By Lambert E. Feher, etc., A. Stipsicz

Those lectures introduce a few well known fields in topology. the subjects mentioned are interrelated with glossy physics and comprise works of 4 top researchers. the unique lectures offered on the convention at Budapest are enlarged with appendices to make those notes self-contained.

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The main assumption for studying the evolution is that each two organisms share a common ancestry. The more similar their protein sequences are the more recent was their common ancestor. The likelihood of the event of amino acid i substituted by amino acid j is estimated by using blocks of evolutionarily related protein sequences from various databases. edu/education/courses/introtobio (accessed 8 December 2009) 1-letter 3-letter Protein residue Codons A B C D E F G H I K L M N P Q R S T V W X Y Z ∗ Ala Asp, Asn Cys Asp Glu Phe Gly His Ile Lys Leu Met Asn Pro Gln Arg Ser Thr Val Trp Xaa Tyr Glu, Gln STOP Alanine Asp.

A. 3. 2 Probabilistic Statistics Perspective In classical mathematical statistics, a set of numbers X = {x1 , x2 , . . , xN } is usually considered a random sample from a population defined by probabilistic distribution with density f(x), in which each element xi is sampled independently from the others. This involves an assumption that each observation xi is modeled by the distribution f(xi ) so that the mean’s model is the average of distributions f(xi ). The population analogues to the mean and variance are defined over function f(x) so that the mean, median and the midrange are unbiased estimates of the population mean.

4 The Fuller Projection, or Dymaxion Map, displays spherical data on a flat surface of a polyhedron using a low-distortion transformation. Landmasses are presented with no interruption 24 Fig. 5 A conformal map: the angle between any two lines on the sphere is the same between their projected counterparts on the map; in particular, each parallel crosses meridians at right angles; and also, the sizes at any point are the same in all directions Fig. 6 The Table Lens machine: highlighting a fragment by disproportionally enlarging it (see Card et al.