The VMPC function is a combination of triple permutation composition and integer addition. It differs from a simple triple permutation composition with one integer addition operation performed on some of the elements of the permutation. The consequence of this addition operation is corruption of cycle structure of the transformed permutation the fundamental source of the function's resistance t...

IL-23 and IL-12 are heterodimeric cytokines which share the p40 subunit, but which have unique second subunits, IL-23p19 and IL-12p35. Since p40 is required for the development of the Th1 type response necessary for resistance to Toxoplasma gondii, studies were performed to assess the role of IL-23 in resistance to this pathogen. Increased levels of IL-23 were detected in mice infected with T. ...

In this paper we define a variant of the Ising model in which spins are replaced with permutations. The energy between two is function relative disorder one spin, permutation, to other. This motivated by complexity measure for declarative systems. For such systems state permutation and sorting measures average sequential neighbouring states. To use symmetrized version descent statistic that has...

An elusive permutation group is a transitive permutation group with no fixed point free elements of prime orders. In this paper we proved that each minimal normal subgroup of an elusive permutation group with squarefree degree is abelian. As an almost immediate consequence, it follows that there are no elusive permutation groups of degree 2pq where p, q are distinct odd primes.

We consider the relation between various permutation statistics and properties of permutation tableaux. We answer some of the open problems of Steingŕımsson and Williams [8], in particular, on the distribution of the bistatistic of numbers of rows and essential ones in permutation tableaux. We also consider and enumerate sets of permutation tableaux related to some pattern restrictions on permu...

Psoriasis is a chronic, immune-mediated disease affecting more than 100 million people worldwide and up to 2.2% of the UK population. The aetiology of psoriasis is thought to originate from an interplay of genetic, environmental, infectious and lifestyle factors. The manner in which genetic and environmental factors interact to contribute to the molecular disease mechanisms has remained elusive...