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

Holographic c-theorems in arbitrary dimensions

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flows is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.Comment: 62 pages, 4 figures, few typo's correcte

Perineal descent and patients’ symptoms of anorectal dysfunction, pelvic organ prolapse, and urinary incontinence

Contains fulltext : 89793.pdf (publisher's version ) (Closed access)INTRODUCTION AND HYPOTHESIS: The aim of this dynamic magnetic resonance (MR) imaging study was to assess the relation between the position and mobility of the perineum and patients' symptoms of pelvic floor dysfunction. METHODS: Patients' symptoms were measured with the use of validated questionnaires. Univariate logistic regression analyses were used to study the relationship between the questionnaires domain scores and the perineal position on dynamic MR imaging, as well as baseline characteristics (age, body mass index, and parity). RESULTS: Sixty-nine women were included in the analysis. Only the domain score genital prolapse was associated with the perineal position on dynamic MR imaging. This association was strongest at rest. CONCLUSIONS: Pelvic organ prolapse symptoms were associated with the degree of descent of the perineum on dynamic MR imaging. Perineal descent was not related to anorectal and/or urinary incontinence symptoms.1 juni 201

A search for ultrahigh-energy neutrinos associated with astrophysical sources using the third flight of ANITA

The ANtarctic Impulsive Transient Antenna (ANITA) long-duration balloon experiment is sensitive to interactions of ultrahigh-energy (E>1018 eV) neutrinos in the Antarctic ice sheet. The third flight of ANITA, lasting 22 days, began in December 2014. We develop a methodology to search for energetic neutrinos spatially and temporally coincident with potential source classes in ANITA data. This methodology is applied to several source classes: the potential IceCube-identified neutrino sources TXS 0506+056 and NGC 1068, flaring high-energy blazars reported by the Fermi All-Sky Variability Analysis, gamma-ray bursts, and supernovae. Among searches within the five source classes, one candidate was identified as associated with SN 2015D, although not at a statistically significant level. We proceed to place upper limits on the source classes. We further comment on potential application of this methodology to more sensitive future instruments

An analysis of a tau-neutrino hypothesis for the near-horizon cosmic-ray-like events observed by ANITA-IV

We present the results of a simulation of the acceptance of the Antarctic Impulsive Transient Antenna (ANITA) to possible υτ point source fluxes detected via τ-lepton-induced air showers. This investigation is framed around the detection of four upward-going extensive air shower events observed very close to the horizon in ANITA-IV. These four events as well as the overall diffuse and point source exposure to Earth-skimming υτ are also compared against published ultrahigh-energy neutrino limits from the Pierre Auger Observatory. We find that while these four events were detected at sky coordinates close to ANITA’s maximum υτ sensitivity and were not simultaneously visible by Auger, the implied fluence necessary for ANITA to observe these events is in tension with limits set by Auger across a wide range of energies and is additionally in tension with ANITA’s Askaryan in-ice neutrino channel above 1019 eV

Analysis of a tau neutrino origin for the near-horizon air shower events observed by the fourth flight of the Antarctic Impulsive Transient Antenna

We study in detail the sensitivity of the Antarctic Impulsive Transient Antenna (ANITA) to possible Formula Presented point source fluxes detected via Formula Presented-lepton-induced air showers. This investigation is framed around the observation of four upward-going extensive air shower events very close to the horizon seen in ANITA-IV. We find that these four upgoing events are not observationally inconsistent with Formula Presented-induced EASs from Earth-skimming Formula Presented both in their spectral properties as well as in their observed locations on the sky. These four events as well as the overall diffuse and point source exposure to Earth-skimming Formula Presented are also compared against published ultrahigh-energy neutrino limits from the Pierre Auger Observatory. While none of these four events occurred at sky locations simultaneously visible by Auger, the implied fluence necessary for ANITA to observe these events is in strong tension with limits set by Auger across a wide range of energies and is additionally in tension with ANITA’s Askaryan in-ice neutrino channel above Formula Presented. We conclude by discussing some of the technical challenges with simulating and analyzing these near horizon events and the potential for future observatories to observe similar events

Methyl-donor depletion of head and neck cancer cells in vitro establishes a less aggressive tumour cell phenotype

PURPOSE: DNA methylation plays a fundamental role in the epigenetic control of carcinogenesis and is, in part, influenced by the availability of methyl donors obtained from the diet. In this study, we developed an in-vitro model to investigate whether methyl donor depletion affects the phenotype and gene expression in head and neck squamous cell carcinoma (HNSCC) cells. METHODS: HNSCC cell lines (UD-SCC2 and UPCI-SCC72) were cultured in medium deficient in methionine, folate, and choline or methyl donor complete medium. Cell doubling-time, proliferation, migration, and apoptosis were analysed. The effects of methyl donor depletion on enzymes controlling DNA methylation and the pro-apoptotic factors death-associated protein kinase-1 (DAPK1) and p53 upregulated modulator of apoptosis (PUMA) were examined by quantitative-PCR or immunoblotting. RESULTS: HNSCC cells cultured in methyl donor deplete conditions showed significantly increased cell doubling times, reduced cell proliferation, impaired cell migration, and a dose-dependent increase in apoptosis when compared to cells cultured in complete medium. Methyl donor depletion significantly increased the gene expression of DNMT3a and TET-1, an effect that was reversed upon methyl donor repletion in UD-SCC2 cells. In addition, expression of DAPK1 and PUMA was increased in UD-SCC2 cells cultured in methyl donor deplete compared to complete medium, possibly explaining the observed increase in apoptosis in these cells. CONCLUSION: Taken together, these data show that depleting HNSCC cells of methyl donors reduces the growth and mobility of HNSCC cells, while increasing rates of apoptosis, suggesting that a methyl donor depleted diet may significantly affect the growth of established HNSCC

The role of prostaglandin E2 (PGE 2) in toll-like receptor 4 (TLR4)-mediated colitis-associated neoplasia

<p>Abstract</p> <p>Background</p> <p>We have previously found that TLR4-deficient (TLR4-/-) mice demonstrate decreased expression of mucosal PGE ₂and are protected against colitis-associated neoplasia. However, it is still unclear whether PGE ₂is the central factor downstream of TLR4 signaling that promotes intestinal tumorigenesis. To further elucidate critical downstream pathways involving TLR4-mediated intestinal tumorigenesis, we examined the effects of exogenously administered PGE ₂in TLR4-/- mice to see if PGE ₂bypasses the protection from colitis-associated tumorigenesis.</p> <p>Method</p> <p>Mouse colitis-associated neoplasia was induced by azoxymethane (AOM) injection followed by two cycles of dextran sodium sulfate (DSS) treatment. Two different doses of PGE ₂(high dose group, 200 μg, n = 8; and low dose group, 100 μg, n = 6) were administered daily during recovery period of colitis by gavage feeding. Another group was given PGE ₂during DSS treatment (200 μg, n = 5). Inflammation and dysplasia were assessed histologically. Mucosal Cox-2 and amphiregulin (AR) expression, prostanoid synthesis, and EGFR activation were analyzed.</p> <p>Results</p> <p>In control mice treated with PBS, the average number of tumors was greater in WT mice (n = 13) than in TLR4-/- mice (n = 7). High dose but not low dose PGE ₂treatment caused an increase in epithelial proliferation. 28.6% of PBS-treated TLR4-/- mice developed dysplasia (tumors/animal: 0.4 ± 0.2). By contrast, 75.0% (tumors/animal: 1.5 ± 1.2, P < 0.05) of the high dose group and 33.3% (tumors/animal: 0.3 ± 0.5) of the low dose group developed dysplasia in TLR4-/- mice. Tumor size was also increased by high dose PGE ₂treatment. Endogenous prostanoid synthesis was differentially affected by PGE ₂treatment during acute and recovery phases of colitis. Exogenous administration of PGE ₂increased colitis-associated tumorigenesis but this only occurred during the recovery phase. Lastly, PGE ₂treatment increased mucosal expression of AR and Cox-2, thus inducing EGFR activation and forming a positive feedback mechanism to amplify mucosal Cox-2.</p> <p>Conclusions</p> <p>These results highlight the importance of PGE ₂as a central downstream molecule involving TLR4-mediated intestinal tumorigenesis.</p