Matroids and Quantum Secret Sharing Schemes

A secret sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum secret sharing schemes. In addition to providing a new perspective on quantum secret sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum secret sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum secret sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure state quantum secret sharing scheme with information rate one

Ideal hierarchical secret sharing schemes

Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention from the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization deals with the properties of the hierarchically minimal sets of the access structure, which are the minimal qualified sets whose participants are in the lowest possible levels in the hierarchy. By using our characterization, it can be efficiently checked whether any given hierarchical access structure that is defined by its hierarchically minimal sets is ideal. We use the well known connection between ideal secret sharing and matroids and, in particular, the fact that every ideal access structure is a matroid port. In addition, we use recent results on ideal multipartite access structures and the connection between multipartite matroids and integer polymatroids. We prove that every ideal hierarchical access structure is the port of a representable matroid and, more specifically, we prove that every ideal structure in this family admits ideal linear secret sharing schemes over fields of all characteristics. In addition, methods to construct such ideal schemes can be derived from the results in this paper and the aforementioned ones on ideal multipartite secret sharing. Finally, we use our results to find a new proof for the characterization of the ideal weighted threshold access structures that is simpler than the existing one.Peer ReviewedPostprint (author's final draft

Microplate tectonics and environmental factors as distribution drivers in Western Mediterranean freshwater planarians

AIM: Species biogeography mainly focuses on palaeogeographical events, while environmental factors are generally overlooked despite their importance in species diversification. Here, we use an integrative approach to understand how palaeogeographical and environmental processes shape species distribution and focus on freshwater planarians as the model system. LOCATION: Western Mediterranean. TAXON: Dugesia METHODS: We inferred the phylogenetic relationships of most known Dugesia species in the area using six molecular markers. We then estimated their divergence times and reconstructed their ancestral distribution ranges. We also performed environmental niche modelling analyses using Dugesia subtentaculata as a model to evaluate the effects of several hydro-environmental variables and the likely existence of interspecific competition on Dugesia distributions. RESULTS: Our results provide a new phylogenetic scheme for Dugesia from the Western Mediterranean and show that the time splits between the lineages and their putative ancestral distribution ranges are correlated with microplate tectonic dynamics within the region during the Oligocene–Miocene period. Our environmental niche modelling analyses indicate that the type of land cover and the slope of the terrain are the most important abiotic factors driving the distribution of Dugesia from this region. Finally, we found a partial niche overlap between D. subtentaculata and two other common planarian species from the Iberian Peninsula. MAIN CONCLUSIONS: The microplate tectonic dynamics of the Western Mediterranean during the Oligocene–Miocene period, together with the position of the mountain ranges and posterior climate changes, may have played crucial roles in driving the biogeographical history of Dugesia in this region. Moreover, both interspecific competition and changes in fluvial characteristics driven by human activities may affect the current diversity and distribution of Dugesia in the Western Mediterranean. This study highlights the importance of integrating different types of information to study the biogeographical history of a species. <br

Time-resolved broadband analysis of slow-light propagation and superluminal transmission of electromagnetic waves in three-dimensional photonic crystals

A time-resolved analysis of the amplitude and phase of THz pulses propagating through three-dimensional photonic crystals is presented. Single-cycle pulses of THz radiation allow measurements over a wide frequency range, spanning more than an octave below, at and above the bandgap of strongly dispersive photonic crystals. Transmission data provide evidence for slow group velocities at the photonic band edges and for superluminal transmission at frequencies in the gap. Our experimental results are in good agreement with finite-difference-time-domain simulations.Comment: 7 pages, 11 figure

Overlapping and Distinct Roles of PRR7 and PRR9 in the Arabidopsis Circadian Clock

AbstractThe core mechanism of the circadian oscillators described to date rely on transcriptional negative feedback loops with a delay between the negative and the positive components [1–3]. In plants, the first suggested regulatory loop involves the transcription factors CIRCADIAN CLOCK-ASSOCIATED 1 (CCA1) and LATE ELONGATED HYPOCOTYL (LHY) and the pseudo-response regulator TIMING OF CAB EXPRESSION 1 (TOC1/PRR1)[4]. TOC1 is a member of the Arabidopsis circadian-regulated PRR gene family [5,6]. Analysis of single and double mutants in PRR7 and PRR9 indicates that these morning-expressed genes play a dual role in the circadian clock, being involved in the transmission of light signals to the clock and in the regulation of the central oscillator. Furthermore, CCA1 and LHY had a positive effect on PRR7 and PRR9 expression levels, indicating that they might form part of an additional regulatory feedback loop. We propose that the Arabidopsis circadian oscillator is composed of several interlocking positive and negative feedback loops, a feature of clock regulation that appears broadly conserved between plants, fungi, and animals

Cyanobacteria and their secondary metabolites in three freshwater reservoirs in the United Kingdom

Background Bloom-forming cyanobacteria occur globally in aquatic environments. They produce diverse bioactive metabolites, some of which are known to be toxic. The most studied cyanobacterial toxins are microcystins, anatoxin, and cylindrospermopsin, yet more than 2000 bioactive metabolites have been identified to date. Data on the occurrence of cyanopeptides other than microcystins in surface waters are sparse. Results We used a high-performance liquid chromatography-high-resolution mass spectrometry/tandem mass spectrometry (HPLC-HRMS/MS) method to analyse cyanotoxin and cyanopeptide profiles in raw drinking water collected from three freshwater reservoirs in the United Kingdom. A total of 8 cyanopeptides were identified and quantified using reference standards. A further 20 cyanopeptides were identified based on a suspect-screening procedure, with class-equivalent quantification. Samples from Ingbirchworth reservoir showed the highest total cyanopeptide concentrations, reaching 5.8, 61, and 0.8 µg/L in August, September, and October, respectively. Several classes of cyanopeptides were identified with anabaenopeptins, cyanopeptolins, and microcystins dominating in September with 37%, 36%, and 26%, respectively. Samples from Tophill Low reservoir reached 2.4 µg/L in September, but remained below 0.2 µg/L in other months. Samples from Embsay reservoir did not exceed 0.1 µg/L. At Ingbirchworth and Tophill Low, the maximum chlorophyll-a concentrations of 37 µg/L and 22 µg/L, respectively, and cyanobacterial count of 6 × 10 cells/mL were observed at, or a few days after, peak cyanopeptide concentrations. These values exceed the World Health Organization's guideline levels for relatively low probability of adverse health effects, which are defined as 10 µg/L chlorophyll-a and 2 × 10 cells/mL. Conclusions This data is the first to present concentrations of anabaenopeptins, cyanopeptolins, aeruginosins, and microginins, along with icrocystins, in U.K. reservoirs. A better understanding of those cyanopeptides that are abundant in drinking water reservoirs can inform future monitoring and studies on abatement efficiency during water treatment

Optimal non-perfect uniform secret sharing schemes

A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this end, we extend the known connections between polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information that every subset of participants obtains about the secret value. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, the ones whose values depend only on the number of participants, generalize the threshold access structures. Our main result is to determine the optimal information ratio of the uniform access functions. Moreover, we present a construction of linear secret sharing schemes with optimal information ratio for the rational uniform access functions.Peer ReviewedPostprint (author's final draft

Enhanced 2,4-D metabolism in two resistant papaver rhoeas populations from Spain

Corn poppy (Papaver rhoeas), the most problematic broadleaf weed in winter cereals in Southern Europe, has developed resistance to the widely-used herbicide, 2,4-D. The first reported resistance mechanism in this species to 2,4-D was reduced translocation from treated leaves to the rest of the plant. However, the presence of other non-target site resistance (NTSR) mechanisms has not been investigated up to date. Therefore, the main objective of this research was to reveal if enhanced 2,4-D metabolism is also present in two Spanish resistant (R) populations to synthetic auxins. With this aim, HPLC experiments at two 2,4-D rates (600 and 2,400 g ai ha−1) were conducted to identify and quantify the metabolites produced and evaluate possible differences in 2,4-D degradation between resistant (R) and susceptible (S) plants. Secondarily, to determine the role of cytochrome P450 in the resistance response, dose-response experiments were performed using malathion as its inhibitor. Three populations were used: S, only 2,4-D R (R-703) and multiple R to 2,4-D and ALS inhibitors (R-213). HPLC studies indicated the presence of two hydroxy metabolites in these R populations in shoots and roots, which were not detected in S plants, at both rates. Therefore, enhanced metabolism becomes a new NTSR mechanism in these two P. rhoeas populations from Spain. Results from the dose-response experiments also showed that pre-treatment of R plants with the cytochrome P450 (P450) inhibitor malathion reversed the phenotype to 2,4-D from resistant to susceptible in both R populations. Therefore, it could be hypothesized that a malathion inhibited P450 is responsible of the formation of the hydroxy metabolites detected in the metabolism studies. This and previous research indicate that two resistant mechanisms to 2,4-D could be present in populations R-703 and R-213: reduced translocation and enhanced metabolism. Future experiments are required to confirm these hypotheses, understand the role of P450, and the relationship between both NTSR mechanisms. On this basis, selection pressure with synthetic auxins bears the risk of promoting the evolution enhanced metabolism in Papaver rhoeas.The authors gratefully acknowledge Du Pont (C16006) for funding the experiments. They thank M. Tricas, J. Recasens, M. Casamitjana, B. Singla, and the students of El Carme high-school for their help in trials. Special thanks to the reviewers and editor for their suggestions to improve the manuscript

HTLV-1 proviral load in infective dermatitis associated with HTLV-1 does not increase after the development of HTLV-1-associated myelopathy/tropical spastic paraparesis and does not decrease after IDH remission

Introduction Infective dermatitis associated with HTLV-1 (IDH) is a recurrent eczema which affects children vertically infected with HTLV-1. In Bahia, Brazil, we recently reported that 47% of IDH patients also develop juvenile HTLV-1-associated myelopathy/tropical spastic paraparesis (HAM/TSP), a progressive disabling disorder which is typically reported in adult HTLV-1 carriers. IDH may also predispose to adult T-cell leukemia/lymphoma, a neoplasm associated with HTLV-1. The factors relating to the development of HTLV-1-associated juvenile diseases have not yet been defined. HTLV-1 proviral load (PVL) is one of the main parameters related to the development of HTLV-1 associated diseases in adults. In the current study, we investigated the role of PVL in IDH and juvenile HAM/TSP. Methodology/Principal findings This is a cohort study that included fifty-nine HTLV-1 infected children and adolescents, comprising 16 asymptomatic carriers, 18 IDH patients, 20 patients with IDH and HAM/TSP (IDH/HAM/TSP) and five with HAM/TSP. These patients were followed-up for up to 14 years (median of 8 years). We found that PVL in IDH and IDH/HAM/TSP patients were similarly higher than PVL in juvenile asymptomatic carriers (p<0.0001). In those IDH patients who developed HAM/TSP during follow-up, PVL levels did not vary significantly. HAM/TSP development did not occur in those IDH patients who presented high levels of PVL. IDH remission was associated with an increase of PVL. Inter-individual differences in PVL were observed within all groups. However, intra-individual PVL did not fluctuate significantly during follow-up. Conclusions/Significance High PVL in IDH patients was not necessary indicative of progression to HAM/TSP. PVL did not decrease after IDH remission. The maintenance of high PVL after remission could favor early development of ATL. Therefore, IDH patients would have to be followed-up even after remission of IDH and for a long period of time.This work was supported by the Fundação de Amparo à Pesquisa do Estado da Bahia (FAPESB, www.fapesb.ba.gov.br) [Grant number RED0028/2012 to L.F.], Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, www.cnpq.br)[Grant number 409985/ 2016-3 to A.L.B.]. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska Marie Curie grant (https://ec.europa.eu) [agreement number 799850 to L.F.] The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript