Lattice

Single frequency estimation is a long-studied problem with application domains including radar, sonar, telecommunications, astronomy and medicine. One method of estimation, called phase unwrapping, attempts to estimate the frequency by performing linear regression on the phase of the received signal. This procedure is complicated by the fact that the received phase is 'wrapped' modulo 2 and therefore must be 'unwrapped' before the regression can be performed. In this paper, we propose an estimator that performs phase unwrapping in the least squares sense. The estimator is shown to be strongly consistent and its asymptotic distribution is derived. We then show that the problem of computing the least squares phase unwrapping is related to a problem in algorithmic number theory known as the nearest lattice point problem. We derive a polynomial time algorithm that computes the least squares estimator. The results of various simulations are described for different values of sample size and SNR.

Let V denote V (n, q), the vector space of dimension n over GF(q). A subspace partition of V is a collection Π of subspaces of V such that every nonzero vector in V is contained in exactly one subspace belonging to Π. The set P (V) of all subspace partitions of V is a lattice with minimum and maximum elements 0 and 1 respectively. In this paper, we show that the number of elements in P (V) is congruent to the number of all set partitions of {1,. .. , n} modulo q − 1. Moreover, we show that the Möbius number µ n,q (0, 1) of P (V) is congruent to (−1) n−1 (n − 1)! (the Möbius number of set partitions of {1,. .. , n}) modulo q − 1.

Lattices are regular arrangements of points in n-dimensional space, whose study appeared in the 19th century in both number theory and crystallography. Since the appearance of the celebrated Lenstra-Lenstra-Lovász lattice basis reduction algorithm twenty years ago, lattices have had surprising applications in cryptology. Until recently, the applications of lattices to cryptology were only negative, as lattices were used to break various cryptographic schemes. Paradoxically, several positive cryptographic applications of lattices have emerged in the past five years: there now exist public-key cryptosystems based on the hardness of lattice problems, and lattices play a crucial rôle in a few security proofs. In this talk, we will try to survey the main examples of the two faces of lattices in cryptology. The full material of this talk appeared in [2]. A preliminary version can be found in [1].

In this study, quantitative models for monomer/water and the corresponding polymer/water interfaces were developed. The monomer/water interface was modeled within the framework proposed by Fu and Li (Chem. Eng. Sci. 44 (1989) 1519) for organic liquid/water interfaces. We took a similar approach with that which others used to simulate micelle formation of surfactants and block polymers in developing the model for the polymer/water interface. In this model, the Gibbs free energy of interfacial formation was decomposed into two components: transfer free energy of a polymer segment to the interface and mixing free energy within the interface. Interfacial tensions were then estimated using concentration gradient theory. The ratio of the number of total nearest neighbors of a site in a lattice within the interface to that located in each of the adjacent planes was found to be the important correlating factor. It was shown that this ratio for monomer/water interfaces and that for polymer/water interfaces are linearly related. The polymer in the interface is likely to be in the form of short polymer segments (2-4 monomer units) rather than dangling chain ends. The estimation of polymer/water interfacial tension from the models established in this work is in reasonable agreement with experimental observation.

Let L be a D-lattice, i.e. a lattice ordered effect algebra, and let BV be the Banach space of all real-valued functions of bounded variation on L (vanishing at 0) endowed with the variation norm. We prove the existence of a continuous Aumann-Shapley value ϕ on bv NA, the subspace of BV spanned by all functions of the form f • µ, where µ : L → [0, 1] is a nonatomic σ-additive modular measure and f : [0, 1] → R is of bounded variation and continuous at 0 and at 1. Mathematics Subject Classification (2000). 28A12, 06C15, 91A12. A. Basile et al. Positivity (D1) a b is defined if and only if b ≤ a; (D2) If b = b c. Vol. 12 (2008) On the Aumann-Shapley value 615

As said by Archimedes give me a long enough lever and a fulcrum and I shall move the world A bell crank lever is a connector component which is used to change the direction of force applied on to a component. the motion of it can be restricted to various angles most commonly used angles being 90 degrees and 180 degrees. thus, undergoing high working comprehensive and tensile stress. we try to analyze the stresses induced in the bell crank lever based on conventional design methods and strengthen them by lattice structure design. the applications being from automotive to aircraft sectors due to its compact fitting and high stress tolerate capacity and as a light weight component.

We introduce the framework of ordered read-write locks, ORWL, that are characterized by two main features: a strict FIFO policy for access and the attribution of access to lock-handles instead of processes or threads. These two properties allow applications to have a controlled pro-active access to resources and thereby to achieve a high degree of asynchronicity between different tasks of the same application. For the case of iterative computations with many parallel tasks which access their resources in a cyclic pattern we provide a generic technique to implement them by means of ORWL. We show that the possible execution patterns for such a system correspond to a combinatorial lattice structure and that this lattice is finite iff the configuration contains a potential deadlock. In addition, we provide efficient algorithms: one that allows for a deadlock-free initialization of such a system and another one for the detection of deadlocks in an already initialized system. Calculs itératifs avec des verrous ordonnés de lecteur/écriture Résumé : Nous présentons la structure des verrous ordonnés de lecture/écriture, ORWL, qui sont caractérisés par deux fonctionnalités principales : une politique d'accès FIFO stricte et une attribution des accès à des gestionnaires de verrou plutôt qu'à des processus ou des threads. Ces deux propriétés permettent aux applications d'avoir un contrôle dynamique de l'accès aux ressources et donc de parvenir à un haut niveau d'asynchronisme entre les différentes tâches d'une même application. Dans le cas de calculs itératifs avec beaucoup de tâches parallèles accédant à leurs ressources selon un motif cyclique, nous proposons une technique générique d'implémentation avec des ORWL. Nous montrons que les schémas d'exécution possibles pour un tel système forment un treillis combinatoire et que ce treillis est fini si et seulement si la configuration contient un interblocage potentiel. De plus, nous proposons deux algorithmes efficaces : l'un pour une initialisation sans interblocage d'un tel système et l'autre pour la détection d'interblocage dans un système déjà initialisé.

This paper describes a technique for identiÿcation of the knowledge structures implicit in scientiÿc data and further develops the supporting methodology for analysis of fuzzy relational structures using the mathematical theory of Fuzzy Relations and Generalized Morphism. Initial knowledge elicited using repertory grid with semiotic descriptors is transformed to fuzzy relational knowledge structures which capture semantic relationships in a problem domain by means of BK-product. In analysis, the fuzzy relational structures computed in the di erent sized domains or those computed by means of various fuzzy logics can be analyzed using generalized morphism; namely (global) structure embedding, or structure preserving as well as meta analysis of fuzzy relational structures. The result of meta analysis is represented as the Hasse Diagram structure of meta relations by classifying equivalent classes of fuzzy relational structures. The paper is concluded with a case study using real-life engineering data from the aviation industry.

Louis Hjelmslev en sus Prolegómenos a una teoría del lenguaje anticipa los fundamentos de una teoría semiótica axiomáticamente consistente. El andamiaje teórico construido por Hjelmslev busca conformar un 'álgebra lingüística' cuyo principio de articulación es la relación de ...

Third-generation low-emittance storage-ring light sources based on double- and triple-bend cells and undulator magnets have been in operation around the world for more than two decades. On the horizon is a new generation based on the multi-bend achromat (MBA) lattice concept promising two to three orders of magnitude higher brightness than is available in today's sources. In this paper, the challenges inherent in designing MBA lattices, as well as potential solutions, are described. Topics covered include lattice concepts, scaling of storage-ring performance, brightness optimization, nonlinear dynamics, beam lifetime and injection schemes.

This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher connectivity receive special attention. Graphs embeddable in the cubic lattice of arbitrary dimension, and graphs embeddable in the triangular or hexagonal lattice of the plane are also discussed. Results concerning the case when not all, but just some longest paths or cycles are intersected, for example two or three of them, are also reported.

De nombreux modèles ont été proposés pour la modélisation de données multidimensionnelles dans les entrepôts. Ces propositions considèrent une même fonction d'agrégation pour déterminer les valeurs d'une mesure aux différents niveaux de granularité de l'espace multidimensionnel. Nous proposons un nouveau modèle conceptuel plus flexible supportant des agrégations multiples différentiées. L'agrégation multiple permet d'associer à une même mesure, une fonction d'agrégation différente pour chaque axe d'analyse. L'agrégation différentiée autorise des agrégations spécifiques à chaque niveau de granularité. Le modèle proposé repose sur des formalismes graphiques suffisamment expressifs pour contrôler la validité des fonctions d'agrégation qui peuvent être distributives, algébriques ou holistiques. Nous montrons également comment la modélisation conceptuelle peut être exploitée au niveau logique R-OLAP pour construire efficacement des treillis de pré-agrégats. ABSTRACT. Many models have been proposed for multidimensional data warehouses modeling. These propositions consider the same aggregate function to determine the values of a measure with different levels of granularity of the multidimensional space. We propose a new conceptual model for multidimensional representation of data supporting multiple differentiated aggregations. Multiple aggregation allows to associate to the same measure, a different aggregation function for each axis of analysis. Differentiated aggregation allows specific aggregations at each level of granularity. The proposed model is based on graphical formalisms expressive enough to control the validity of aggregate functions that can be distributive, algebraic and holistic. We also show how conceptual modeling can be exploited in logic R-OLAP to build effectively lattices of pre-aggregates. MOTS-CLÉS : système décisionnels, base de données multidimensionnelles, modélisation conceptuelle d'entrepôt de données, mécanismes d'agrégations multiples dans les treillis multidimensionnels.

There are five known classes of lattice equations that hold in every infinite dimensional Hilbert space underlying quantum systems: generalised orthoarguesian, Mayet's EA, Godowski, Mayet-Godowski, and Mayet's E equations. We obtain a result which opens a possibility that the first two classes coincide. We devise new algorithms to generate Mayet-Godowski equations that allow us to prove that the fourth class properly includes the third. An open problem related to the last class is answered. Finally, we show some new results on the Godowski lattices characterising the third class of equations.

We investigate the dissolution of artificial fractures with three-dimensional, pore-scale numerical simulations. The fluid velocity in the fracture space was determined from a lattice-Boltzmann method, and a stochastic solver was used for the transport of dissolved species. Numerical simulations were used to study conditions under which long conduits (wormholes) form in an initially rough but spatially homogeneous fracture. The effects of flow rate, mineral dissolution rate and geometrical properties of the fracture were investigated, and the optimal conditions for wormhole formation determined.

NTRU is a very efficient public-key cryptosystem based on polynomial arithmetic. Its security is related to the hardness of lattice problems in a very special class of lattices. This article is motivated by an interesting peculiar property of NTRU lattices. Namely, we show that NTRU lattices are proportional to the so-called symplectic lattices. This suggests to try to adapt the classical reduction theory to symplectic lattices, from both a mathematical and an algorithmic point of view. As a first step, we show that orthogonalization techniques (Cholesky, Gram-Schmidt, QR factorization, etc.) which are at the heart of all reduction algorithms known, are all compatible with symplecticity, and that they can be significantly sped up for symplectic matrices. Surprisingly, by doing so, we also discover a new integer Gram-Schmidt algorithm, which is faster than the usual algorithm for all matrices. Finally, we study symplectic variants of the celebrated LLL reduction algorithm, and obtain interesting speed ups.

Lattice-based signature schemes following the Goldreich–Goldwasser–Halevi (GGH) design have the unusual property that each signature leaks information on the signer’s secret key, but this does not necessarily imply that such schemes are insecure. At Eurocrypt ’03, Szydlo proposed a potential attack by showing that the leakage reduces the key-recovery problem to that of distinguishing integral quadratic forms. He proposed a

The main results of this paper interpret mixed volumes of lattice polytopes as mixed multiplicities of ideals and mixed multiplicities of ideals as Samuel's multiplicities. In particular, we can give a purely algebraic proof of Bernstein's theorem which asserts that the number of common zeros of a system of Laurent polynomial equations in the torus is bounded above by the mixed volume of their Newton polytopes.

In his grammar of ancient Sanskrit, Pān. ini represents the phonological classes as intervals of a list. This representation method and especially the actual list constructed by Pān. ini, which is called thé Sivasūtras, earns universal admiration. The legend says that godŚiva revealed theŚivasūtras to Pān. ini in order to let him start developing his grammar of Sanskrit. A question still discussed is whether it is possible to shorten theŚivasūtras. In the course of this paper, I am going to prove that this question can be reduced to a question about the graphtheoretical form of a particular formal concept lattice. Furthermore, I show how theŚivasūtras can be reconstructed from Pān. ini's grammar.

Setting n i = n (for all i) in these expressions yields a new proof of a recent result of Duchi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension.

In this study, magnesia stabilized zirconia based nanocrystalline ceramics were produced through a polymer precursor route using gadolinium and boron. The powders were characterized during the various steps by structural and morphological techniques (FT-IR, XRD, and SEM). XRD results proved that a tetragonal phase is predominant for all samples with varying magnesium contents and no monoclinic zirconia solid solution appears. The crystallite sizes of the samples were calculated using Scherrer equation. The smallest crystallite size was obtained for the sample containing Zr/Mg/Ce/Gd/B ratio of 82/0/10/8/0. The lattice parameters were calculated for cubic, tetragonal, hexagonal, and orthorhombic structures. SEM results show all the samples have spherical grains. The average grain diameters were calculated for all the samples. The smallest average grain diameter was obtained for the sample containing Zr/Mg/Ce/Gd/B ratio of 82/0/10/8/0.

We consider special subclasses of the class of Lindelöf Σ-spaces obtained by imposing restrictions on the weight of the elements of compact covers that admit countable networks: A space X is in the class LΣ( � κ) if it admits a cover by compact subspaces of weight κ and a countable network for the cover. We restrict our attention to κ ≤ ω. In the case κ = ω, the class includes the class of metrizably fibered spaces considered by Tkachuk, and the P-approximable spaces considered by Tkačenko. The case κ = 1 corresponds to the spaces of countable network weight, but even the case κ = 2 gives rise to a nontrivial class of spaces. The relation of known classes of compact spaces to these classes is considered. It is shown that not every Corson compact of weight ℵ1 is in the class LΣ( ≤ ω), answering a question of Tkachuk. As well, we study whether certain compact spaces in LΣ( ≤ ω) have dense metrizable subspaces, partially answering a question of Tkačenko. Other interesting results and e...

In this paper, we present a new methodology to adapt any kind of lattice reduction algorithms to deal with the modular knapsack problem. In general, the modular knapsack problem can be solved using a lattice reduction algorithm, when its density is low. The complexity of lattice reduction algorithms to solve those problems is upper-bounded in the function of the lattice dimension and the maximum norm of the input basis. In the case of a low density modular knapsack-type basis, the weight of maximum norm is mainly from its first column. Therefore, by distributing the weight into multiple columns, we are able to reduce the maximum norm of the input basis. Consequently, the upper bound of the time complexity is reduced. To show the advantage of our methodology, we apply our idea over the floating-point LLL (L 2 ) algorithm. We bring the complexity from O(d 3+ε β 2 + d 4+ε β) to O(d 2+ε β 2 + d 4+ε β) for ε < 1 for the low density knapsack problem, assuming a uniform distribution, where d is the dimension of the lattice, β is the bit length of the maximum norm of knapsack-type basis. We also provide some techniques when dealing with a principal ideal lattice basis, which can be seen as a special case of a low density modular knapsack-type basis.

Several authors have examined connections among 132-avoiding permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we find analogues for some of these results for permutations π avoiding 132 and 1223 (there is no occurrence π i < π j < π j+1 such that 1 ≤ i ≤ j − 2) and provide a combinatorial interpretation for such permutations in terms of lattice paths. Using tools developed to prove these analogues, we give enumerations and generating functions for permutations which avoid both 132 and 1223, and certain additional patterns. We also give generating functions for permutations avoiding 132 and 1223 and containing certain additional patterns exactly once. In all cases we express these generating functions in terms of Chebyshev polynomials of the second kind.

In this paper, we provide an unified view of two definitions of digital lines in 3D via the use of lattice theory and specific projections of the lattice Z 3. We use this unified vision to explain the extension of the definition of Voss [1] to an arbitrary dimension and we show how to extend the definition of Figueiredo and Reveillès [2] to an arbitrary dimension.

We describe a novel volumetric global illumination framework based on the Face-Centered Cubic (FCC) lattice. An FCC lattice has important advantages over a Cartesian lattice. It has higher packing density in the frequency domain, which translates to better sampling efficiency. Furthermore, it has the maximal possible kissing number (equivalent to the number of nearest neighbors of each site), which provides optimal 3D angular discretization among all lattices. We employ a new two-pass (illumination and rendering) global illumination scheme on an FCC lattice. This scheme exploits the angular discretization to greatly simplify the computation in multiple scattering and to minimize illumination information storage. The GPU has been utilized to further accelerate the rendering stage. We demonstrate our new framework with participating media and volume rendering with multiple scattering, where both are significantly faster than traditional techniques with comparable quality.

It is shown how a log concave sequence generates a log super-modular function on the lattice being the direct product of two finite chains. The FKG inequality is applied to this function, and results in an inequality that is a 2-dimensional version of an inequality shown by Seymour and Welsh (1975).

Digital Logic: Logic functions, Minimization, Design and synthesis of combinational and sequential circuits; Number representation and computer arithmetic (fixed and floating point). Computer Organization and Architecture: Machine instructions and addressing modes, ALU and data-path, CPU control design, Memory interface, I/O interface (Interrupt and DMA mode), Instruction pipelining, Cache and main memory, Secondary storage.

In this paper, an optimal aggregation and counter-aggregation (drill-down) methodology is proposed on multidimensional data cube. The main idea is to aggregate on smaller cuboids after partitioning those depending on the cardinality of the individual dimensions. Based on the operations to make these partitions, a Galois Connection is identified for formal analysis that allow to guarantee the soundness of optimizations of storage space and time complexity for the abstraction and concretization functions defined on the lattice structure. Our contribution can be seen as an application to OLAP operations on multidimensional data model in the Abstract Interpretation framework.

Bayesian probability theory is an inference calculus, which originates from a generalization of inclusion on the Boolean lattice of logical assertions to a degree of inclusion represented by a real number. Dual to this lattice is the distributive lattice of questions constructed from the ordered set of down-sets of assertions, which forms the foundation of the calculus of inquiry-a generalization of information theory. In this paper we introduce this novel perspective on these spaces in which machine learning is performed and discuss the relationship between these results and several proposed generalizations of information theory in the literature.

Up to now, any attempt to use Gröbner bases in the design of public key cryptosystems has failed, as anticipated by a classical paper of B. Barkee et al.; we show why, and show that the only residual hope is to use binomial ideals, i.e. lattices. We propose two lattice-based cryptosystems that will show the usefulness of multivariate polynomial algebra and Gröbner bases in the construction of public key cryptosystems. The first one tries to revive two cryptosystems Polly Cracker and GGH, that have been considered broken, through a hybrid; the second one improves a cryptosystem (NTRU) that only has heuristic and challenged evidence of security, providing evidence that the extension cannot be broken with some of the standard lattice tools that can be used to break some reduced form of NTRU. Because of the bounds on length, we only sketch the construction of these two cryptosystems, and leave many details of the construction of private and public keys, of the proofs and of the security considerations to forthcoming technical papers.

Internet of things (IoT) deals with massive collected data. Most of these data are personality information that needs to be protected from hacking and unauthorized access. In other hand, these massive data needs processing speed. To meet these requirements, this paper provides modifications on NTRU public key cryptosystem to prevent LLL algorithm from recover the plain text from known cipher text.The method is based on a specific swapping process in the encryption process to thwart it. In addition to use suggest a method that can generatedynamic sequences of keys in a parallel manner that use to encrypt the data in IoT environment applications.

Introduction. Semilattice semantics for relevant logics were discovered independently by Routley and Urquhart over 10 years ago. A semilattice semantics was first published in [10], where the weak theory of implication of [8] and [3] (i.e., R -, the pure implication fragment of the system R of relevant implication) is shown to be consistent and complete with respect to it. That result was extended in [11]. But the semantics is explored in greatest detail in [12]. As reported in [4], Fine outfitted the positive semilattice semantics for R, with a suitable Hilbert-style axiomatisation. (We refer to the system as UR+.)l In 1980 Charlwood supplied a subscripted system of natural deduction. (See [1] and [2].) A subscripted Gentzen system was devised in [5] and [6]. Obviously, the central idea of the semilattice semantics is to impose relevant-style valuations on a semilattice (with an identity) used as the underlying model structure. However, in [12] the contractionless2 semantics are obtained (quite reasonably) by dropping the idempotence postulate and thus changing the relatively simple semilattice structure into a commutative monoid. Here we show that the semilattice structure can be regained for positive, contractionless relevant implication.3 Although we have no proofs as yet, we think that this semantics will pave the way for showing completeness for the corresponding subscripted Gentzen and natural deduction systems, as well as the Hilbert-style axiomatization, URW+.4 Contractionless semilattice semantics. For the original semantics of [12], let a UR W+ -model structure (UR W+ -m.s.) be a triple <K, 0, v > with K a set, 0 E K and v a binary operation on K satisfying the following postulates: p1. 0 V X = X.

A three dimensional, multigroup, neutron diffusion theory based computer code NEMSQR (Nodal Expansion Method for SQuare geometry) is developed for square geometry in order to perform reactor core calculation. The code is based on Nodal Expansion Method (NEM). In this method, an inhomogeneous matrix equation, which involves spatial moments of nodal flux distribution and surface averaged partial currents across the nodal surfaces, is derived using fourth order polynomial approximation to spatial dependence of nodal flux. Discontinuity factor is incorporated into the code to reduce homogenization error. This code is used for calculation of effective multiplication factor, neutron flux (both direct and adjoint flux), integral kinetics parameters and subcritical count in presence of external neutron source. The numerical studies reported here for several benchmark problems related to light water reactor as well as fast breeder reactor demonstrate the accuracy of the code.

This paper gives a isomorphic representation of the subtheories RT − , RT − EC, and RT of Asher and Vieu’s first-order ontology of mereotopology RT0. It corrects and extends previous work on the representation of these mereotopologies. We develop the theory of p-ortholattices – lattices that are both orthocomplemented and pseudocomplemented – and show that the identity (x·y) ∗ = x ∗ +y ∗ defines the natural class of Stonian p-ortholattices. Equivalent conditions for a p-ortholattice to be Stonian are given. The main contribution of the paper consists of a representation theorem for RT − as Stonian p-ortholattices. Moreover, it is shown that the class of models of RT − EC is isomorphic to the non-distributive Stonian p-ortholattices and a representation of RT is given by a set of four algebras of which one need to be a subalgebra of the present model. As corollary we obtain that Axiom (A11) – existence of two externally connected regions – is in fact a theorem of the remaining axioms...

Cet article pr~sente une nouvelle mdthode de codage audionum6rique h faible retard et & d~bit rdduit pour des applications ~mergentes en tdldcommunication telles que l'audioconfgrence ou la vidgoconf(rence. Le codeur dgveloppd permet de traiter des signaux g~n&iques (parole, musique, sons d'accompagnement, sons d'ambiance,...) un d~bit de 64 kbit/s avec un retard de codage et d~codage aux environs de 5 ms dans la bande de fr6quence 20-15000 Hz. Ce codeur s'articule sur une d~composition en sous-bandes du signal d'entrde assocMe g~ un codage de la parole de type LD-r L'introduction d' un modkle psychoacoustique permet de d~terminer le d~bit optimal gt allouer g~ chacune des sous-bandes en fonction des caractdristiques propres de l'audition humaine. Pour satisfaire la demande de ddbit requise par le modkle psychoacoustique et pour rdduire la complexit~ algorithmique induite par cette structure de codage, nous avons prdsentd une nouvelle mdthode de quantification vectorielle bas~e sur les rYseaux rdguliers de points. Cette mdthode pennet de quantifier le signal rdsiduel au sein du codeur LO-CELP sans effectuer de recherche trop complexe du meilleur quantificateur. Des tests objectifs et subjectifs ont dt# r~alisds sur des sYquences sonores critiques utilis~es par l'tso. Des tests formels ont montrY que la qualit6 du codeur proposd est comparable aux meilleures implantations de la norme MPEG-I, touche 11, avec l'avantage, pour la solution propos6e, d'avoir un retard de codage et d6codage beaucoup plus faible (5 ms).

The meaning of many k.inds of expressions In programming languages can be tak.en as elements of cerra in spaces of ••partial" objects. In this report these spaces are modeled in one universal domain Pw. the set of all subsets of the integers. This domain renders the connection of Ihis semantic theory with the ordinary theory of number theoretic (especially general recursive) funClIons clear and straightforward.

A detailed understanding of the coupling between fluid and solid mechanics is important for understanding many processes in Earth sciences. Numerical models are a popular means for exploring these processes, but most models do not adequately handle all aspects of this coupling. This paper presents the application of a micromechanically based fluid-solid coupling scheme, lattice-Boltzmann discrete element method (LBDEM), for porous media simulation. The LBDEM approach couples the lattice-Boltzmann method for fluid mechanics and a discrete element method for solid mechanics. At the heart of this coupling is a previously developed boundary condition that has never been applied to coupled fluid-solid mechanics in porous media. Quantitative comparisons of model results to a one-dimensional analytical solution for fluid flow in a slightly deformable medium indicate a good match to the predicted continuum-scale fluid diffusion-like profile. Coupling of the numerical formulation is demonstrated through simulation of porous medium consolidation with the model capturing poroelastic behavior, such as the coupling between applied stress and fluid pressure rise. Finally, the LBDEM model is used to simulate the genesis and propagation of natural hydraulic fractures. The model provides insight into the relationship between fluid flow and propagation of fractures in strongly coupled systems. The LBDEM model captures the dominant dynamics of fluid-solid micromechanics of hydraulic fracturing and classes of problems that involve strongly coupled fluid-solid behavior.

Digital Logic: Logic functions, Minimization, Design and synthesis of combinational and sequential circuits; Number representation and computer arithmetic (fixed and floating point). Computer Organization and Architecture: Machine instructions and addressing modes, ALU and data-path, CPU control design, Memory interface, I/O interface (Interrupt and DMA mode), Instruction pipelining, Cache and main memory, Secondary storage.

In this paper, we study the security of multi-prime RSA whose modulus is N = p1p2 pr for r 3 with small prime difference of size N . In ACISP 2013, Zhang and Takagi showed a Fermat-like factoring attack, which can directly factor N for &lt; 1 r2. We improve this bound to theoretically achieve &lt; 2 r(r+2) by a new factoring attack. Furthermore, we also analyse specific MPRSA with imbalanced prime factors. Experimental results are provided to show the efficiency of our attack.

Lattices are regular arrangements of points in n-dimensional space, whose study appeared in the 19th century in both number theory and crystallography. Since the appearance of the celebrated Lenstra-Lenstra-Lovász lattice basis reduction algorithm twenty years ago, lattices have had surprising applications in cryptology. Until recently, the applications of lattices to cryptology were only negative, as lattices were used to break various cryptographic schemes. Paradoxically, several positive cryptographic applications of lattices have emerged in the past five years: there now exist public-key cryptosystems based on the hardness of lattice problems, and lattices play a crucial rôle in a few security proofs. In this talk, we will try to survey the main examples of the two faces of lattices in cryptology. The full material of this talk appeared in [2]. A preliminary version can be found in [1].