Nothing in Biology makes sense without the flavour of Mathematics

The elements of mathematical language are on the whole precise and unambigous. In the history of science, one can see that the development of any branch of science begins from the largely descriptive, goes on to become explanatory at the qualitative level, and finally becomes explanatory at the quantitative level. With the application of mathematical principles, physics made the transition from a qualitative to a quantitative science about 3 to 4 centuries ago; biology is making the transition now. Mathematical biology is today a fast growing, well recognized, albeit not clearly defined subject. To my mind, it is the most exciting modern application of mathematics

Variational Sequential Monte Carlo

Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. In this paper we present a new approximating family of distributions, the variational sequential Monte Carlo (VSMC) family, and show how to optimize it in variational inference. VSMC melds variational inference (VI) and sequential Monte Carlo (SMC), providing practitioners with flexible, accurate, and powerful Bayesian inference. The VSMC family is a variational family that can approximate the posterior arbitrarily well, while still allowing for efficient optimization of its parameters. We demonstrate its utility on state space models, stochastic volatility models for financial data, and deep Markov models of brain neural circuits

Multifaceted approach to evaluate the relationship among closely related forms of Drosophila

Drosophila is a suitable system to study different facets of population differentiation. Drosophila sulfurigaster, Drosophila bilimbata, Drosophila albostrigata, Drosophila neonasuta and Drosophila pulaua are morphologically indistinguishable members of the orbital sheen complex of the nasuta subgroup of Drosophila. They are distributed in different parts of south east Asia. The evolutionary inter-relationship between these closely related forms will be discussed with reference to karyotypes, heterochromatin, satellite DNA, population fitness, ecogenetic divergence and isozyme variations

Karyology of a few species of South Indian acridids. II. Male germ line karyotypic instability in Gastrimargus

Gastrimargus africanus orientalis, an acridid grasshopper has revealed the existence of karyotypic mosaicism in the male germ line cells of a few individuals with 2n=23, 19, 21, 25 and 27 chromosomes. Details of this chromosomal instability are presented in this paper

Teaching and learning genetics withDrosophila. 4. Pattern of inheritance of characters when there is interaction of genes or linkage of genes

This article does not have an abstract

Teaching and learning genetics with Drosophila. 2. Mutant phenotypes of Drosophila melanogaster

The first part of this series [1] looked at why the fruitfly Drosophila is such an excellent eukaryotic model system for genetic studies. Of the many important attributes of this fly, which have earned it the title 'Cinderella of Genetics', the availability of innumerable number of mutant genetic stocks of D. melanogaster is an extremely useful and important one. These different mutants are of immense help to study various aspects of inheritance, as we shall see in this and subsequent articles

OSTEOARTHRITIC SUBCHONDRAL BONE MARROW HISTOLOGY. LESSONS FROM CHANGES IN ALKAPTONURIA

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Control dependence for extended finite state machines

Though there has been nearly three decades of work on program slicing, there has been comparatively little work on slicing for state machines. One of the primary challenges that currently presents a barrier to wider application of state machine slicing is the problem of determining control dependence. We survey existing related definitions, introducing a new definition that subsumes one and extends another. We illustrate that by using this new definition our slices respect Weiser slicing’s termination behaviour. We prove results that clarify the relationships between our definition and older ones, following this up with examples to motivate the need for these differences

Patterns of replication in the neo-sex chromosomes of Drosophila nasuta albomicans

Drosophila nasuta albomicans (with 2n=6), contains a pair of metacentric neo-sex chromosomes. Phylogenetically these are products of centric fusion between ancestral sex (X, Y) chromosomes and an autosome (chromosome 3). The polytene chromosome complement of males with a neo-X- and neo-Y-chromosomes has revealed asynchrony in replication between the two arms of the neo-sex chromosomes. The arm which represents the ancestral X-chromosome is faster replicating than the arm which represents ancestral autosome. The latter arm of the neo-sex chromosome is synchronous with other autosomes of the complement. We conclude that one arm of the neo-X/Y is still mimicking the features of an autosome while the other arm has the features of a classical X/Y-chromosome. This X-autosome translocation differs from the other evolutionary X-autosome translocations known in certain species of Drosophila

Incipient sexual isolation in the nasuta-albomicans complex of Drosophila: mating preference in male-, female- and multiple-choice mating experiments

Interracial divergence is an important facet of speciation. The nasuta-albomicans complex of Drosophila with sixteen morphologically identical, karyotypically different but cross-fertile races is an excellent system to study a few dimensions of raciation. Drosophila nasuta nasuta, Drosophila nasuta albomicans, Cytorace 1, Cytorace 2, Cytorace 3 and Cytorace 4 of this subgroup have been subjected to male-, female- and multiple-choice mating experiments. Out of 8456 crosses conducted, 7185 had successful matings. The overall impression is that mating is far from random amongst these six closely related races of the nasuta-albomicans complex. The males of D. n. albomicans, Cytorace 1 and Cytorace 4 in male-choice, the females of Cytorace 1 and Cytorace 2 in female-choice, and the males and females of D. n. nasuta, D. n. albomicans, Cytorace 1 and Cytorace 4 against the males and females of Cytorace 2 in multiple-choice experiments, had significantly more homogamic matings than expected. Thus in this study of evolutionary experimentation on raciation under laboratory conditions, we have documented the initiation of preference for con-specific matings among closely related and independently evolving members of the nasuta-albomicans complex of Drosophila