On Hankel Transform of Generalized Mathieu Series

Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20

Representations of Inverse Functions by the Integral Transform with the Sign Kernel

Mathematics Subject Classification: Primary 30C40

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.

On Y. Nievergelt's Inversion Formula for the Radon Transform

Mathematics Subject Classification 2010: 42C40, 44A12.

Bochner-Hecke Theorems for the Weinstein Transform and Application

MSC 2010: 42B10, 44A15

Hough Transform Approach to Identification of Flare Stars in Multi-exposure Plate Images

ACM Computing Classification System (1998): I.2.8 , I.2.10, I.5.1, J.2.

Generalized Backscattering and the Lax-Phillips Transform

2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.

α-Mellin Transform and One of Its Applications

MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45

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.

Fault diagnosis scheme for open-circuit faults in switched reluctance motor drives using fast Fourier transform algorithm with bus current detection

Reliability of power converters is of crucial importance in switched reluctance motor drives used for safety-critical applications. Open-circuit faults in power converters will cause the motor to run in unbalanced states, and if left untreated, they will lead to damage to the motor and power modules, and even cause a catastrophic failure of the whole drive system. This study is focused on using a single current sensor to detect open-circuit faults accurately. An asymmetrical half-bridge converter is considered in this study and the faults of single-phase open and two-phase open are analysed. Three different bus positions are defined. On the basis of a fast Fourier transform algorithm with Blackman window interpolation, the bus current spectrums before and after open-circuit faults are analysed in details. Their fault characteristics are extracted accurately by the normalisations of the phase fundamental frequency component and double phase fundamental frequency component, and the fault characteristics of the three bus detection schemes are also compared. The open-circuit faults can be located by finding the relationship between the bus current and rotor position. The effectiveness of the proposed diagnosis method is validated by the simulation results and experimental tests.

Civilizing the tropics: The highlanders' failed attempt to transform the Colombian Amazon, 1850--1930

The subject of this dissertation is the nature of the environmental transformations, both symbolic and physical, that took place in Colombia between 1850 and 1930. This period begins with the attempt by the Colombian elite to leave behind colonial ties, overcome economic disorganization, and link Colombia to the international market. These efforts were part of a general project to “civilize” this tropical country. The period closes with the transition toward an industrialization and urbanization process led by the Colombian state during the 1930s. ^ Frequently, environmental studies as an academic field are dominated by biological concerns. However, most environmental thinking accepts their interdisciplinary nature. Under this framework not only spatial but also symbolic concerns are key elements in understanding environmental transformations. ^ This study finds that despite several attempts to transform the Colombian landscape physically, most of the substantive changes were localized and circumscribed to the Andean region. Other changes were mainly symbolic. This dissertation thus uses the Amazon as one of several regions that did not experience significant changes in the forest canopy. While highlanders originally dreamed of the Amazon as an untapped El Dorado, their failed attempts to exploit the region caused them to imagine it as a nightmarish “green hell”. ^ This dissertation concentrates on three pairs of concepts: tropicality/civilization, landscape/territory, and symbolic/material changes. It presents both a general vision of Colombia and case studies of three regions: Cundinamarca, and Cauca Valley are used to compare with the Amazon region that is developed at length. Whereas mainstream Colombian histories have either fixated on the Andean highlands or, in a relegated second place, on the Caribbean region, this dissertation attempts to significantly contribute to the historiography of Colombia by focusing on the largely neglected Amazonian region. ^ To understand imageries about Colombia's landscape, the dissertation relies on travel writings, chorographic descriptions and maps. It also makes uses legal documents and other published primary sources, including literary pieces and memoirs. ^

Annotated record of the detailed examination of Mn deposits from COCOTOW Expedition stations in the intersection of the Siqueiros Transform Fault and the East Pacific Rise

A near-bottom geological and geophysical survey was conducted at the western intersection of the Siqueiros Transform Fault and the East Pacific Rise. Transform-fault shear appears to distort the east flank of the rise crest in an area north of the fracture zone. In ward-facing scarps trend 335° and do not parallel the regional axis of spreading. Small-scale scarps reveal a hummocky bathymetry. The center of spreading is not a central peak but rather a 20-40 m deep, 1 km wide valley superimposed upon an 8 km wide ridge-crest horst. Small-scale topography indicates widespread volcanic flows within the valley. Two 0.75 km wide blocks flank the central valley. Fault scarps are more dominant on the western flank. Their alignment shifts from directions intermediate to parallel to the regional axis of spreading (355°). A median ridge within the fracture zone has a fault-block topography similar to that of the East Pacific Rise to the north. Dominant eastward-facing scarps trending 335° are on the west flank. A central depression, 1 km wide and 30 m deep, separates the dominantly fault-block regime of the west from the smoother topography of the east flank. This ridge originated by uplift due to faulting as well as by volcanism. Detailed mapping was concentrated in a perched basin (Dante's Hole) at the intersection of the rise crest and the fracture zone. Structural features suggest that Dante's Hole is an area subject to extreme shear and tensional drag resulting from transition between non-rigid and rigid crustal behavior. Normal E-W crustal spreading is probably taking place well within the northern confines of the basin. Possible residual spreading of this isolated rise crest coupled with shear drag within the transform fault could explain the structural isolation of Dante's Hole from the remainder of the Siqueiros Transform Fault.

Identification of unusual events in multi-channel bridge monitoring data using wavelet transform and outlier analysis

Peer reviewed