia (AML), its effect on disease progression has not been studied systematically. In a small retrospective analysis, we found that 6-MP could induce marked haematological improvement in a considerable number of AML patients who were not treated with intensive remission induction courses. Due to the inherent limitations of retrospective analyses, we then investigated prospectively in 51 consecutive patients over a 3-year period in a single centre, to what extent, oral 6-MP 250 mg twice a week could be beneficial to AML patients who were not-or no longer-eligible for intensive chemotherapy. Clinical response was scored according to changes in blood cell counts and dependency on blood transfusions. Thirteen patients (25%) were considered responders since they showed an increased platelet count from the first month after initiation of 6-MP onwards and they became independent of blood transfusions after 3 months. This effect lasted for 13 (range 7-30+) months. Median overall survival of this subgroup was 16.5 (6-33+) months. Ten patients (20%) had a shorter or incomplete response and a survival of 12 (6-30) months. Seven patients were lost to follow-up. Twenty-one (41%) failed to respond and survived for 4 (1.5-17) months. The response seemed not to be affected by previous chemotherapy, history of myelodysplasia, or karyotype abnormalities, but high leukocyte count initially was unfavourable. 6-MP thus can induce marked improvement of blood cell counts in a considerable proportion of AML patients who are not eligible for intensive chemotherapy, leading to good quality of life and a significant prolongation of survival.</p

The longitudinal link between popularity, likeability, fear of negative evaluation and social avoidance across adolescence

This study investigated the longitudinal bidirectional associations between likeability, popularity, fear of negative evaluation, and social avoidance, to aid in preventing the negative consequences and persistent trajectories of low social status and heightened social anxiety. In total, 1741 adolescents in grades 7–9 participated at 3 yearly waves. A self-report questionnaire measured fear of negative evaluation. Peer nominations assessed likeability, popularity, and social avoidance. Lower popularity predicted more avoidance, and vice versa. More avoidance was related to lower likeability over time. Being less popular and/or more liked by peers, increased fear of negative evaluation. Support for a transactional model between social anxiety and social status was found, but distinguishing different social status and social anxiety components is necessary

Human cooperation in groups: variation begets variation

Many experiments on human cooperation have revealed that individuals differ systematically in their tendency to cooperate with others. It has also been shown that individuals condition their behaviour on the overall cooperation level of their peers. Yet, little is known about how individuals respond to heterogeneity in cooperativeness in their neighbourhood. Here, we present an experimental study investigating whether and how people respond to heterogeneous behaviour in a public goods game. We find that a large majority of subjects does respond to heterogeneity in their group, but they respond in quite different ways. Most subjects contribute less to the public good when the contributions of their peers are more heterogeneous, but a substantial fraction of individuals consistently contributes more in this case. In addition, we find that individuals that respond positively to heterogeneity have a higher general cooperation tendency. The finding that social responsiveness occurs in different forms and is correlated with cooperativeness may have important implications for the outcome of cooperative interactions

On the nature of candidate luminous blue variables in M33

Luminous blue variables (LBVs) are expected to play an important role in massive stellar evolution as well as being the progenitors of some of the most luminous supernovae known. In this paper we provide a multiwavelength study of the population of (candidate) LBVs identified within M33. New spectra provide an observational baseline of >4yr with respect to published data, which is well suited to identifying LBV outbursts. Multi-epoch optical and mid-IR surveys of M33 further constrain the variability of the sample and permit a search for dusty circumstellar ejecta. Spectroscopic and photometric variability appears common amongst the sample, although in many cases further observations will be required to determine its physical origin. Nevertheless, we report a new outburst of M33 Var C, while the transition of the WNLh star B517 to a cooler B supergiant phase between 1993-2010 confirms an LBV classification. Proof-of-concept quantitative analysis is provided for Romano's star; the results being consistent with the finding that its bolometric luminosity varies during its LBV excursions. The combination of the temperature and luminosity of two stars, the B hypergiant [HS80] 110A and the cool hypergiant B324, appears to be in violation of the empirical Humphreys-Davidson limit. Mid-IR observations demonstrate that a number of candidates appear associated with hot circumstellar dust, although no objects as extreme as Eta Carinae are identified. The combined multiwavelength dataset suggests that the population of LBVs studied is contaminated by stars demonstrating the B[e] phenomenon. Of these, a subset of optically faint, low luminosity stars associated with hot dust are of particular interest since they appear similar to the likely progenitors of SN 2008S and the 2008 NGC300 transient, albeit suffering less intrinsic extinction. [ABRIDGED]Comment: 23 pages, 14 figures, accepted for publication in Astronomy and Astrophysic

What's in a name; Genetic structure in Solanum section Petota studied using population-genetic tools

Background - The taxonomy and systematic relationships among species of Solanum section Petota are complicated and the section seems overclassified. Many of the presumed (sub)species from South America are very similar and they are able to exchange genetic material. We applied a population genetic approach to evaluate support for subgroups within this material, using AFLP data. Our approach is based on the following assumptions: (i) accessions that may exchange genetic material can be analyzed as if they are part of one gene pool, and (ii) genetic differentiation among species is expected to be higher than within species. Results - A dataset of 566 South-American accessions (encompassing 89 species and subspecies) was analyzed in two steps. First, with the program STRUCTURE 2.2 in an 'unsupervised' procedure, individual accessions were assigned to inferred clusters based on genetic similarity. The results showed that the South American members of section Petota could be arranged in 16 clusters of various size and composition. Next, the accessions within the clusters were grouped by maximizing the partitioning of genetic diversity among subgroups (i.e., maximizing Fst values) for all available individuals of the accessions (2767 genotypes). This two-step approach produced an optimal partitioning into 44 groups. Some of the species clustered as genetically distinct groups, either on their own, or combined with one or more other species. However, accessions of other species were distributed over more than one cluster, and did not form genetically distinct units. Conclusions - We could not find any support for 43 species (almost half of our dataset). For 28 species some level of support could be found varying from good to weak. For 18 species no conclusions could be drawn as the number of accessions included in our dataset was too low. These molecular data should be combined with data from morphological surveys, with geographical distribution data, and with information from crossing experiments to identify natural units at the species level. However, the data do indicate which taxa or combinations of taxa are clearly supported by a distinct set of molecular marker data, leaving other taxa unsupported. Therefore, the approach taken provides a general method to evaluate the taxonomic system in any species complex for which molecular data are available

Modified Delphi procedure-based expert consensus on endpoints for an international disease registry for Metachromatic Leukodystrophy:The European Metachromatic Leukodystrophy initiative (MLDi)

BACKGROUND: Metachromatic Leukodystrophy (MLD) is a rare lysosomal disorder. Patients suffer from relentless neurological deterioration leading to premature death. Recently, new treatment modalities, including gene therapy and enzyme replacement therapy, have been developed. Those advances increase the need for high-quality research infrastructure to adequately compare treatments, execute post-marketing surveillance, and perform health technology assessments (HTA). To facilitate this, a group of MLD experts started the MLD initiative (MLDi) and initiated an academia-led European MLD registry: the MLDi. An expert-based consensus procedure, namely a modified Delphi procedure, was used to determine the data elements required to answer academic, regulatory, and HTA research questions. RESULTS: Three distinct sets of data elements were defined by the 13-member expert panel. The minimal set (n = 13) contained demographics and basic disease characteristics. The core set (n = 55) included functional status scores in terms of motor, manual, speech and eating abilities, and causal and supportive treatment characteristics. Health-related quality of life scores were included that were also deemed necessary for HTA. The optional set (n = 31) contained additional clinical aspects, such as findings at neurological examination, detailed motor function, presence of peripheral neuropathy, gall bladder involvement and micturition. CONCLUSION: Using a modified Delphi procedure with physicians from the main expert centers, consensus was reached on a core set of data that can be collected retrospectively and prospectively. With this consensus-based approach, an important step towards harmonization was made. This unique dataset will support knowledge about the disease and facilitate regulatory requirements related to the launch of new treatments. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s13023-022-02189-w

Stochastic Responses May Allow Genetically Diverse Cell Populations to Optimize Performance with Simpler Signaling Networks

Two theories have emerged for the role that stochasticity plays in biological responses: first, that it degrades biological responses, so the performance of biological signaling machinery could be improved by increasing molecular copy numbers of key proteins; second, that it enhances biological performance, by enabling diversification of population-level responses. Using T cell biology as an example, we demonstrate that these roles for stochastic responses are not sufficient to understand experimental observations of stochastic response in complex biological systems that utilize environmental and genetic diversity to make cooperative responses. We propose a new role for stochastic responses in biology: they enable populations to make complex responses with simpler biochemical signaling machinery than would be required in the absence of stochasticity. Thus, the evolution of stochastic responses may be linked to the evolvability of different signaling machineries.National Institutes of Health (U.S.). Pioneer Awar