It has often been remarked that turbulence is a subject of great scientific and technological importance, and yet one of the least understood (e.g. McComb 1990). To an outsider this may seem strange, since the basic physical laws of fluid mechanics are well established, an excellent mathematical model is available in the Navier-Stokes equations, and the results of well over a century of increasingly sophisticated experiments are at our disposal. One major difficulty, of course, is that the governing equations are nonlinear and little is known about their solutions at high Reynolds number, even in simple geometries. Even mathematical questions as basic as existence and uniqueness are unsettled in three spatial dimensions (cf Temam 1988). A second problem, more important from the physical viewpoint, is that experiments and the available mathematical evidence all indicate that turbulence involves the interaction of many degrees of freedom over broad ranges of spatial and temporal scales. One of the problems of turbulence is to derive this complex picture from the simple laws of mass and momentum balance enshrined in the NavierStokes equations. It was to this that Ruelle & Takens (1971) contributed with their suggestion that turbulence might be a manifestation in physical

/pdf/the-proper-orthogonal-decomposition-in-the-analysis-of-44vs42u998.pdf

The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows

Hexaploid bread wheat (Triticum aestivum L. em. Thell) is one of the world's most important crop plants and displays a very low level of intraspecific polymorphism. We report the development of highly polymorphic microsatellite markers using procedures optimized for the large wheat genome. The isolation of microsatellite-containing clones from hypomethylated regions of the wheat genome increased the proportion of useful markers almost twofold. The majority (80%) of primer sets developed are genome-specific and detect only a single locus in one of the three genomes of bread wheat (A, B, or D). Only 20% of the markers detect more than one locus. A total of 279 loci amplified by 230 primer sets were placed onto a genetic framework map composed of RFLPs previously mapped in the reference population of the International Triticeae Mapping Initiative (ITMI) Opata 85 x W7984. Sixty-five microsatellites were mapped at a LOD >2.5, and 214 microsatellites were assigned to the most likely intervals. Ninety-three loci were mapped to the A genome, 115 to the B genome, and 71 to the D genome. The markers are randomly distributed along the linkage map, with clustering in several centromeric regions.

https://www.genetics.org/content/genetics/149/4/2007.full.pdf

A microsatellite map of wheat.

[1] The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.

/pdf/advanced-spectral-methods-for-climatic-time-series-4hxv68i0r0.pdf

Advanced spectral methods for climatic time series

A software tool was developed for the identification of simple sequence repeats (SSRs) in a barley (Hordeum vulgare L.) EST (expressed sequence tag) database comprising 24,595 sequences. In total, 1,856 SSR-containing sequences were identified. Trimeric SSR repeat motifs appeared to be the most abundant type. A subset of 311 primer pairs flanking SSR loci have been used for screening polymorphisms among six barley cultivars, being parents of three mapping populations. As a result, 76 EST-derived SSR-markers were integrated into a barley genetic consensus map. A correlation between polymorphism and the number of repeats was observed for SSRs built of dimeric up to tetrameric units. 3′-ESTs yielded a higher portion of polymorphic SSRs (64%) than 5′-ESTs did. The estimated PIC (polymorphic information content) value was 0.45 ± 0.03. Approximately 80% of the SSR-markers amplified DNA fragments in Hordeum bulbosum, followed by rye, wheat (both about 60%) and rice (40%). A subset of 38 EST-derived SSR-markers comprising 114 alleles were used to investigate genetic diversity among 54 barley cultivars. In accordance with a previous, RFLP-based, study, spring and winter cultivars, as well as two- and six-rowed barleys, formed separate clades upon PCoA analysis. The results show that: (1) with the software tool developed, EST databases can be efficiently exploited for the development of cDNA-SSRs, (2) EST-derived SSRs are significantly less polymorphic than those derived from genomic regions, (3) a considerable portion of the developed SSRs can be transferred to related species, and (4) compared to RFLP-markers, cDNA-SSRs yield similar patterns of genetic diversity.

Exploiting EST databases for the development and characterization of gene-derived SSR-markers in barley (Hordeum vulgare L.).

A microsatellite consensus map was constructed by joining four independent genetic maps of bread wheat. Three of the maps were F1-derived, doubled-haploid line populations and the fourth population was ‘Synthetic’ × ‘Opata’, an F6-derived, recombinant-inbred line population. Microsatellite markers from different research groups including the Wheat Microsatellite Consortium, GWM, GDM, CFA, CFD, and BARC were used in the mapping. A sufficient number of common loci between genetic maps, ranging from 52 to 232 loci, were mapped on different populations to facilitate joining the maps. Four genetic maps were developed using MapMaker V3.0 and JoinMap V3.0. The software CMap, a comparative map viewer, was used to align the four maps and identify potential errors based on consensus. JoinMap V3.0 was used to calculate marker order and recombination distances based on the consensus of the four maps. A total of 1,235 microsatellite loci were mapped, covering 2,569 cM, giving an average interval distance of 2.2 cM. This consensus map represents the highest-density public microsatellite map of wheat and is accompanied by an allele database showing the parent allele sizes for every marker mapped. This enables users to predict allele sizes in new breeding populations and develop molecular breeding and genomics strategies.

A high-density microsatellite consensus map for bread wheat (Triticum aestivum L.)

The genetic map is a tool to quantify the distance between genes on a chromosome, based on the observed frequency of crossovers during cell division.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1469-1809.1943.tb02321.x

The estimation of map distances from recombination values.

Had DDK followed up on this paper in a more systematic manner, and if attribution had been given more properly, the Karhunen–Loeve theorem may well have been known more widely as the Kosambi–Karhunen–Loeve theorem.

Statistics in Function Space

of long-established principles brought up to date, based upon the actual methods employed as by Ajatasatru's brahmin minister Vassakara against the ancient Licchavis. Though the overwhelming and irresistible Mauryan army could simply flatten out opposition on the field of battle, earlier Magadhan kings had found that circumspection would cost less in men and money. For the rest, nomadic herding tribesmen not in permanent occupation of land, neither engaged in agriculture nor sufficiently well armed to be a military danger, continued to exist. Megasthenes states that these pastoralists were one of the seven major classes of the Indian population in the third century B.C. Some of the Arthasastra methods, including strong drink and poison, were used in the U.S.A. against the 'Redskins' for much the same reasons as in ancient Magadha. 6.3. Administration of the Land The Arthasastra must appear strange and unreal to those who visualise the Indian countryside in its later form. The unit of administration was the janapada, which might now be translated district. The original meaning 'seat of a tribe' no longer applied. Tribal settlers had often merged into a far wider peasantry. The districts did not touch each other, but were separated by considerable forests inhabited solely by food-gathering atavika savages. The forest between villages of the same janapada would supply fuel, timber, hay, game, edible produce, and grazing, but was normally clear of dangerous humans. The frontiers of each janapada were heavily guarded against attack, whether a raid by the savages or foreign invasion. Movements and intentions of the savages would be spied out by special agents, usually disguised as hermits; if too powerful but nevertheless ripe for change to food production, the forest tribes could be subverted by the methods of the last section. These disjointed janapada internal frontiers of the kingdom were as important as the boundaries with other kingdoms till the third century B.C. Trade caravans between janapadas had to pay customs duties at the points of entry and of exit. Every individual crossing the janapada frontier had to produce a duly stamped official pass, to be obtained only for good reasons by paying a heavy fee. The high ministers and boards of local officials belonged to the janapada they administered. Occasionally, a top governor might seem to be a stranger like the Persian Tushaspha under Candragupta Maurya, but a long; line of rapidly Indianised foreigners later held the same post at Girnar, presumably because there was a powerful settlement of Iranians in that area. The administration was duplicated, janapada by janapada. The highest officials held the rank of minister to the king; the officials just below them sat in boards (bahumukhyah, noted by the Greeks). The men destined for top appointments were carefully chosen and examined for intelligence, honesty, courage, loyalty, and weakness in the way of money, women, vices, or ambition, through temptations held out by secret provocateurs. The special qualities and defects of each were docketed. Every official was spied upon for the whole of his career. Spies disguised as men of substance, penitents, or ordinary citizens ascertained public opinion, even helped mould it at need. This was a substitute for the public opinion poll and newspaper editorial campaigns of some modern countries. The lower bureaucracy extended to the registrar of every village or of each block of streets in town. Every such 'guardian' (gopa) had to keep a full record of births, deaths, movements of any person into or out of his registry. Strangers and guests, stray travellers, traders, any sudden access of wealth or suspicious behaviour on the part of any person had at once to be reported and closely watched. There were spies in every traders' caravan. The king was omniscient; nothing was allowed to escape the notice of royal agents. Any news item of interest or importance was conveyed immediately to headquarters by messenger or carrier pigeon and orders passed to the proper official by the same methods. The janapada lands fell into two distinct categories: those paying rashtra taxes; and the sita lands settled as well as farmed directly under crown supervision. The former had developed out of earlier Aryan tribal settlements. They normally had their own small headquarters city to which surrounding farmlands supplied the necessary produce. The administration here was allowed to run along traditional lines provided no practice endangered the power of the emperor. Among these rashtra units were the 'free cities' reported by the Greeks, understanding the words in the sense of Aristotle's 'free states' where oligarchs ruled by sanction of the people. Some, under Mauryan hegemony, issued their own coins with a mint-mark of the central treasury; the wheel-symbol of sovereignty that appeared on royal coins was replaced by tiny human figures, or by a shield and arrows. The rashtra taxes were also based on former tradition, though now FIG. 12. Silver 'Tribal' coins, struck by people who had not an immediate king though under the ultimate suzerainty (in this case) of the second Mauryan emperor Bindusara (who defeated Seleukos Nikator). Such coinage tallies with the existence of Indian 'free cities' mentioned by Megasthenes. gathered by a special minister of the king. Some villages paid a single commutation tax, individual shares being settled by the residents among themselves. The main assessment was the sixth portion of the harvest. A tax "for army rations" represented the tribal contributions that had formerly supported local levies; the bali evolved out of traditional gifts to the king at the tribal yajna some taxes had emerged out of presents to the chief at the birth of a son, convocation of a general assembly, etc. The chief and the (volunteer but practised) tribal army had often disappeared; nevertheless the new state regularly collected every one of the old taxes. The state also levied a tax on orchards and a nominal tax as compensation for supposed damage to crops by herds; a cess was charged for water-works (dams, canals reservoirs) constructed at state expense. Some of these taxes are confirmed by the inscriptions: Asoka freed Lummini village of the bali and reduced the sixth to an eighth of the harvest ('because the Buddha was born here'). The personal gifts, etc., reappeared or continued as baronial prerogatives in feudal times. The situation was entirely different in sita lands. These soon formed so great a proportion of the cultivated area that Greek visitors (who must have gone to Patna along the Ganges and not by the gradually deserted uttarapatha land route) believed all land belonged to the Indian king. The Arthasastra king vigorously promoted the direct settlement of wastelands, whether former clearing that had reverted to jungle or virgin soil cleared for the first time. The settlers might be immigrants from outside the janapada given special inducements to settle, or sudra families deported forcibly from the king's own domains, whether overcrowded town slums or overpopulated villages. We know that some w ere taken and resettled under compulsion from newly conquered lands, for the precise verb (apavah) is used by Asoka to describe the results of his Kalinga campaign. However, these villagers were not slaves, not even serfs, but free settlerswith restrictions on such freedom of action as might cause fiscal losses. The new villages were to be three miles or so apart, with the precise boundaries between villages carefully demarcated, whether all the land was cleared or not. The settlement unit was a village of between 100 and 500 sudra peasant (karshaka) families each, so grouped that villages could protect each other. There were administrative headquarters, presumably with garrisons, for groups of every 10, 200, 400, and 800 villages. It might be that Sisupalgarh was established as a town of the last kind; the details have yet to be checked by comparison against the Arthasastra, but the archaeological date is the third century B.C. The land in each crown village was assigned only for life to the holder. It would not be reassigned if he were the first to clear it and would go to his heirs if properly cultivated. The holding could not be transferred by the assignee without special permission; any failure to cultivate might result in reassignment of the field to someone else. The sita taxes might be remitted when the clearing and settlement was new, or in times of distress. Otherwise, they were much heavier than in the rashtra, the least being a fifth of the harvest, while up to one-third would be charged for lands irrigated by the state. Timber, forest produce, fish, game, and elephants were reserved for the state. The elephant forests were riot cleared; anyone convicted of killing an elephant would be put to death. The elephant was indispensable to the army, not only in battle but for heavy transport, building bridges, and heavy auxiliary duties; in addition, there was the prestige value. Officials, veterinarians and doctors, state messengers and the like could be allotted a holding of sita land for the duration of service; but they had no ownership rights and could not even mortgage the plot. Land under cultivation for a long time was to be directly fanned, if it fell vacant, by the minister of crown lands (for the particular janapada) with hired labour and penal slaves who were thus allowed to work out their sentences or their fines. There was no large-scale slave labour as such; penal slaves, however, could be sold for the prescribed term. Unfarmed lands could also be assigned on half-shares, generally to those who had nothing to supply but their bodily labour. The seed would be deducted and the womenfolk of the assignees subject to work at milling the grain taken by the state as its portion. Apparently the representative of the state arranged even for tools and oxen in such ca

/pdf/the-culture-and-civilisation-of-ancient-india-in-historical-g3w43h2wge.pdf

The culture and civilisation of ancient India in historical outline

An Introduction to the Study of Indian History

After DDK returned to India, he kept up his contacts with well-known European mathematicians such as T. Levi-Civita and E. Cartan, who also communicated his papers to professional journals. This paper appears to have been sent to Elie Cartan prior to publication, and the ensuing correspondence resulted in this paper by Kosambi and a note by Cartan being published back-to-back in Zeitschrift (see the next chapter). Along with a later paper by S.S. Chern in the Bulletin des Sciences Mathematiques, 63, 206–212 (1939) these papers lay the foundations of the Kosambi-Cartan-Chern theory.

D. D. Kosambi

Papers

The estimation of map distances from recombination values.

Statistics in Function Space

The culture and civilisation of ancient India in historical outline

An Introduction to the Study of Indian History

Parallelism and path-spaces