On the existence and implications of an inverse folding code in proteins.

The existence of a code relating the set of possible sequences at a given position in a protein backbone to the local structure at that location is investigated. It is shown that only 73% of 4-C alpha structure fragments in a sample of 114 protein structures exhibit a preference for a particular set of sequences. The remaining structures can accommodate essentially any sequence. The structures that encode specific sequence distributions include the classical "secondary" structures, with the notable exception of planar (beta) bends. It is suggested that this has implications as to the mechanism of folding in proteins with extensive sheet/barrel structure. The possible role of structures that do not encode specific sequences as mutation hot spots is noted.

Discourses upon the existence and attributes of God.

Mode of access: Internet.

Discourses upon the existence and attributes of God /

Includes index.

Discourses upon the existence and attributes of God /

Includes index.

Natural theology: or, Evidences of the existence and attributes of the Deity, collected from the appearances of nature.

Part 2 has title: Illustrations of Paley's natural theology, with descriptive letter press. By James Paxton ... Boston, Hilliard, Gray Little, and Wilkins, 1830.

Natural theology : or, Evidences of the existence and attributes of the Deity, collected from the appearances of nature /

Mode of access: Internet.

Natural theology, or Evidences of the existence and attributes of the Deity, collected from the appearances of nature.

Mode of access: Internet.

Natural theology: or, Evidences of the existence and attributes of the Deity, collected from the appearances of nature.

Dedication dated July, 1802.

Natural theology: or, Evidences of the existence and attributes of the Deity, collected from the appearances of nature.

Preface signed: J. W. [i.e. John Ware]

Letters to the Rev. William E. Channing, D.D., on the existence and agency of fallen spirits.

Mode of access: Internet.

Natural theology: or, Evidences of the existence and attributes of the Deity,

Mode of access: Internet.

Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.

On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.