Search

The mission of theoretical cryptography is to define and construct provably secure cryptographic protocols and schemes. Without proofs of security, cryptographic constructs offer no guarantees whatsoever and no basis for evaluation and comparison. As most security proofs necessarily come in the form of a reduction between the security claim and an intractability assumption, such proofs are ultimately only as good as the assumptions they are based on. Thus, the complexity implications of every assumption we utilize should be of significant substance, and serve as the yard stick for the value of our proposals. Lately, the field of cryptography has seen a sharp increase in the number of new assumptions that are often complex to define and difficult to interpret. At times, these assumptions are hard to untangle from the constructions which utilize them. We believe that the lack of standards of what is accepted as a reasonable cryptographic assumption can be harmful to the credibility of our field. Therefore, there is a great need for measures according to which we classify and compare assumptions, as to which are safe and which are not. In this paper, we propose such a classification and review recently suggested assumptions in this light. This follows the footsteps of Naor Crypto 2003. Our governing principle is relying on hardness assumptions that are independent of the cryptographic constructions.

In this paper, I use administrative data to estimate the number of deaths, the number of infections, and mortality rates from COVID-19 in Lombardia, the hot spot of the disease in Italy and Europe. The information will assist policy makers in reaching correct decisions and the public in adopting appropriate behaviors. As the available data suffer from sample selection bias, I use partial identification to derive the above quantities. Partial identification combines assumptions with the data to deliver a set of admissible values or bounds. Stronger assumptions yield stronger conclusions but decrease the credibility of the inference. Therefore, I start with assumptions that are always satisfied, then I impose increasingly more restrictive assumptions. Using my preferred bounds, during March 2020 in Lombardia, there were between 10,000 and 18,500 more deaths than in previous years. The narrowest bounds of mortality rates from COVID-19 are between 0.1 and 7.5%, much smaller than the 17.5% discussed in earlier reports. This finding suggests that the case of Lombardia may not be as special as some argue.

Purpose Preference-based measures are essential for producing quality-adjusted life years (QALYs) that are widely used for economic evaluations. In the absence of such measures, mapping algorithms can be applied to estimate utilities from disease-specific measures. This paper aims to develop mapping algorithms between the MacNew Heart Disease Quality of Life Questionnaire (MacNew) instrument and the English and the US-based EQ-5D-5L value sets. Methods Individuals with heart disease were recruited from six countries: Australia, Canada, Germany, Norway, UK and the US in 2011/12. Both parametric and non-parametric statistical techniques were applied to estimate mapping algorithms that predict utilities for MacNew scores from EQ-5D-5L value sets. The optimal algorithm for each country-specific value set was primarily selected based on root mean square error (RMSE), mean absolute error (MAE), concordance correlation coefficient (CCC), and r-squared. Leave-one-out cross-validation was conducted to test the generalizability of each model. Results For both the English and the US value sets, the one-inflated beta regression model consistently performed best in terms of all criteria. Similar results were observed for the cross-validation results. The preferred model explained 59 and 60% for the English and the US value set, respectively. Linear equating provided predicted values that were equivalent to observed values. Conclusions The preferred mapping function enables to predict utilities for MacNew data from the EQ-5D-5L value sets recently developed in England and the US with better accuracy. This allows studies, which have included the MacNew to be used in cost-utility analyses and thus, the comparison of services with interventions across the health system.

We consider the problem of optimal partisan gerrymandering: a legislator in charge of redrawing the boundaries of equal-sized congressional districts wants to ensure the best electoral outcome for his own party. The so-called gerrymanderer faces two issues: the number of districts is finite and there is uncertainty at the level of each district. Solutions to this problem consists in cracking favorable voters in as many districts as possible to get tight majorities, and in packing unfavorable voters in the remaining districts. The optimal payoff of the gerrymanderer tends to increase as the uncertainty decreases and the number of districts is large. With an infinite number of districts, this problem boils down to concavifying a function, similarly to the optimal Bayesian persuasion problem. We introduce a measure of fairness and show that optimal gerrymandering is accordingly closer to uniform districting (full cracking), which is most unfair, than to community districting (full packing), which is very fair.

In this research, a dataset including 29 ketone-based covalent inhibitors with SARS-CoV-1 3CLpro inhibition activity was used to develop high predictive QSAR models. Twenty-two molecules were put in train set and seven molecules in test set. By using stepwise MLR method for molecules in train set, four molecular descriptors including Mor26p, Hy, GATS7p and Mor04v were selected to build QSAR models. MLR and ANN methods were used to create QSAR models for predicting the activity of molecules in both train and test sets. Both QSAR models were validated by calculating several statistical parameters. R2 values for the test set of MLR and ANN models were 0.93 and 0.95, respectively, and RMSE values for their test sets were 0.24 and 0.17, respectively. Other calculated statistical parameters (especially \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_{F3}^{2}$$\end{document}QF32 parameter) show that created ANN model has more predictive power with respect to developed MLR model (with four descriptor). Calculated leverages for all molecules show that predicted pIC50 (by both QSAR models) for all molecules is acceptable, and drawn residuals plots show that there is no systematic error in building both QSAR modes. Also, based on developed MLR model, used molecular descriptors were interpreted.

Finite mixtures of generalized linear models are commonly fitted by maximum likelihood and the EM algorithm. The estimation process and subsequent inferential and classification procedures can be badly affected by the occurrence of outliers. Actually, contamination in the sample at hand may lead to severely biased fitted components and poor classification accuracy. In order to take into account the potential presence of outliers, a robust fitting strategy is proposed that is based on the weighted likelihood methodology. The technique exhibits a satisfactory behavior in terms of both fitting and classification accuracy, as confirmed by some numerical studies and real data examples.

Graphical abstract Most drugs are no longer produced in their own countries by the pharmaceutical companies, but by contract manufacturers or at manufacturing sites in countries that can produce more cheaply. This not only makes it difficult to trace them back but also leaves room for criminal organizations to fake them unnoticed. For these reasons, it is becoming increasingly difficult to determine the exact origin of drugs. The goal of this work was to investigate how exactly this is possible by using different spectroscopic methods like nuclear magnetic resonance and near- and mid-infrared spectroscopy in combination with multivariate data analysis. As an example, 56 out of 64 different paracetamol preparations, collected from 19 countries around the world, were chosen to investigate whether it is possible to determine the pharmaceutical company, manufacturing site, or country of origin. By means of suitable pre-processing of the spectra and the different information contained in each method, principal component analysis was able to evaluate manufacturing relationships between individual companies and to differentiate between production sites or formulations. Linear discriminant analysis showed different results depending on the spectral method and purpose. For all spectroscopic methods, it was found that the classification of the preparations to their manufacturer achieves better results than the classification to their pharmaceutical company. The best results were obtained with nuclear magnetic resonance and near-infrared data, with 94.6%/99.6% and 98.7/100% of the spectra of the preparations correctly assigned to their pharmaceutical company or manufacturer. Supplementary Information The online version contains supplementary material available at 10.1007/s00216-021-03249-z.

One of the major sources of uncertainty in large-scale crop modeling is the lack of information capturing the spatiotemporal variability of crop sowing dates. Remote sensing can contribute to reducing such uncertainties by providing essential spatial and temporal information to crop models and improving the accuracy of yield predictions. However, little is known about the impacts of the differences in crop sowing dates estimated by using remote sensing (RS) and other established methods, the uncertainties introduced by the thresholds used in these methods, and the sensitivity of simulated crop yields to these uncertainties in crop sowing dates. In the present study, we performed a systematic sensitivity analysis using various scenarios. The LINTUL-5 crop model implemented in the SIMPLACE modeling platform was applied during the period 2001–2016 to simulate maize yields across four provinces in South Africa using previously defined scenarios of sowing dates. As expected, the selected methodology and the selected threshold considerably influenced the estimated sowing dates (up to 51 days) and resulted in differences in the long-term mean maize yield reaching up to 1.7 t ha−1 (48% of the mean yield) at the province level. Using RS-derived sowing date estimations resulted in a better representation of the yield variability in space and time since the use of RS information not only relies on precipitation but also captures the impacts of socioeconomic factors on the sowing decision, particularly for smallholder farmers. The model was not able to reproduce the observed yield anomalies in Free State (Pearson correlation coefficient: 0.16 to 0.23) and Mpumalanga (Pearson correlation coefficient: 0.11 to 0.18) in South Africa when using fixed and precipitation rule-based sowing date estimations. Further research with high-resolution climate and soil data and ground-based observations is required to better understand the sources of the uncertainties in RS information and to test whether the results presented herein can be generalized among crop models with different levels of complexity and across distinct field crops.

We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of sum-of-squares relaxations. Exploiting the polynomial kernel technique, we obtain a quadratic improvement of the known convergence rate by Reznick and Doherty and Wehner. Specifically, we show that the rate of convergence is no worse than $$O(d^2/\ell ^2)$$ O ( d 2 / ℓ 2 ) in the regime $$\ell = \Omega (d)$$ ℓ = Ω ( d ) where $$\ell $$ ℓ is the level of the hierarchy and d the dimension, solving a problem left open in the recent paper by de Klerk and Laurent (arXiv:1904.08828 ). Importantly, our analysis also works for matrix-valued polynomials on the sphere which has applications in quantum information for the Best Separable State problem. By exploiting the duality relation between sums of squares and the Doherty–Parrilo–Spedalieri hierarchy in quantum information theory, we show that our result generalizes to nonquadratic polynomials the convergence rates of Navascués, Owari and Plenio.

The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An in 1997. These assume that either the convex or the concave part, or both, are evaluated by one of their subgradients. In this paper we propose an algorithm which allows the evaluation of both the concave and the convex part by their proximal points. Additionally, we allow a smooth part, which is evaluated via its gradient. In the spirit of primal-dual splitting algorithms, the concave part might be the composition of a concave function with a linear operator, which are, however, evaluated separately. For this algorithm we show that every cluster point is a solution of the optimization problem. Furthermore, we show the connection to the Toland dual problem and prove a descent property for the objective function values of a primal-dual formulation of the problem. Convergence of the iterates is shown if this objective function satisfies the Kurdyka--\L ojasiewicz property. In the last part, we apply the algorithm to an image processing model.

Strategies used in artificial grammar learning can shed light into the abilities of different species to extract regularities from the environment. In the A(X)nB rule, A and B items are linked but assigned to different positional categories and separated by distractor items. Open questions are how widespread is the ability to extract positional regularities from A(X)nB patterns, which strategies are used to encode positional regularities and whether individuals exhibit preferences for absolute or relative position encoding. We used visual arrays to investigate whether cotton-top tamarins (Saguinus oedipus) can learn this rule and which strategies they use. After training on a subset of exemplars, half of the tested monkeys successfully generalized to novel combinations. These tamarins discriminated between categories of tokens with different properties (A, B, X) and detected a positional relationship between non-adjacent items even in the presence of novel distractors. Generalization, though, was incomplete, since we observed a failure with items that during training had always been presented in reinforced arrays. The pattern of errors revealed that successful subjects used visual similarity with training stimuli to solve the task, and that tamarins extracted the relative position of As and Bs rather than their absolute position, similarly to what observed in other species. Relative position encoding appears to be the default strategy in different tasks and taxa.

Purpose Despite practised for decades, the planning of osteotomy around the knee, commonly using the Mikulicz-Line, is only empirically based, clinical outcome inconsistent and the target angle still controversial. A better target than the angle of frontal-plane static leg alignment might be the external frontal-plane lever arm (EFL) of the knee adduction moment. Hypothetically assessable from frontal-plane-radiograph skeleton dimensions, it might depend on the leg-alignment angle, the hip-centre-to-hip-centre distance, the femur- and tibia-length. Methods The target EFL to achieve a medial compartment force ratio of 50% during level-walking was identified by relating in-vivo-measurement data of knee-internal loads from nine subjects with instrumented prostheses to the same subjects’ EFLs computed from frontal-plane skeleton dimensions. Adduction moments derived from these calculated EFLs were compared to the subjects’ adduction moments measured during gait analysis. Results Highly significant relationships (0.88 ≤ R2 ≤ 0.90) were found for both the peak adduction moment measured during gait analysis and the medial compartment force ratio measured in vivo to EFL calculated from frontal-plane skeleton dimensions. Both correlations exceed the respective correlations with the leg alignment angle, EFL even predicts the adduction moment’s first peak. The guideline EFL for planning osteotomy was identified to 0.349 times the epicondyle distance, hence deducing formulas for individualized target angles and Mikulicz-Line positions based on full-leg radiograph skeleton dimensions. Applied to realistic skeleton geometries, widespread results explain the inconsistency regarding correction recommendations, whereas results for average geometries exactly meet the most-consented “Fujisawa-Point”. Conclusion Osteotomy outcome might be improved by planning re-alignment based on the provided formulas exploiting full-leg-radiograph skeleton dimensions.

This work presents a new extension to B-Splines that enables them to model functions on directed tree graphs such as non-braided river networks. The main challenge of the application of B-splines to graphs is their definition in the neighbourhood of nodes with more than two incident edges. Achieving that the B-splines are continuous at these points is non-trivial. For both, simplification reasons and in view of our application, we limit the graphs to directed tree graphs. To fulfil the requirement of continuity, the knots defining the B-Splines need to be located symmetrically along the edges with the same direction. With such defined B-Splines, we approximate the topography of the Mekong River system from scattered height data along the river. To this end, we first test and validate successfully the method with synthetic water level data, with and without added annual signal. The quality of the resulting heights is assessed besides others by means of root mean square errors (RMSE) and mean absolute differences (MAD). The RMSE values are 0.26 m and 1.05 m without and with added annual variation respectively and the MAD values are even lower with 0.11 m and 0.60 m. For the second test, we use real water level observations measured by satellite altimetry. Again, we successfully estimate the river topography, but also discuss the short comings and problems with unevenly distributed data. The unevenly distributed data leads to some very large outliers close to the upstream ends of the rivers tributaries and in regions with rapidly changing topography such as the Mekong Falls. Without the outlier removal the standard deviation of the resulting heights can be as large as 50 m with a mean value of 15.73 m. After the outlier removal the mean standard deviation drops to 8.34 m.

Second-order work analyses, based on elasto-plastic models, have been frequently carried out leading to the result that failure may occur before the limit yield condition is encountered. In this article, second-order work investigations are carried out with barodesy regarding standard element tests and finite element applications. In barodesy, it was shown—like in hypoplasticity and elasto-plasticity—that second-order work may vanish at stress states inside the critical limit surface. For boundary value problems, an end-to-end shear band of vanishing second-order work marks situations, where failure is imminent.

There is an explosion in the number of labs analyzing cannabinoids in marijuana (Cannabis sativa L., Cannabaceae) but existing methods are inefficient, require expert analysts, and use large volumes of potentially environmentally damaging solvents. The objective of this work was to develop and validate an accurate method for analyzing cannabinoids in cannabis raw materials and finished products that is more efficient and uses fewer toxic solvents. An HPLC-DAD method was developed for eight cannabinoids in cannabis flowers and oils using a statistically guided optimization plan based on the principles of green chemistry. A single-laboratory validation determined the linearity, selectivity, accuracy, repeatability, intermediate precision, limit of detection, and limit of quantitation of the method. Amounts of individual cannabinoids above the limit of quantitation in the flowers ranged from 0.02 to 14.9% w/w, with repeatability ranging from 0.78 to 10.08% relative standard deviation. The intermediate precision determined using HorRat ratios ranged from 0.3 to 2.0. The LOQs for individual cannabinoids in flowers ranged from 0.02 to 0.17% w/w. This is a significant improvement over previous methods and is suitable for a wide range of applications including regulatory compliance, clinical studies, direct patient medical services, and commercial suppliers. Electronic supplementary material The online version of this article (doi:10.1007/s00216-017-0256-3) contains supplementary material, which is available to authorized users.

The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G = (V, E)$$\end{document}G=(V,E) and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with respect to the distances d. The method of choice for solving the TSP to optimality is a branch and cut approach. Usually the integrality constraints are relaxed first and all separation processes to identify violated inequalities are done on fractional solutions. In our approach we try to exploit the impressive performance of current ILP-solvers and work only with integer solutions without ever interfering with fractional solutions. We stick to a very simple ILP-model and relax the subtour elimination constraints only. The resulting problem is solved to integer optimality, violated constraints (which are trivial to find) are added and the process is repeated until a feasible solution is found. In order to speed up the algorithm we pursue several attempts to find as many relevant subtours as possible. These attempts are based on the clustering of vertices with additional insights gained from empirical observations and random graph theory. Computational results are performed on test instances taken from the TSPLIB95 and on random Euclidean graphs.

Objectives The traditional time trade-off (TTO) method has some problems in the valuation of health states considered worse than dead. The aim of our study is to compare two TTO variants that address this issue: lead-time and lag-time TTO. Methods Quota sampling was undertaken in June 2011 in Buenos Aires as part of the EQ-5D-5L Multinational Pilot Study. Respondents were randomly assigned to one of the TTO variants with two blocks of five EQ-5D-5L health states. Tasks were administered using a web-based digital aid (EQ-VT) administered in a group interview. Results A total of 387 participants were included [mean age 38.85 (SD: 13.97); 53.14 % females]. The mean observed values ranged from 0.44 (0.59) for state 21111 to 0.02 (0.76) for state 53555 in the lead-time group and between 0.53 (0.52) and 0.08 (0.76) in the lag-time group. There were no statistically significant differences in the values between TTO variants, except for a significant difference of 0.19 for state 33133. In both variants, marked peaks were observed around the value 0 across all states, with a higher percentage of 0 responses in the last state valued, suggesting ordering effects. Conclusions No important differences were found between TTO variants regarding values for EQ-5D-5L health states, suggesting that they could be equivalent variants. However, differences between the two methods may have been obscured by other aspects of the study design affecting the characteristics of the data.

We construct a stabilized finite-element method to compute flow and finite-strain deformations in an incompressible poroelastic medium. We employ a three-field mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewise-linear approximation for the displacements and fluid flux, and piecewise-constant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.

The real-time measurement of biomass has been addressed since many years. The quantification of biomass in the induction phase of a recombinant bioprocess is not straight forward, since biological burden, caused by protein expression, can have a significant impact on the cell morphology and physiology. This variability potentially leads to poor generalization of the biomass estimation, hence is a very important issue in the dynamic field of process development with frequently changing processes and producer lines. We want to present a method to quantify “biomass” in real-time which avoids off-line sampling and the need for representative training data sets. This generally applicable soft-sensor, based on first principles, was used for the quantification of biomass in induced recombinant fed-batch processes. Results were compared with “state of the art” methods to estimate the biomass concentration and the specific growth rate µ. Gross errors such as wrong stoichiometric assumptions or sensor failure were detected automatically. This method allows for variable model coefficients such as yields in contrast to other process models, hence does not require prior experiments. It can be easily adapted to a different growth stoichiometry; hence the method provides good generalization, also for induced culture mode. This approach estimates the biomass (or anabolic bioconversion) in induced fed-batch cultures in real-time and provides this key variable for process development for control purposes.

In this paper we propose an improved efficient approximation scheme for the multiple knapsack problem (MKP). Given a set ${\mathcal A}$ of n items and set ${\mathcal B}$ of m bins with possibly different capacities, the goal is to find a subset $S \subseteq{\mathcal A}$ of maximum total profit that can be packed into ${\mathcal B}$ without exceeding the capacities of the bins. Chekuri and Khanna presented a PTAS for MKP with arbitrary capacities with running time $n^{O(1/\epsilon^8 \log(1/\epsilon))}$ . Recently we found an efficient polynomial time approximation scheme (EPTAS) for MKP with running time $2^{O(1/\epsilon^5 \log(1/\epsilon))} poly(n)$ . Here we present an improved EPTAS with running time $2^{O(1/\epsilon \log^4(1/\epsilon))} + poly(n)$ . If the integrality gap between the ILP and LP objective values for bin packing with different sizes is bounded by a constant, the running time can be further improved to $2^{O(1/\epsilon \log^2(1/\epsilon))} + poly(n)$ .

Let be a complex algebraic hypersurface in not passing through the point . The generators of the fundamental group and the relations among them are described in terms of the real cone over with apex at . This description is a generalization to the algebraic case of Wirtinger's corepresentation of the fundamental group of a knot in . A new proof of Zariski's conjecture about commutativity of the fundamental group for a projective nodal curve is given in the second part of the paper based on the description of the generators and the relations in the group obtained in the first part.

This paper contributes to the environmental literature by (i) demonstrating that the estimated coefficients and the statistical significance of the non-leading terms in quadratic, cubic, and quartic logarithmic environmental Kuznets curve (EKC) specifications are arbitrary and should therefore not be used to choose the preferred specification and (ii) detailing a proposed general-to-specific type methodology for choosing the appropriate specifications when attempting to estimate higher-order polynomials such as cubic and quartic logarithmic EKC relationships. Testing for the existence and shape of the well-known EKC phenomenon is a hot topic in the environmental economics literature. The conventional approach widely employs quadratic and cubic specifications and more recently also the quartic specification, where the variables are in logarithmic form. However, it is important that researchers understand whether the estimated EKC coefficients, turning points, and elasticities are statistically acceptable, economically interpretable, and comparable. In addition, it is vital that researchers have a clear structured non-arbitrary methodology for determining the preferred specification and hence shape of the estimated EKC. We therefore show mathematically and empirically the arbitrary nature of estimated non-leading coefficients in quadratic, cubic, and quartic logarithmic EKC specifications, being dependent upon the units of measurement chosen for the independent variables (e.g. dependent upon a rescaling of the variables such as moving from $m to $bn). Consequently, the practice followed in many previously papers, whereby the estimates of the non-leading terms are used in the decision to choose the preferred specification of an estimated EKC relationship, is incorrect and should not be followed since it potentially could lead to misleading conclusions. Instead, it should be based upon the sign and statistical significance of the estimated coefficients of the leading terms, the location of turning point(s), and the sign and statistical significance of the estimated elasticities. Furthermore, we suggest that researchers should follow a proposed general-to-specific type methodology for choosing the appropriate order of polynomials when attempting to estimate higher-order polynomial logarithmic EKCs. Supplementary Information The online version contains supplementary material available at 10.1007/s11356-021-13463-y.

In this paper, new concepts of covering of fuzzy graphs are introduced. The definitions of fuzzy covering maps and fuzzy covering graphs of fuzzy graphs are given. Some special types of fuzzy covering graphs are discussed. Some important theorems to find out the fuzzy covering maps as well as fuzzy covering graphs for different types of fuzzy graphs are described. On the basis of the present situation during the current pandemic COVID-19, the world economic status is highly disruptive and deeply affected by the lock-down process. So, this topic is catching the eye for being an application part of this paper. Also, there are globally seventeen goals to sustain our development, which contain the eighth goal ‘Decent Work and Economic Growth’ having effect on the economy of the world. For this reason, the eighth sustainable development goal is combined with the economic impact of the pandemic for the discussion in the application part. Then some strategies are made to overcome this condition in a better way and perform all the steps to get a better situation in near future.

In this paper we consider Susceptible \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document}→ Infectious \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document}→ Recovered (SIR) epidemics on random graphs with clustering. To incorporate group structure of the underlying social network, we use a generalized version of the configuration model in which each node is a member of a specified number of triangles. SIR epidemics on this type of graph have earlier been investigated under the assumption of homogeneous infectivity and also under the assumption of Poisson transmission and recovery rates. We extend known results from literature by relaxing the assumption of homogeneous infectivity both in individual infectivity and between different kinds of neighbours. An important special case of the epidemic model analysed in this paper is epidemics in continuous time with arbitrary infectious period distribution. We use branching process approximations of the spread of the disease to provide expressions for the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0, the probability of a major outbreak and the expected final size. In addition, the impact of random vaccination with a perfect vaccine on the final outcome of the epidemic is investigated. We find that, for this particular model, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0 equals the perfect vaccine-associated reproduction number. Generalizations to groups larger than three are discussed briefly.

In a previous paper (Graham et al. in J Comput Phys 230:3668-3694, 2011), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random coefficients. This method was based on combining quasi-Monte Carlo (QMC) methods for computing the expected values with circulant embedding methods for sampling the random field on a regular grid. It was found capable of handling fluid flow problems in random heterogeneous media with high stochastic dimension, but no convergence theory was provided. This paper provides a convergence analysis for the method in the case when the QMC method is a specially designed randomly shifted lattice rule. The convergence result depends on the eigenvalues of the underlying nested block circulant matrix and can be independent of the number of stochastic variables under certain assumptions. In fact the QMC analysis applies to general factorisations of the covariance matrix to sample the random field. The error analysis for the underlying fully discrete finite element method allows for locally refined meshes (via interpolation from a regular sampling grid of the random field). Numerical results on a non-regular domain with corner singularities in two spatial dimensions and on a regular domain in three spatial dimensions are included.

Several lattice-based cryptosystems require to sample from a discrete Gaussian distribution over the integers. Existing methods to sample from such a distribution either need large amounts of memory or they are very slow. In this paper we explore a different method that allows for a flexible time-memory trade-off, offering developers freedom in choosing how much space they can spare to store precomputed values. We prove that the generated distribution is close enough to a discrete Gaussian to be used in lattice-based cryptography. Moreover, we report on an implementation of the method and compare its performance to existing methods from the literature. We show that for large standard deviations, the Ziggurat algorithm outperforms all existing methods.

This paper presents a combined structure for using real, complex, and binary valued vectors for semantic representation. The theory, implementation, and application of this structure are all significant. For the theory underlying quantum interaction, it is important to develop a core set of mathematical operators that describe systems of information, just as core mathematical operators in quantum mechanics are used to describe the behavior of physical systems. The system described in this paper enables us to compare more traditional quantum mechanical models (which use complex state vectors), alongside more generalized quantum models that use real and binary vectors. The implementation of such a system presents fundamental computational challenges. For large and sometimes sparse datasets, the demands on time and space are different for real, complex, and binary vectors. To accommodate these demands, the Semantic Vectors package has been carefully adapted and can now switch between different number types comparatively seamlessly. This paper describes the key abstract operations in our semantic vector models, and describes the implementations for real, complex, and binary vectors. We also discuss some of the key questions that arise in the field of quantum interaction and informatics, explaining how the wide availability of modelling options for different number fields will help to investigate some of these questions.

We compute the channel capacity of non-binary fingerprinting under the Marking Assumption, in the limit of large coalition size c. The solution for the binary case was found by Huang and Moulin. They showed that asymptotically, the capacity is 1/(c 2 2ln 2), the interleaving attack is optimal and the arcsine distribution is the optimal bias distribution. In this paper we prove that the asymptotic capacity for general alphabet size q is (q¿-¿1)/(c 2 2ln q). Our proof technique does not reveal the optimal attack or bias distribution. The fact that the capacity is an increasing function of q shows that there is a real gain in going to non-binary alphabets.

A graph G is a support for a hypergraph $H = (V, \mathcal{S})$ if the vertices of G correspond to the vertices of H such that for each hyperedge $S_i \in \mathcal{S}$ the subgraph of G induced by Si is connected. G is a planar support if it is a support and planar. Johnson and Pollak [9] proved that it is NP-complete to decide if a given hypergraph has a planar support. In contrast, there are polynomial time algorithms to test whether a given hypergraph has a planar support that is a path, cycle, or tree. In this paper we present an algorithm which tests in polynomial time if a given hypergraph has a planar support that is a tree where the maximal degree of each vertex is bounded. Our algorithm is constructive and computes a support if it exists. Furthermore, we prove that it is already NP-hard to decide if a hypergraph has a 3-outerplanar support.

A natural way to draw two planar graphs whose vertex sets are matched is to assign each matched pair a unique y-coordinate. In this paper we introduce the concept of such matched drawings, which are a relaxation of simultaneous geometric embeddings with mapping. We study which classes of graphs allow matched drawings and show that (i) two 3-connected planar graphs or a 3-connected planar graph and a tree may not be matched drawable, while (ii) two trees or a planar graph and a planar graph of some special families—such as unlabeled level planar (ULP) graphs or the family of "carousel graphs"—are always matched drawable. Research partially supported by the MIUR Project "MAINSTREAM: Algorithms for massive information structures and data streams".

It is well-known, due to the work of Girard and Coquand, that adding polymorphic domains to higher order logic, HOL, or its type theoretic variant ¿HOL, renders the logic inconsistent. This is known as Girard’s paradox, see [4]. But there is also another presentation of higher order logic, in its type theoretic variant called ¿PRED¿, to which polymorphic domains can be added safely, Both ¿HOL and ¿PRED¿ are well-known type systems and in this paper we study why ¿HOL with polymorphic domains is inconsistent and why nd ¿PRED¿ with polymorphic domains remains consistent. We do this by describing a simple model for the latter and we show why this can not be a model of the first.

Although Constraint Programming (CP) is considered a useful tool for tackling combinatorial problems, its lack of flexibility when dealing with uncertainties and preferences is still a matter for research. Several formal frameworks for soft constraints have been proposed within the CP community: all of them seem to be theoretically solid, but few practical implementations exist. In this paper we present an implementation for Mozart of one of these frameworks, which is based on a semiring structure. We explain how the soft constraints constructs were adapted to the propagation process that Mozart performs, and show how they can be transparently integrated with current Mozart hard propagators. Additionally, we show how over-constrained problems can be successfully relaxed and solved, and how preferences can be added to a problem, while keeping the formal model as a direct reference.

This paper presents a deterministic, strongly polynomial time algorithm for computing the matrix rank for a class of symbolic matrices (whose entries are polynomials over a field). This class was introduced, in a different language, by Lovasz [16] in his study of flats in matroids, and proved a duality theorem putting this problem in \(NP \cap coNP\). As such, our result is another demonstration where “good characterization” in the sense of Edmonds leads to an efficient algorithm. In a different paper Lovasz [17] proved that all such symbolic rank problems have efficient probabilistic algorithms, namely are in BPP. As such, our algorithm may be interpreted as a derandomization result, in the long sequence special cases of the PIT (Polynomial Identity Testing) problem. Finally, Lovasz and Yemini [20] showed how the same problem generalizes the graph rigidity problem in two dimensions. As such, our algorithm may be seen as a generalization of the well-known deterministic algorithm for the latter problem. There are two somewhat unusual technical features in this paper. The first is the translation of Lovasz’ flats problem into a symbolic rank one. The second is the use of submodular optimization for derandomization. We hope that the tools developed for both will be useful for related problems, in particular for better understanding of graph rigidity in higher dimensions.

In two recent papers by Veitch and Roy and by Borgs, Chayes, Cohn, and Holden, a new class of sparse random graph processes based on the concept of graphexes over \(\sigma \)-finite measure spaces has been introduced. In this paper, we introduce a metric for graphexes that generalizes the cut metric for the graphons of the dense theory of graph convergence. We show that a sequence of graphexes converges in this metric if and only if the sequence of graph processes generated by the graphexes converges in distribution. In the course of the proof, we establish a regularity lemma and determine which sets of graphexes are precompact under our metric. Finally, we establish an identifiability theorem, characterizing when two graphexes are equivalent in the sense that they lead to the same process of random graphs.

Quantile regression estimates conditional quantiles and has wide applications in the real world. Estimating high conditional quantiles is an important problem. The regular quantile regression (QR) method often designs a linear or non-linear model, then estimates the coefficients to obtain the estimated conditional quantiles. This approach may be restricted by the linear model setting. To overcome this problem, this paper proposes a direct nonparametric quantile regression method with five-step algorithm. Monte Carlo simulations show good efficiency for the proposed direct QR estimator relative to the regular QR estimator. The paper also investigates two real-world examples of applications by using the proposed method. Studies of the simulations and the examples illustrate that the proposed direct nonparametric quantile regression model fits the data set better than the regular quantile regression method.

In this paper we consider the following topics related to results of Laszlo Fejes Toth: (1) The Tammes problem and Fejes Toth’s bound on circle packings; (2) Fejes Toth’s problem on maximizing the minimum distance between antipodal pairs of points on the sphere; (3) Fejes Toth’s problem on the maximum kissing number of packings on the sphere; (4) The Fejes Toth–Sachs problem on the one-sided kissing numbers; (5) Fejes Toth’s papers on the isoperimetric problem for polyhedra.

In this paper we present some new complexity results on the routing time of a graph under the routing via matching model. This is a parallel routing model which was introduced by Alon et al. [1]. The model can be viewed as a communication scheme on a distributed network. The nodes in the network can communicate via matchings (a step), where a node exchanges data (pebbles) with its matched partner. Let G be a connected graph with vertices labeled from \(\{1,...,n\}\) and the destination vertices of the pebbles are given by a permutation \(\pi \). The problem is to find a minimum step routing scheme for the input permutation \(\pi \). This is denoted as the routing time \(rt(G,\pi )\) of G given \(\pi \). In this paper we characterize the complexity of some known problems under the routing via matching model and discuss their relationship to graph connectivity and clique number. We also introduce some new problems in this domain, which may be of independent interest.

The paper addresses the problem of computing maximal conditional expected accumulated rewards until reaching a target state briefly called maximal conditional expectations in finite-state Markov decision processes where the condition is given as a reachability constraint. Conditional expectations of this type can, e.g., stand for the maximal expected termination time of probabilistic programs with non-determinism, under the condition that the program eventually terminates, or for the worst-case expected penalty to be paid, assuming that at least three deadlines are missed. The main results of the paper are i a polynomial-time algorithm to check the finiteness of maximal conditional expectations, ii PSPACE-completeness for the threshold problem in acyclic Markov decision processes where the task is to check whether the maximal conditional expectation exceeds a given threshold, iii a pseudo-polynomial-time algorithm for the threshold problem in the general cyclic case, and iv an exponential-time algorithm for computing the maximal conditional expectation and an optimal scheduler.

The main contribution of this paper, is a new key enumeration algorithm that combines the conceptual simplicity of the rank estimation algorithm of Glowacz et al. (from FSE 2015) and the parallelizability of the enumeration algorithm of Bogdanov et al. (SAC 2015) and Martin et al. (from ASIACRYPT 2015). Our new algorithm is based on histograms. It allows obtaining simple bounds on the (small) rounding errors that it introduces and leads to straightforward parallelization. We further show that it can minimize the bandwidth of distributed key testing by selecting parameters that maximize the factorization of the lists of key candidates produced by the enumeration, which can be highly beneficial, e.g. if these tests are performed by a hardware coprocessor. We also put forward that the conceptual simplicity of our algorithm translates into efficient implementations (that slightly improve the state-of-the-art). As an additional consolidating effort, we finally describe an open source implementation of this new enumeration algorithm, combined with the FSE 2015 rank estimation one, that we make available with the paper.

GOST 28147-89 is a well-known block cipher. Its large key size of 256 bits and incredibly low implementation cost make it a plausible alternative for AES-256 and triple DES. Until 2010 "despite considerable cryptanalytic efforts spent in the past 20 years", GOST was not broken see [30]. Accordingly, in 2010 GOST was submitted to ISO 18033 to become a worldwide industrial encryption standard. In paper we focus on the question of how far one can go in a dedicated Depth-First-Search approach with several stages of progressive guessing and filtering with successive distinguishers. We want to design and optimized guess-then-truncated differential attack on full 32-bit GOST and make as efficient as we can.The main result of this paper is a single-key attack against full 32-round 256-bit GOST with time complexity of $$2^{179}$$ which is substantially faster than any other known single key attack on GOST.

The running time of a quantum walk search algorithm depends on both the structure of the search space graph and the configuration of marked locations. While the first dependence has been studied in a number of papers, the second dependence remains mostly unstudied. We study search by quantum walks on the two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [AKR05]. The original paper analyses one and two marked locations only. We move beyond two marked locations and study the behaviour of the algorithm for an arbitrary configuration of marked locations. In this paper, we prove two results showing the importance of how the marked locations are arranged. First, we present two placements of k marked locations for which the number of steps of the algorithm differs by a factor of $$\varOmega \sqrt{k}$$. Second, we present two configurations of k and $$\sqrt{k}$$ marked locations having the same number of steps and probability to find a marked location.

The decorrelation theory provides a different point of view on the security of block cipher primitives. Results on some statistical attacks obtained in this context can support or provide new insight on the security of symmetric cryptographic primitives. In this paper, we study, for the first time, the multidimensional linear attacks as well as the truncated differential attacks in this context. We show that the cipher should be decorrelated of order two to be resistant against some multidimensional linear and truncated differential attacks. Previous results obtained with this theory for linear, differential, differential-linear and boomerang attacks are also resumed and improved in this paper.

In the "The curse of simultaneity", Paes Leme at al. show that there are interesting classes of games for which sequential decision making and corresponding subgame perfect equilibria avoid worst case Nash equilibria, resulting in substantial improvements for the price of anarchy. This is called the sequential price of anarchy. A handful of papers have lately analysed it for various problems, yet one of the most interesting open problems was to pin down its value for network congestion games, where the price of anarchy equals 5/2. The main contribution of this paper is the surprising result that the sequential price of anarchy is unbounded even for linear symmetric routing games, thereby showing that sequentiality can be arbitrarily worse than simultaneity for this important class of games. Complementing this unboundedness result we solve an open problem in the area by establishing that the (regular) price of anarchy for linear symmetric routing games equals 5/2. Additionally, we prove that in these games, even with two players, computing the outcome of a subgame perfect equilibrium is NP-hard. The latter explains, to some extent, the difficulty of analyzing subgame perfect equilibria.

The parity of the length of paths and cycles is a classical and well-studied topic in graph theory and theoretical computer science. The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with a group label on each arc. Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero disjoint paths and cycles. In this paper, we present a solution to finding an $s$--$t$ path in a group-labeled graph with two labels forbidden. This also leads to an elementary solution to finding a zero path in a ${\mathbb Z}_3$-labeled graph, which is the first nontrivial case of finding a zero path. This situation in fact generalizes the 2-disjoint paths problem in undirected graphs, which also motivates us to consider that setting. More precisely, we provide a polynomial-time algorithm for testing whether there are at most two possible labels of $s$--$t$ paths in a group-labeled graph or not, and finding $s$--$t$ paths attaining at least three distinct labels if exist. The algorithm is based on a necessary and sufficient condition for a group-labeled graph to have exactly two possible labels of $s$--$t$ paths, which is the main technical contribution of this paper.

In this paper, we construct an infinitary variant of the relational model of linear logic, where the exponential modality is interpreted as the set of finite or countable multisets. We explain how to interpret in this model the fixpoint operator Y as a Conway operator alternatively defined in an inductive or a coinductive way. We then extend the relational semantics with a notion of color or priority in the sense of parity games. This extension enables us to define a new fixpoint operator Y combining both inductive and coinductive policies. We conclude the paper by mentionning a connection between the resulting model of λ-calculus with recursion and higher-order model-checking.

In the present paper, we propose Abstract Algebraic Logic (AAL) as a general logical framework for Judgment Aggregation. Our main contribution is a generalization of Herzberg’s algebraic approach to characterization results on judgment aggregation and propositional-attitude aggregation, characterizing certain Arrovian classes of aggregators as Boolean algebra and MV-algebra homomorphisms, respectively. The characterization result of the present paper applies to agendas of formulas of an arbitrary selfextensional logic. This notion comes from AAL, and encompasses a vast class of logics, of which classical, intuitionistic, modal, many-valued and relevance logics are special cases. To each selfextensional logic \(\mathcal{S}\), a unique class of algebras \(\mathbb{A}\mathrm{lg}\mathcal{S}\) is canonically associated by the general theory of AAL. We show that for any selfextensional logic \(\mathcal{S}\) such that \(\mathbb{A}\mathrm{lg}\mathcal{S}\) is closed under direct products, any algebra in \(\mathbb{A}\mathrm{lg}\mathcal{S}\) can be taken as the set of truth values on which an aggregation problem can be formulated. In this way, judgment aggregation on agendas formalized in classical, intuitionistic, modal, many-valued and relevance logic can be uniformly captured as special cases. This paves the way to the systematic study of a wide array of “realistic agendas” made up of complex formulas, the propositional connectives of which are interpreted in ways which depart from their classical interpretation. This is particularly interesting given that, as observed by Dietrich, nonclassical (subjunctive) interpretation of logical connectives can provide a strategy for escaping impossibility results.

This paper proposes a compact and efficient \(GF(2^8)\) inversion circuit design based on a combination of non-redundant and redundant Galois Field (GF) arithmetic. The proposed design utilizes redundant GF representations, called Polynomial Ring Representation (PRR) and Redundantly Represented Basis (RRB), to implement \(GF(2^8)\) inversion using a tower field \(GF((2^4)^2)\). In addition to the redundant representations, we introduce a specific normal basis that makes it possible to map the former components for the 16th and 17th powers of input onto logic gates in an efficient manner. The latter components for \(GF(2^4)\) inversion and \(GF(2^4)\) multiplication are then implemented by PRR and RRB, respectively. The flexibility of the redundant representations provides efficient mappings from/to the \(GF(2^8)\). This paper also evaluates the efficacy of the proposed circuit by means of gate counts and logic synthesis with a 65 nm CMOS standard cell library and comparisons with conventional circuits, including those with tower fields \(GF(((2^2)^2)^2)\). Consequently, we show that the proposed circuit achieves approximately 40 % higher efficiency in terms of area-time product than the conventional best \(GF(((2^2)^2)^2)\) circuit excluding isomorphic mappings. We also demonstrate that the proposed circuit achieves the best efficiency (i.e., area-time product) for an AES encryption S-Box circuit including isomorphic mappings.

Many algorithms for multi-criteria top-\(k\) query processing with ranking predicates have been proposed, but little effort has been directed toward genericity, i.e. supporting any type of access to the lists of predicate scores (sorted and/or random), or any access cost settings. In this paper we propose a general approach to exact and approximate generic top-\(k\) processing. To this end, we propose a general framework (GF) for generic top-\(k\) processing, able to express any top-\(k\) algorithm and present within this framework a first comparison between generic algorithms. In previous work, we proposed BreadthRefine (BR), a generic algorithm that considers the current top-\(k\) candidates as a whole instead of focusing on the best candidate for score refinement, then we compared it with specific top-\(k\) algorithms. In this paper, we propose two variants of existing generic strategies and experimentally compare them with the BR breadth-first strategy, showing that BR leads to better execution costs. We also extend the notion of \(\theta \)-approximation to the GF framework and present a first experimental study of the approximation potential of top-\(k\) algorithms on early stopping.