Secret Sharing Schemes with a large number of players from Toric Varieties

A general theory for constructing linear secret sharing schemes over a finite field \Fq from toric varieties is introduced. The number of players can be as large as $(q-1)^r-1$ for $r\geq 1$. We present general methods for obtaining the reconstruction and privacy thresholds as well as conditions for multiplication on the associated secret sharing schemes. In particular we apply the method on certain toric surfaces. The main results are ideal linear secret sharing schemes where the number of players can be as large as $(q-1)^2-1$. We determine bounds for the reconstruction and privacy thresholds and conditions for strong multiplication using the cohomology and the intersection theory on toric surfaces.Comment: 15 pages, 4 figures. arXiv admin note: text overlap with arXiv:1203.454

Quantum Codes from Toric Surfaces

A theory for constructing quantum error correcting codes from Toric surfaces by the Calderbank-Shor-Steane method is presented. In particular we study the method on toric Hirzebruch surfaces. The results are obtained by constructing a dualizing differential form for the toric surface and by using the cohomology and the intersection theory of toric varieties. In earlier work the author developed methods to construct linear error correcting codes from toric varieties and derive the code parameters using the cohomology and the intersection theory on toric varieties. This method is generalized in section to construct linear codes suitable for constructing quantum codes by the Calderbank-Shor-Steane method. Essential for the theory is the existence and the application of a dualizing differential form on the toric surface. A.R. Calderbank, P.W. Shor and A.M. Steane produced stabilizer codes from linear codes containing their dual codes. These two constructions are merged to obtain results for toric surfaces. Similar merging has been done for algebraic curves with different methods by A. Ashikhmin, S. Litsyn and M.A. Tsfasman.Comment: IEEE copyrigh

Secret Sharing Schemes with Strong Multiplication and a Large Number of Players from Toric Varieties

This article consider Massey's construction for constructing linear secret sharing schemes from toric varieties over a finite field Fq with q elements. The number of players can be as large as (q − 1) r − 1 for r ≥ 1. The schemes have strong multiplication, such schemes can be utilized in the domain of multiparty computation. We present general methods to obtain the reconstruction and privacy thresholds as well as conditions for multiplication on the associated secret sharing schemes. In particular we apply the method on certain toric surfaces. The main results are ideal linear secret sharing schemes where the number of players can be as large as (q − 1) 2 − 1, we determine bounds for the reconstruction and privacy thresholds and conditions for strong multiplication using the cohomology and the intersection theory on toric surfaces

Hydrodynamics of confined colloidal fluids in two dimensions

We apply a hybrid Molecular Dynamics and mesoscopic simulation technique to study the dynamics of two dimensional colloidal discs in confined geometries. We calculate the velocity autocorrelation functions, and observe the predicted $t^{-1}$ long time hydrodynamic tail that characterizes unconfined fluids, as well as more complex oscillating behavior and negative tails for strongly confined geometries. Because the $t^{-1}$ tail of the velocity autocorrelation function is cut off for longer times in finite systems, the related diffusion coefficient does not diverge, but instead depends logarithmically on the overall size of the system.Comment: RevTex 13 pages, 9 figure

Influence of reed beds (Phragmites australis) and submerged vegetation on pike (Esox lucius)

Eutrophication and reduced grazing have led to an expansion of the common reed (Phragmites australis) in ar-chipelago areas in the Baltic Sea, while at the same time the composition of submerged vegetation has changed. Although reed is important as nursery habitat for many fish species, extensive emergent vegetation may reduce biodiversity and abundance of predatory fish. Pike (Esox lucius) is a predatory fish whose larvae and young-of -the-year find both food and shelter in reed but use different micro-habitats during different life-stages. Here we investigate the influence of reed and submerged vegetation on abundance and body size of adult pike during the spawning season. We predicted that coastal bays with extensive but heterogeneous reed beds with higher cover of submerged vegetation would have more and larger pike than bays with smaller, homogenous reed belts or with less submerged vegetation. To test these predictions, we estimated abundance and size-structure of adult pike from catches in angling fishing among 22 bays in the Stockholm archipelago at the Swedish Baltic Sea coast. Our analyses show that catches of adult pike were positively associated with both extensive reed beds and cover of rooted submerged vegetation. However, pike size was not correlated with any vegetation variable, but instead increased with wave exposure and bay area. Our study suggests that reed beds and submerged vegetation are important for adult pike during the spawning season, and even the most extensive reed beds had no evident negative effect on pike populations. We could not see any clear relationship between emergent reed habitat and cover of submerged vegetation among the studied bays, and conclude that to maintain pike population during the spawning season it is important that coastal bays have sufficient amounts of both reed beds and rooted submerged vegetation

INITIAL SCREENING FOR BEDWETTING: THE USE OF QUESTIONNAIRES AND VOIDING DIARIES First results from a National Belgian study

Title Initial screening for bedwetting: the use of questionnaires and voiding diaries. First results from a National Belgian study Authors S. Karamaria2, N. Ranguelov3, P. Hansen4, V. De Boe5, P. Verleyen6, J. Vande Walle1,2, L. Dossche2, A. Bael7,8 1Department of Pediatric Nephrology, UZ Gent, Ghent, 2Ghent University, 3Department of Pediatrics, Cliniques Universitaires St-Luc, Université Catholique de Louvain, Brussels, 4Department of Pediatrics, CHU Tivoli, La Louvière, 5Department of Urology, UZ Brussel, Brussels, 6Department of Urology, AZ Groeninge, Kortrijk, 7Department of Pediatrics, Pediatric Nephrology, ZNA Koningin Paola Kinderziekenhuis, Antwerp; 8Faculty of Medicine, University of Antwerp, Antwerp Background International guidelines have a consensus that stratification of nocturnal enuresis (NE) into non-monosymptomatic (NMNE) and monosymptomatic (MNE) is mandatory at intake to optimize therapeutic approach. This stratification is based on clinical parameters (presence or absence of Lower Urinary Tract Symptoms (LUTS) respectively). To identify clinical parameters a checklist (Clinical Management Tool (CMT)) and/or voiding diaries based on home recordings can be used. However, these recordings can be time consuming and difficult for the family. Moreover, the added value to the CMT, especially in treatment naïve patients, is rather expert opinion than evidence based. Methods The aim of this study run in 7 Belgian Hospitals, was to document in treatment naïve NE patients >5 years: 1) The prevalence of MNE vs NMNE 2) the added value and correlation of CMT and/or diary in differentiating NE. Two study visits were scheduled: At visit 1 CMT was obtained, after a thorough medical history and basic assessments. If daytime incontinence and/or LUTS were identified, the diagnosis was NMNE. After the 1st study visit, a 2day voiding diary (fluid intake, voiding volumes, incontinence) was registered at home. During the second study visit, this diary was evaluated; if the micturition frequency was >8 or <3 and/or there was daytime incontinence, the diagnosis was NMNE. Results In total 109 children were included, of which19 were lost in follow up. Mean age was 7,7 (±2); 62 were boys (68,9%) and 27 were girls (30%). 68 (75, 6%) were included at a non-University center. Based on the CMT 13 children were diagnosed as MNE (16,7%) and 75 children as NMNE (83,3%). Based on the diary 16 children were diagnosed as MNE (17,8%) and 74 children as NMNE (82,2%). 25 children (27,8%) had the same diagnosis with both methods Regarding the presence or not of LUTS we observed significant inconsistencies between the CMT and the diary. Specifically there was fair agreement between the two modalities for urge (κ=0,219), moderate agreement for daytime incontinence (κ=0,432) and no agreement for abnormal voiding frequency (8 voidings/day) between what the parents answered on the CMT and what they registered in the diary (κ=-0,057). Conclusion NMNE is more frequent than MNE in treatment naïve patients. CMT alone versus CMT + diary had a different sensitivity and specificity of identifying LUTS : in absence of validation of the importance by a therapeutic trial outcome, we state that we can only consider patients as MNE when and CMT and diary do not demonstrate LUTS