Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure

GVC: efficient random access compression for gene sequence variations

Background: In recent years, advances in high-throughput sequencing technologies have enabled the use of genomic information in many fields, such as precision medicine, oncology, and food quality control. The amount of genomic data being generated is growing rapidly and is expected to soon surpass the amount of video data. The majority of sequencing experiments, such as genome-wide association studies, have the goal of identifying variations in the gene sequence to better understand phenotypic variations. We present a novel approach for compressing gene sequence variations with random access capability: the Genomic Variant Codec (GVC). We use techniques such as binarization, joint row- and column-wise sorting of blocks of variations, as well as the image compression standard JBIG for efficient entropy coding. Results: Our results show that GVC provides the best trade-off between compression and random access compared to the state of the art: it reduces the genotype information size from 758 GiB down to 890 MiB on the publicly available 1000 Genomes Project (phase 3) data, which is 21% less than the state of the art in random-access capable methods. Conclusions: By providing the best results in terms of combined random access and compression, GVC facilitates the efficient storage of large collections of gene sequence variations. In particular, the random access capability of GVC enables seamless remote data access and application integration. The software is open source and available at https://github.com/sXperfect/gvc/

Lymphoadenopathy during Lyme Borreliosis Is Caused by Spirochete Migration-Induced Specific B Cell Activation

Lymphadenopathy is a hallmark of acute infection with Borrelia burgdorferi, a tick-borne spirochete and causative agent of Lyme borreliosis, but the underlying causes and the functional consequences of this lymph node enlargement have not been revealed. The present study demonstrates that extracellular, live spirochetes accumulate in the cortical areas of lymph nodes following infection of mice with either host-adapted, or tick-borne B. burgdorferi and that they, but not inactivated spirochetes, drive the lymphadenopathy. The ensuing lymph node response is characterized by strong, rapid extrafollicular B cell proliferation and differentiation to plasma cells, as assessed by immunohistochemistry, flow cytometry and ELISPOT analysis, while germinal center reactions were not consistently observed. The extrafollicular nature of this B cell response and its strongly IgM-skewed isotype profile bear the hallmarks of a T-independent response. The induced B cell response does appear, however, to be largely antigen-specific. Use of a cocktail of recombinant, in vivo-expressed B. burgdorferi-antigens revealed the robust induction of borrelia-specific antibody-secreting cells by ELISPOT. Furthermore, nearly a quarter of hybridomas generated from regional lymph nodes during acute infection showed reactivity against a small number of recombinant Borrelia-antigens. Finally, neither the quality nor the magnitude of the B cell responses was altered in mice lacking the Toll-like receptor adaptor molecule MyD88. Together, these findings suggest a novel evasion strategy for B. burgdorferi: subversion of the quality of a strongly induced, potentially protective borrelia-specific antibody response via B. burdorferi's accumulation in lymph nodes

On two stronger versions of Dejean's conjecture

Repetition threshold is the smallest number RT(n) such that infinitely many n-ary words contain no repetition of order greater than RT(n). These "extremal" repetition-free words are called threshold words. All values of RT(n) are now known, since the celebrated Dejean's conjecture (1972) was finally settled in 2009. We study two questions about threshold words. First, does the number of n-ary threshold words grow exponentially with length? This is the case for 3 ≤ n ≤ 10, and a folklore conjecture suggests an affirmative answer for all n ≥ 3. Second, are there infinitely many n-ary threshold words containing only finitely many different repetitions of order RT(n)? The answer is "yes" for n = 3, but nothing was previously known about bigger alphabets. For odd n = 7,9,...,101, we prove the strongest possible result in this direction. Namely, there are exponentially many n-ary threshold words containing no repetitions of order RT(n) except for the repeats of just one letter. © 2012 Springer-Verlag

Antibody-Mediated Disease Remission in the Mouse Model of Lyme Borreliosis

In the mouse model of Lyme borreliosis, the host immune response during infection with Borrelia burgdorferi results in the remission of carditis and arthritis, as well as global reduction of spirochete numbers in tissues, without elimination of infection (28). These events were recapitulated by passive transfer of immune serum from infected immunocompetent mice or T-cell-deficient mice to severe combined immunodeficient (SCID) mice. Previous studies have shown that immune serum is reactive against arthritis-related protein (Arp) and that Arp antiserum induces arthritis remission (16). However, although immune serum from T-cell-deficient mice induced disease remission, it was not reactive against Arp, suggesting that antibody to another antigen may be responsible. T-cell-deficient mouse immune serum was reactive to decorin binding protein A (DbpA). Therefore, DbpA antiserum was tested to determine its ability to induce disease remission in SCID mice. Antisera to Arp or DbpA induced both carditis and arthritis remission but did not significantly reduce spirochete numbers in tissues, based upon quantitative flaB DNA analysis, nor did treatment affect RNA levels of several genes, including arp and dbpA. Immunohistochemical labeling of spirochetes in hearts and joints during disease remission induced by adoptive transfer of lymphocytes, passive transfer of immune serum, or passive transfer of DbpA antiserum revealed that such treatment resulted in elimination of spirochetes from heart base and synovium but not vascular walls, tendons, or ligaments. These results suggest that Arp and DbpA antibodies may be active as disease-resolving components in immune serum but antibody against other antigens may be involved in reductions of spirochetes in tissues