On the Galerkin/Finite-Element Method for the Serre Equations

A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-nonlinear regime. The fully-discrete scheme utilizes the Galerkin / finite-element method based on smooth periodic splines in space, and an explicit fourth-order Runge–Kutta method in time. Computations compared with exact solitary and cnoidal wave solutions show that the scheme achieves the optimal orders of accuracy in space and time. These computations also show that the stability of this scheme does not impose very restrictive conditions on the temporal stepsize. In addition, solitary, cnoidal, and dispersive shock waves are studied in detail using this numerical scheme for the Serre system and compared with the ‘classical’ Boussinesq system for small-amplitude shallow water waves. The results show that the interaction of solitary waves in the Serre system is more inelastic. The efficacy of the numerical scheme for modeling dispersive shocks is shown by comparison with asymptotic results. These results have application to the modeling of shallow water waves of intermediate or large amplitude.     

Multi-input Functional Encryption in the Private-Key Setting: Stronger Security from Weaker Assumptions

We construct a general-purpose multi-input functional encryption scheme in the private-key setting. Namely, we construct a scheme where a functional key corresponding to a function f enables a user holding encryptions of \(x_1, \ldots , x_t\) to compute \(f(x_1, \ldots , x_t)\) but nothing else. This is achieved starting from any general-purpose private-key single-input scheme (without any additional assumptions) and is proven to be adaptively secure for any constant number of inputs t. Moreover, it can be extended to a super-constant number of inputs assuming that the underlying single-input scheme is sub-exponentially secure. Instantiating our construction with existing single-input schemes, we obtain multi-input schemes that are based on a variety of assumptions (such as indistinguishability obfuscation, multilinear maps, learning with errors, and even one-way functions), offering various trade-offs between security assumptions and functionality. Previous and concurrent constructions of multi-input functional encryption schemes either rely on stronger assumptions and provided weaker security guarantees (Goldwasser et al. in Advances in cryptology—EUROCRYPT, 2014; Ananth and Jain in Advances in cryptology—CRYPTO, 2015), or relied on multilinear maps and could be proven secure only in an idealized generic model (Boneh et al. in Advances in cryptology—EUROCRYPT, 2015). In comparison, we present a general transformation that simultaneously relies on weaker assumptions and guarantees stronger security.     

Functional Encryption for Randomized Functionalities in the Private-Key Setting from Minimal Assumptions

We present a construction of a private-key functional encryption scheme for any family of randomized functionalities based on any such scheme for deterministic functionalities that is sufficiently expressive. Instantiating our construction with existing schemes for deterministic functionalities, we obtain schemes for any family of randomized functionalities based on a variety of assumptions (including the LWE assumption, simple assumptions on multilinear maps, and even the existence of any one-way function) offering various trade-offs between security and efficiency. Previously, Goyal et al. (Proceedings of the 12th theory of cryptography conference (TCC), pp 325–351, 2015) constructed a public-key functional encryption scheme for any family of randomized functionalities based on indistinguishability obfuscation. One of the key insights underlying our work is that, in the private-key setting, a sufficiently expressive functional encryption scheme may be appropriately utilized for implementing proof techniques that were so far implemented based on obfuscation assumptions [such as the punctured programming technique of Sahai and Waters (Proceedings of the 46th annual ACM symposium on theory of computing (STOC), pp. 475–484, 2014)]. We view this as a contribution of independent interest that may be found useful in other settings as well.     

Anti-proliferative activities,phytochemical levels and fruit quality of pepper (Capsicum spp.) following prolonged storage

Peppers are rich in health-promoting phytochemicals, which are involved in the defence mechanisms against cancer. To select a lead variety of pepper with anti-proliferative activity against colon cancer cells and liver cancer cells, high antioxidant activity, and high concentrations of capsaicin, flavonoids and phenolics, we compared these attributes in nine different pepper accessions belonging to Capsicum annuum and C. chinense. Quality parameters such as weight loss and total soluble solids content were tested as well. The different parameters were determined immediately after harvest and after prolonged storage and marketing simulation. A significant variation of these traits was detected among the accessions. C. chinense line 1745 had the highest antioxidant activity, the highest levels of capsaicin and flavonoids, a high and specific anti-cancer activity, and the lowest weight loss level during postharvest storage. It is proposed that line 1745 has potential for use as a source for health-promoting traits and should be further evaluated for use as a nutraceutical for the prevention and treatment of colon and liver cancers.     

Function suggests nano-structure: towards a unified theory for secretion rate,a statistical mechanics approach

The inventory of secretory granules along the plasma membrane can be viewed as maintained in two restricted compartments. The release-ready pool represents docked granules available for an initial stage of fast, immediate secretion, followed by a second stage of granule set-aside secretion pool, with significantly slower rate. Transmission electron microscopy ultra-structural investigations correlated with electrophysiological techniques and mathematical modelling have allowed the categorization of these secretory vesicle compartments, in which vesicles can be in various states of secretory competence. Using the above-mentioned approaches, the kinetics of single vesicle exocytosis can be worked out. The ultra-fast kinetics, explored in this study, represents the immediately available release-ready pool, in which granules bound to the plasma membrane are exocytosed upon Ca²⁺ influx at the SNARE rosette at the base of porosomes. Formalizing Dodge and Rahamimoff findings on the effect of calcium concentration and incorporating the effect of SNARE transient rosette size, we postulate that secretion rate (rate), the number (X) of intracellular calcium ions available for fusion, calcium capacity (0 ≤ M ≤ 5) and the fusion nano-machine size (as measured by the SNARE rosette size K) satisfy the parsimonious M–K relation rate ≈ C × [Ca²⁺]^min(X,M)e^−K/2.     

Guided Sampling via Weak Motion Models and Outlier Sample Generation for Epipolar Geometry Estimation

The problem of automatic robust estimation of the epipolar geometry in cases where the correspondences are contaminated with a high percentage of outliers is addressed. This situation often occurs when the images have undergone a significant deformation, either due to large rotation or wide baseline of the cameras. An accelerated algorithm for the identification of the false matches between the views is presented. The algorithm generates a set of weak motion models (WMMs). Each WMM roughly approximates the motion of correspondences from one image to the other. The algorithm represents the distribution of the median of the geometric distances of a correspondence to the WMMs as a mixture model of outlier correspondences and inlier correspondences. The algorithm generates a sample of outlier correspondences from the data. This sample is used to estimate the outlier rate and to estimate the outlier pdf. Using these two pdfs the probability that each correspondence is an inlier is estimated. These probabilities enable guided sampling. In the RANSAC process this guided sampling accelerates the search process. The resulting algorithm when tested on real images achieves a speedup of between one or two orders of magnitude. This work was supported partly by grant 01-99-08430 of the Israeli Space Agency through the Ministry of Science Culture and Sports of Israel.     

Optimal design of the inspection buffer for an unreliable process

Placing an inspection buffer immediately after an unreliable process subject to failure protects the process customers from receiving non-conforming products. Such protection is achieved by screening the buffer contents whenever a shift in the process is detected. Previous studies have suggested that, if properly designed, such buffers can reduce overall costs. In this paper we make two types of contributions to the study of inspection buffers. First, we refine the model proposed by Klastorin et al. (1993), by incorporating a more efficient way of sampling, a more realistic objective function and more accurate cost expressions. Second, we provide analytical results to assist in the calculation of the economically optimal buffer size. Specifically, these include conditions for determining whether an inspection buffer is at all justified and a theorem for bounding the search for the optimal buffer size. The performance of the search bound and the sensitivity of the model are examined computationally.     

Bacterial community composition and structure of biofilms developing on nanofiltration membranes applied to wastewater treatment

The structure and microbial communities of biofilms developing on cross-flow nanofiltration (NF) membranes at different temperatures (20, 25 or 34 degrees C) and operation lengths (8h-24days) were studied. Feedwater comprised tertiary quality wastewater effluent or synthetic media mimicking effluents of intermediate quality. After each run, the membranes were autopsied for bacterial enumeration, bacterial community composition and microscopy visualization (SEM, CLSM and AFM/NSOM). Community composition was analyzed by polymerase chain reaction-denaturing gradient gel electrophoresis (PCR-DGGE) coupled with sequence analysis of 16S rRNA gene fragments from dominant bands. Deposition of polysaccharides and initial bacterial colonization were observed within 8h, whereas developed biofilms markedly affecting membrane permeability were evident from days 2-3 onwards. Regardless of applied conditions, the heterotrophic plate counts in the biofilm were 3-4x10(6)CFU/cm(2) and the thickness of the biofouling layer was 20-30microm. From a total of 22 sequences obtained from 14 independent experiments, most species identified were Gram negative (19 of 22 sequences). Proteobacteria were found to be a prevalent group in all cases (16 of 22 sequences) and among it, the beta-subclass was the most predominant (8 sequences), followed by the gamma-subclass (5 sequences). Pseudomonas/Burkholderia, Ralstonia, Bacteroidetes and Sphingomonas were the dominant groups found in most cases. Even though the microbial population might be important with respect to biofouling patterns, membrane permeability decline seems to be more substantially influenced by the formation and accumulation of exopolymeric substances (EPS).