The smallest sets of points not determined by their X-rays

Let $F$ be an $n$-point set in $\mathbb{K}^d$ with $\mathbb{K}\in\{\mathbb{R},\mathbb{Z}\}$ and $d\geq 2$. A (discrete) X-ray of $F$ in direction $s$ gives the number of points of $F$ on each line parallel to $s$. We define $\psi_{\mathbb{K}^d}(m)$ as the minimum number $n$ for which there exist $m$ directions $s_1,...,s_m$ (pairwise linearly independent and spanning $\mathbb{R}^d$) such that two $n$-point sets in $\mathbb{K}^d$ exist that have the same X-rays in these directions. The bound $\psi_{\mathbb{Z}^d}(m)\leq 2^{m-1}$ has been observed many times in the literature. In this note we show $\psi_{\mathbb{K}^d}(m)=O(m^{d+1+\varepsilon})$ for $\varepsilon>0$. For the cases $\mathbb{K}^d=\mathbb{Z}^d$ and $\mathbb{K}^d=\mathbb{R}^d$, $d>2$, this represents the first upper bound on $\psi_{\mathbb{K}^d}(m)$ that is polynomial in $m$. As a corollary we derive bounds on the sizes of solutions to both the classical and two-dimensional Prouhet-Tarry-Escott problem. Additionally, we establish lower bounds on $\psi_{\mathbb{K}^d}$ that enable us to prove a strengthened version of R\'enyi's theorem for points in $\mathbb{Z}^2$

Mariner 9 data storage subsystem flight performance summary

The performance is summarized of the Mariner 9 Data Storage Subsystem (DSS) throughout the primary and extended missions. Information presented is limited to reporting of anomalies which occurred during the playback sequences. Tables and figures describe the anomalies (dropouts, missing and added bits, in the imaging data) as a function of time (accumulated tape passes). The data results indicate that the performance of the DSS was satisfactory and within specification throughout the mission. The data presented is taken from the Spacecraft Team Incident/Surprise Anomaly Log recorded during the mission. Pertinent statistics concerning the tape transport performance are given. Also presented is a brief description of DSS operation, particularly that related to the recorded anomalies. This covers the video data encoding and how it is interpreted/decoded by ground data processing and the functional operation of the DSS in abnormal conditions such as loss of lock to the playback signal

Systems development methods and usability in Norway: An industrial perspective

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2007 Springer Berlin HeidelbergThis paper investigates the relationship between traditional systems development methodologies and usability, through a survey of 78 Norwegian IT companies. Building on previous research we proposed two hypotheses; (1) that software companies will generally pay lip service to usability, but do not prioritize it in industrial projects, and (2) that systems development methods and usability are perceived as not being integrated. We find support for both hypotheses. Thus, the use of systems development methods is fairly stable, confirming earlier research. Most companies do not use a formal method, and of those who do, the majority use their own method. Generally, the use of methods is rather pragmatic: Companies that do not use formal methods report that they use elements from such methods. Further, companies that use their own method import elements from standardised methods into their own

Combining Cognitive and Noncognitive Assessments to Predict First Year GPA and Persistence in Community College Students

Standard assessments of cognitive ability have been the preferred method of assessing the probability of student achievement at community colleges, but there is a growing trend in the use of noncognitive factors to assess student potential. Factors related to a student’s race/ethnicity and family income have been shown to be correlated with placement tests scores and high school grades. There is a gap in the literature about the use of noncognitive measures in conjunction with standardized placement tests to predict the achievement and persistence of community college students. The purpose of this study was to examine the strength of cognitive and noncognitive measures of placement to predict the achievement and persistence. The researcher used hierarchical linear regression analyses with Sedlacek’s Non-Cognitive Questionnaire (NCQ), SAT or multiple measures, and demographic data as independent variables and first semester GPA and persistence to second year as dependent variables. Data were further analyzed for descriptive statistics, collinearity and normal distribution. Noncognitive factors knowledge acquired in a field and realistic self-appraisal were positive correlated with GPA across race/ethnicity. Work hours were negatively correlated with academic success, as was placement at the lowest level through multiple measures due to low high school GPA. Results differed in some ways from previous literature, finding self-reported leadership experience negatively correlated with student persistence. It is recommended that institutional leaders promote practices and services such as flexible schedules, financial support structures, and proficiency-based pedagogy

CONVEX-BODIES, ECONOMIC CAP COVERINGS, RANDOM POLYTOPES

Let K be a convex compact body with nonempty interior in the d-dimensional Euclidean space Rd and let x1, …, xn be random points in K, independently and uniformly distributed. Define Kn = conv {x1, …, xn}. Our main concern in this paper will be the behaviour of the deviation of vol Kn from vol K as a function of n, more precisely, the expectation of the random variable vol (K\Kn). We denote this expectation by E (K, n)

The vertices of the knapsack polytope

AbstractThe number of vertices of a polytope associated to the Knapsack integer programming problem is shown to be small. An algorithm for finding these vertices is discussed

Almost ellipsoidal sections and projections of convex bodies

In (1) Dvoretsky proved, using very ingenious methods, that every centrally symmetric convex body of sufficiently high dimension contains a central k-dimensional section which is almost spherical. Here we shall extend this result (Corollary to Theorem 2) to k-dimensional sections through an arbitrary interior point of any convex bod