Information capacity of the Hopfield model

The information capacity of general forms of memory is formalized. The number of bits of information that can be stored in the Hopfield model of associative memory is estimated. It is found that the asymptotic information capacity of a Hopfield network of N neurons is of the order N^3b. The number of arbitrary state vectors that can be made stable in a Hopfield network of N neurons is proved to be bounded above by N

Placing the Common Era in a Holocene context: millennial to centennial patterns and trends in the hydroclimate of North America over the past 2000 years

A synthesis of 93 hydrologic records from across North and Central America, and adjacent tropical and Arctic islands, reveals centennial to millennial trends in the regional hydroclimates of the Common Era (CE; past 2000 years). The hydrological records derive from materials stored in lakes, bogs, caves, and ice from extant glaciers, which have the continuity through time to preserve low-frequency ( \u3e 100 year) climate signals that may extend deeper into the Holocene. The most common pattern, represented in 46 (49 %) of the records, indicates that the centuries before 1000 CE were drier than the centuries since that time. Principal component analysis indicates that millennial-scale trends represent the dominant pattern of variance in the southwestern US, northeastern US, mid-continent, Pacific Northwest, Arctic, and tropics, although not all records within a region show the same direction of change. The Pacific Northwest and the southernmost tier of the tropical sites tended to dry toward present, as many other areas became wetter than before. In 22 records (24 %), the Medieval Climate Anomaly period (800–1300 CE) was drier than the Little Ice Age (1400–1900 CE), but in many cases the difference was part of the longer millennial-scale trend, and, in 25 records (27 %), the Medieval Climate Anomaly period represented a pluvial (wet) phase. Where quantitative records permitted a comparison, we found that centennial-scale fluctuations over the Common Era represented changes of 3–7% in the modern interannual range of variability in precipitation, but the accumulation of these long-term trends over the entirety of the Holocene caused recent centuries to be significantly wetter, on average, than most of the past 11 000 years

A paleolimnological assessment of the diatom communities of Lake Opeongo, Ontario, Canada

grantor: University of TorontoLake Opeongo is an oligotrophic lake in Algonquin Provincial Park, Ontario, Canada (45°42' N, 78°22' W). Limnological conditions over the past 300 years were tracked using diatoms preserved in the sediments and applying diatom-based transfer functions to infer total phosphorus (TP). Before European settlement, Lake Opeongo was highly oligotrophic, with the diatom community consisting of 'Cyclotella stelligera' complex with subdominants ' Tabellaria flocculosa' IIIp and 'Aulacoseira distans'. No changes occurred until ca. 1956 when the diatom community shifted to the current mesotrophic assemblage consisting of 'Asterionella formosa ' with lesser amounts of 'Cyclotella bodanica' var ' lemanica, C. stelligera' complex, 'Fragilaria crotonensis' and 'T. flocculosa' IIIp. This shift could have occurred due to increased direct human impacts on the watershed; increased post-war fertilizer use; global warming, including changes in the thermal conditions of the lake; and trophic level changes caused by human manipulation of the fish community of the lake.M.Sc

Placing the Common Era in a Holocene context: millennial to centennial patterns and trends in the hydroclimate of North America over the past 2000 years

A synthesis of 93 hydrologic records from across North and Central America, and adjacent tropical and Arctic islands, reveals centennial to millennial trends in the regional hydroclimates of the Common Era (CE; past 2000 years). The hydrological records derive from materials stored in lakes, bogs, caves, and ice from extant glaciers, which have the continuity through time to preserve low-frequency ( \u3e 100 year) climate signals that may extend deeper into the Holocene. The most common pattern, represented in 46 (49 %) of the records, indicates that the centuries before 1000 CE were drier than the centuries since that time. Principal component analysis indicates that millennial-scale trends represent the dominant pattern of variance in the southwestern US, northeastern US, mid-continent, Pacific Northwest, Arctic, and tropics, although not all records within a region show the same direction of change. The Pacific Northwest and the southernmost tier of the tropical sites tended to dry toward present, as many other areas became wetter than before. In 22 records (24 %), the Medieval Climate Anomaly period (800–1300 CE) was drier than the Little Ice Age (1400–1900 CE), but in many cases the difference was part of the longer millennial-scale trend, and, in 25 records (27 %), the Medieval Climate Anomaly period represented a pluvial (wet) phase. Where quantitative records permitted a comparison, we found that centennial-scale fluctuations over the Common Era represented changes of 3–7% in the modern interannual range of variability in precipitation, but the accumulation of these long-term trends over the entirety of the Holocene caused recent centuries to be significantly wetter, on average, than most of the past 11 000 years

Minnesota isopoll maps from the pre-settlement AD 1870 and modern core-top samples.

<p>The nine taxa showing the greatest changes in relative abundance (%) after Euro-American settlement according to St. Jacques et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113806#pone.0113806.ref005" target="_blank">5</a>] are presented. Interpolation based on natural neighbor interpolation (Matlab 2012).</p

The Bias and Signal Attenuation Present in Conventional Pollen-Based Climate Reconstructions as Assessed by Early Climate Data from Minnesota, USA

<div><p>The inference of past temperatures from a sedimentary pollen record depends upon the stationarity of the pollen-climate relationship. However, humans have altered vegetation independent of changes to climate, and consequently modern pollen deposition is a product of landscape disturbance and climate, which is different from the dominance of climate-derived processes in the past. This problem could cause serious signal distortion in pollen-based reconstructions. In the north-central United States, direct human impacts have strongly altered the modern vegetation and hence the pollen rain since Euro-American settlement in the mid-19^th century. Using instrumental temperature data from the early 1800s from Fort Snelling (Minnesota), we assessed the signal distortion and bias introduced by using the conventional method of inferring temperature from pollen assemblages in comparison to a calibration set from pre-settlement pollen assemblages and the earliest instrumental climate data. The early post-settlement calibration set provides more accurate reconstructions of the 19^th century instrumental record, with less bias, than the modern set does. When both modern and pre-industrial calibration sets are used to reconstruct past temperatures since AD 1116 from pollen counts from a varve-dated record from Lake Mina, Minnesota, the conventional inference method produces significant low-frequency (centennial-scale) signal attenuation and positive bias of 0.8-1.7°C, resulting in an overestimation of Little Ice Age temperature and likely an underestimation of the extent and rate of anthropogenic warming in this region. However, high-frequency (annual-scale) signal attenuation exists with both methods. Hence, we conclude that any past pollen spectra from before Euro-American settlement in this region should be interpreted using a pre-Euro-American settlement pollen set, paired to the earliest instrumental climate records. It remains to be explored how widespread this problem is when conventional pollen-based inference methods are used, and consequently how seriously regional manifestations of global warming have been underestimated with traditional pollen-based techniques.</p></div

Comparisons of the reconstructions to each other and the early instrumental data.

<p>Student’s <i>t</i>-tests and <i>F</i>-tests of the AD 1820–1876 means (<i>µ_1, µ₂</i>) and standard deviations (<i>σ₁, σ₂</i>) of the February and May 1870-based and modern-based reconstructions and the annual instrumental temperatures, the latter averaged as the pollen samples were according to the varve counts. Bold denotes significance at the 0.05 level.</p><p>Comparisons of the reconstructions to each other and the early instrumental data.</p

Residuals of the reconstructed 1870 pollen sets from hindcasting and cross-validation.

<p>The reconstructions from hindcasting (i.e., the application of the modern calibration set to the pre-settlement 1870 pollen samples for each of the 133 sites) minus their paired observed AD 1895–1924 temperatures (°C) for (a) February and (b) May are shown. Also shown are the reconstructions from leave-one-out cross-validation (i.e., the application of the pre-settlement 1870 calibration set to the 1870 pollen samples for each of the 133 sites) minus their paired observed AD 1895–1924 temperatures (°C) for (c) February and (d) May.</p

Fort Snelling, Minnesota, USA, monthly climate normals comparisons.

<p>Shown are the differences between the AD 1895–1924 temperature means minus the AD 1840–1869 temperature means, and the AD 1961–1990 temperature means minus the AD 1840–1869 temperature means for each month and annually. Temperatures in °C; two-sided <i>t</i>-tests assuming equal variances, with 58 degrees of freedom; bold denotes significance at the 0.05 level.</p><p>Fort Snelling, Minnesota, USA, monthly climate normals comparisons.</p