Open circular billiards and the Riemann hypothesis

A comparison of escape rates from one and from two holes in an experimental container (e.g. a laser trap) can be used to obtain information about the dynamics inside the container. If this dynamics is simple enough one can hope to obtain exact formulas. Here we obtain exact formulas for escape from a circular billiard with one and with two holes. The corresponding quantities are expressed as sums over zeroes of the Riemann zeta function. Thus we demonstrate a direct connection between recent experiments and a major unsolved problem in mathematics, the Riemann hypothesis.Comment: 5 pages, 4 embedded postscript figures; v2: more explicit on how the Reimann Hypothesis arises from a comparison of one and two hole escape rate

The Proposed Biological Station at the Tortugas

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Response of Microorganisms to Hot Crude Oil Spills on a Subarctic Taiga Soil

This study was conducted on the short-term effects of seasonal spills of hot Prudhoe Bay crude oil on microorganisms in a taiga soil in interior Alaska. Following a winter spill, the filamentous fungal populations were inhibited whereas the heterotrophic bacterial populations were stimulated. After a summer spill there was an initial depression of both the filamentous fungal and bacterial populations followed by a general enhancement. In both oil spill plots, yeasts; along with the denitrifying, proteolytic, oil-utilizing, and cellulose-utilizing microorganisms; were favorably affected by the oil. Soil respiration was also enhanced in the oiled plots. An extended period of study is required to fully evaluate the impact of oil on the soil microflora and the role of these microorganisms in recovery of oil-inundated areas in subarctic ecosystems

Spatiotemporal relationships of coyotes and free-ranging domestic cats as indicators of conflict in Culver City, California

As habitat generalists, urban coyote (Canis latrans) populations often utilize an abundance of diverse food sources in cities. Within southern California, domestic cats (Felis catus) comprise a higher proportion of coyote diets than in other studied urban areas throughout the United States. However, it is unclear which ecological factors contribute to higher rates of cat depredation by coyotes in this region. While previous research suggests that coyote presence may have a negative effect on free-ranging domestic cat distributions, few studies have determined whether urban green spaces affect coyote or free-ranging domestic cat occurrence and activity within a predominantly urbanized landscape. We placed 20 remote wildlife cameras across a range of green spaces and residential sites in Culver City, California, an area of Los Angeles County experiencing pronounced coyote-domestic cat conflict. Using data collected across 6 months from 2019–2020, we assessed the influence of green space and prey species (i.e., cottontail rabbits (Sylvilagus spp.) and domestic cats) on coyote habitat use and activity. Coyotes exhibited a preference for sites with higher amounts of green space, while domestic cat habitat use was high throughout our study region. Although cottontail rabbit habitat use was also highly associated with urban green space, neither cottontails nor domestic cats appeared to temporally overlap significantly with coyotes. Unlike other cities where coyotes and domestic cats exhibit strong habitat partitioning across the landscape, domestic cats and coyotes spatially overlapped in green space fragments throughout Culver City. We suggest that this pattern of overlap may be responsible for the frequent cases of domestic cat depredation by coyotes in Culver City

Fluctuation of left ventricular thresholds and required safety margin for left ventricular pacing with cardiac resynchronization therapy

AIMS: Fluctuations in left ventricular (LV) thresholds with cardiac resynchronization therapy (CRT) are unknown. The LV capture management (LVCM) algorithm automatically measures LV thresholds on a daily basis and offers the opportunity to analyse threshold fluctuations. METHODS AND RESULTS: A total of 282 patients implanted with a Medtronic Concerto CRT-D device were prospectively studied. Device data were collected at periodic visits, including daily thresholds from the preceding 14 days and weekly threshold ranges since implantation, acquired by the LVCM algorithm up to 12 months' follow-up. Overall, LV thresholds remained relatively stable, with 189/208 (91%) patients having a maximum increase in threshold of > or = 1.0 V at any time between their 1 and 6 month visits and 127/135 (94%) between the 6 and 12 month visits. However, increase in threshold was significantly affected by LV threshold amplitude. Of the 170 patients with a 1 month threshold of > or = 2.0 V, 159 (94%) had increases of >1.0 V up to their 6 month visit, whereas 8/38 (21%) patients with or = 2.0 V) LV thresholds, a safety margin of 1.0 V is sufficient to ensure LV capture if phrenic nerve stimulation is an issue, and may be even lower in devices with auto-adaptive capture management algorithms. However, the margin should be greater in patients with higher thresholds because of larger fluctuations. Left ventricular capture management may be particularly useful in these patients to ensure LV capture without sacrificing device longevity

A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution - II

We present a semi-decision procedure to tackle first order differential equations, with Liouvillian functions in the solution (LFOODEs). As in the case of the Prelle-Singer procedure, this method is based on the knowledge of the integrating factor structure.Comment: 11 pages, late