Bridging gap between standard and differential polynomial approximation: The case of bin-packing

AbstractThe purpose of this paper is mainly to prove the following theorem: for every polynomial time algorithm running in time T(n) and guaranteeing standard-approximation ratio ϱ for bin-packing, there exists an algorithm running in time O(nT(n)) and achieving differential-approximation ratio 2 − ϱ for BP. This theorem has two main impacts. The first one is “operational”, deriving a polynomial time differential-approximation schema for bin-packing. The second one is structural, establishing a kind of reduction (to our knowledge not existing until now) between standard approximation and differential one

On the complexity of the multiple stack TSP, kSTSP

The multiple Stack Travelling Salesman Problem, STSP, deals with the collect and the deliverance of n commodities in two distinct cities. The two cities are represented by means of two edge-valued graphs (G1,d2) and (G2,d2). During the pick-up tour, the commodities are stored into a container whose rows are subject to LIFO constraints. As a generalisation of standard TSP, the problem obviously is NP-hard; nevertheless, one could wonder about what combinatorial structure of STSP does the most impact its complexity: the arrangement of the commodities into the container, or the tours themselves? The answer is not clear. First, given a pair (T1,T2) of pick-up and delivery tours, it is polynomial to decide whether these tours are or not compatible. Second, for a given arrangement of the commodities into the k rows of the container, the optimum pick-up and delivery tours w.r.t. this arrangement can be computed within a time that is polynomial in n, but exponential in k. Finally, we provide instances on which a tour that is optimum for one of three distances d1, d2 or d1+d2 lead to solutions of STSP that are arbitrarily far to the optimum STSP

Maternal age effect and severe germ-line bottleneck in the inheritance of human mitochondrial DNA

The manifestation of mitochondrial DNA (mtDNA) diseases depends on the frequency of heteroplasmy (the presence of several alleles in an individual), yet its transmission across generations cannot be readily predicted owing to a lack of data on the size of the mtDNA bottleneck during oogenesis. For deleterious heteroplasmies, a severe bottleneck may abruptly transform a benign (low) frequency in a mother into a disease-causing (high) frequency in her child. Here we present a high-resolution study of heteroplasmy transmission conducted on blood and buccal mtDNA of 39 healthy mother–child pairs of European ancestry (a total of 156 samples, each sequenced at ∼20,000× per site). On average, each individual carried one heteroplasmy, and one in eight individuals carried a disease-associated heteroplasmy, with minor allele frequency ≥1%. We observed frequent drastic heteroplasmy frequency shifts between generations and estimated the effective size of the germ-line mtDNA bottleneck at only ∼30–35 (interquartile range from 9 to 141). Accounting for heteroplasmies, we estimated the mtDNA germ-line mutation rate at 1.3 × 10−8 (interquartile range from 4.2 × 10−9 to 4.1 × 10−8) mutations per site per year, an order of magnitude higher than for nuclear DNA. Notably, we found a positive association between the number of heteroplasmies in a child and maternal age at fertilization, likely attributable to oocyte aging. This study also took advantage of droplet digital PCR (ddPCR) to validate heteroplasmies and confirm a de novo mutation. Our results can be used to predict the transmission of disease-causing mtDNA variants and illuminate evolutionary dynamics of the mitochondrial genome

The complexity of the Pk partition problem and related problems in bipartite graphs

International audienceIn this paper, we continue the investigation made in [MT05] about the approximability of Pk partition problems, but focusing here on their complexity. Precisely, we aim at designing the frontier between polynomial and NP-complete versions of the Pk partition problem in bipartite graphs, according to both the constant k and the maximum degree of the input graph. We actually extend the obtained results to more general classes of problems, namely, the minimum k-path partition problem and the maximum Pk packing problem. Moreover, we propose some simple approximation algorithms for those problems

The Diversity of Religious Diversity. Using Census and NCS Methodology in Order to Map and Assess the Religious Diversity of a Whole Country

Religious diversity is often captured in “mapping studies” that use mostly qualitative methods in order to map and assess the religious communities in a given area. While these studies are useful, they often present weaknesses in that they treat only limited geographic regions, provide limited possibilities for comparing across religious groups and cannot test theories. In this article, we show how a census and a quantitative national congregations study (NCS) methodology can be combined in order to map and assess the religious diversity of a whole country (Switzerland), overcoming the problems mentioned above. We outline the methodological steps and selected results concerning organizational, geographic, structural, and cultural diversity

Ellipticine cytotoxicity to cancer cell lines — a comparative study

Ellipticine is a potent antineoplastic agent exhibiting multiple mechanisms of action. This anticancer agent should be considered a pro-drug, whose pharmacological efficiency and/or genotoxic side effects are dependent on its cytochrome P450 (CYP)- and/or peroxidase-mediated activation to species forming covalent DNA adducts. Ellipticine can also act as an inhibitor or inducer of biotransformation enzymes, thereby modulating its own metabolism leading to its genotoxic and pharmacological effects. Here, a comparison of the toxicity of ellipticine to human breast adenocarcinoma MCF-7 cells, leukemia HL-60 and CCRF-CEM cells, neuroblastoma IMR-32, UKF-NB-3 and UKF-NB-4 cells and U87MG glioblastoma cells and mechanisms of its action to these cells were evaluated. Treatment of all cells tested with ellipticine resulted in inhibition of cell growth and proliferation. This effect was associated with formation of two covalent ellipticine-derived DNA adducts, identical to those formed by 13-hydroxy- and 12-hydroxyellipticine, the ellipticine metabolites generated by CYP and peroxidase enzymes, in MCF-7, HL-60, CCRF-CEM, UKF-NB-3, UKF-NB-4 and U87MG cells, but not in neuroblastoma UKF-NB-3 cells. Therefore, DNA adduct formation in most cancer cell lines tested in this comparative study might be the predominant cause of their sensitivity to ellipticine treatment, whereas other mechanisms of ellipticine action also contribute to its cytotoxicity to neuroblastoma UKF-NB-3 cells

Unprocessed Viral DNA Could Be the Primary Target of the HIV-1 Integrase Inhibitor Raltegravir

Integration of HIV DNA into host chromosome requires a 3′-processing (3′-P) and a strand transfer (ST) reactions catalyzed by virus integrase (IN). Raltegravir (RAL), commonly used in AIDS therapy, belongs to the family of IN ST inhibitors (INSTIs) acting on IN-viral DNA complexes (intasomes). However, studies show that RAL fails to bind IN alone, but nothing has been reported on the behaviour of RAL toward free viral DNA. Here, we assessed whether free viral DNA could be a primary target for RAL, assuming that the DNA molecule is a receptor for a huge number of pharmacological agents. Optical spectroscopy, molecular dynamics and free energy calculations, showed that RAL is a tight binder of both processed and unprocessed LTR (long terminal repeat) ends. Complex formation involved mainly van der Waals forces and was enthalpy driven. Dissociation constants (Kds) revealed that RAL affinity for unbound LTRs was stronger than for bound LTRs. Moreover, Kd value for binding of RAL to LTRs and IC50 value (half concentration for inhibition) were in same range, suggesting that RAL binding to DNA and ST inhibition are correlated events. Accommodation of RAL into terminal base-pairs of unprocessed LTR is facilitated by an extensive end fraying that lowers the RAL binding energy barrier. The RAL binding entails a weak damping of fraying and correlatively of 3′-P inhibition. Noteworthy, present calculated RAL structures bound to free viral DNA resemble those found in RAL-intasome crystals, especially concerning the contacts between the fluorobenzyl group and the conserved 5′C4pA33′ step. We propose that RAL inhibits IN, in binding first unprocessed DNA. Similarly to anticancer drug poisons acting on topoisomerases, its interaction with DNA does not alter the cut, but blocks the subsequent joining reaction. We also speculate that INSTIs having viral DNA rather IN as main target could induce less resistance

DNA and histone deacetylases as targets for neuroblastoma treatment

Neuroblastoma, a tumor of the peripheral sympathetic nervous system, is the most frequent solid extra cranial tumor in children and is a major cause of death from neoplasia in infancy. Still little improvement in therapeutic options has been made, requiring a need for the development of new therapies. In our laboratory, we address still unsettled questions, which of mechanisms of action of DNA-damaging drugs both currently use for treatment of human neuroblastomas (doxorubicin, cis-platin, cyclophosphamide and etoposide) and another anticancer agent decreasing growth of neuroblastomas in vitro, ellipticine, are predominant mechanism(s) responsible for their antitumor action in neuroblastoma cell lines in vitro. Because hypoxia frequently occurs in tumors and strongly correlates with advanced disease and poor outcome caused by chemoresistance, the effects of hypoxia on efficiencies and mechanisms of actions of these drugs in neuroblastomas are also investigated. Since the epigenetic structure of DNA and its lesions play a role in the origin of human neuroblastomas, pharmaceutical manipulation of the epigenome may offer other treatment options also for neuroblastomas. Therefore, the effects of histone deacetylase inhibitors on growth of neuroblastoma and combination of these compounds with doxorubicin, cis-platin, etoposide and ellipticine as well as mechanisms of such effects in human neuroblastona cell lines in vitro are also investigated. Such a study will increase our knowledge to explain the proper function of these drugs on the molecular level, which should be utilized for the development of new therapies for neuroblastomas

An Introduction to Temporal Graphs: An Algorithmic Perspective

A \emph{temporal graph} is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed as a sequence $G_1,G_2\ldots,G_l$ of static graphs over the same (static) set of nodes $V$. Though static graphs have been extensively studied, for their temporal generalization we are still far from having a concrete set of structural and algorithmic principles. Recent research shows that many graph properties and problems become radically different and usually substantially more difficult when an extra time dimension in added to them. Moreover, there is already a rich and rapidly growing set of modern systems and applications that can be naturally modeled and studied via temporal graphs. This, further motivates the need for the development of a temporal extension of graph theory. We survey here recent results on temporal graphs and temporal graph problems that have appeared in the Computer Science community