Results of n-alkane biomarker analyses and paleoclimate reconstruction

The current study presents quantitative reconstructions of tree cover, annual precipitation and mean July temperature derived from the pollen record from Lake Billyakh (65°17'N, 126°47'E, 340 m above sea level) spanning the last ca. 50 kyr. The reconstruction of tree cover suggests presence of woody plants through the entire analyzed time interval, although trees played only a minor role in the vegetation around Lake Billyakh prior to 14 kyr BP (<5%). This result corroborates low percentages of tree pollen and low scores of the cold deciduous forest biome in the PG1755 record from Lake Billyakh. The reconstructed values of the mean temperature of the warmest month ~8-10 °C do not support larch forest or woodland around Lake Billyakh during the coldest phase of the last glacial between ~32 and ~15 kyr BP. However, modern cases from northern Siberia, ca. 750 km north of Lake Billyakh, demonstrate that individual larch plants can grow within shrub and grass tundra landscape in very low mean July temperatures of about 8 °C. This makes plausible our hypothesis that the western and southern foreland of the Verkhoyansk Mountains could provide enough moist and warm microhabitats and allow individual larch specimens to survive climatic extremes of the last glacial. Reconstructed mean values of precipitation are about 270 mm/yr during the last glacial interval. This value is almost 100 mm higher than modern averages reported for the extreme-continental north-eastern Siberia east of Lake Billyakh, where larch-dominated cold deciduous forest grows at present. This suggests that last glacial environments around Lake Billyakh were never too dry for larch to grow and that the summer warmth was the main factor, which limited tree growth during the last glacial interval. The n-alkane analysis of the Siberian plants presented in this study demonstrates rather complex alkane distribution patterns, which challenge the interpretation of the fossil records. In particular, extremely low n-alkane concentrations in the leaves of local coniferous trees and shrubs suggest that their contribution to the litter and therefore to the fossil lake sediments might be not high enough for tracing the Quaternary history of the needleleaved taxa using the n-alkane biomarker method.

n-Alkan-2-ones in peat-forming plants from the Roñanzas ombrotrophic bog (Asturias, northern Spain)

We determined the distribution of lipids (n-alkanes and n-alkan-2-ones) in present-day peat-formingplants in the RoñanzasBog in northernSpain. Consistent with the observation of others, most Sphagnum (moss) species alkanes maximized at C23, whereas the other plants maximized at higher molecular weight (C27 to C31). We show for the first time that plants other than seagrass and Sphagnum moss contain n-alkan-2-ones. Almost all the species analysed showed an n-alkan-2-one distribution between C21 and C31 with an odd/even predominance, maximizing at C27 or C29, except ferns, which maximized at lower molecular weight (C21–C23). We also observed that microbial degradation can be a major contributor to the n-alkan-2-one distribution in sediments as opposed to a direct input of ketones from plants

DCT Type-III for Multicarrier Modulation

In this paper we propose the use of Discrete Cosine Transform Type-III (DCT3) for multicarrier modulation. There are two DCT3 (even and odd) and, for each of them, we derive the expressions for both prefix and suffix to be appended into each data symbol to be transmitted. Moreover, DCT3 are closely related to the corresponding inverse DCT Type-II even and odd. Furthermore, we give explicit expressions for the 1-tap per subcarrier equalizers that must be implemented at the receiver to perform the channel equalization in the frequency-domain. As a result, the proposed DCT3-based multicarrier modulator can be used as an alternative to DFT-based systems to perform Orthogonal Frequency-Division Multiplexing or Discrete Multitone Modulation

Phase transition in the countdown problem

We present a combinatorial decision problem, inspired by the celebrated quiz show called Countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.

Theoretical Stark broadening parameters for spectral lines arising from the 2p5ns, 2p5np and 2p5nd electronic configurations of MgIII

In the present work we report theoretical Stark widths and shifts calculated using the Griem semi-empirical approach, corresponding to 237 spectral lines of MgIII. Data are presented for an electron density of 1017 cm?3 and temperatures T = 0.5?10.0 (104 K). The matrix elements used in these calculations have been determined from 23 configurations of MgIII: 2s22p6, 2s22p53p, 2s22p54p, 2s22p54f and 2s22p55f for even parity and 2s22p5ns (n = 3?6), 2s22p5nd (n = 3?9), 2s22p55g and 2s2p6np (n = 3?8) for odd parity. For the intermediate coupling (IC) calculations, we use the standard method of least-squares fitting from experimental energy levels by means of the Cowan computer code. Also, in order to test the matrix elements used in our calculations, we present calculated values of 70 transition probabilities of MgIII spectral lines and 14 calculated values of radiative lifetimes of MgIII levels. There is good agreement between our calculations and experimental radiative lifetimes. Spectral lines of MgIII are relevant in astrophysics and also play an important role in the spectral analysis of laboratory plasma. Theoretical trends of the Stark broadening parameter versus the temperature for relevant lines are presented. No values of Stark parameters can be found in the bibliography.

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed