Packing Returning Secretaries

We study online secretary problems with returns in combinatorial packing domains with $n$ candidates that arrive sequentially over time in random order. The goal is to accept a feasible packing of candidates of maximum total value. In the first variant, each candidate arrives exactly twice. All $2n$ arrivals occur in random order. We propose a simple 0.5-competitive algorithm that can be combined with arbitrary approximation algorithms for the packing domain, even when the total value of candidates is a subadditive function. For bipartite matching, we obtain an algorithm with competitive ratio at least $0.5721 - o(1)$ for growing $n$, and an algorithm with ratio at least $0.5459$ for all $n \ge 1$. We extend all algorithms and ratios to $k \ge 2$ arrivals per candidate. In the second variant, there is a pool of undecided candidates. In each round, a random candidate from the pool arrives. Upon arrival a candidate can be either decided (accept/reject) or postponed (returned into the pool). We mainly focus on minimizing the expected number of postponements when computing an optimal solution. An expected number of $\Theta(n \log n)$ is always sufficient. For matroids, we show that the expected number can be reduced to $O(r \log (n/r))$, where $r \le n/2$ is the minimum of the ranks of matroid and dual matroid. For bipartite matching, we show a bound of $O(r \log n)$, where $r$ is the size of the optimum matching. For general packing, we show a lower bound of $\Omega(n \log \log n)$, even when the size of the optimum is $r = \Theta(\log n)$.Comment: 23 pages, 5 figure

A structural theorem for local algorithms with applications to coding, testing, and privacy

We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and PCPs of proximity. Namely, we show that the structure of every algorithm that makes $q$ adaptive queries and satisfies a natural robustness condition admits a sample-based algorithm with $n^{1- 1/O(q^2 \log^2 q)}$ sample complexity, following the definition of Goldreich and Ron (TOCT 2016). We prove that this transformation is nearly optimal. Our theorem also admits a scheme for constructing privacy-preserving local algorithms. %Along the way, we obtain a sunflower-based combinatorial representation of robust local algorithms. Using the unified view that our structural theorem provides, we obtain results regarding various types of local algorithms, including the following. - We strengthen the state-of-the-art lower bound for relaxed locally decodable codes, obtaining an \emph{exponential} improvement on the dependency in query complexity; this resolves an open problem raised by Gur and Lachish (SICOMP 2021). - We show that any (constant-query) testable property admits a sample-based tester with sublinear sample complexity; this resolves a problem left open in a work of Fischer, Lachish, and Vasudev (FOCS 2015), bypassing an exponential blowup caused by previous techniques in the case of adaptive testers. - We prove that the known separation between proofs of proximity and testers is essentially maximal; this resolves a problem left open by Gur and Rothblum (ECCC 2013, Computational Complexity 2018) regarding sublinear-time delegation of computation. Our techniques strongly rely on relaxed sunflower lemmas and the Hajnal–Szemer\'{e}di theorem

Transmission dynamics of Tasmanian devil facial tumor disease may lead to disease-induced extinction

Most pathogens threatening to cause extinction of a host species are maintained on one or more reservoir hosts, in addition to the species that is threatened by disease. Further, most conventional host–pathogen theory assumes that transmission is related to host density, and therefore a pathogen should become extinct before its sole host. Tasmanian devil facial tumor disease is a recently emerged infectious cancer that has led to massive population declines and grave concerns for the future persistence of this largest surviving marsupial carnivore. Here we report the results of mark–recapture studies at six sites and use these data to estimate epidemiological parameters critical to both accurately assessing the risk of extinction from this disease and effectively managing this disease threat. Three sites were monitored from before or close to the time of disease arrival, and at three others disease was well established when trapping began, in one site for at least 10 years. We found no evidence for sex-specific differences in disease prevalence and little evidence of consistent seasonal variation in the force of infection. At all sites, the disease was maintained at high levels of prevalence (>50% in 2–3-year-old animals), despite causing major population declines. We also provide the first estimates of the basic reproductive rate R0 for this disease. Using a simple age-structured deterministic model, we show that our results are not consistent with transmission being proportional to the density of infected hosts but are consistent with frequency-dependent transmission. This conclusion is further supported by the observation that local disease prevalence in 2–3-year-olds still exceeds 50% at a site where population density has been reduced by up to 90% in the past 12 years. These findings lend considerable weight to concerns that this host-specific pathogen will cause the extinction of the Tasmanian devil. Our study highlights the importance of rapidly implementing monitoring programs to determine how transmission depends on host density and emphasizes the need for ongoing management strategies involving a disease-free “insurance population,” along with ongoing field monitoring programs to confirm whether local population extinction occur

A structural theorem for local algorithms with applications to coding, testing, and privacy

We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and PCPs of proximity. Namely, we show that the structure of every algorithm that makes q adaptive queries and satisfies a natural robustness condition admits a sample-based algorithm with n 1−1/O(q 2 log2 q) sample complexity, following the definition of Goldreich and Ron (TOCT 2016). We prove that this transformation is nearly optimal. Our theorem also admits a scheme for constructing privacy-preserving local algorithms. Using the unified view that our structural theorem provides, we obtain results regarding various types of local algorithms, including the following. We strengthen the state-of-the-art lower bound for relaxed locally decodable codes, obtaining an exponential improvement on the dependency in query complexity; this resolves an open problem raised by Gur and Lachish (SODA 2020). We show that any (constant-query) testable property admits a sample-based tester with sublinear sample complexity; this resolves a problem left open in a work of Fischer, Lachish, and Vasudev (FOCS 2015) by extending their main result to adaptive testers. We prove that the known separation between proofs of proximity and testers is essentially maximal; this resolves a problem left open by Gur and Rothblum (ECCC 2013, Computational Complexity 2018) regarding sublinear-time delegation of computation. Our techniques strongly rely on relaxed sunflower lemmas and the Hajnal–Szemer´edi theorem

Instruments of RT-2 Experiment onboard CORONAS-PHOTON and their test and evaluation II: RT-2/CZT payload

Cadmium Zinc Telluride (CZT) detectors are high sensitivity and high resolution devices for hard X-ray imaging and spectroscopic studies. The new series of CZT detector modules (OMS40G256) manufactured by Orbotech Medical Solutions (OMS), Israel, are used in the RT-2/CZT payload onboard the CORONAS-PHOTON satellite. The CZT detectors, sensitive in the energy range of 20 keV to 150 keV, are used to image solar flares in hard X-rays. Since these modules are essentially manufactured for commercial applications, we have carried out a series of comprehensive tests on these modules so that they can be confidently used in space-borne systems. These tests lead us to select the best three pieces of the 'Gold' modules for the RT-2/CZT payload. This paper presents the characterization of CZT modules and the criteria followed for selecting the ones for the RT-2/CZT payload. The RT-2/CZT payload carries, along with three CZT modules, a high spatial resolution CMOS detector for high resolution imaging of transient X-ray events. Therefore, we discuss the characterization of the CMOS detector as well.Comment: 26 pages, 19 figures, Accepted for publication in Experimental Astronomy (in press

Demographic profiles and environmental drivers of variation relate to individual breeding state in a long-lived trans-oceanic migratory seabird, the Manx shearwater

Understanding the points in a species breeding cycle when they are most vulnerable to environmental fluctuations is key to understanding interannual demography and guiding effective conservation and management. Seabirds represent one of the most threatened groups of birds in the world, and climate change and severe weather is a prominent and increasing threat to this group. We used a multi-state capture-recapture model to examine how the demographic rates of a long-lived trans-oceanic migrant seabird, the Manx shearwater Puffinus puffinus, are influenced by environmental conditions experienced at different stages of the annual breeding cycle and whether these relationships vary with an individual's breeding state in the previous year (i.e., successful breeder, failed breeder and non-breeder). Our results imply that populations of Manx shearwaters are comprised of individuals with different demographic profiles, whereby more successful reproduction is associated with higher rates of survival and breeding propensity. However, we found that all birds experienced the same negative relationship between rates of survival and wind force during the breeding season, indicating a cost of reproduction (or central place constraint for non-breeders) during years with severe weather conditions. We also found that environmental effects differentially influence the breeding propensity of individuals in different breeding states. This suggests individual spatio-temporal variation in habitat use during the annual cycle, such that climate change could alter the frequency that individuals with different demographic profiles breed thereby driving a complex and less predictable population response. More broadly, our study highlights the importance of considering individual-level factors when examining population demography and predicting how species may respond to climate change

Demographic profiles and environmental drivers of variation relate to individual breeding state in a long-lived trans-oceanic migratory seabird, the Manx shearwater.

Understanding the points in a species breeding cycle when they are most vulnerable to environmental fluctuations is key to understanding interannual demography and guiding effective conservation and management. Seabirds represent one of the most threatened groups of birds in the world, and climate change and severe weather is a prominent and increasing threat to this group. We used a multi-state capture-recapture model to examine how the demographic rates of a long-lived trans-oceanic migrant seabird, the Manx shearwater Puffinus puffinus, are influenced by environmental conditions experienced at different stages of the annual breeding cycle and whether these relationships vary with an individual's breeding state in the previous year (i.e., successful breeder, failed breeder and non-breeder). Our results imply that populations of Manx shearwaters are comprised of individuals with different demographic profiles, whereby more successful reproduction is associated with higher rates of survival and breeding propensity. However, we found that all birds experienced the same negative relationship between rates of survival and wind force during the breeding season, indicating a cost of reproduction (or central place constraint for non-breeders) during years with severe weather conditions. We also found that environmental effects differentially influence the breeding propensity of individuals in different breeding states. This suggests individual spatio-temporal variation in habitat use during the annual cycle, such that climate change could alter the frequency that individuals with different demographic profiles breed thereby driving a complex and less predictable population response. More broadly, our study highlights the importance of considering individual-level factors when examining population demography and predicting how species may respond to climate change

New Insights into the Role of MHC Diversity in Devil Facial Tumour Disease

Devil facial tumour disease (DFTD) is a fatal contagious cancer that has decimated Tasmanian devil populations. The tumour has spread without invoking immune responses, possibly due to low levels of Major Histocompatibility Complex (MHC) diversity in Tasmanian devils. Animals from a region in north-western Tasmania have lower infection rates than those in the east of the state. This area is a genetic transition zone between sub-populations, with individuals from north-western Tasmania displaying greater diversity than eastern devils at MHC genes, primarily through MHC class I gene copy number variation. Here we test the hypothesis that animals that remain healthy and tumour free show predictable differences at MHC loci compared to animals that develop the disease

Genomic Restructuring in the Tasmanian Devil Facial Tumour: Chromosome Painting and Gene Mapping Provide Clues to Evolution of a Transmissible Tumour

Devil facial tumour disease (DFTD) is a fatal, transmissible malignancy that threatens the world's largest marsupial carnivore, the Tasmanian devil, with extinction. First recognised in 1996, DFTD has had a catastrophic effect on wild devil numbers, and intense research efforts to understand and contain the disease have since demonstrated that the tumour is a clonal cell line transmitted by allograft. We used chromosome painting and gene mapping to deconstruct the DFTD karyotype and determine the chromosome and gene rearrangements involved in carcinogenesis. Chromosome painting on three different DFTD tumour strains determined the origins of marker chromosomes and provided a general overview of the rearrangement in DFTD karyotypes. Mapping of 105 BAC clones by fluorescence in situ hybridisation provided a finer level of resolution of genome rearrangements in DFTD strains. Our findings demonstrate that only limited regions of the genome, mainly chromosomes 1 and X, are rearranged in DFTD. Regions rearranged in DFTD are also highly rearranged between different marsupials. Differences between strains are limited, reflecting the unusually stable nature of DFTD. Finally, our detailed maps of both the devil and tumour karyotypes provide a physical framework for future genomic investigations into DFTD

Prevalence and genetic diversity of Avipoxvirus in house sparrows in Spain

Avipoxvirus (APV) is a fairly common virus affecting birds that causes morbidity and mortality in wild and captive birds. We studied the prevalence of pox-like lesions and genetic diversity of APV in house sparrows (Passer domesticus) in natural, agricultural and urban areas in southern Spain in 2013 and 2014 and in central Spain for 8 months (2012±2013). Overall, 3.2% of 2,341 house sparrows visually examined in southern Spain had cutaneous lesions consistent with avian pox. A similar prevalence (3%) was found in 338 birds from central Spain. Prevalence was higher in hatch-year birds than in adults. We did not detect any clear spatial or temporal patterns of APV distribution. Molecular analyses of poxvirus-like lesions revealed that 63% of the samples were positive. Molecular and phylogenetic analyses of 29 DNA sequences from the fpv167 gene, detected two strains belonging to the canarypox clade (subclades B1 and B2) previously found in Spain. One of them appears predominant in Iberia and North Africa and shares 70% similarity to fowlpox and canarypox virus. This APV strain has been identified in a limited number of species in the Iberian Peninsula, Morocco and Hungary. The second one has a global distribution and has been found in numerous wild bird species around the world. To our knowledge, this represents the largest study of avian poxvirus disease in the broadly distributed house sparrow and strongly supports the findings that Avipox prevalence in this species in South and central Spain is moderate and the genetic diversity low.This study was funded by the Spanish Ministry of Science and Innovation (Project CGL2010-15734/BOS), the Spanish Ministry of Economy and Competitiveness (Project CGL2013-41642-P/BOS) and the Innovation and Development Agency of Andalusia (Spain) (P11-RNM-7038). Grants were awarded to JMP (Juan de la Cierva- JCI-2012-11868) and MAJM (FPIBES-2011-047609), Spanish Ministry of Economy and Competitiveness; RAJW (CEI-PICATA2012), CEI Campus of International Excellence; MM (FPU12/0568), Spanish Ministry of Education, Culture and Sports. RAJW was supported by the Craaford Foundation (grant 20160971) during the writing of this publication. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript