A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency

This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave) when composed in parallel. The algebra of rely/guarantee concurrency then becomes an instantiation of the more abstract algebra. Many of the core properties needed for rely/guarantee reasoning can be shown to hold in the abstract algebra where their proofs are simpler and hence allow a higher degree of automation. The algebra has been encoded in Isabelle/HOL to provide a basis for tool support for program verification. In rely/guarantee concurrency, programs are specified to guarantee certain behaviours until assumptions about the behaviour of their environment are violated. When assumptions are violated, program behaviour is unconstrained (aborting), and guarantees need no longer hold. To support these guarantees a second synchronous operator, weak conjunction, was introduced: both processes in a weak conjunction must agree to take each atomic step, unless one aborts in which case the whole aborts. In developing the laws for parallel and weak conjunction we found many properties were shared by the operators and that the proofs of many laws were essentially the same. This insight led to the idea of generalising synchronisation to an abstract operator with only the axioms that are shared by the parallel and weak conjunction operator, so that those two operators can be viewed as instantiations of the abstract synchronisation operator. The main differences between parallel and weak conjunction are how they combine individual atomic steps; that is left open in the axioms for the abstract operator.Comment: Extended version of a Formal Methods 2016 paper, "An algebra of synchronous atomic steps

pairwise alignments of mtDNAs of domestic animals

pairwise alignments of mtDNAs of domestic animal

Mitochondrial DNA sequence variation in Iranian native dogs

<p>The dog mtDNA diversity picture from wide geographical sampling but from a small number of individuals per region or breed, displayed little geographical correlation and high degree of haplotype sharing between very distant breeds. For a clear picture, we extensively surveyed Iranian native dogs (<i>n</i> = 305) in comparison with published European (<i>n</i> = 443) and Southwest Asian (<i>n</i> = 195) dogs. Twelve haplotypes related to haplogroups A, B and C were shared by Iranian, European, Southwest Asian and East Asian dogs. In Iran, haplotype and nucleotide diversities were highest in east, southeast and northwest populations while western population had the least. Sarabi and Saluki dog populations can be assigned into haplogroups A, B, C and D; Qahderijani and Kurdi to haplogroups A, B and C, Torkaman to haplogroups A, B and D while Sangsari and Fendo into haplogroups A and B, respectively. Evaluation of population differentiation using pairwise <i>F</i>_ST generally revealed no clear population structure in most Iranian dog populations. The genetic signal of a recent demographic expansion was detected in East and Southeast populations. Further, in accordance with previous studies on dog-wolf hybridization for haplogroup d2 origin, the highest number of d2 haplotypes in Iranian dog as compared to other areas of Mediterranean basin suggests Iran as the probable center of its origin. Historical evidence showed that Silk Road linked Iran to countries in South East Asia and other parts of the world, which might have probably influenced effective gene flow within Iran and these regions. The medium nucleotide diversity observed in Iranian dog calls for utilization of appropriate management techniques in increasing effective population size.</p

Median-joining networks of eight Y-STRs within NRY haplogroups R-M17 and R-M124.

<p>Sizes of the circles are proportional to haplotypes frequencies. The lengths of the lines are proportional to the number of mutational steps.</p

NRY and mtDNA haplogroup profiles for the Chams and the Kinhs.

<p>For mtDNA haplogroups, M* includes M17, M20, M21d, M22, M33c, M50, M51, M71, M72, M73, and M77; N* includes N21 and N23; R* includes R22 and R23 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036437#pone.0036437-Peng1" target="_blank">[10]</a>.</p

PCA plot based on NRY haplogroup frequencies of 45 populations in southern China and Southeast Asia.

<p>PCA plot based on NRY haplogroup frequencies of 45 populations in southern China and Southeast Asia.</p

Classification tree of 26 NRY haplogroups along with their frequencies (%) in four populations.

<p>Haplogroup defining markers are given along the branches; corresponding markers genotyped in Karafet et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036437#pone.0036437-Karafet1" target="_blank">[27]</a> are noted in brackets. The names of haplogroups are shown to the right of the branches using the mutation-based nomenclature of the Karafet et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036437#pone.0036437-Karafet2" target="_blank">[35]</a>.</p

General information for 57 populations in southern China and Southeast Asia.

<p>Note:</p>¶<p>genomic DNA was extracted and purified at the laboratory of the Immunophysiopathology Department, Hanoi Medical University;</p>§<p>requests for the data access could be directed to the authors;</p>†<p>Timor was excluded in PCA and MDS analyses because of fewer sample size;</p>*<p>populations were genotyped with the lower Y-SNPs resolution, and were not considered in PCA.</p

MDS plot of 53 populations with <i>R</i>_ST genetic distances based on eight common Y-STRs.

<p>For population information, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036437#pone-0036437-t001" target="_blank">Table 1</a>. Because of severe genetic drift <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036437#pone.0036437-Karafet1" target="_blank">[27]</a>, populations Taiwan, Nias, and Mentawai that were resolved as the outliers in the initial analyses and were excluded.</p

Admixture analysis of the two populations from southern Vietnam.

<p>Note:</p>¶<p>admixture coefficient;</p>†<p>bootstrap average and standard deviation of the admixture coefficient were obtained by bootstrap with 1000 replications.</p