Cutting a part from many measures

Holmsen, Kyncˇl and Valculescu recently conjectured that if a finite set X with in points in Rd that is colored by m different colors can be partitioned into n subsets of i points each, such that each subset contains points of at least d different colors, then there exists such a partition of X with the additional property that the convex hulls of the n subsets are pairwise disjoint. We prove a continuous analogue of this conjecture, generalized so that each subset contains points of at least c different colors, where we also allow c to be greater than d. Furthermore, we give lower bounds on the fraction of the points each of the subsets contains from c different colors. For example, when n ≤ 2, d ≤ 2, c ≤ d with m ≤ n(c - d) d are integers, and µ1, . . . ,µm are m positive finite absolutely continuous measures on Rd , we prove that there exists a partition of Rd into n convex pieces which equiparts the measures µ1, . . . ,µd−1, and in addition every piece of the partition has positive measure with respect to at least c of the measures µ1, . . . ,µm . 2010 Mathematics Subject Classification: 52C35, 51M20 (primary); 55R20, 55N25 (secondary

Dominant negative phenotype of Bacillus thuringiensis Cry1Ab, Cry11Aa and Cry4Ba mutants suggest hetero-oligomer formation among different Cry toxins.

Background - Bacillus thuringiensis Cry toxins are used worldwide in the control of different insect pests important in agriculture or in human health. The Cry proteins are pore-forming toxins that affect the midgut cell of target insects. It was shown that non-toxic Cry1Ab helix a-4 mutants had a dominant negative (DN) phenotype inhibiting the toxicity of wildtype Cry1Ab when used in equimolar or sub-stoichiometric ratios (1:1, 0.5:1, mutant:wt) indicating that oligomer formation is a key step in toxicity of Cry toxins. Methodology/Principal Findings - The DN Cry1Ab-D136N/T143D mutant that is able to block toxicity of Cry1Ab toxin, was used to analyze its capacity to block the activity against Manduca sexta larvae of other Cry1 toxins, such as Cry1Aa, Cry1Ac, Cry1Ca, Cry1Da, Cry1Ea and Cry1Fa. Cry1Ab-DN mutant inhibited toxicity of Cry1Aa, Cry1Ac and Cry1Fa. In addition, we isolated mutants in helix a-4 of Cry4Ba and Cry11Aa, and demonstrate that Cry4Ba-E159K and Cry11Aa-V142D are inactive and completely block the toxicity against Aedes aegypti of both wildtype toxins, when used at sub-stoichiometric ratios, confirming a DN phenotype. As controls we analyzed Cry1Ab-R99A or Cry11Aa-E97A mutants that are located in helix a-3 and are affected in toxin oligomerization. These mutants do not show a DN phenotype but were able to block toxicity when used in 10:1 or 100:1 ratios (mutant:wt) probably by competition of binding with toxin receptors. Conclusions/Significance - We show that DN phenotype can be observed among different Cry toxins suggesting that may interact in vivo forming hetero-oligomers. The DN phenotype cannot be observed in mutants affected in oligomerization, suggesting that this step is important to inhibit toxicity of other toxin

Testing for distributional features in varying coefficient panel data models

This article provides several tests for skewness and kurtosis for the error terms in a one-way fixed-effects varying coefficient panel data model. To obtain these tests, estimators of higher-order moments of both error components are obtained as solutions of estimating equations. Additionally, to obtain the nonparametric residuals, a local constant estimator based on a pairwise differencing transformation is proposed. The asymptotic properties of these estimators and tests are established. The proposed estimators and test statistics are augmented by simulation studies, and they are also illustrated in an empirical analysis regarding the technical efficiency of European Union companies.The authors would like to thank two anonymous referees for their very helpful comments and suggestions. Furthermore, the authors gratefully acknowledge financial support from the Programa Estatal de Fomento de la Investigaci´on Cient´ıfica y T´ecnica de Excelencia/Spanish Ministry of Economy and Competitiveness. Ref. ECO2016-76203-C2-1-P. In addition, this work is part of the Research Project APIE 1/2015-17: “New methods for the empirical analysis of financial markets” of the Santander Financial Institute (SANFI) of UCEIF Foundation resolved by the University of Cantabria and funded with sponsorship from Banco Santander. Stute’s work was partly done while he was on leave at BCAM, the Basque Center of Applied Mathematics in Bilba

Perineural liposomal bupivacaine for postoperative pain control in patients undergoing upper extremity orthopedic surgery: A prospective and randomized pilot study

Background: Upper extremity surgery is commonly performed in the ambulatory setting and is associated with moderate to severe postoperative pain. Methods: Patients scheduled for upper extremity orthopedic surgery with a peripheral nerve block were randomized to receive either an ultrasound-guided single-injection supraclavicular block or ultrasound-guided median, ulnar, and radial nerve blocks (forearm blocks) performed at the level of the mid to proximal forearm with liposomal bupivacaine (Exparel) combined with a short-acting supraclavicular block. A sham block was performed in an attempt to blind enrollees in the control group. We administered the EuroQol 5D-5L questionnaire preoperatively and on postoperative days 1-3 and considered the results the primary outcome of our investigation. Block procedure times, postanesthesia care unit (PACU) length of stay, instances of nausea/vomiting, need for narcotic administration, and patient satisfaction were also assessed. Results: We observed no significant differences in postoperative EuroQol scores between the 2 groups and no significant differences in patient demographics, PACU length of stay, or side effects in the PACU. In some instances, the short-acting supraclavicular block resolved in the PACU, and these patients reported higher pain scores and required titration of analgesics prior to discharge. Conclusion: Larger prospective studies are needed to determine the safety and efficacy of liposomal bupivacaine in patients undergoing upper extremity surgery. Liposomal bupivacaine is currently only approved for local anesthetic infiltration use

Direct semi-parametric estimation of fixed effects panel data varying coefficient models.

In this paper, we present a new technique to estimate varying coefficient models of unknown form in a panel data framework where individual effects are arbitrarily correlated with the explanatory variables in an unknown way. The estimator is based on first differences and then a local linear regression is applied to estimate the unknown coefficients. To avoid a non-negligible asymptotic bias, we need to introduce a higher-dimensional kernel weight. This enables us to remove the bias at the price of enlarging the variance term and, hence, achieving a slower rate of convergence. To overcome this problem, we propose a one-step backfitting algorithm that enables the resulting estimator to achieve optimal rates of convergence for this type of problem. It also exhibits the so-called oracle efficiency property. We also obtain the asymptotic distribution. Because the estimation procedure depends on the choice of a bandwidth matrix, we also provide a method to compute this matrix empirically. The Monte Carlo results indicate the good performance of the estimator in finite samples

Identification of a Novel Aminopeptidase P-Like Gene (OnAPP) Possibly Involved in Bt Toxicity and Resistance in a Major Corn Pest (Ostrinia nubilalis)

Studies to understand the Bacillus thuringiensis (Bt) resistance mechanism in European corn borer (ECB, Ostrinia nubilalis) suggest that resistance may be due to changes in the midgut-specific Bt toxin receptor. In this study, we identified 10 aminopeptidase-like genes, which have previously been identified as putative Bt toxin receptors in other insects and examined their expression in relation to Cry1Ab toxicity and resistance. Expression analysis for the 10 aminopeptidase-like genes revealed that most of these genes were expressed predominantly in the larval midgut, but there was no difference in the expression of these genes in Cry1Ab resistant and susceptible strains. This suggested that altered expression of these genes was unlikely to be responsible for resistance in these ECB strains. However, we found that there were changes in two amino acid residues of the aminopeptidase-P like gene (OnAPP) involving Glu305 to Lys305 and Arg307 to Leu307 in the two Cry1Ab-resistant strains as compared with three Cry1Ab-susceptible strains. The mature OnAPP contains 682 amino acid residues and has a putative signal peptide at the N-terminus, a predicted glycosylphosphatidyl-inositol (GPI)-anchor signal at the C-terminal, three predicted N-glycosylation sites at residues N178, N278 and N417, and an O-glycosylation site at residue T653. We used a feeding based-RNA interference assay to examine the role of the OnAPP gene in Cry1Ab toxicity and resistance. Bioassays of Cry1Ab in larvae fed diet containing OnAPP dsRNA resulted in a 38% reduction in the transcript level of OnAPP and a 25% reduction in the susceptibility to Cry1Ab as compared with larvae fed GFP dsRNA or water. These results strongly suggest that the OnAPP gene could be involved in binding the Cry1Ab toxin in the ECB larval midgut and that mutations in this gene may be associated with Bt resistance in these two ECB strains

Critically short telomeres and toxicity of chemotherapy in early breast cancer

Cumulative toxicity from weekly paclitaxel (myalgia, peripheral neuropathy, fatigue) compromises long-term administration. Preclinical data suggest that the burden of critically short telomeres ( 21.9% CSTs) had 2-fold higher number of neuropathy (P = 0.04) or fatigue (P = 0.019) episodes and >3-fold higher number of myalgia episodes (P = 0.005). The average telomere length was unrelated to the incidence of side effects.The percentage of CSTs, but not the average telomere size, is associated with weekly paclitaxel-derived toxicity.This work was supported by the Fondo de Investigación Sanitaria [FIS PI10/00288 and FIS PI13/00430]; AECC Scientific Foundation [Beca de Retorno-2010, to MQF]; Spanish Ministry of Economy and Competitiveness Projects [SAF2013-45111-R]; Madrid Regional Government Projects [S2010/BMD- 2303]; AXA Research Found; Fundación Botin; AVON Spain; and Boehringer-Ingelheim Spain.S