Relative Entropy in Biological Systems

In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe the dynamics of a population or probability distribution. Under suitable assumptions, the distribution will approach an equilibrium with the passage of time. Relative entropy - that is, the Kullback--Leibler divergence, or various generalizations of this - provides a quantitative measure of how far from equilibrium the system is. We explain various theorems that give conditions under which relative entropy is nonincreasing. In biochemical applications these results can be seen as versions of the Second Law of Thermodynamics, stating that free energy can never increase with the passage of time. In ecological applications, they make precise the notion that a population gains information from its environment as it approaches equilibrium.Comment: 20 page

Network Models

Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of networks. We show that each network model gives rise to an operad, whose operations are ways of assembling a network of the given kind from smaller parts. Such operads, and their algebras, can serve as tools for designing networks. Technically, a network model is a lax symmetric monoidal functor from the free symmetric monoidal category on some set to $\mathbf{Cat}$, and the construction of the corresponding operad proceeds via a symmetric monoidal version of the Grothendieck construction.Comment: 46 page

On the changing shape of the Australian mortality curve

Over the course of the twentieth century, mortality rates in Australia have shown substantial improvements at all ages. The improvements which have taken place at different ages, however, have not occurred at a uniform pace, and as a result, the shapes of the national mortality curves have varied over time. The most noticeable change for males has been the development of an ‘accident hump’ in the late teens and early twenties mid-century, the growth of this ‘hump’ in the 1960s and 1970s, and its sudden disappearance, or transformation into a ‘bulge’, in the late 1980s. This paper examines the reasons for the disappearance of the male ‘accident hump’, and the changes in mortality by cause which have occurred over the decade to 1992 and influenced the level and shape of the whole mortality curve both for males and for females. Extrapolating the trends observed for the various cause-specific mortality rates obtains projected life tables for Australian males and females in the year 2002

Some Methods Of Improving Attendance In The Negro Public Schools Of Bowie County

According to statistics of the United States Office of Education, in each 100 pupils enrolled in the elementary and secondary school, approximately 15 are absent daily} that is, the percentage of average daily attendance is approximately 85\u3e and the percentage of non-attendance is approximately 15. Without the combined efforts of parents, teachers, and other members of the community, it is agreed among educators that irregular attendance will continue to grow. Changing state aid from a population to attendance basis causes schools to pay more attention to slow and problem pupils, said Sturgeon, who is on leave as superintendent of New Boston Schools. These often were discouraged from coming to school. Now a child is worth 90^ to the school every day he comes to class, said Sturgeon. Principals no longer jump for joy when the problem child quits school. They\u27re trying to help them along. Prior to the enactment of the Gilmer-Aiken laws in Texas, emphasis was placed on census enumeration, as census enumeration was the basis for the allocation of money and teachers in the public schools of Texas. Since the enactment of the Gilmer-Aiken laws, more emphasis is being placed on attendance, as attendance is being used as the chief basis for allocation of money and teachers in the public schools of Texas

A study of marine exploitation in prehistoric Scotland, with special reference to marine shells and their archaeological contexts

The history of the study of marine exploitation in Scotland is outlined prior to the presentation of an overview of the evidence for its practice in both earlier and later prehistory. This overview is based on a corpus of Scottish prehistoric sites known to include evidence for marine exploitation. Marine shells are found on a variety of archaeological sites, many of which cannot be described as shell middens. They are defined in this work as sites given over to the primary processing and consumption of marine resources, most obviously represented by marine shells. A simple classificatory system is introduced in order to allow further discussion of the similarities and differences between various types of deposits. The material culture related to marine exploitation is discussed and ethnohistorical sources are used to demonstrate some of the ways in which similar elements of material culture have been utilised in more recent times. Issues discussed here include not only shellfish exploitation but also whaling, fishing and the use of seaweeds. The utilisation of various kinds of raw materials, of both terrestrial and marine origin, are discussed and their contextual relationship to marine resource residues considered. Discussion will then move on to focus more closely on a number of aspects relating to marine exploitation in both early and later prehistory. The 'Obanian' sites in Oban and Oronsay are used as a case study to examine the implications of shell middens being used over long periods of time and as places for burial. The results of survey and excavation work carried out on the 'Obanian' shell midden on Risga are used to supplement a discussion on the nature and role of shell middens. Discussion of the later period is centred upon a contextual study of settlement sites and the relationship between marine and terrestrial resources is discussed. This work draws to a close by considering the role of marine resources in prehistoric ritual practice. The implications of the deposition of marine shells in chambered tombs and the construction of chambered tombs over shell middens are discussed. In the later period the redeposition of midden material appears to play an important part in the development of substantial settlement complexes and may represent a change in the nature of ritual behaviour. The concluding chapter isolates what are felt to be the most important issues raised by this work