New Upper Bound for the Edge Folkman Number Fe(3,5;13)

2000 Mathematics Subject Classification: 05C55.

Bound dissipative-pulse evolution in the all-normal dispersion fiber laser using a 45° tilted fiber grating

The formation and evolution of bound dissipative pulses in the all-normal dispersion Yb-fiber laser based on a novel 45° tilted fiber grating (TFG) are first investigated both numerically and experimentally. Based on the nonlinear polarization rotation technique, the TFG and two polarization controllers (PCs) are exploited for stable self-started passive mode locking. Numerical results show that the formation of bound-state pulses in the all-normal dispersion region is the progress of soliton shaping through the dispersive waves and follows the soliton energy quantization effect. Theoretical and experimental results demonstrate that the formation mechanism of bound-state pulses can be attributed to the high pump strength and effective filter bandwidth. The obtained bound-state dissipative pulses with quasi-rectangular spectral profile have fixed pulse separation as a function of pump power. © 2013 Astro Ltd.

A lower bound on the per soliton capacity of the nonlinear optical fibre channel

A closed-form expression for a lower bound on the per soliton capacity of the nonlinear optical fibre channel in the presence of (optical) amplifier spontaneous emission (ASE) noise is derived. This bound is based on a non-Gaussian conditional probability density function for the soliton amplitude jitter induced by the ASE noise and is proven to grow logarithmically as the signal-to-noise ratio increases.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Multicolour nonlinearly bound chirped dissipative solitons

The dissipative soliton regime is one of the most advanced ways to generate high-energy femtosecond pulses in mode-locked lasers. On the other hand, the stimulated Raman scattering in a fibre laser may convert the excess energy out of the coherent dissipative soliton to a noisy Raman pulse, thus limiting its energy. Here we demonstrate that intracavity feedback provided by re-injection of a Raman pulse into the laser cavity leads to formation of a coherent Raman dissipative soliton. Together, a dissipative soliton and a Raman dissipative soliton (of the first and second orders) form a two (three)-colour stable complex with higher total energy and broader spectrum than those of the dissipative soliton alone. Numerous applications can benefit from this approach, including frequency comb spectroscopy, transmission lines, seeding femtosecond parametric amplifiers, enhancement cavities and multiphoton fluorescence microscopy.

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(Table 1) Physical oceanography during Lance cruise LA99/2 in the marginal ice zone of the Barents Sea

Zooplankton was studied on eight stations in the marginal ice zone (MIZ) of the Barents Sea, in May 1999, along two transects across the ice edge. On each station, physical background measurements and zooplankton samples were taken every 6 h over a 24 h period at five discrete depth intervals. Cluster analysis revealed separation of open water stations from all ice stations as well as high similarity level among replicates belonging to particular station. Based on five replicates per station, analysis of variance (ANOVA) confirmed significant differences (P < 0.05) in abundances of the main mesozooplankton taxa among stations. Relations between the zooplankton community and environmental parameters were established using redundancy analysis (CANOCO). In total, 55% of mesozooplankton variability within studied area was explained by eight variables with significant conditional effects: depth stratum, fluorescence, temperature, salinity, bottom depth, latitude, bloom situation, and ice concentration. GLM models supported supposition about clear and negative relationship between concentration of Oithona similis, and overall mesozooplankton diversity The analyses showed a dynamic relationship between mesozooplankton distribution and hydrological conditions on short-term scale. Furthermore, our study demonstrated that variability in the physical environment of dynamic MIZ of the Barents Sea has measurable effect on the Arctic pelagic ecosystem.

Biogenic opal, carbonat concentrations and stable oxygen isotope ratios of foraminifera from sediment cores of the Southern Ocean

We present records of biogenic opal percentage and burial rate in 12 piston cores from the Atlantic and Indian sectors of the Southern Ocean. These records provide a detailed, quantitative description of changing patterns of opal deposition over the last 450 kyr. The striking regional coherence of these records suggests that dissolution in the deep sea and sediment pore waters does not obscure the surface productivity signal, and therefore these opal time series can be used in combination with other surface water tracers to make inferences about the chemistry and circulation of the Southern Ocean under different global climate conditions. Three broad depositional patterns can be distinguished. Northernmost records (39°-42°S latitude) are characterized by enhanced opal burial during glacial periods and strong 41 kyr periodicity. Records from cores just north of the present Antarctic Polar Front (46°-49°S) show even larger increases in opal burial rate during glacial intervals, but have variance concentrated in the 100 and 23 kyr bands. Southernmost records (51°-55°S) are completely out of phase with those to the north, with greatly reduced opal burial rates during glacial periods. Taken as a whole, the opal records show no evidence for the increased total Antarctic productivity predicted by recent geochemical models of atmospheric CO2 variability. The areal expansion of Southern Ocean sea ice over the present zone of high siliceous productivity provides one plausible explanation for the glacial-interglacial opal patterns. The excess silica not taken up in this zone during glacial periods would contribute to greater nutrient availability and thus higher productivity in the subantarctic region. However, local circulation changes may act to modify this basic signal, possibly accounting for the observed differences in the opal variance spectra.

Stable carbon and oxygen isotope ratios of planktonic foraminifera from the equatorial Atlantic

Carbon isotopic records of nutrient-depleted surface water place constraints on the past fertility of the oceans and on past atmospheric pCO2 levels. The best records of nutrient-depleted delta13C are obtained from planktonic foraminifera living in the thick mixed layers of the western equatorial and tropical Atlantic Ocean. We have produced a composite, stacked Globigerinoides sacculifer delta13C record from the equatorial Atlantic, which exhibits significant spectral power at the 100,000- and 41,000-year Milankovitch periods, but no power at the 23,000-year period. Similar to the record presented by Shackleton and Pisias [1985], surface-deep ocean Delta delta13C produced with the G. sacculifer record leads the delta18O ice volume record. However, the glacial-interglacial amplitudes of Delta delta13C differ between our record and Shackleton and Pisias [1985] record. Although large changes in Delta delta13C occur in the equatorial Atlantic during early stages of the last three glacial cycles, surface-deep Delta delta13C at glacial maxima (18O stage 2, late stage 6, and late stage 8) was only about 0.2? greater than during the subsequent interglacial. Our results imply that nutrient-driven pCO2 changes account for about one third of the pCO2 decrease observed in ice cores, and consequently, Delta delta13C should not be used as a proxy pCO2 index. Enough variance in the ice core pCO2 records remains to be explained that conclusions about pCO2 and ice volume phase relationships should also be reexamined. As much as 40 ppm pCO2 change still has not been accounted for by models of past physics and chemistry of the ocean.

Relative abundance of dinoflagellate cysts in surface sediments and dinoflagellate counts from three sediment cores from the Atlantic sector of the Southern Ocean

In this study we investigate the potential of organic-walled dinoflagellate cysts (dinocysts) as tools for quantifying past sea-surface temperatures (SST) in the Southern Ocean. For this purpose, a dinocyst reference dataset has been formed, based on 138 surface sediment samples from different circum-Antarctic environments. The dinocyst assemblages of these samples are composed of phototrophic (gonyaulacoid) and heterotrophic (protoperidinioid) species that provide a broad spectrum of palaeoenvironmental information. The relationship between the environmental parameters in the upper water column and the dinocyst distribution patterns of individual species has been established using the statistical method of Canonical Correspondence Analysis (CCA). Among the variables tested, summer SST appeared to correspond to the maximum variance represented in the dataset. To establish quantitative summer SST reconstructions, a Modern Analogue Technique (MAT) has been performed on data from three Late Quaternary dinocyst records recovered from locations adjacent to prominent oceanic fronts in the Atlantic sector of the Southern Ocean. These dinocyst time series exhibit periodic changes in the dinocyst assemblage during the last two glacial/interglacial-cycles. During glacial conditions the relative abundance of protoperidinioid cysts was highest, whereas interglacial conditions are characterised by generally lower cyst concentrations and increased relative abundance of gonyaulacoid cysts. The MAT palaeotemperature estimates show trends in summer SST changes following the global oxygen isotope signal and a strong correlation with past temperatures of the last 140,000 years based on other proxies. However, by comparing the dinocyst results to quantitative estimates of summer SSTs based on diatoms, radiolarians and foraminifer-derived stable isotope records it can be shown that in several core intervals the dinocyst-based summer SSTs appeared to be extremely high. In these intervals the dinocyst record seems to be highly influenced by selective degradation, leading to unusual temperature ranges and to unrealistic palaeotemperatures. We used the selective degradation index (kt-index) to determine those intervals that have been biased by selective degradation in order to correct the palaeotemperature estimates. We show that after correction the dinocyst based SSTs correspond reasonably well with other palaeotemperature estimates for this region, supporting the great potential of dinoflagellate cysts as a basis for quantitative palaeoenvironmental studies.

Expanded GHOST database

In this study we review a global set of alkenone- and foraminiferal Mg/Ca-derived sea surface temperatures (SST) records from the Holocene and compare them with a suite of published Eemian SST records based on the same approach. For the Holocene, the alkenone SST records belong to the actualized GHOST database (Kim, J.-H., Schneider R.R., 2004). The actualized GHOST database not only confirms the SST changes previously described but also documents the Holocene temperature evolution in new oceanic regions such as the Northwestern Atlantic, the eastern equatorial Pacific, and the Southern Ocean. A comparison of Holocene SST records stemming from the two commonly applied paleothermometry methods reveals contrasting - sometimes divergent - SST evolution, particularly at low latitudes where SST records are abundant enough to infer systematic discrepancies at a regional scale. Opposite SST trends at particular locations could be explained by out-of-phase trends in seasonal insolation during the Holocene. This hypothesis assumes that a strong contrast in the ecological responses of coccolithophores and planktonic foraminifera to winter and summer oceanographic conditions is the ultimate reason for seasonal differences in the origin of the temperature signal provided by these organisms. As a simple test for this hypothesis, Eemian SST records are considered because the Holocene and Eemian time periods experienced comparable changes in orbital configurations, but had a higher magnitude in insolation variance during the Eemian. For several regions, SST changes during both interglacials were of a similar sign, but with higher magnitudes during the Eemian as compared to the Holocene. This observation suggests that the ecological mechanism shaping SST trends during the Holocene was comparable during the penultimate interglacial period. Although this "ecology hypothesis" fails to explain all of the available results, we argue that any other mechanism would fail to satisfactorily explain the observed SST discrepancies among proxies.