Maximum Number Of Points Research Articles

Allowing examinee choice in educational testing

Achievement tests sometimes entertain examinee choice – a situation where an examinee is presented with a set of items among which s/he has to choose one (or few) to answer that will be scored in her/his total test score. Basic assumption is that choice items are equivalent regarding both content and psychometric characteristics and therefore it doesn't matter which particular item examinee selects. Choice items often also share same maximum number of points and examinee score on a test is usually achieved by summing scores from all items taken by the examinee regardless of their combination. Choice items present conceptual problems like why enabling choice when items should be equivalent in the first place and methodological ones like how item scores from different combinations of items should contribute to comparable total score on test. Author used Rasch's model within Item Response Theory framework to test the assumption of equivalence of choice items by scaling all item difficulties on same scale. Physics 2008 and 2009 tests from Slovenian General Matura examination are analyzed as an example to explore equivalence of choice items. Differences in difficulty of choice items in those tests are presented and discussed. It seems that examinee choice still doesn't work in educational testing and should be avoided when possible.

On the maximum number of points at least one unit away from each other in the unit n-cube

We present a very short survey of known results and many new estimates and results on the maximum number of points that can be chosen in the n-dimensional unit cube so that every distance between them is at least 1.

Caps with free pairs of points

We say that two points x, y of a cap C form a free pair of points if any plane containing x and y intersects C in at most three points. For given N and q, we denote by m2+ (N, q) the maximum number of points in a cap of PG(N, q) that contains at least one free pair of points. It is straightforward to prove that m2+ (N, q) ≤ (qN-1 + 2q − 3)/(q − 1), and it is known that this bound is sharp for q = 2 and all N. We use geometric constructions to prove that this bound is sharp for all q when N ≤ 4. We briefly survey the motivation for constructions of caps with free pairs of points which comes from the area of statistical experimental design.

Intersection of ACM-curves in ℙ3

Abstract In this note we address the problem of determining the maximum number of points of intersection of two arithmetically Cohen–Macaulay curves in ℙ3. We give a sharp upper bound for the maximum number of points of intersection of two irreducible arithmetically Cohen–Macaulay curves Ct and Ct–r in ℙ3 defined by the maximal minors of a t × (t + 1), resp. (t – r ) × (t – r + 1), matrix with linear entries, provided Ct–r has no linear series of degree and dimension n ≥ t – r.

Top-k spatial joins

Given two spatial data sets A and B, a top-k spatial join retrieves the k objects from A or B that intersect the largest number of objects from the other data set. Depending on the application requirements, there exist several variations of the problem. For instance, B may be a point data set, and the goal may be to retrieve the regions of A that contain the maximum number of points. The processing of such queries with conventional spatial join algorithms is expensive. However, several improvements are possible based on the fact that we only require a small subset of the result (instead of all intersection/containments pairs). In this paper, we propose output-sensitive algorithms for top-k spatial joins that utilize a variety of optimizations for reducing the overhead.

Optimal projections onto grids and finite resolution images

The problem of determining nice (regular, simple, minimum crossing, and monotonic) and non-degenerate (with distinct x-coordinate, non-collinear, non-cocircular, and non-parallel) orthogonal and perspective images of a set of points or a set of disjoint line segments has been studied extensively in the literature for the theoretical case of infinite resolution images [J. Vis. Commun. Image Represent. 10 (2) (1999) 155; Int. J. Math. Algorithms 2 (2001) 227; J. Vis. Commun. Image Represent. 12 (4) (2001) 387; J. Vis. Commun. Image Represent.]. In this paper we propose to extend the study of this type of problems to the case where the images have finite resolution. Applications dealing with such images are common in practice, in fields such as computer graphics and computer vision. We derive algorithms that solve three related problems, both exactly and approximately. Given a set P in the plane or in the space, find a graduated line, a line partitioned into unit length intervals, so that the maximum number of points of P that are projected into a single interval is minimized. In space we also study the variant where we want to project P onto a graduated plane, a plane partitioned into unit squares.

The cubic curves of PG(2, 3)

We consider the cubic curves of PG(2, 3) and we prove that those containing the maximum number of points of PG(2, 3), irreducible over PG(2, Γ3), are two.

On some singular irreducible cubics of PG(2, 2)

We prove that only one irreducible cubic, either with a node or with a cusp or with an isolated double point, containing the maximum number of points of PG(2, 2) exists.

An appraisal of the quality of referral letters from general dental practitioners to a temporomandibular disorder clinic.

To assess the usefulness of referral letters from general dental practitioners (GDPs) to a clinic seeing referrals related to temporomandibular disorders. A retrospective analysis of all referral letters received by the TMD clinic at Manchester Dental Hospital over a ten-week period. The new patient referral letters to the TMD clinic were examined against suggested criteria of 16 points of information considered to be useful by clinicians working in the clinic. The letters were then assessed using a quality scale based on the level of useful information given in the letter, and using this scale, classified into groups of 'very helpful', 'some help' or 'a little helpful'. Out of the 100 letters analysed, the majority (94) proved to be a 'little helpful' for the TMD clinician; that is to say, the letter included only 0-4 points (out of 16) regarded as important information for the specialist. The maximum number of points of information contained in a letter was nine. No letters were categorised as 'very helpful' for the clinician, and only 6% of the referral letters were considered to provide some help (5-12 points). During the period of the study, in general, referral letters to the TMD clinic concerned contained insufficient information. The introduction of a referral pro forma, produced by the TMD clinic, and guidelines might improve the quality of referrals.

The Maximum Number of Points on a Curve of Genus 4 over is 25

AbstractWe prove that the maximum number of rational points on a smooth, geometrically irreducible genus 4 curve over the field of 8 elements is 25. The body of the paper shows that 27 points is not possible by combining techniques from algebraic geometry with a computer verification. The appendix shows that 26 points is not possible by examining the zeta functions.

On the irreducible cubics containing the maximum number of points of a Fano plane

We prove that two irreducible cubics containing the maximum number of points, that is five, of a Fano plane exist and result to be projectively equivalent.

The Largest Cap in AG (4, 4) and Its Uniqueness

We show that 40 is the maximum number of points of a cap in AG(4, 4). Up to semi-linear transformations there is only one such 40-cap. Its group of automorphisms is a semidirect product of an elementary abelian group of order 16 and the alternating group A5.

Improved Algorithms for Uniform Partitions of Points

We consider the following one- and two-dimensional bucketing problems: Given a set S of n points inR 1 orR 2 and a positive integer b, distribute the points of S into b equal-size buckets so that the maximum number of points in a bucket is minimized. Suppose at most.n=b/C1 points lie in each bucket in an optimal solution. We present algorithms whose time complexities depend on b and1. No prior knowledge of1 is necessary for our algorithms. For the one-dimensional problem, we give a deterministic algorithm that achieves a running time of O.b 4 .1 2 C log n/C n/. For the two-dimensional problem, we present a Monte Carlo algorithm that runs in subquadratic time for small values of b and1. The previous algorithms, by Asano and Tokuyama (1), searched the entire parameterized space and required˜.n 2 / time in the worst case even for constant values of b and1. We also present a subquadratic algorithm for the special case of the two-dimensional problem when bD 2. 1. Introduction. We consider geometric optimization problems that do not seem to have any nice properties like convexity and have a large number of distinct global optimal solutions. Consequently, it is hard to develop a search strategy that will avoid examining all the optimum solutions (or more likely near-optimal solutions). However, if there are few optimal solutions, we may be able to prune the search space. This may lead to more efficient algorithms that are output-sensitive in the sense that the running time of the algorithm depends on the number of optimal solutions. Since we do not know the optimum solution to begin with, we can try to estimate the optima by some means, say, random-sampling, and then use that to prune the search space. The success of such an approach depends on how effectively we estimate the optima. In this paper we consider the problem of partitioning a set of points in R 1 orR 2 into equal-size buckets, so that the maximum number of points in a bucket is minimized. These problems were earlier studied in (1) and (4), and they arise in the construction of optimal hash functions; see the aforementioned references for details.

The number of two-dimensional maxima

Let n points be placed uniformly at random in a subset A of the plane. A point is said to be maximal in the configuration if no other point is larger in both coordinates. We show that, for large n and for many sets A, the number of maximal points is approximately normally distributed. The argument uses Stein's method, and is also applicable in higher dimensions.

The number of two-dimensional maxima

Letnpoints be placed uniformly at random in a subsetAof the plane. A point is said to be maximal in the configuration if no other point is larger in both coordinates. We show that, for largenand for many setsA, the number of maximal points is approximately normally distributed. The argument uses Stein's method, and is also applicable in higher dimensions.

A Fast Algorithm for k -Nearest Neighbor Problem on a Reconfigurable Mesh Computer

Given a set S of m points stored on a reconfigurable mesh computer of size n×n, one point per processing element (PE). In this paper we present a parallel method for solving the k-Nearest Neighbor problem (k-NN). This method permits each point of S to know its k-NN (0<k<m). The corresponding algorithm requires that each PE must have 2k registers where it stores the (x,y) coordinates of its k-NN in a given order. This algorithm has a complexity of O(log h+k2) times, where h is a maximal number of points within a row of the mesh. This complexity is reduced to O(k2) times, using an appropriate procedure which demonstrates the power of the reconfiguration operations carried out by the processors, and the polymorphic properties of the mesh.

Limit Theorems for the Number of Maxima in Random Samples from Planar Regions

We prove that the number of maximal points in a random sample taken uniformly and independently from a convex polygon is asymptotically normal in the sense of convergence in distribution. Many new results for other planar regions are also derived. In particular, precise Poisson approximation results are given for the number of maxima in regions bounded above by a nondecreasing curve.

Size functions of subgeometry-closed classes of representable combinatorial geometries

Let ex q ( G; n) be the maximum number of points in a rank-n geometry (simple matroid) that is representable over GF( q) and that has no restriction isomorphic to the geometry G. We find ex q ( G; n) for several infinite families of geometries G, and we show that if G is a binary affine geometry, then lim n→∞ ex 2(G;n) 2 n−1 =0.

NOTE - A Min-Max Relation for Monotone Path Systems in Simple Regions

-plane which bounds the simple polygonal (closed) region D. Let T and B be two finite, disjoint, equicardinal sets of points of D. We give a min-max relation for the maximum number of points of T and B which can be joined by a MPS in D, and a polytime algorithm for finding such a MPS.

On Maximum-sized k-Regular Matroids

Let k be an integer exceeding one. The class of k-regular matroids is a generalization of the classes of regular and near-regular matroids. A simple rank-r regular matroid has the maximum number of points if and only if it is isomorphic to M(Kr+1), the cycle matroid of the complete graph on r+1 vertices. A simple rank-r near-regular matroid has the maximum number of points if and only if it is isomorphic to the simplification of \(\), that is, the simplification of the matroid obtained, geometrically, by freely adding a point to a 3-point line of M(Kr+2) and then contracting this point. This paper determines the maximum number of points that a simple rank-r k-regular matroid can have and determines all such matroids having this number. With one exception, there is exactly one such matroid. This matroid is isomorphic to the simplification of \(\), that is, the simplification of the matroid obtained, geometrically, by freely adding k independent points to a flat of M(Kr+k+1) isomorphic to M(Kk+2) and then contracting each of these points.