Distribution of trace values and two-weight, self-orthogonal codes over GF (p,2)

The uniform distribution of the trace map lends itself very well to the construction of binary and non-binary codes from Galois fields and Galois rings. In this paper we study the distribution of the trace map with the argument ax 2 over the Galois field GF(p,2). We then use this distribution to construct two-weight, self-orthogonal, trace codes

Transitions in coral reef accretion rates linked to intrinsic ecological shifts on turbid-zone nearshore reefs

Nearshore coral communities within turbid settings are typically perceived to have limited reef-building capacity. However, several recent studies have reported reef growth over millennial time scales within such environments and have hypothesized that depth-variable community assemblages may act as equally important controls on reef growth as they do in clear-water settings. Here, we explicitly test this idea using a newly compiled chronostratigraphic record (31 cores, 142 radiometric dates) from seven proximal (but discrete) nearshore coral reefs located along the central Great Barrier Reef (Australia). Uniquely, these reefs span distinct stages of geomorphological maturity, as reflected in their elevations below sea level. Integrated age-depth and ecological data sets indicate that contemporary coral assemblage shifts, associated with changing light availability and wave exposure as reefs shallowed, coincided with transitions in accretion rates at equivalent core depths. Reef initiation followed a regional ∼1 m drop in sea level (1200–800 calibrated yr B.P.) which would have lowered the photic floor and exposed new substrate for coral recruitment by winnowing away fine seafloor sediments. We propose that a two-way feedback mechanism exists where past growth history influences current reef morphology and ecology, ultimately driving future reef accumulation and morphological change. These findings provide the first empirical evidence that nearshore reef growth trajectories are intrinsically driven by changes in coral community structure as reefs move toward sea level, a finding of direct significance for predicting the impacts of extrinsically driven ecological change (e.g., coral-algal phase shifts) on reef growth potential within the wider coastal zone on the Great Barrier Reef

Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform

We enumerate the inequivalent self-dual additive codes over GF(4) of blocklength n, thereby extending the sequence A090899 in The On-Line Encyclopedia of Integer Sequences from n = 9 to n = 12. These codes have a well-known interpretation as quantum codes. They can also be represented by graphs, where a simple graph operation generates the orbits of equivalent codes. We highlight the regularity and structure of some graphs that correspond to codes with high distance. The codes can also be interpreted as quadratic Boolean functions, where inequivalence takes on a spectral meaning. In this context we define PAR_IHN, peak-to-average power ratio with respect to the {I,H,N}^n transform set. We prove that PAR_IHN of a Boolean function is equivalent to the the size of the maximum independent set over the associated orbit of graphs. Finally we propose a construction technique to generate Boolean functions with low PAR_IHN and algebraic degree higher than 2.Comment: Presented at Sequences and Their Applications, SETA'04, Seoul, South Korea, October 2004. 17 pages, 10 figure

Cycling injury risk in London: A case-control study exploring the impact of cycle volumes, motor vehicle volumes, and road characteristics including speed limits.

Cycling injury risk is an important topic, but few studies explore cycling risk in relation to exposure. This is largely because of a lack of exposure data, in other words how much cycling is done at different locations. This paper helps to fill this gap. It reports a case-control study of cycling injuries in London in 2013-2014, using modelled cyclist flow data alongside datasets covering some characteristics of the London route network. A multilevel binary logistic regression model is used to investigate factors associated with injury risk, comparing injury sites with control sites selected using the modelled flow data. Findings provide support for 'safety in numbers': for each increase of a natural logarithmic unit (2.71828) in cycling flows, an 18% decrease in injury odds was found. Conversely, increased motor traffic volume is associated with higher odds of cycling injury, with one logarithmic unit increase associated with a 31% increase in injury odds. Twenty-mile per hour compared with 30mph speed limits were associated with 21% lower injury odds. Residential streets were associated with reduced injury odds, and junctions with substantially higher injury odds. Bus lanes do not affect injury odds once other factors are controlled for. These data suggest that speed limits of 20 mph may reduce cycling injury risk, as may motor traffic reduction. Further, building cycle routes that generate new cycle trips should generate 'safety in numbers' benefits

Measuring the state of disaster philanthropy 2021: Data to drive decisions

Each year, the Center for Disaster Philanthropy (CDP) and Candid analyze global disaster-related funding from foundations, bilateral and multilateral donors, U.S. government agencies, corporations, and donations through donor-advised funds (DAFs) and online platforms. We analyze funding according to a taxonomy that classifies giving by type of disaster and disaster assistance strategy, allowing us to identify funding gaps and areas of opportunity, so that crisis-affected communities have resources for immediate relief and to build back stronger than before. This year's report focuses on funding in FY 2019. Philanthropy plays a crucial role in supporting the long-term recovery of individuals and communities affected by disasters. This year, and moving forward, this annual report offers specific, actionable takeaways for how donors can maximize their disaster-related giving. These insights are based on findings from the data and the latest recommendations from CDP about effective disaster funding