Polynomial matrices, representations, and linear system theory

Frequency domain analogies, polynomial matrices, and linear system

Nonlinear software sensor for monitoring genetic regulation processes with noise and modeling errors

Nonlinear control techniques by means of a software sensor that are commonly used in chemical engineering could be also applied to genetic regulation processes. We provide here a realistic formulation of this procedure by introducing an additive white Gaussian noise, which is usually found in experimental data. Besides, we include model errors, meaning that we assume we do not know the nonlinear regulation function of the process. In order to illustrate this procedure, we employ the Goodwin dynamics of the concentrations [B.C. Goodwin, Temporal Oscillations in Cells, (Academic Press, New York, 1963)] in the simple form recently applied to single gene systems and some operon cases [H. De Jong, J. Comp. Biol. 9, 67 (2002)], which involves the dynamics of the mRNA, given protein, and metabolite concentrations. Further, we present results for a three gene case in co-regulated sets of transcription units as they occur in prokaryotes. However, instead of considering their full dynamics, we use only the data of the metabolites and a designed software sensor. We also show, more generally, that it is possible to rebuild the complete set of nonmeasured concentrations despite the uncertainties in the regulation function or, even more, in the case of not knowing the mRNA dynamics. In addition, the rebuilding of concentrations is not affected by the perturbation due to the additive white Gaussian noise and also we managed to filter the noisy output of the biological systemComment: 21 pages, 7 figures; also selected in vjbio of August 2005; this version corrects a misorder in the last three references of the published versio

Geometric and algebraic properties of minimal bases of singular systems

For a general singular system with an associated pencil T(S), a complete classification of the right polynomial vector pairs x(s), u(s)), connected with the N{script}r{T(S)}, rational vector space, is given according to the proper-nonproper property, characterising the relationship of the degrees of those two vectors. An integral part of the classification of right pairs is the development of the notions of canonical and normal minimal bases for N{script}r{T(S)} and N{script}r{R(S)} rational vector spaces, where R(s) is the state restriction pencil of Se[E, A, B]. It is shown that the notions of canonical and normal minimal bases are equivalent; the first notion characterises the pure algebraic aspect of the classification, whereas the second is intimately connected to the real geometry properties and the underlying generation mechanism of the proper and nonproper state vectors x(s). The results describe the algebraic and geometric dimensions of the invariant partitioning of the set of reachability indices of singular systems. The classification of all proper and nonproper polynomial vectors x(s) induces a corresponding classification for the reachability spaces to proper-nonproper and results related to the possible dimensions feedback-spectra assignment properties of them are also given. The classification of minimal bases introduces new feedback invariants for singular systems, based on the real geometry of polynomial minimal bases, and provides an extension of the standard theory for proper systems (Warren, M.E., & Eckenberg, A.E. (1975)

Building Babies - Chapter 16

In contrast to birds, male mammals rarely help to raise the offspring. Of all mammals, only among rodents, carnivores, and primates, males are sometimes intensively engaged in providing infant care (Kleiman and Malcolm 1981). Male caretaking of infants has long been recognized in nonhuman primates (Itani 1959). Given that infant care behavior can have a positive effect on the infant’s development, growth, well-being, or survival, why are male mammals not more frequently involved in “building babies”? We begin the chapter defining a few relevant terms and introducing the theory and hypotheses that have historically addressed the evolution of paternal care. We then review empirical findings on male care among primate taxa, before focusing, in the final section, on our own work on paternal care in South American owl monkeys (Aotus spp.). We conclude the chapter with some suggestions for future studies.Deutsche Forschungsgemeinschaft (HU 1746/2-1) Wenner-Gren Foundation, the L.S.B. Leakey Foundation, the National Geographic Society, the National Science Foundation (BCS-0621020), the University of Pennsylvania Research Foundation, the Zoological Society of San Dieg

The evolution of pair-living, sexual monogamy, and cooperative infant care: Insights from research on wild owl monkeys, titis, sakis, and tamarins

“Monogamy” and pair bonding have long been of interest to anthropologists and primatologists. Their study contributes to our knowledge of human evolutionary biology and social evolution without the cultural trappings associated with studying human societies directly. Here, we first provide an overview of theoretical considerations, followed by an evaluation of recent comparative studies of the evolution of “social monogamy”; we are left with serious doubts about the conclusions of these studies that stem from the often poor quality of the data used and an overreliance on secondary sources without vetting the data therein. We then describe our field research program on four “monogamous” platyrrhines (owl monkeys, titis, sakis, and tamarins), evaluate how well our data support various hypotheses proposed to explain “monogamy,” and compare our data to those reported on the same genera in comparative studies. Overall, we found a distressing lack of agreement between the data used in comparative studies and data from the literature for the taxa that we work with. In the final section, we propose areas of research that deserve more attention. We stress the need for more high‐quality natural history data, and we urge researchers to be cautious about the uncritical use of variables of uncertain internal validity. Overall, it is imperative that biological anthropologists establish and follow clear criteria for comparing and combining results from published studies and that researchers, reviewers, and editors alike comply with these standards to improve the transparency, reproducibility, and interpretability of causal inferences made in comparative studies.Division of Behavioral and Cognitive Sciences; National Institute of Child Health and Human Development; National Institutes of Agin