51 research outputs found
Short rainbow cycles for families of matchings and triangles
No full textA generalization of the famous Caccetta–Häggkvist conjecture, suggested by Aharoni, is that any family (Formula presented.) of sets of edges in (Formula presented.), each of size (Formula presented.), has a rainbow cycle of length at most (Formula presented.). In works by the author with Aharoni and by the author with Aharoni, Berger, Chudnovsky, and Zerbib, it was shown that asymptotically this can be improved to (Formula presented.) if all sets are matchings of size 2, or all are triangles. We show that the same is true in the mixed case, that is, if each (Formula presented.) is either a matching of size 2 or a triangle. We also study the case that each (Formula presented.) is a matching of size 2 or a single edge, or each (Formula presented.) is a triangle or a single edge, and in each of these cases we determine the threshold proportion between the types, beyond which the rainbow girth goes from linear to logarithmic
Solving Constraints on the Intermediate Result of Decimal Floating-Point Operations
No full textThe draft revision of the IEEE Standard for Floating-Point Arithmetic (IEEE P754) includes a definition for dec-imal floating-point (FP) in addition to the widely used bi-nary FP specification. The decimal standard raises new concerns with regard to the verification of hardware- and software-based designs. The verification process normally emphasizes intricate cor-ner cases and uncommon events. The decimal format intro-duces several new classes of such events in addition to those characteristic of binary FP. Our work addresses the following problem: Given a dec-imal floating-point operation, a constraint on the interme-diate result, and a constraint on the representation selected for the result, find random inputs for the operation that yield an intermediate result compatible with these specifications. The paper supplies efficient analytic solutions for addi-tion and for some cases of multiplication and division. We provide probabilistic algorithms for the remaining cases. These algorithms prove to be efficient in the actual imple-mentation.
A note on the edge cover number and independence number in hypergraphs
No full textAbstractConsider a hypergraph of rank r>2 with m edges, independence number α and edge cover number ρ. We prove the inequalityρ⩽(r-2)m+αr-1.One application of this inequality is a special case of a conjecture of Aharoni and the first author extending Ryser's Conjecture to matroids
FPgen - A Test Generation Framework for Datapath Floating-Point Verification
No full textFPgen is a new test generation framework targeted toward the verification of the floating-point (FP) datapath, through the generation of test cases. This framework provides the capacity to define virtually any architectural FP coverage model, consisting of verification tasks. The tool supplies strong constraint solving capabilities, allowing the generation of random tests that target these tasks. We present an overview of FPgen's functionality, describe the results of its use for the verification of several FP units, and compare its efficiency with existing test generators. 1
Coloring the intersection of two matroids
No full textA result from Aharoni and the first author of this paper [Trans. Amer. Math. Soc. 358 (2006), pp. 4895-4917] states that for any two positive integers p, q, where p divides q, if a matroid M is p-colorable and a matroid N is q-colorable then M ∩ N is (p + q)-colorable. In this paper we show that the assumption that p divides q is in fact redundant, and we also prove that M ∩ N is even p + q list-colorable. The result uses topology and relies on a new parameter yielding a lower bound for the topological connectivity of the intersection of two matroids
Coloring the intersection of two matroids
No full textA result \cite{matcomp} from 2006 of Aharoni and the first author of this
paper states that for any two natural numbers p, q, where p divides q, if a
matroid M is p-colorable and a matroid N is q-colorable then M \cap N is
(p+q)-colorable. In this paper we show that the assumption that p divides q is
in fact redundant, and we also prove that M \cap N is even p+q list-colorable.
The result uses topology and relies on a new parameter yielding a lower bound
for the topological connectivity of the intersection of two matroids.Comment: 8 page
Hypnotherapy and non-verbal communication
No full textIncludes bibliographical references (pages 35-38)The purpose of this project was to develop a course\ud
in the areas of hypnotherapy and non-verbal communication\ud
for the graduate students in the Counseling and Guidance\ud
Program at California State University, Northridge. It\ud
was developed to acquaint students with these areas that\ud
are useful as tools in individual and family counseling. The reasons for developing such a course were:1) The areas of hypnotherapy and non-verbal??communication\ud
are not given sufficient attention in the Counseling and\ud
Guidance Program, and 2) students expressed an interest in gaining skills in these fields.\ud
The course was taught in a seminar fashion by the\ud
author over a six-week period. Seventeen students\ud
attended. Specific theories and topics were presented\ud
and discussed, along with practical experience in each\ud
area. An extensive course outline was developed for\ud
teaching this information in a three-unit course.\ud
The response of the students to the class was\ud
determined through the use of an evaluation form and\ud
student's personal comments regarding the class.\ud
It was concluded that there is a definite need for\ud
such a course in this program and that students would like\ud
to see such a course offered by the Educational Psychology\ud
Department as a three-unit course
Hypnotherapy and non-verbal communication
No full textThe purpose of this project was to develop a course in the areas of hypnotherapy and non-verbal communication for the graduate students in the Counseling and Guidance Program at California State University, Northridge. It was developed to acquaint students with these areas that are useful as tools in individual and family counseling. The reasons for developing such a course were:1) The areas of hypnotherapy and non-verbal·communication are not given sufficient attention in the Counseling and Guidance Program, and 2) students expressed an interest in gaining skills in these fields. The course was taught in a seminar fashion by the author over a six-week period. Seventeen students attended. Specific theories and topics were presented and discussed, along with practical experience in each area. An extensive course outline was developed for teaching this information in a three-unit course. The response of the students to the class was determined through the use of an evaluation form and student's personal comments regarding the class. It was concluded that there is a definite need for such a course in this program and that students would like to see such a course offered by the Educational Psychology Department as a three-unit course.California State University, Northridge. Department of Education.Includes bibliographical references (pages 35-38
- …
