A Technique for Obtaining True Approximations for kk-Center with Covering Constraints

There has been a recent surge of interest in incorporating fairness aspects into classical clustering problems. Two recently introduced variants of the $k$-Center problem in this spirit are Colorful $k$-Center, introduced by Bandyapadhyay, Inamdar, Pai, and Varadarajan, and lottery models, such as the Fair Robust $k$-Center problem introduced by Harris, Pensyl, Srinivasan, and Trinh. To address fairness aspects, these models, compared to traditional $k$-Center, include additional covering constraints. Prior approximation results for these models require to relax some of the normally hard constraints, like the number of centers to be opened or the involved covering constraints, and therefore, only obtain constant-factor pseudo-approximations. In this paper, we introduce a new approach to deal with such covering constraints that leads to (true) approximations, including a $4$-approximation for Colorful $k$-Center with constantly many colors---settling an open question raised by Bandyapadhyay, Inamdar, Pai, and Varadarajan---and a $4$-approximation for Fair Robust $k$-Center, for which the existence of a (true) constant-factor approximation was also open. We complement our results by showing that if one allows an unbounded number of colors, then Colorful $k$-Center admits no approximation algorithm with finite approximation guarantee, assuming that $\mathrm{P} \neq \mathrm{NP}$. Moreover, under the Exponential Time Hypothesis, the problem is inapproximable if the number of colors grows faster than logarithmic in the size of the ground set

Estimation of colorectal adenoma recurrence with dependent censoring

<p>Abstract</p> <p>Background</p> <p>Due to early colonoscopy for some participants, interval-censored observations can be introduced into the data of a colorectal polyp prevention trial. The censoring could be dependent of risk of recurrence if the reasons of having early colonoscopy are associated with recurrence. This can complicate estimation of the recurrence rate.</p> <p>Methods</p> <p>We propose to use midpoint imputation to convert interval-censored data problems to right censored data problems. To adjust for potential dependent censoring, we use information from auxiliary variables to define risk groups to perform the weighted Kaplan-Meier estimation to the midpoint imputed data. The risk groups are defined using two risk scores derived from two working proportional hazards models with the auxiliary variables as the covariates. One is for the recurrence time and the other is for the censoring time. The method described here is explored by simulation and illustrated with an example from a colorectal polyp prevention trial.</p> <p>Results</p> <p>We first show that midpoint imputation under an assumption of independent censoring will produce an unbiased estimate of recurrence rate at the end of the trial, which is often the main interest of a colorectal polyp prevention trial, and then show in simulations that the weighted Kaplan-Meier method using the information from auxiliary variables based on the midpoint imputed data can improve efficiency in a situation with independent censoring and reduce bias in a situation with dependent censoring compared to the conventional methods, while estimating the recurrence rate at the end of the trial.</p> <p>Conclusion</p> <p>The research in this paper uses midpoint imputation to handle interval-censored observations and then uses the information from auxiliary variables to adjust for dependent censoring by incorporating them into the weighted Kaplan-Meier estimation. This approach can handle a situation with multiple auxiliary variables by deriving two risk scores from two working PH models. Although the idea of this approach might appear simple, the results do show that the weighted Kaplan-Meier approach can gain efficiency and reduce bias due to dependent censoring.</p

Immunohistochemical localization of collagen types I and VI in human skin wounds

A total of 74 human skin wounds were investigated and collagen types I and VI were localized in the wound area by immunohistochemistry. Collagen type I appeared in the form of ramifying string-like structures after approximately 5–6 days, but positive reactions in the form of a spot-like staining around isolated fibroblasts also occurred in a skin wound aged 4 days. Collagen VI was detectable after a post-infliction interval of at least 3 days showing a strongly positive reacting network associated with fibroblasts in the wound area. Both collagens appeared almost constantly after a wound age of 6–7 clays and could also be found in wounds aged a few months. Therefore, although a positive reaction for collagen type I in the form of string-like and ramifying structures around wound fibroblasts indicates a wound age of at least 5–6 days, a spot-like positive staining for collagen type I cannot exclude a wound age of at least 4 days. A positive staining for collagen type VI represents a post-infliction time of 3 days or more. The almost constant appearance of these collagen types suggests that negative results in a sufficient number of specimens indicate a wound age of less than 6–7 days, but cannot completely exclude longer post-infliction intervals. Since collagen type I and VI are also found in the granulation/scar tissue of lesions with advanced wound age, the immunohistochemical analysis of these proteins provides no further information for an age determination of older skin wounds

Ultrasonic Imaging and the Long Wavelength Phase

Elastodynamic and acoustic wave scattering play an essential role in various inspection methods such as sonar and ultrasonic tomography. Recently there has been considerable interest in the implications of long wavelength elastodynamic scattering for the characterization of flaws in elastic solids [1-6]. If the scattering amplitude is expanded as a power series in the frequency, the leading term is real and varies as the frequency squared. The next term varies as the frequency cubed and is purely imaginary. The evaluation of the phase variation in the long wavelength limit requires the ratio of these terms. Most effort to date has been invested in understanding the dependence of the coefficient of the frequency squared term on the size, shape, orientation and material properties of the scatterer. Richardson [3] and Kohn and Rice [4] have shown that, for an anisotropic elastic inclusion in an otherwise isotropic and homogeneous elastic space, the coefficient depends on at most 22 parameters. In addition, efficient numerical programs have been constructed to evaluate this coefficient for ellipsoidal inclusions. Other work has related it to the stress intensity factor for flaws which are crack-like [5]

Electrostatically gated membrane permeability in inorganic protocells

Although several strategies are now available to produce functional microcompartments analogous to primitive cell-like structures, little progress has been made in generating protocell constructs with self-controlled membrane permeability. Here we describe the preparation of water-dispersible colloidosomes based on silica nanoparticles and delineated by a continuous semipermeable inorganic membrane capable of self-activated, electrostatically gated permeability. We use crosslinking and covalent grafting of a pH-responsive copolymer to generate an ultrathin elastic membrane that exhibits selective release and uptake of small molecules. This behaviour, which depends on the charge of the copolymer coronal layer, serves to trigger enzymatic dephosphorylation reactions specifically within the protocell aqueous interior. This system represents a step towards the design and construction of alternative types of artificial chemical cells and protocell models based on spontaneous processes of inorganic self-organization

Selective-logging and oil palm: Multitaxon impacts, biodiversity indicators, and trade-offs for conservation planning

Strong global demand for tropical timber and agricultural products has driven large-scale logging and subsequent conversion of tropical forests. Given that the majority of tropical landscapes have been or will likely be logged, the protection of biodiversity within tropical forests thus depends on whether species can persist in these economically exploited lands, and if species cannot persist, whether we can protect enough primary forest from logging and conversion. However, our knowledge of the impact of logging and conversion on biodiversity is limited to a few taxa, often sampled in different locations with complex land-use histories, hampering attempts to plan cost-effective conservation strategies and to draw conclusions across taxa. Spanning a land-use gradient of primary forest, once- and twice-logged forests, and oil palm plantations, we used traditional sampling and DNA metabarcoding to compile an extensive data set in Sabah, Malaysian Borneo for nine vertebrate and invertebrate taxa to quantify the biological impacts of logging and oil palm, develop cost-effective methods of protecting biodiversity, and examine whether there is congruence in response among taxa. Logged forests retained high species richness, including, on average, 70% of species found in primary forest. In contrast, conversion to oil palm dramatically reduces species richness, with significantly fewer primary-forest species than found on logged forest transects for seven taxa.Using a systematic conservation planning analysis, we show that efficient protection of primary-forest species is achieved with land portfolios that include a large proportion of logged-forest plots. Protecting logged forests is thus a cost-effective method of protecting an ecologically and taxonomically diverse range of species, particularly when conservation budgets are limited. Six indicator groups (birds, leaf-litter ants, beetles, aerial hymenopterans, flies, and true bugs) proved to be consistently good predictors of the response of the other taxa to logging and oil palm. Our results confidently establish the high conservation value of logged forests and the low value of oil palm. Cross-taxon congruence in responses to disturbance also suggests that the practice of focusing on key indicator taxa yields important information of general biodiversity in studies of logging and oil palm

Estimation of Recurrence of Colorectal Adenomas with Dependent Censoring Using Weighted Logistic Regression

In colorectal polyp prevention trials, estimation of the rate of recurrence of adenomas at the end of the trial may be complicated by dependent censoring, that is, time to follow-up colonoscopy and dropout may be dependent on time to recurrence. Assuming that the auxiliary variables capture the dependence between recurrence and censoring times, we propose to fit two working models with the auxiliary variables as covariates to define risk groups and then extend an existing weighted logistic regression method for independent censoring to each risk group to accommodate potential dependent censoring. In a simulation study, we show that the proposed method results in both a gain in efficiency and reduction in bias for estimating the recurrence rate. We illustrate the methodology by analyzing a recurrent adenoma dataset from a colorectal polyp prevention trial

Characterization and Comparison of 2 Distinct Epidemic Community-Associated Methicillin-Resistant Staphylococcus aureus Clones of ST59 Lineage.

Sequence type (ST) 59 is an epidemic lineage of community-associated (CA) methicillin-resistant Staphylococcus aureus (MRSA) isolates. Taiwanese CA-MRSA isolates belong to ST59 and can be grouped into 2 distinct clones, a virulent Taiwan clone and a commensal Asian-Pacific clone. The Taiwan clone carries the Panton-Valentine leukocidin (PVL) genes and the staphylococcal chromosomal cassette mec (SCCmec) VT, and is frequently isolated from patients with severe disease. The Asian-Pacific clone is PVL-negative, carries SCCmec IV, and a frequent colonizer of healthy children. Isolates of both clones were characterized by their ability to adhere to respiratory A549 cells, cytotoxicity to human neutrophils, and nasal colonization of a murine and murine sepsis models. Genome variation was determined by polymerase chain reaction of selected virulence factors and by multi-strain whole genome microarray. Additionally, the expression of selected factors was compared between the 2 clones. The Taiwan clone showed a much higher cytotoxicity to the human neutrophils and caused more severe septic infections with a high mortality rate in the murine model. The clones were indistinguishable in their adhesion to A549 cells and persistence of murine nasal colonization. The microarray data revealed that the Taiwan clone had lost the ø3-prophage that integrates into the β-hemolysin gene and includes staphylokinase- and enterotoxin P-encoding genes, but had retained the genes for human immune evasion, scn and chps. Production of the virulence factors did not differ significantly in the 2 clonal groups, although more α-toxin was expressed in Taiwan clone isolates from pneumonia patients. In conclusion, the Taiwan CA-MRSA clone was distinguished by enhanced virulence in both humans and an animal infection model. The evolutionary acquisition of PVL, the higher expression of α-toxin, and possibly the loss of a large portion of the β-hemolysin-converting prophage likely contribute to its higher pathogenic potential than the Asian-Pacific clone

Heterologous production of curcuminoids

Curcuminoids, components of the rhizome of turmeric, show several beneficial biological activities, including anticarcinogenic, antioxidant, anti-inflammatory, and antitumor activities. Despite their numerous pharmaceutically important properties, the low natural abundance of curcuminoids represents a major drawback for their use as therapeutic agents. Therefore, they represent attractive targets for heterologous production and metabolic engineering. The understanding of biosynthesis of curcuminoids in turmeric made remarkable advances in the last decade, and as a result, several efforts to produce them in heterologous organisms have been reported. The artificial biosynthetic pathway (e.g., in Escherichia coli) can start with the supplementation of the amino acid tyrosine or phenylalanine or of carboxylic acids and lead to the production of several natural curcuminoids. Unnatural carboxylic acids can also be supplemented as precursors and lead to the production of unnatural compounds with possibly novel therapeutic properties. In this paper, we review the natural conversion of curcuminoids in turmeric and their production by E. coli using an artificial biosynthetic pathway. We also explore the potential of other enzymes discovered recently or already used in other similar biosynthetic pathways, such as flavonoids and stilbenoids, to increase curcuminoid yield and activity.We acknowledge financial support from the Strategic Project PEst-OE/EQB/LA0023/2013, project reference RECI/BBB-EBI/0179/2012 (project number FCOMP-01-0124-FEDER-027462), project SYNBIOBACTHER (PTDC/EBB-BIO/102863/2008), and a doctoral grant (SFRH/BD/51187/ 2010) to J. L. Rodrigues, funded by Fundacao para a Ciencia e a Tecnologia. We thank the MIT-Portugal Program for support given to J. L. Rodrigues