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

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

Assembling evidence for identifying reservoirs of infection

Many pathogens persist in multihost systems, making the identification of infection reservoirs crucial for devising effective interventions. Here, we present a conceptual framework for classifying patterns of incidence and prevalence, and review recent scientific advances that allow us to study and manage reservoirs simultaneously. We argue that interventions can have a crucial role in enriching our mechanistic understanding of how reservoirs function and should be embedded as quasi-experimental studies in adaptive management frameworks. Single approaches to the study of reservoirs are unlikely to generate conclusive insights whereas the formal integration of data and methodologies, involving interventions, pathogen genetics, and contemporary surveillance techniques, promises to open up new opportunities to advance understanding of complex multihost systems

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

Detection, prevalence, and transmission of avian hematozoa in waterfowl at the Arctic/sub-Arctic interface: co-infections, viral interactions, and sources of variation

Background The epidemiology of avian hematozoa at high latitudes is still not well understood, particularly in sub-Arctic and Arctic habitats, where information is limited regarding seasonality and range of transmission, co-infection dynamics with parasitic and viral agents, and possible fitness consequences of infection. Such information is important as climate warming may lead to northward expansion of hematozoa with unknown consequences to northern-breeding avian taxa, particularly populations that may be previously unexposed to blood parasites. Methods We used molecular methods to screen blood samples and cloacal/oropharyngeal swabs collected from 1347 ducks of five species during May-August 2010, in interior Alaska, for the presence of hematozoa, Influenza A Virus (IAV), and IAV antibodies. Using models to account for imperfect detection of parasites, we estimated seasonal variation in prevalence of three parasite genera (Haemoproteus, Plasmodium, Leucocytozoon) and investigated how co-infection with parasites and viruses were related to the probability of infection. Results We detected parasites from each hematozoan genus in adult and juvenile ducks of all species sampled. Seasonal patterns in detection and prevalence varied by parasite genus and species, age, and sex of duck hosts. The probabilities of infection for Haemoproteus and Leucocytozoon parasites were strongly positively correlated, but hematozoa infection was not correlated with IAV infection or serostatus. The probability of Haemoproteus infection was negatively related to body condition in juvenile ducks; relationships between Leucocytozoon infection and body condition varied among host species. Conclusions We present prevalence estimates for Haemoproteus, Leucocytozoon, and Plasmodium infections in waterfowl at the interface of the sub-Arctic and Arctic and provide evidence for local transmission of all three parasite genera. Variation in prevalence and molecular detection of hematozoa parasites in wild ducks is influenced by seasonal timing and a number of host traits. A positive correlation in co-infection of Leucocytozoon and Haemoproteus suggests that infection probability by parasites in one or both genera is enhanced by infection with the other, or that encounter rates of hosts and genus-specific vectors are correlated. Using size-adjusted mass as an index of host condition, we did not find evidence for strong deleterious consequences of hematozoa infection in wild ducks.Geological Survey (U.S.) (Wildlife Program of the Ecosystem Mission Area)U.S. Fish and Wildlife ServiceDelta Waterfowl FoundationInstitute for Wetland and Waterfowl ResearchIcahn School of Medicine at Mount Sinai (Center for Research on Influenza Pathogenesis)Center of Excellence for Influenza Research and Surveillance (contracts HHSN272201400008C and HHSN266200700010C

Beak and feather disease virus in wild and captive parrots: an analysis of geographic and taxonomic distribution and methodological trends

Psittacine beak and feather disease (PBFD) has emerged in recent years as a major threat to wild parrot populations and is an increasing concern to aviculturists and managers of captive populations. Pathological and serological tests for screening for the presence of beak and feather disease virus (BFDV) are a critical component of efforts to manage the disease and of epidemiological studies. Since the disease was first reported in the mid-1970s, screening for BFDV has been conducted in numerous wild and captive populations. However, at present, there is no current and readily accessible synthesis of screening efforts and their results. Here, we consolidate information collected from 83 PBFD- and BFDV-based publications on the primary screening methods being used and identify important knowledge gaps regarding potential global disease hotspots. We present trends in research intensity in this field and critically discuss advances in screening techniques and their applications to both aviculture and to the management of threatened wild populations. Finally, we provide an overview of estimates of BFDV prevalence in captive and wild flocks alongside a complete list of all psittacine species in which the virus has been confirmed. Our evaluation highlights the need for standardised diagnostic tests and more emphasis on studies of wild populations, particularly in view of the intrinsic connection between global trade in companion birds and the spread of novel BFDV strains into wild populations. Increased emphasis should be placed on the screening of captive and wild parrot populations within their countries of origin across the Americas, Africa and Asia

A STRUCTURAL THEOREM FOR LOCAL ALGORITHMS WITH APPLICATIONS TO CODING, TESTING, AND VERIFICATION

We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and probabilistically checkable proofs 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 n1-1/O(q2 log2 q) sample complexity, following the definition of Goldreich and Ron [ACM Trans. Comput. Theory, 8 (2016), 7]. 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 [SIAM J. Comput., 50 (2021), pp. 788-813]. 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 [Proceedings of the 56th Annual Symposium on Foundations of Computer Science, IEEE, 2015, pp. 1163-1182], 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 [Proceedings of the 8th Innovations in Theoretical Computer Science Conference, 2017, pp. 39:1-39:43; Comput. Complexity, 27 (2018), pp. 99-207] regarding sublinear-time delegation of computation. Our techniques strongly rely on relaxed sunflower lemmas and the Hajnal-Szemerédi theorem