An Improved Interactive Streaming Algorithm for the Distinct Elements Problem

The exact computation of the number of distinct elements (frequency moment $F_0$) is a fundamental problem in the study of data streaming algorithms. We denote the length of the stream by $n$ where each symbol is drawn from a universe of size $m$. While it is well known that the moments $F_0,F_1,F_2$ can be approximated by efficient streaming algorithms, it is easy to see that exact computation of $F_0,F_2$ requires space $\Omega(m)$. In previous work, Cormode et al. therefore considered a model where the data stream is also processed by a powerful helper, who provides an interactive proof of the result. They gave such protocols with a polylogarithmic number of rounds of communication between helper and verifier for all functions in NC. This number of rounds $\left(O(\log^2 m) \;\text{in the case of} \;F_0 \right)$ can quickly make such protocols impractical. Cormode et al. also gave a protocol with $\log m +1$ rounds for the exact computation of $F_0$ where the space complexity is $O\left(\log m \log n+\log^2 m\right)$ but the total communication $O\left(\sqrt{n}\log m\left(\log n+ \log m \right)\right)$. They managed to give $\log m$ round protocols with $\operatorname{polylog}(m,n)$ complexity for many other interesting problems including $F_2$, Inner product, and Range-sum, but computing $F_0$ exactly with polylogarithmic space and communication and $O(\log m)$ rounds remained open. In this work, we give a streaming interactive protocol with $\log m$ rounds for exact computation of $F_0$ using $O\left(\log m \left(\,\log n + \log m \log\log m\,\right)\right)$ bits of space and the communication is $O\left( \log m \left(\,\log n +\log^3 m (\log\log m)^2 \,\right)\right)$. The update time of the verifier per symbol received is $O(\log^2 m)$.Comment: Submitted to ICALP 201

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

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

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

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

Inference of the infection status of individuals using longitudinal testing data from cryptic populations: Towards a probabilistic approach to diagnosis

Effective control of many diseases requires the accurate detection of infected individuals. Confidently ascertaining whether an individual is infected can be challenging when diagnostic tests are imperfect and when some individuals go for long periods of time without being observed or sampled. Here, we use a multi-event capture-recapture approach to model imperfect observations of true epidemiological states. We describe a method for interpreting potentially disparate results from individuals sampled multiple times over an extended period, using empirical data from a wild badger population naturally infected with Mycobacterium bovis as an example. We examine the effect of sex, capture history and current and historical diagnostic test results on the probability of being truly infected, given any combination of diagnostic test results. In doing so, we move diagnosis away from the traditional binary classification of apparently infected versus uninfected to a probability-based interpretation which is updated each time an individual is re-sampled. Our findings identified temporal variation in infection status and suggest that capture probability is influenced by year, season and infection status. This novel approach to combining ecological and epidemiological data may aid disease management decision-making by providing a framework for the integration of multiple diagnostic test data with other information

Natural Killer Cell Mediated Cytotoxic Responses in the Tasmanian Devil

The Tasmanian devil (Sarcophilus harrisii), the world's largest marsupial carnivore, is under threat of extinction following the emergence of an infectious cancer. Devil facial tumour disease (DFTD) is spread between Tasmanian devils during biting. The disease is consistently fatal and devils succumb without developing a protective immune response. The aim of this study was to determine if Tasmanian devils were capable of forming cytotoxic antitumour responses and develop antibodies against DFTD cells and foreign tumour cells. The two Tasmanian devils immunised with irradiated DFTD cells did not form cytotoxic or humoral responses against DFTD cells, even after multiple immunisations. However, following immunisation with xenogenic K562 cells, devils did produce cytotoxic responses and antibodies against this foreign tumour cell line. The cytotoxicity appeared to occur through the activity of natural killer (NK) cells in an antibody dependent manner. Classical NK cell responses, such as innate killing of DFTD and foreign cancer cells, were not observed. Cells with an NK-like phenotype comprised approximately 4 percent of peripheral blood mononuclear cells. The results of this study suggest that Tasmanian devils have NK cells with functional cytotoxic pathways. Although devil NK cells do not directly recognise DFTD cancer cells, the development of antibody dependent cell-mediated cytotoxicity presents a potential pathway to induce cytotoxic responses against the disease. These findings have positive implications for future DFTD vaccine research