Randomness and degrees of irregularity.

The fundamental question "Are sequential data random?" arises in myriad contexts, often with severe data length constraints. Furthermore, there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness--e.g., to evaluate the efficacy of therapy in medicine. We address both these issues from a computable framework via a quantification of regularity. ApEn (approximate entropy), defining maximal randomness for sequences of arbitrary length, indicating the applicability to sequences as short as N = 5 points. An infinite sequence formulation of randomness is introduced that retains the operational (and computable) features of the finite case. In the infinite sequence setting, we indicate how the "foundational" definition of independence in probability theory, and the definition of normality in number theory, reduce to limit theorems without rates of convergence, from which we utilize ApEn to address rates of convergence (of a deficit from maximal randomness), refining the aforementioned concepts in a computationally essential manner. Representative applications among many are indicated to assess (i) random number generation output; (ii) well-shuffled arrangements; and (iii) (the quality of) bootstrap replicates.

Targeting Gβγ signaling in arterial vascular smooth muscle proliferation: A novel strategy to limit restenosis

Restenosis continues to be a major problem limiting the effectiveness of revascularization procedures. To date, the roles of heterotrimeric G proteins in the triggering of pathological vascular smooth muscle (VSM) cell proliferation have not been elucidated. βγ subunits of heterotrimeric G proteins (Gβγ) are known to activate mitogen-activated protein (MAP) kinases after stimulation of certain G protein-coupled receptors; however, their relevance in VSM mitogenesis in vitro or in vivo is not known. Using adenoviral-mediated transfer of a transgene encoding a peptide inhibitor of Gβγ signaling (βARKct), we evaluated the role of Gβγ in MAP kinase activation and proliferation in response to several mitogens, including serum, in cultured rat VSM cells. Our results include the striking finding that serum-induced proliferation of VSM cells in vitro is mediated largely via Gβγ. Furthermore, we studied the effects of in vivo adenoviral-mediated βARKct gene transfer on VSM intimal hyperplasia in a rat carotid artery restenosis model. Our in vivo results demonstrated that the presence of the βARKct in injured rat carotid arteries significantly reduced VSM intimal hyperplasia by 70%. Thus, Gβγ plays a critical role in physiological VSM proliferation, and targeted Gβγ inhibition represents a novel approach for the treatment of pathological conditions such as restenosis.

Interleaved concatenated codes: New perspectives on approaching the Shannon limit

The last few years have witnessed a significant decrease in the gap between the Shannon channel capacity limit and what is practically achievable. Progress has resulted from novel extensions of previously known coding techniques involving interleaved concatenated codes. A considerable body of simulation results is now available, supported by an important but limited theoretical basis. This paper presents a computational technique which further ties simulation results to the known theory and reveals a considerable reduction in the complexity required to approach the Shannon limit.

Minimum size limit for useful locomotion by free-swimming microbes

Formulas are derived for the effect of size on a free-swimming microbe’s ability to follow chemical, light, or temperature stimuli or to disperse in random directions. The four main assumptions are as follows: (i) the organisms can be modeled as spheres, (ii) the power available to the organism for swimming is proportional to its volume, (iii) the noise in measuring a signal limits determination of the direction of a stimulus, and (iv) the time available to determine stimulus direction or to swim a straight path is limited by rotational diffusion caused by Brownian motion. In all cases, it is found that there is a sharp size limit below which locomotion has no apparent benefit. This size limit is estimated to most probably be about 0.6 μm diameter and is relatively insensitive to assumed values of the other parameters. A review of existing descriptions of free-floating bacteria reveals that the smallest of 97 motile genera has a mean length of 0.8 μm, whereas 18 of 94 nonmotile genera are smaller. Similar calculations have led to the conclusion that a minimum size also exists for use of pheromones in mate location, although this size limit is about three orders of magnitude larger. In both cases, the application of well-established physical laws and biological generalities has demonstrated that a common feature of animal behavior is of no use to small free-swimming organisms.

A Single Limit Dextrinase Gene Is Expressed Both in the Developing Endosperm and in Germinated Grains of Barley1

The single gene encoding limit dextrinase (pullulan 6-glucanohydrolase; EC 3.2.1.41) in barley (Hordeum vulgare) has 26 introns that range in size from 93 to 822 base pairs. The mature polypeptide encoded by the gene has 884 amino acid residues and a calculated molecular mass of 97,417 D. Limit dextrinase mRNA is abundant in gibberellic acid-treated aleurone layers and in germinated grain. Gibberellic acid response elements were found in the promoter region of the gene. These observations suggest that the enzyme participates in starch hydrolysis during endosperm mobilization in germinated grain. The mRNA encoding the enzyme is present at lower levels in the developing endosperm of immature grain, a location consistent with a role for limit dextrinase in starch synthesis. Enzyme activity was also detected in developing grain. The limit dextrinase has a presequence typical of transit peptides that target nascent polypeptides to amyloplasts, but this would not be expected to direct secretion of the mature enzyme from aleurone cells in germinated grain. It remains to be discovered how the enzyme is released from the aleurone and whether another enzyme, possibly of the isoamylase group, might be equally important for starch hydrolysis in germinated grain.

Glutamate antagonists limit tumor growth

Neuronal progenitors and tumor cells possess propensity to proliferate and to migrate. Glutamate regulates proliferation and migration of neurons during development, but it is not known whether it influences proliferation and migration of tumor cells. We demonstrate that glutamate antagonists inhibit proliferation of human tumor cells. Colon adenocarcinoma, astrocytoma, and breast and lung carcinoma cells were most sensitive to the antiproliferative effect of the N-methyl-d-aspartate antagonist dizocilpine, whereas breast and lung carcinoma, colon adenocarcinoma, and neuroblastoma cells responded most favorably to the α-amino-3-hydroxy-5-methyl-4-isoxazole-propionate antagonist GYKI52466. The antiproliferative effect of glutamate antagonists was Ca2+ dependent and resulted from decreased cell division and increased cell death. Morphological alterations induced by glutamate antagonists in tumor cells consisted of reduced membrane ruffling and pseudopodial protrusions. Furthermore, glutamate antagonists decreased motility and invasive growth of tumor cells. These findings suggest anticancer potential of glutamate antagonists.

The growth of demand will limit output growth for food over the next quarter century

The rate of growth of world food demand will be much slower for 1990–2010 than it was for the prior three decades. The major factor determining the increase in food demand is population growth. Income growth has a much smaller effect. From 1960 to 1990, population growth accounted for approximately three fourths of the growth in demand or use of grain. For 1990–2010, it is anticipated that population growth will account for nearly all of the increase in world demand for grain. The rate of population growth from 1990 to 2020 is projected to be at an annual rate of 1.3% compared with 1.9% for 1960 to 1990—a decline of more than 30%. World per capita use of grain will increase very little—perhaps by 4%. The increase in grain use is projected to be 40% less than in 1960–1990. It is anticipated that real grain prices will decline during the period, although not nearly as much as the 40% decline in the previous three decades. Concern has been expressed concerning the deterioration of the quality and productivity of the world’s farmland. A study for China and Indonesia indicates that there has been no significant change in the productive capacity of the land over the past 50 years. Contrary to numerous claims, the depth of the topsoil has not changed, indicating that erosion has had little or no impact.

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.

Binding site size limit of the 2:1 pyrrole-imidazole polyamide-DNA motif.

Polyamides containing N-methylimidazole (Im) and N-methylpyrrole (Py) amino acids can be combined in antiparallel side-by-side dimeric complexes for sequence-specific recognition in the minor groove of DNA. Six polyamides containing three to eight rings bind DNA sites 5-10 bp in length, respectively. Quantitative DNase I footprint titration experiments demonstrate that affinity maximizes and is similar at ring sizes of five, six, and seven. Sequence specificity decreases as the length of the polyamides increases beyond five rings. These results provide useful guidelines for the design of new polyamides that bind longer DNA sites with enhanced affinity and specificity.