Topology of geometric joins

We consider the geometric join of a family of subsets of the Euclidean space. This is a construction frequently used in the (colorful) Carath\'eodory and Tverberg theorems, and their relatives. We conjecture that when the family has at least $d+1$ sets, where $d$ is the dimension of the space, then the geometric join is contractible. We are able to prove this when $d$ equals $2$ and $3$, while for larger $d$ we show that the geometric join is contractible provided the number of sets is quadratic in $d$. We also consider a matroid generalization of geometric joins and provide similar bounds in this case

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

Prediction of blood-based biomarkers and subsequent design of bisulfite PCR-LDR-qPCR assay for breast cancer detection

This work is licensed under a Creative Commons Attribution 4.0 International License.Background Interrogation of site-specific CpG methylation in circulating tumor DNAs (ctDNAs) has been employed in a number of studies for early detection of breast cancer (BrCa). In many of these studies, the markers were identified based on known biology of BrCa progression, and interrogated using methyl-specific PCR (MSP), a technique involving bisulfite conversion, PCR, and qPCR. Methods In this report, we are demonstrating the development of a novel assay (Multiplex Bisulfite PCR-LDR-qPCR) which can potentially offer improvements to MSP, by integrating additional steps such as ligase detection reaction (LDR), methylated CpG target enrichment, carryover protection (use of uracil DNA glycosylase), and minimization of primer-dimer formation (use of ribose primers and RNAseH2). The assay is designed to for breast cancer-specific CpG markers identified through integrated analyses of publicly available genome-wide methylation datasets for 31 types of primary tumors (including BrCa), as well as matching normal tissues, and peripheral blood. Results Our results indicate that the PCR-LDR-qPCR assay is capable of detecting ~ 30 methylated copies of each of 3 BrCa-specific CpG markers, when mixed with excess amount unmethylated CpG markers (~ 3000 copies each), which is a reasonable approximation of BrCa ctDNA overwhelmed with peripheral blood cell-free DNA (cfDNA) when isolated from patient plasma. The bioinformatically-identified CpG markers are located in promoter regions of NR5A2 and PRKCB, and a non-coding region of chromosome 1 (upstream of EFNA3). Additional bioinformatic analyses would reveal that these methylation markers are independent of patient race and age, and positively associated with signaling pathways associated with BrCa progression (such as those related to retinoid nuclear receptor, PTEN, p53, pRB, and p27). Conclusion This report demonstrates the potential utilization of bisulfite PCR-LDR-qPCR assay, along with bioinformatically-driven biomarker discovery, in blood-based BrCa detection

Predicting erythropoietin resistance in hemodialysis patients with type 2 diabetes

<p>Background: Resistance to ESAs (erythropoietin stimulating agents) is highly prevalent in hemodialysis patients with diabetes and associated with an increased mortality. The aim of this study was to identify predictors for ESA resistance and to develop a prediction model for the risk stratification in these patients.</p> <p>Methods: A post-hoc analysis was conducted of the 4D study, including 1015 patients with type 2 diabetes undergoing hemodialysis. Determinants of ESA resistance were identified by univariate logistic regression analyses. Subsequently, multivariate models were performed with stepwise inclusion of significant predictors from clinical parameters, routine laboratory and specific biomarkers.</p> <p>Results: In the model restricted to clinical parameters, male sex, shorter dialysis vintage, lower BMI, history of CHF, use of ACE-inhibitors and a higher heart rate were identified as independent predictors of ESA resistance. In regard to routine laboratory markers, lower albumin, lower iron saturation, higher creatinine and higher potassium levels were independently associated with ESA resistance. With respect to specific biomarkers, higher ADMA and CRP levels as well as lower Osteocalcin levels were predictors of ESA resistance.</p> <p>Conclusions: Easily obtainable clinical parameters and routine laboratory parameters can predict ESA resistance in diabetic hemodialysis patients with good discrimination. Specific biomarkers did not meaningfully further improve the risk prediction of ESA resistance. Routinely assessed data can be used in clinical practice to stratify patients according to the risk of ESA resistance, which may help to assign appropriate treatment strategies.</p&gt

Potential energy threshold for nano-hillock formation by impact of slow highly charged ions on a CaF2_2(111) surface

We investigate the formation of nano-sized hillocks on the (111) surface of CaF$_2$ single crystals by impact of slow highly charged ions. Atomic force microscopy reveals a surprisingly sharp and well-defined threshold of potential energy carried into the collision of about 14 keV for hillock formation. Estimates of the energy density deposited suggest that the threshold is linked to a solid-liquid phase transition (``melting'') on the nanoscale. With increasing potential energy, both the basal diameter and the height of the hillocks increase. The present results reveal a remarkable similarity between the present predominantly potential-energy driven process and track formation by the thermal spike of swift ($\sim$ GeV) heavy ions.Comment: 10 pages, 2 figure

Synthesis of Novel Peptide Inhibitors of Thrombin-induced Platelet Activation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65762/1/j.1747-0285.2006.00442.x.pd

Mixed integer programming in production planning with backlogging and setup carryover : modeling and algorithms

This paper proposes a mixed integer programming formulation for modeling the capacitated multi-level lot sizing problem with both backlogging and setup carryover. Based on the model formulation, a progressive time-oriented decomposition heuristic framework is then proposed, where improvement and construction heuristics are effectively combined, therefore efficiently avoiding the weaknesses associated with the one-time decisions made by other classical time-oriented decomposition algorithms. Computational results show that the proposed optimization framework provides competitive solutions within a reasonable time

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

The Epigravettian chronology and the human population of eastern Central Europe during MIS2

Human Origin