The intersection problem for star designs

We determine those triples (m, II, k) of integers for which there are two m-star designs on the same n-set having exactly k stars in common.

The intersection problem for K_4-e designs

A G-design of order n is a pair (P,B) where P is the vertex set of the complete graph K-n and B is an edge-disjoint decomposition of K-n into copies of the simple graph G. Following design terminology, we call these copies ''blocks''. Here K-4 - e denotes the complete graph K-4 with one edge removed. It is well-known that a K-4 - e design of order n exists if and only if n = 0 or 1 (mod 5), n greater than or equal to 6. The intersection problem here asks for which k is it possible to find two K-4 - e designs (P,B-1) and (P,B-2) of order n, with \B-1 boolean AND B-2\ = k, that is, with precisely k common blocks. Here we completely solve this intersection problem for K-4 - e designs.

The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

Solving a signalized traffic intersection problem with an hyperbolic penalty function

Mathematical Program with Complementarity Constraints (MPCC) finds many applications in fields such as engineering design, economic equilibrium and mathematical programming theory itself. A queueing system model resulting from a single signalized intersection regulated by pre-timed control in traffic network is considered. The model is formulated as an MPCC problem. A MATLAB implementation based on an hyperbolic penalty function is used to solve this practical problem, computing the total average waiting time of the vehicles in all queues and the green split allocation. The problem was codified in AMPL.

Complexité raffinée du problème d'intersection d'automates

Le problème d'intersection d'automates consiste à vérifier si plusieurs automates finis déterministes acceptent un mot en commun. Celui-ci est connu PSPACE-complet (resp. NL-complet) lorsque le nombre d'automates n'est pas borné (resp. borné par une constante). Dans ce mémoire, nous étudions la complexité du problème d'intersection d'automates pour plusieurs types de langages et d'automates tels les langages unaires, les automates à groupe (abélien), les langages commutatifs et les langages finis. Nous considérons plus particulièrement le cas où chacun des automates possède au plus un ou deux états finaux. Ces restrictions permettent d'établir des liens avec certains problèmes algébriques et d'obtenir une classification intéressante de problèmes d'intersection d'automates à l'intérieur de la classe P. Nous terminons notre étude en considérant brièvement le cas où le nombre d'automates est fixé.

Differential geometry of intersection curves in R(4) of three implicit surfaces

We present algorithms for computing the differential geometry properties of intersection Curves of three implicit surfaces in R(4), using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive t, n, b(1), b(2) vectors and curvatures (k(1), k(2), k(3)) for transversal intersections of the intersection problem. (C) 2008 Elsevier B.V. All rights reserved.

A maximal domain of preferences for tops-only rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

Evaluating the Relationship between the Driver and Roadway to Address Rural Intersection Safety using the SHRP 2 Naturalistic Driving Study Data, RB05-013, 2016

Rural intersections account for 30% of crashes in rural areas and 6% of all fatal crashes, representing a significant but poorly understood safety problem. Transportation agencies have traditionally implemented countermeasures to address rural intersection crashes but frequently do not understand the dynamic interaction between the driver and roadway and the driver factors leading to these types of crashes. The Second Strategic Highway Research Program (SHRP 2) conducted a large-scale naturalistic driving study (NDS) using instrumented vehicles. The study has provided a significant amount of on-road driving data for a range of drivers. The present study utilizes the SHRP 2 NDS data as well as SHRP 2 Roadway Information Database (RID) data to observe driver behavior at rural intersections first hand using video, vehicle kinematics, and roadway data to determine how roadway, driver, environmental, and vehicle factors interact to affect driver safety at rural intersections. A model of driver braking behavior was developed using a dataset of vehicle activity traces for several rural stop-controlled intersections. The model was developed using the point at which a driver reacts to the upcoming intersection by initiating braking as its dependent variable, with the driver’s age, type and direction of turning movement, and countermeasure presence as independent variables. Countermeasures such as on-pavement signing and overhead flashing beacons were found to increase the braking point distance, a finding that provides insight into the countermeasures’ effect on safety at rural intersections. The results of this model can lead to better roadway design, more informed selection of traffic control and countermeasures, and targeted information that can inform policy decisions. Additionally, a model of gap acceptance was attempted but was ultimately not developed due to the small size of the dataset. However, a protocol for data reduction for a gap acceptance model was determined. This protocol can be utilized in future studies to develop a gap acceptance model that would provide additional insight into the roadway, vehicle, environmental, and driver factors that play a role in whether a driver accepts or rejects a gap.

Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

Cognitive competence and life course change in multi-problem adolescents

The dissertation reports on two studies. The purpose of Study I was to develop and evaluate a measure of cognitive competence (the Critical Problem Solving Skills Scale – Qualitative Extension) using Relational Data Analysis (RDA) with a multi-ethnic, adolescent sample. My study builds on previous work that has been conducted to provide evidence for the reliability and validity of the RDA framework in evaluating youth development programs (Kurtines et al., 2008). Inter-coder percent agreement among the TOC and TCC coders for each of the category levels was moderate to high, with a range of .76 to .94. The Fleiss' kappa across all category levels was from substantial agreement to almost perfect agreement, with a range of .72 to .91. The correlation between the TOC and the TCC demonstrated medium to high correlation, with a range of r(40)=.68, p<.001 to r(40)=.79, p<.001. Study II reports an investigation of a positive youth development program using an Outcome Mediation Cascade (OMC) evaluation model, an integrated model for evaluating the empirical intersection between intervention and developmental processes. The Changing Lives Program (CLP) is a community supported positive youth development intervention implemented in a practice setting as a selective/indicated program for multi-ethnic, multi-problem at risk youth in urban alternative high schools in the Miami Dade County Public Schools (M-DCPS). The 259 participants for this study were drawn from the CLP's archival data file. The study used a structural equation modeling approach to construct and evaluate the hypothesized model. Findings indicated that the hypothesized model fit the data (χ2 (7) = 5.651, p = .83; RMSEA = .00; CFI = 1.00; WRMR = .319). My study built on previous research using the OMC evaluation model (Eichas, 2010), and the findings are consistent with the hypothesis that in addition to having effects on targeted positive outcomes, PYD interventions are likely to have progressive cascading effects on untargeted problem outcomes that operate through effects on positive outcomes.