Maximum rectilinear convex subsets

Let P be a set of n points in the plane. We consider a variation of the classical Erd\H os-Szekeres problem, presenting efficient algorithms with O(n3) running time and O(n2) space complexity that compute (1) a subset S of P such that the boundary of the rectilinear convex hull of S has the maximum number of points from P, (2) a subset S of P such that the boundary of the rectilinear convex hull of S has the maximum number of points from P and its interior contains no element of P, (3) a subset S of P such that the rectilinear convex hull of S has maximum area and its interior contains no element of P, and (4) when each point of P is assigned a weight, positive or negative, a subset S of P that maximizes the total weight of the points in the rectilinear convex hull of S. We also revisit the problems of computing a maximum area orthoconvex polygon and computing a maximum area staircase polygon, amidst a point set in a rectangular domain. We obtain new and simpler algorithms to solve both problems with the same complexity as in the state of the art

Bichromatic Discrepancy via Convex Partitions

Let R be a set of red points and B a set of blue points on the plane. In this paper we introduce a new concept for measuring how mixed the elements of S = R â\u88ª B are. The discrepancy of a set X â\u8a\u82 S is ||X â\u88© R | â\u88\u92 |X â\u88© B||. We say that a partition Π = {S1, S2,..., Sk} of S is convex if the convex hulls of its members are pairwise disjoint. The discrepancy of a convex partition of S is the minimum discrepancy of the sets Si. The discrepancy of S is the discrepancy of the convex partition of S with maximum discrepancy. We study the problem of computing the discrepancy of a bichromatic point set. We divide the study in general convex partitions for both general set of points and points in convex position, and also when the partition is given by a line. In this case we prove that this problem is 3SUM-hard

Confirmation of the spectral excess in DAMIC at SNOLAB with skipper CCDs

International audienceWe present results from a 3.1 kg-day target exposure of two charge-coupled devices (CCDs), each with 24 megapixels and skipper readout, deployed in the DAMIC (DArk Matter In CCDs) setup at SNOLAB. With a reduction in pixel readout noise of a factor of 10 relative to the previous detector, we investigate the excess population of low-energy bulk events previously observed above expected backgrounds. We address the dominant systematic uncertainty of the previous analysis through a depth fiducialization designed to reject surface backgrounds on the CCDs. The measured bulk ionization spectrum confirms with higher significance the presence of an excess population of low-energy events in the CCD target with characteristic rate of ${\sim}7$ events per kg-day and electron-equivalent energies of ${\sim}80~$eV, whose origin remains unknown

Confirmation of the spectral excess in DAMIC at SNOLAB with skipper CCDs

International audienceWe present results from a 3.1 kg-day target exposure of two charge-coupled devices (CCDs), each with 24 megapixels and skipper readout, deployed in the DAMIC (DArk Matter In CCDs) setup at SNOLAB. With a reduction in pixel readout noise of a factor of 10 relative to the previous detector, we investigate the excess population of low-energy bulk events previously observed above expected backgrounds. We address the dominant systematic uncertainty of the previous analysis through a depth fiducialization designed to reject surface backgrounds on the CCDs. The measured bulk ionization spectrum confirms with higher significance the presence of an excess population of low-energy events in the CCD target with characteristic rate of ${\sim}7$ events per kg-day and electron-equivalent energies of ${\sim}80~$eV, whose origin remains unknown

Confirmation of the spectral excess in DAMIC at SNOLAB with skipper CCDs

International audienceWe present results from a 3.1 kg-day target exposure of two charge-coupled devices (CCDs), each with 24 megapixels and skipper readout, deployed in the DAMIC (DArk Matter In CCDs) setup at SNOLAB. With a reduction in pixel readout noise of a factor of 10 relative to the previous detector, we investigate the excess population of low-energy bulk events previously observed above expected backgrounds. We address the dominant systematic uncertainty of the previous analysis through a depth fiducialization designed to reject surface backgrounds on the CCDs. The measured bulk ionization spectrum confirms with higher significance the presence of an excess population of low-energy events in the CCD target with characteristic rate of ${\sim}7$ events per kg-day and electron-equivalent energies of ${\sim}80~$eV, whose origin remains unknown

Genetic landscape of 6089 inherited retinal dystrophies affected cases in Spain and their therapeutic and extended epidemiological implications

Inherited retinal diseases (IRDs), defined by dysfunction or progressive loss of photoreceptors, are disorders characterized by elevated heterogeneity, both at the clinical and genetic levels. Our main goal was to address the genetic landscape of IRD in the largest cohort of Spanish patients reported to date. A retrospective hospital-based cross-sectional study was carried out on 6089 IRD affected individuals (from 4403 unrelated families), referred for genetic testing from all the Spanish autonomous communities. Clinical, demographic and familiar data were collected from each patient, including family pedigree, age of appearance of visual symptoms, presence of any systemic findings and geographical origin. Genetic studies were performed to the 3951 families with available DNA using different molecular techniques. Overall, 53.2% (2100/3951) of the studied families were genetically characterized, and 1549 different likely causative variants in 142 genes were identified. The most common phenotype encountered is retinitis pigmentosa (RP) (55.6% of families, 2447/4403). The most recurrently mutated genes were PRPH2, ABCA4 and RS1 in autosomal dominant (AD), autosomal recessive (AR) and X-linked (XL) NON-RP cases, respectively; RHO, USH2A and RPGR in AD, AR and XL for non-syndromic RP; and USH2A and MYO7A in syndromic IRD. Pathogenic variants c.3386G > T (p.Arg1129Leu) in ABCA4 and c.2276G > T (p.Cys759Phe) in USH2A were the most frequent variants identified. Our study provides the general landscape for IRD in Spain, reporting the largest cohort ever presented. Our results have important implications for genetic diagnosis, counselling and new therapeutic strategies to both the Spanish population and other related populations

Genetic landscape of 6089 inherited retinal dystrophies affected cases in Spain and their therapeutic and extended epidemiological implications

Inherited retinal diseases (IRDs), defined by dysfunction or progressive loss of photoreceptors, are disorders characterized by elevated heterogeneity, both at the clinical and genetic levels. Our main goal was to address the genetic landscape of IRD in the largest cohort of Spanish patients reported to date. A retrospective hospital-based cross-sectional study was carried out on 6089 IRD affected individuals (from 4403 unrelated families), referred for genetic testing from all the Spanish autonomous communities. Clinical, demographic and familiar data were collected from each patient, including family pedigree, age of appearance of visual symptoms, presence of any systemic findings and geographical origin. Genetic studies were performed to the 3951 families with available DNA using different molecular techniques. Overall, 53.2% (2100/3951) of the studied families were genetically characterized, and 1549 different likely causative variants in 142 genes were identified. The most common phenotype encountered is retinitis pigmentosa (RP) (55.6% of families, 2447/4403). The most recurrently mutated genes were PRPH2, ABCA4 and RS1 in autosomal dominant (AD), autosomal recessive (AR) and X-linked (XL) NON-RP cases, respectively; RHO, USH2A and RPGR in AD, AR and XL for non-syndromic RP; and USH2A and MYO7A in syndromic IRD. Pathogenic variants c.3386G > T (p.Arg1129Leu) in ABCA4 and c.2276G > T (p.Cys759Phe) in USH2A were the most frequent variants identified. Our study provides the general landscape for IRD in Spain, reporting the largest cohort ever presented. Our results have important implications for genetic diagnosis, counselling and new therapeutic strategies to both the Spanish population and other related populations