Set Of Intersections Research Articles

Probabilistic quorums for dynamic systems

A quorum system is a set of sets such that every two sets in the quorum system intersect. Quorum systems are well known building blocks for maintaining information in a distributed system while providing high availability and good load balance. Probabilistic Quorum Systems (PQS) are variants of quorum systems that relax the strict intersection requirement. They are particularly attractive for large scale systems due to their simplicity and highly efficient availability--load balance tradeoff. We introduce scalable techniques that maintain a PQS in a highly decentralized and highly dynamic setting. We address two challenges. First we show how PQS can be realized efficiently even when each process maintains knowledge of only a constant number of other members. Second, we provide algorithms that adaptively evolve the quorums to adjust to the changes in the system caused by processes leaving and joining the system over time.

Static analysis based on formal models and incremental computation in Go programming

Computer-Go programs have high computational costs for static analysis, even though most intersections of the board remain unchanged by one move. Therefore, incremental computation as well as theoretical models are essential features for static analysis. This paper describes some formal models for static analysis, and explores how incremental computation is applied to the static analysis in Go programs. The static analysis in this paper includes (1) recognizing blocks and groups of stones and evaluating their properties, (2) determining the life and death of a group by numerical features, (3) finding the numbers of regions enclosed by the groups based on Euler's formula, and (4) analysing capturing races ( semeai) and sekis based on an abstract description called the semeai graph. Several operations on the sets of intersections on the board are used for defining the notions on Go boards as well as for describing the analysis methods.

Intersective sets and Diophantine approximation

Intersective sets and Diophantine approximation

On random perturbation of some intersective sets

Given a subset S of Z and a sequence I = (I n) n=1 ∞ of intervals of increasing length contained in Z, let b ( S , I ) = lim sup ⁡ | I n | → ∞ | S ∩ I n | | I n | and let b(S) = sup I b(S, I), where the supremum is taken over all sequences I = (I n) n=1 ∞ of increasing length contained in Z. We call b(S) the Banach density of S. We will say that a sequence of natural numbers k = (κ n) n=1 ∞ is multiply intersective, if given any subset E of the natural numbers of positive Banach density, there exists another subset R of Z with lim ⁡ N → ∞ | R ∩ [ 1 , N ] | N existing and not less than b(E), such that for each finite subset { n 1, , n r} of R we have b ( E ∩ ( E + k n 1 ) ∩ ... ∩ ( E + k n r ) ) > 0. Let #x003B8; = (θ n) n=1 ∞ be a suitable sequence of N-valued independent, idemically distributed random variables. In this paper we show that if (κ n) n=1 ∞ is multiply intersective, then so is (k n + θ n) n=1 ∞ for almost all θ = (θ n) n=1 ∞

Directed self-organized critical patterns emerging from fractional Brownian paths

We discuss a family of clusters C corresponding to the region whose boundary is formed by a fractional Brownian path y( i) and by the moving average function y n(i)≡ 1 n ∑ k=0 n−1y(i−k) . Our model generates fractal directed patterns showing spatio-temporal complexity, and we demonstrate that the cluster area, length and duration exhibit the characteristic scaling behavior of SOC clusters. The function C n ( i) acts as a magnifying lens, zooming in (or out) the ‘avalanches’ formed by the cluster construction rule, where the magnifying power of the zoom is set by the value of the amplitude window n. On the basis of the construction rule of the clusters C n(i)≡y(i)− y n(i) and of the relationship among the exponents, we hypothesize that our model might be considered to be a generalized stochastic directed model, including the Dhar–Ramaswamy (DR) model and the stochastic models as particular cases. As in the DR model, the growth and annihilation of our clusters are obtained from the set of intersections of two random walk paths, and we argue that our model is a variant of the directed self-organized criticality scheme of the DR model.

Anomalous dispersion of electromagnetic eigenwaves in a sandwich structure with a gap

A system of two different isotropic dielectric plates aligned parallel to each other and separated by a gap is considered. For a sufficiently large gap, electromagnetic eigenwaves in the plates are virtually independent and dispersion curves for the studied system are characterized by an infinite set of intersections. A decrease in the gap thickness leads to coupling between the wave fields and the disappearance of the intersection points due to divergence of the dispersion curves. Each of the dispersion curves of the spectrum transformed under the action of coupling is formed by a set of adjacent portions of initially independent branches corresponding to different plates. A gradual change in the frequency along one of the new dispersion curves results in a periodic displacement of the localization zone of the wave field from one plate to the other.

Set Systems and Dissimilarities

Different one–one correspondences exist between classes of indexed clustering structures (such as indexed hierarchies) and classes of dissimilarities (such as ultrametrics). Following the line developed in previous works (i.e., Johnson (1967), Diday (1984, 1986), Bertrand and Diday (1991), Batbedat (1988), Bandelt and Dress (1994)), we associate each pseudo-dissimilarityδ defined on a finite set E with the set system of all maximal linked subsets of E. This provides a one–one correspondence that maps the set of pseudo-dissimilarities onto the collection of all the valued set systems (S, f) that satisfy two conditions. One of these conditions was introduced by Batbedat (1988) and is related to the characterization of 2-conformity in hypergraphs (see also Bandelt and Dress (1994)). We introduce the other condition which requires the index f to be a weak index. Our approach includes a characterization of the valued set systems (S, f) such that S contains (respectively is contained in) the set of all finite nonempty intersections of maximal linked subsets with respect to the pseudo-dissimilarity induced by the pair (S, f).

The Committed Word: Literature and Public Values

During past century, literary education, often divorced from rhetoric, has grown increasingly distant from practice of language in statecraft, law, religion, and ethics. Yet literature and rhetoric retain open, independent powers to enhance what Emerson calls the conduct of life. In these provocative essays, James Engell argues that a more complete literary training can foster a heightened sense of shared social experience, an awareness of diverse views, a love of language, and a more powerful ability to express values we enshrine or debate. Revealing a set of deep intersections among literature, politics, rhetoric, and public deliberation of values, he explores how dedicated individuals of different callings resort to heightened language in order to secure knowledge, test beliefs, consider policy, and promote action. Through profiles of Lincoln, Burke, Swift, Hume, Lowth, Vico, and others, Engell explores political and ethical involvement of writers with their culture in order to reestablish links between literary qualities of language and means by which we challenge power and secure liberty. He presents a cogent argument for a different, expanded kind of literary education, suggesting that training in rhetoric, now often misunderstood or neglected, can serve common good without becoming mired in partisan squabbles or academic pedantry. Despite dominance of visual media in our society, observes Engell, difficult problems we face must be resolved through language. By presenting writers who use resourceful language to engage political contests and cultural issues, he contributes to ongoing debates in education, politics, and culture without subscribing to easy labels of left and right or traditional versus innovative. He demonstrates imaginative ways to apply time-tested literary techniques to a changing world, making use of past yet in a way that past could not predict. This passionately argued book calls for a shift in ways we teach and regard literature.

Distributed and cooperative fuzzy controllers for traffic intersections group

This paper presents a fuzzy traffic controller for a set of intersections and its simulation results. The controller of an intersection controls its own traffic and cooperates with its neighbors. It gets information from its traffic detectors and its neighbors. Using this information, the fuzzy rule base system gives optimal signals. It manages phase sequences and phase lengths adaptively to its neighbors' as well as its own traffic conditions. To carry out the performance evaluation of the controller, a simulator for intersection groups has been developed. The proposed method is compared with the vehicle actuated method which is one of the typical conventional methods. The average delay time of a vehicle is used as a performance index. The simulation results show good performance in the case of time-varying traffic patterns and heavy traffic conditions.

Etale cohomology of toric varieties defined by infinite fans

Toric varieties are a special class of normal rational varieties defined by means of a combinatorial object called a fan. The fan defining the variety gives a designated open cover and a dictionary describing how the open sets in the cover intersect. When all the open sets in the designated cover and their intersections have trivial cohomology, the cohomology of the whole variety is determined by the fan. In this article we calculate the low degree cohomology on the Zariski and Etale sites of toric varieties over an algebraically closed field of characteristic = 0. These computations extend (with different proofs) most of the results in DeMeyer et al., (1993) where the fan was assumed to be finite. As a result, we show any countable direct product of finite cyclic groups is isomorphic to the cohomological Brauer group of some toric variety. All the definitions and basic facts about toric varieties which we use can be found in Oda (1988).

Quadric shell intersections

The paper considers intersections of natural quadric shells (surfaces with thickness). A natural quadric shell can be thought of as a solid defined by a natural quadric surface and its offset (which is again a quadric). Thus, the intersection of quadric shells is essentially the same as the set of intersections of quadric surfaces and their offsets. An approach is presented to obtain the intersection of any two offset surfaces (of the initial quadrics) in terms of the offset distances. For the intersection of any two shells (which contain the initial quadrics as one of their surfaces), the intersection curve can be obtained directly by substituting the appropriate shell thickness (offset distances) in the general solution.

A construction of some [ n, k, d; q]-codes meeting the Griesmer bound

Let [ n, k, d; q]-code denote a q-ary linear code, with length n, dimension k and minimum distance d. Griesmer's bound is well known as a lower bound on n for given integers k, d and q. Linear codes meeting the Griesmer bound are called optimal linear codes. This paper is a survey on the construction of optimal linear codes. Some relations among optimal linear codes, linear programming, maxhypers and minihypers are investigated. Maxhypers and minihypers are very useful in obtaining and characterizing optimal linear codes. Furthermore, we present many optimal linear codes which are constructed using these relations and l intersectional empty sets.

Offset‐dependent mis‐tie analysis at seismic line intersections

Offset‐dependent line‐intersection displays can be of significant direct interpretive value. On our data set from a proprietary location, use of these displays permits a refined structural interpretation and improves the usefulness of amplitude and amplitude‐versus‐offset displays for direct hydrocarbon detection. The degree of data reproducibility at each intersection may be exposed as a function of offset through the use of prestack and partial‐range stack splice and difference displays. At a set of marine line intersections, after only cursory processing, the range of residual amplitudes found by subtracting strike traces from dip traces is from −20 dB to +6 dB relative to the input. The average is about −8 dB. The poorest line intersection ties occur below the edges of deep bright spots, where velocity anomalies leading to time mis‐ties greater than 10 ms can occur. Shallow near‐surface velocity anomalies, out‐of‐plane arrivals including fault plane reflections, and, occasionally, water reverberation variations contribute locally to the data mis‐ties. Location errors are ubiquitous but of secondary importance, and random noise is more than 20 dB down. A simple and inexpensive routine splice display of line intersection data can be of significant value for quality control, for processing evaluation, and for interpretation. Issues of data reliability, such as screening of amplitude‐versus‐offset (AVO) anomalies by shallow gas and transmission‐path problems for large CMP offsets, as well as other problems in operational and research geophysics, may be addressed by analysis of line intersections in the offset domain.

Ruzsa’s problem on sets of recurrence

The main purpose of this paper is to prove the existence of Poincare sequences of integers which are not van der Corput sets. This problem was considered in I. Ruzsa’s expository article [R1] (1982–83) on correlative and intersective sets. Thus the existence is shown of a positive non-continuous measureμ on the circle which Fourier transform vanishes on a set of recurrence, i.e.S={n ∈Z;\(\hat \mu \)(n)=0} is a set of recurrence but not a van der Corput set. The method is constructive and involves some combinatorial considerations. In fact, we prove that the generic density condition for both properties are the same.

On measures of intersectivity

A set A of positive integers is called (difference) intersective, if A N ( B B ) # 0 whenever B has positive upper density. Here instead of upper density we might equally naturally write lower or asymptotic density; we are going to show that these definitions lead to the same concept, even quantitatively. This is used to show that intersectivity is a "finitary" property. We also show that the situation becomes more complicated if we intend to distinguish between intersective sets, or if we consider sums rather than differences. A denser set than the previously known ones will also be constructed whose differences do not contain any prime-minus-one (this is known to be intersective).

The local structure of a chaotic attractor in four dimensions

A simple system of four ordinary differential equations exhibiting chaotic behavior is introduced. The Lyapunov exponents are approximately 3.34, 0.00, -1.79, and -5.55. Points on the attractor where two variables simultaneously assume prechosen values are located by a numerical integration procedure in which suitable antecedent conditions are obtained by successive approximations. The points are organized into curves, which appear more numerous under higher resolution. A backward integration procedure indicates that a line transverse to the curves intersects each curve rather than passing through gaps, while the set of intersections forms a Cantor set. Thus the attractor appears to be locally the product of three continua and one Cantor set. The continua are found to extend in the expanding, neutral, and less rapidly contracting local directions, while the Cantor set extends in the more rapidly contracting direction.

Arrangements defined by unitary reflection groups

Let V be a complex vector space of dimension I. An arrangement in V is a finite set d of hyperplanes, all containing the origin. Let L = L ( d ) be the set of intersections of elements of ~r Partially order L by reverse inclusion so that L has V as its minimal element and d as its set of atoms. The poset L is a finite geometric lattice with rank function r(X)= dim V/X, XE L. Without loss of generality we assume that N H ~ , H =0 is the maximal element of L and thus L has rank I. The characteristic polynomial z(L, t) of L is defined by

Minkowski-Ebenen mit Spiegelungen

The miquelian Minkowski-planes can be characterized by cycle-reflections. More exactly: If is a non degenerate quadric of index 2 in a 3-dimensional pappian projective space, and if is the set of plane intersections of , which don't contain a line of (the elements of are called cycles), then the incidence-structure is a miquelian Minkowski-plane. In these hold:

Hyperplans poissoniens et compacts de Steiner

A compact convex set in RN is Steiner if it is a finite Minkowski sum of line segments, or a limit of such finite sums, and then satisfies an extension of the Steiner formula. With each Poisson hyperplane stationary process A is uniquely associated a Steiner set M, and for any linear variety V, the Steiner set associated with is the projection of M on V. The density of the order k network Ak (i.e., the set of the intersections of k hyperplanes belonging to A) is linked with simple geometrical properties of M. In the isotropic case, the expression of the covariance measures associated with Ak is derived and compared with the analogous results obtained for (N — k)-dimensional Poisson flats.

Performance of a switching policy applied to a set of intersections

Performance of a switching policy applied to a set of intersections