L\'evy Processes on Quantum Permutation Groups

We describe basic motivations behind quantum or noncommutative probability, introduce quantum L\'evy processes on compact quantum groups, and discuss several aspects of the study of the latter in the example of quantum permutation groups. The first half of this paper is a survey on quantum probability, compact quantum groups, and L\'evy processes on compact quantum groups. In the second half the theory is applied to quantum permutations groups. Explicit examples are constructed and certain classes of such L\'evy processes are classified.Comment: 60 page

One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry

We prove that under a symmetry assumption all cocycles on Hopf *-algebras arise from generating functionals. This extends earlier results of R.Vergnioux and D.Kyed and has two quantum group applications: all quantum L\'evy processes with symmetric generating functionals decompose into a maximal Gaussian and purely non-Gaussian part and the Haagerup property for discrete quantum groups is characterized by the existence of an arbitrary proper cocycle.Comment: 16 pages; v2 corrects a few minor points. The article has been accepted for publication in Mathematische Zeitschrif

Karyotype structure and chromosome fragility in the grass Phleum echinatum Host

Phleum echinatum Host (2n = 2x = 10) is an annual Mediterranean species which differs from other representatives of the genus Phleum by reduced chromosome number, asymmetric karyotype and unusually high amount of DNA in the genome. Chromosomes of this plant were studied using conventional acetic-orcein staining and fluorescence in situ hybridization (FISH). FISH showed the major 35S ribosomal DNA (rDNA) site at the secondary constriction of satellite chromosome (3) and the minor 35S rDNA site near 5S rDNA cluster in the monobrachial chromosome 5. Telomeric repeats were detected at all chromosome ends within secondary constriction in satellited chromosome 3 and at the centromeric regions of chromosomes 1 and 2. Intrachromosomally located telomeric repeats are probably traces of chromosomal rearrangements that have shaped P.echinatum genome; they were prone to breakage which was manifested in chromosome fragmentation. The most distinct telomeric signals, suggesting massive amplification of interstitial telomeric sequences (ITRs), were observed at the nucleolar organizer region (NOR) of the third chromosome pair. Double FISH confirmed co-localization of telomeric and 35S rDNA repeats in this locus characterized by the biggest fragility in the karyotype. Fragile sites of P.echinatum, composed of amplified telomeric repeats, may bear a resemblance to metazoan rare fragile sites enriched in microsatellite repeats

Chromosome numbers in 10 Taraxacum species from Poland

Somatic chromosome numbers are given for the following Taraxacum species: T. pieninicum, 2n=16; T. dentatum, 2n=24; T. fascinans, 2n=24; T. mendax, 2n=40; T. subalpinum, 2n=24; T. telmatophilum, 2n=24; T. cyanolepis, 2n=24; T. fulgidum, 2n=24; T. gentile, 2n=24; and T. undulatum, 2n=24. Chromosome numbers from Poland are published for the first time for T. dentatum, T. fascinans, T. mendax, T. subalpinum, T. telmatophilum, T. cyanolepis, T. fulgidum, T. gentile and T. undulatum

Threshold ECDSA for Decentralized Asset Custody

The surge of interest in decentralization-enabling technologies sparked by the recent success of Bitcoin and other blockchains has led to several new challenges in cryptography and protocol design. One such challenge concerns the widely used digital signature scheme -- ECDSA -- that has in particular been chosen to secure transactions in Bitcoin and several other blockchain systems. To empower decentralized interoperability between such blockchains one would like to implement distributed custody over Bitcoin accounts, which technically can be realized via a threshold ECDSA protocol. Even though several threshold ECDSA protocols already exist, as we argue, due to lack of robustness in signature generation, they are not well suited for deployment scenarios with large committees of parties, out of which a significant fraction might be malicious or prone to DDoS attacks. We propose a new threshold ECDSA protocol that improves upon the state-of-the-art solutions by enabling robustness and fault attributability during signature generation. In addition to that, we improve the signing time and bandwidth of previous solutions by moving expensive operations that are oblivious to the signed message to a separate setup phase. Finally, we back our theoretical results via an empirical evaluation of our protocol in large-scale experiments in LAN and WAN settings

The role of fused thiophene and naphthalene diimide (NDI) in shaping the optical and electrical properties of donor-acceptor polymers

Three polymers with general structure (D-A)n were designed and synthetized to investigate the interaction of strong donors and strong acceptors in polymer chain. They are based on different fused thiophenes (1Th: 4,4′-bis(2-ethylhexyl)-cyclopenta [2,1-b:3,4- ’]dithiophene; 2Th: 4,8-bis [(2-ethylhexyl)oxy]benzo [1,2-b:4,5-b']dithiophene; 3Th: 4,8-bis(4-fluoro-5-(2-ethylhexyl)-thiophen-2-yl)benzo [1,2-b:4,5-b']bisthiophene) and N,N′-bis(2-thylhexyl)-1,8:4,5-naphthalenetetracarboxdiimide (NDI). Fused benzo- and cyclopenta-thiophene derivatives were selected because they are known for their strong electron-donating properties. NDI was coupled with them in polymer chain because it is one of the best known electron withdrawing units. Such combination of donor and acceptor units is one of the strategies for obtaining low band gap conjugated polymers with semiconducting properties for many applications. The interaction of donors and acceptors is a key factor determining the properties of such polymers. The electrochemical and spectroscopic measurement were supported by DFT calculations. Moreover, organic field effect transistors (OFET) were fabricated to demonstrate the feasibility of using the newly developed materials in electronic devices

Karyotype and nuclear DNA content of hexa-, octo-, and duodecaploid lines of Bromus subgen. Ceratochloa

The subgenus Ceratochloa of the genus Bromus includes a number of closely related allopolyploid forms or species that present a difficult taxonomic problem. The present work combines data concerning chromosome length, heterochromatin distribution and nuclear genome size of different 6x, 8x and 12x accessions in this subgenus. Special attention is paid to the karyotype structure and genomic constitution of duodecaploid plants recently found in South America. Hexaploid lineages possess six almost indistinguishable genomes and a nuclear DNA content between 12.72 pg and 15.10 pg (mean 1Cx value = 2.32 pg), whereas octoploid lineages contain the same six genomes (AABBCC) plus two that are characterized by longer chromosomes and a greater DNA content (1Cx = 4.47 pg). Two duodecaploid accessions found in South America resemble each other and apparently differ from the North American duodecaploid B. arizonicus as regards chromosome size and nuclear DNA content (40.00 and 40.50 pg vs. 27.59 pg). These observations suggest that the South American duodecaploids represent a separate evolutionary lineage of the B. subgenus Ceratochloa, unrecognized heretofore

Chromosome landmarks and autosome-sex chromosome translocations in Rumex hastatulus, a plant with XX/XY1Y2 sex chromosome system

Rumex hastatulus is the North American endemic dioecious plant with heteromorphic sex chromosomes. It is differentiated into two chromosomal races: Texas (T) race characterised by a simple XX/XY sex chromosome system and North Carolina (NC) race with a polymorphic XX/XY1Y2 sex chromosome system. The gross karyotype morphology in NC race resembles the derived type, but chromosomal changes that occurred during its evolution are poorly understood. Our C-banding/DAPI and fluorescence in situ hybridization (FISH) experiments demonstrated that Y chromosomes of both races are enriched in DAPI-positive sequences and that the emergence of polymorphic sex chromosome system was accompanied by the break of ancestral Y chromosome and switch in the localization of 5S rDNA, from autosomes to sex chromosomes (X and Y2). Two contrasting domains were detected within North Carolina Y chromosomes: the older, highly heterochromatinised, inherited from the original Y chromosome and the younger, euchromatic, representing translocated autosomal material. The flow-cytometric DNA estimation showed ∼3.5 % genome downsizing in the North Carolina race. Our results are in contradiction to earlier reports on the lack of heterochromatin within Y chromosomes of this species and enable unambiguous identification of autosomes involved in the autosome-heterosome translocation, providing useful chromosome landmarks for further studies on the karyotype and sex chromosome differentiation in this species