Newton’s Unfinished Business: Uncovering the Hidden Powers of Eleven in Pascal’s Triangle

Sir Isaac Newton once observed that the first five rows of Pascal’s Triangle, when concatenated, yield the corresponding powers of eleven. He claimed without proof that subsequent rows also generate powers of eleven. Was he correct? While not all rows can simply be concatenated, the powers of eleven can still be easily derived from each. We have uncovered an algorithm the supports Newton’s claim and will prove its validity for all rows of the Triangle

Newton’s Unfinished Business: Uncovering the Hidden Powers of Eleven in Pascal’s Triangle

Sir Isaac Newton once observed that the first five rows of Pascal’s Triangle, when concatenated, yield the corresponding powers of eleven. He claimed without proof that subsequent rows also generate powers of eleven. Was he correct? While not all rows can simply be concatenated, the powers of eleven can still be easily derived from each. We have uncovered an algorithm the supports Newton’s claim and will prove its validity for all rows of the Triangle

Genetic Variants of Ehrlichia phagocytophila1, Rhode Island and Connecticut

Primers were used to amplify a 561-bp region of the 16S rRNA gene of Ehrlichia phagocytophila from Ixodes scapularis ticks and small mammals collected in Rhode Island and Connecticut. DNA sequences for all 50 E. phagocytophila-positive samples collected from 1996 through 1998 in southwestern Connecticut were identical to the sequence reported for E. phagocytophila DNA from confirmed human cases. In contrast, the sequences from 92 of 123 E. phagocytophila-positive Rhode Island samples collected from 1996 through 1999 included several variants differing by 1-2 nucleotides from that in the agent infecting humans. While 11.9% of 67 E. phagocytophila-positive ticks collected during 1997 in Rhode Island harbored ehrlichiae with sequences identical to that of the human agent, 79.1% had a variant sequence not previously described. The low incidence of human ehrlichiosis in Rhode Island may in part result from interference by these variant ehrlichiae with maintenance and transmission of the true agent of human disease

Division of the genus Chryseobacterium: Observation of discontinuities in amino acid identity values, a possible consequence of major extinction events, guides transfer of nine species to the genus Epilithonimonas, eleven species to the genus Kaistella, and three species to the genus Halpernia gen. nov., with description of Kaistella daneshvariae sp. nov. and Epilithonimonas vandammei sp. nov. derived from clinical specimens

International audienceThe genus Chryseobacterium in the family Weeksellaceae is known to be polyphyletic. Amino acid identity (AAI) values were calculated from whole-genome sequences of species of the genus Chryseobacterium, and their distribution was found to be multi-modal. These naturally-occurring non-continuities were leveraged to standardise genus assignment of these species. We speculate that this multi-modal distribution is a consequence of loss of biodiversity during major extinction events, leading to the concept that a bacterial genus corresponds to a set of species that diversified since the Permian extinction. Transfer of nine species ( Chryseobacterium arachidiradicis , Chryseobacterium bovis, Chryseobacterium caeni, Chryseobacterium hispanicum, Chryseobacterium hominis, Chryseobacterium hungaricum,, Chryseobacterium pallidum and Chryseobacterium zeae ) to the genus Epilithonimonas and eleven ( Chryseobacterium anthropi , Chryseobacterium antarcticum , Chryseobacterium carnis , Chryseobacterium chaponense , Chryseobacterium haifense, Chryseobacterium jeonii, Chryseobacterium montanum , Chryseobacterium palustre , Chryseobacterium solincola , Chryseobacterium treverense and Chryseobacterium yonginense ) to the genus Kaistella is proposed. Two novel species are described: Kaistella daneshvariae sp. nov. and Epilithonimonas vandammei sp. nov. Evidence is presented to support the assignment of Planobacterium taklimakanense to a genus apart from Chryseobacterium, to which Planobacterium salipaludis comb nov. also belongs. The novel genus Halpernia is proposed, to contain the type species Halpernia frigidisoli comb. nov., along with Halpernia humi comb. nov., and Halpernia marina comb. nov

Community-based control of the brown dog tick in a region with high rates of Rocky Mountain spotted fever, 2012-2013.

Rocky Mountain spotted fever (RMSF) transmitted by the brown dog tick (Rhipicephalus sanguineus sensu lato) has emerged as a significant public health risk on American Indian reservations in eastern Arizona. During 2003-2012, more than 250 RMSF cases and 19 deaths were documented among Arizona's American Indian population. The high case fatality rate makes community-level interventions aimed at rapid and sustained reduction of ticks urgent. Beginning in 2012, a two year pilot integrated tick prevention campaign called the RMSF Rodeo was launched in a ∼ 600-home tribal community with high rates of RMSF. During year one, long-acting tick collars were placed on all dogs in the community, environmental acaricides were applied to yards monthly, and animal care practices such as spay and neuter and proper tethering procedures were encouraged. Tick levels, indicated by visible inspection of dogs, tick traps and homeowner reports were used to monitor tick presence and evaluate the efficacy of interventions throughout the project. By the end of year one, <1% of dogs in the RMSF Rodeo community had visible tick infestations five months after the project was started, compared to 64% of dogs in Non-Rodeo communities, and environmental tick levels were reduced below detectable levels. The second year of the project focused on use of the long-acting collar alone and achieved sustained tick control with fewer than 3% of dogs in the RMSF Rodeo community with visible tick infestations by the end of the second year. Homeowner reports of tick activity in the domestic and peridomestic setting showed similar decreases in tick activity compared to the non-project communities. Expansion of this successful project to other areas with Rhipicephalus-transmitted RMSF has the potential to reduce brown dog tick infestations and save human lives

Observed tick counts on dogs during the End-of-Phase evaluations.

<p>Reported as weighted percent frequency (95% confidence interval).</p><p>Observed tick counts on dogs during the End-of-Phase evaluations.</p

Human case incidence of Rocky Mountain spotted fever in the RMSF Rodeo community and Non-Rodeo communities before and after the start of the RMSF Rodeo in April 2012.

<p>Human case incidence of Rocky Mountain spotted fever in the RMSF Rodeo community and Non-Rodeo communities before and after the start of the RMSF Rodeo in April 2012.</p

Observed ticks by life stage in CO₂ traps in the RMSF Rodeo community, n = 5 homes, 3 traps per home.

<p>Observed ticks by life stage in CO₂ traps in the RMSF Rodeo community, n = 5 homes, 3 traps per home.</p