Matrix-free mass spectrometric imaging using laser desorption ionisation Fourier transform ion cyclotron resonance mass spectrometry

Mass spectrometry imaging (MSI) is a powerful tool in metabolomics and proteomics for the spatial localization and identification of pharmaceuticals, metabolites, lipids, peptides and proteins in biological tissues. However, sample preparation remains a crucial variable in obtaining the most accurate distributions. Common washing steps used to remove salts, and solvent-based matrix application, allow analyte spreading to occur. Solvent-free matrix applications can reduce this risk, but increase the possibility of ionisation bias due to matrix adhesion to tissue sections. We report here the use of matrix-free MSI using laser desorption ionisation performed on a 12 T Fourier transform ion cyclotron resonance (FTICR) mass spectrometer. We used unprocessed tissue with no post-processing following thaw-mounting on matrix-assisted laser desorption ionisation (MALDI) indium-tin oxide (ITO) target plates. The identification and distribution of a range of phospholipids in mouse brain and kidney sections are presented and compared with previously published MALDI time-of-flight (TOF) MSI distributions.

New fiber laser architecture with transform-limited nonlinear spectral compression

We numerically demonstrate a new fiber laser architecture supporting spectral compression of negatively chirped pulses in passive normally dispersive fiber. Such a process is beneficial for improving the energy efficiency of the cavity as it prevents narrow spectral filtering from being highly dissipative. The proposed laser design provides an elegant way of generating transform-limited picosecond pulses. © 2012 IEEE.

Digital signal processing based on inverse scattering transform

Through numerical modeling, we illustrate the possibility of a new approach to digital signal processing in coherent optical communications based on the application of the so-called inverse scattering transform. Considering without loss of generality a fiber link with normal dispersion and quadrature phase shift keying signal modulation, we demonstrate how an initial information pattern can be recovered (without direct backward propagation) through the calculation of nonlinear spectral data of the received optical signal. © 2013 Optical Society of America.

Nonlinear signalling networks and cell-to-cell variability transform external signals into broadly distributed or bimodal responses

We show theoretically and experimentally a mechanismbehind the emergence of wide or bimodal protein distributions in biochemical networks with nonlinear input-output characteristics (the dose-response curve) and variability in protein abundance. Large cell-to-cell variation in the nonlinear dose-response characteristics can be beneficial to facilitate two distinct groups of response levels as opposed to a graded response. Under the circumstances that we quantify mathematically, the two distinct responses can coexist within a cellular population, leading to the emergence of a bimodal protein distribution. Using flow cytometry, we demonstrate the appearance of wide distributions in the hypoxia-inducible factor-mediated response network in HCT116 cells. With help of our theoretical framework, we perform a novel calculation of the magnitude of cell-to-cell heterogeneity in the dose-response obtained experimentally. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

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.

Nonlinear Fourier transform for optical communications

The nonlinear Fourier transform, also known as eigenvalue communications, is a transmission and signal processing technique that makes positive use of the nonlinear properties of fibre channels. I will discuss recent progress in this field.

Optical communication based on the periodic nonlinear Fourier transform signal processing

In this work we introduce the periodic nonlinear Fourier transform (PNFT) and propose a proof-of-concept communication system based on it by using a simple waveform with known nonlinear spectrum (NS). We study the performance (addressing the bit-error-rate (BER), as a function of the propagation distance) of the transmission system based on the use of the PNFT processing method and show the benefits of the latter approach. By analysing our simulation results for the system with lumped amplification, we demonstrate the decent potential of the new processing method.

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Periodic nonlinear Fourier transform for fiber-optic communications, Part II:eigenvalue communication

In this paper we propose the design of communication systems based on using periodic nonlinear Fourier transform (PNFT), following the introduction of the method in the Part I. We show that the famous "eigenvalue communication" idea [A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993)] can also be generalized for the PNFT application: In this case, the main spectrum attributed to the PNFT signal decomposition remains constant with the propagation down the optical fiber link. Therefore, the main PNFT spectrum can be encoded with data in the same way as soliton eigenvalues in the original proposal. The results are presented in terms of the bit-error rate (BER) values for different modulation techniques and different constellation sizes vs. the propagation distance, showing a good potential of the technique.

Capacity estimates for optical transmission based on the nonlinear Fourier transform

What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km.