Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

In this lecture we will develop a construction of locally decodable codes developed in three papers by Yekhanin, Raghavendra, and Eframenko respectively (and chronologically). Yekhanin constructed a family of binary locally decodable codes with a 3-query decoding algorithm based on Mersenne primes. Raghavendra simplified Yekhanin’s construction and extended the ideas beyond binary alphabets. Th...

BACKGROUND Medical physics is a relatively small community but it spans great geographical distances, usually with a scarcity of experts whose expertise could greatly benefit students entering into the field. In addition there are many software systems for which an interactive education method would be most advantageous. OBJECTIVE To develop a process to optimally use the Internet for real-ti...

Excited-state conversions were observed from a series of twisted pyrene-substituted tridurylboranes, corresponding to a locally excited (LE) state, a more planar charge transfer (CT) state with a higher fluorescence quantum efficiency, and a more twisted CT state.

We study an approximate version of q-query LDCs (Locally Decodable Codes) over the real numbers and prove lower bounds on the encoding length of such codes. A q-query (α, δ)approximate LDC is a set V of n points in R so that, for each i ∈ [d] there are Ω(δn) disjoint q-tuples (u1, . . . ,uq) in V so that span(u1, . . . ,uq) contains a unit vector whose i’th coordinate is at least α. We prove ex...

Data from the Birmingham Histopathology Data Pool of surgical pathology on the age, sex, and site distributions of various cutaneous and hepatic lesions have been analysed, and the results have been compared with data from the Regional Cancer Registry. Analysis of malignant neoplasms shows that there is no significant difference between the two sources. The results are discussed with reference ...

We study the relation between locally testable and locally decodable codes. Locally testable codes (LTCs) are error-correcting codes for which membership of a given word in the code can be tested probabilistically by examining it in very few locations. Locally decodable codes (LDCs) allow to recover each message entry with high probability by reading only a few entries of a slightly corrupted c...

The Ottawa Regional Cancer Centre offers an Oncology Rehabilitation Program to patients with cancer. Between January 1997 and December 1998, 254 patients with cancer participated in the program. This paper describes the program and its participants. The program's strengths, limitations and future directions are also discussed.

Let m,n > 1 be integers and Pn,m be the point set of the projective (n − 1)-space (defined by [2]) over the ring Zmof integers modulo m. Let An,m = (auv) be the matrix with rows and columns being labeled by Pn,m, where auv = 1 if the inner product 〈u, v〉 = 0 and auv = 0 otherwise. Let Bn,m = An,mA t n,m. The eigenvalues of Bn,m have been studied by [1, 2, 3], where their applications in the stu...