The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor

The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact intervals. It is then demonstrated that a change in the sign of the dichotomy spectrum is associated with a bifurcation from a trivial to a non-trivial mean-square random attractor

Nonlinear inverse synthesis technique for optical links with lumped amplification

The nonlinear inverse synthesis (NIS) method, in which information is encoded directly onto the continuous part of the nonlinear signal spectrum, has been proposed recently as a promising digital signal processing technique for combating fiber nonlinearity impairments. However, because the NIS method is based on the integrability property of the lossless nonlinear Schrödinger equation, the original approach can only be applied directly to optical links with ideal distributed Raman amplification. In this paper, we propose and assess a modified scheme of the NIS method, which can be used effectively in standard optical links with lumped amplifiers, such as, erbium-doped fiber amplifiers (EDFAs). The proposed scheme takes into account the average effect of the fiber loss to obtain an integrable model (lossless path-averaged model) to which the NIS technique is applicable. We found that the error between lossless pathaveraged and lossy models increases linearly with transmission distance and input power (measured in dB). We numerically demonstrate the feasibility of the proposed NIS scheme in a burst mode with orthogonal frequency division multiplexing (OFDM) transmission scheme with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 3.5 dB; these results are comparable to those achievable with multi-step per span digital backpropagation

Regulating Drones Under the First and Fourth Amendments

The FAA Modernization and Reform Act of 2012 requires the Federal Aviation Administration to integrate unmanned aerial vehicles (UAVs), or drones, into the national airspace system by September 2015. Yet perhaps because of their chilling accuracy in targeted killings abroad, perhaps because of an increasing consciousness of diminishing privacy more generally, and perhaps simply because of a fear of the unknown, divergent UAV-restrictive legislation has been proposed in Congress and enacted in a number of states. Given UAV utility and cost-effectiveness over a vast range of tasks, however, widespread commercial use ultimately seems certain. Consequently, it is imperative to understand the constitutional restraints on public flight and constitutional protections afforded to private flight. Unfortunately, although there are a few Fourth Amendment precedents in manned aviation, they are mired not only in 1980s technology but also in the 1980s third party doctrine, and therefore do not reflect more recent Fourth Amendment developments and doctrinal fissures. There is also considerable uncertainty over First Amendment protection of information-gathering—for example, is there a right to record? Further, there is no judicial or scholarly analysis of how UAV flight fits within contemporary First Amendment forum doctrine, a framework that provides a useful starting point for analyzing speech restrictions in government-controlled airspace, but that comes with some uncertainties of its own. It is into this thicket that we dive, and fortunately some clarity emerges. Although the Fourth Amendment third party doctrine hopelessly misunderstands privacy and therefore under-protects our security and liberty interests, the Supreme Court’s manned flyover cases can be mined for a sensible public disclosure doctrine that seems agnostic as to the various Fourth Amendment conceptions: we do not typically require only law enforcement to shield its eyes. Of course, both constitutions and legislation can place special restrictions upon law enforcement, and sometimes doing so makes good sense. But as a general Fourth Amendment matter, the officer may do and see as the citizen would. Hence to understand Fourth Amendment regulation, we must understand how the First Amendment limits government restraint on speech-relevant private UAV flight. Here we analyze the developing right to record and apply contemporary forum doctrine to this novel means of speech and information-gathering. If navigable airspace is treated as a limited public forum, as we propose with some qualification, then the Federal Aviation Administration will have significant—though not unlimited—regulatory leeway to evenhandedly burden speech-related UAV activities where doing so would reasonably promote safe unmanned and manned flight operations. The Agency, however, would likely need further congressional action before it can restrict UAV flight based on privacy rather than safety concerns. As the legality and norms of private flight correspondingly take shape, they will inform Fourth Amendment restrictions on government use

A Spectral Phasor Perspective in Zebrafish Muscle Development

Hyperspectral imaging provides the potential for assessing biochemical interactions in the zebrafish embryo in a label-free manner that extends beyond conventional morphological and molecular phenotyping. It takes advantage of the intrinsic wavelengths emitted or reflected from a sample without the need for extrinsic staining methods. The specific spectral signature from a sample can arise from chemical interactions, molecular bonds and macro-structural arrangements. A challenge in hyperspectral imaging is the large spectral data sets that result from acquiring a spectrum for every pixel within an image. Spectral Phasor offers an efficient representation of the spectral data as vectors in Fourier space, thereby condensing each spectrum into a single point in a 2-D plot. The Spectral Phasor has been successfully applied to hyperspectral data on protein samples, demonstrating changes in fluorescence signatures. This study proposes an application of Spectral Phasor to the zebrafish muscle development. The skeletal muscle system provides an attractive model for the proof-of-principle experiments in the implementation of Spectral Phasor. Skeletal muscle is a highly organized tissue with myofibrils as the functional unit that contributes to the repetitive segment of the myotome. The modularity of these units provides unique landmarks for anchoring the SP data. Our analysis of muscle suggest that SP can be used for staging the skeletal muscle development

Imaging Proteins, Cells, and Tissues Dynamics during Embryogenesis with Two-Photon Light-Sheet Microscopy

Two-photon light sheet microscopy combines nonlinear excitation with the novel sheet-illumination, orthogonal to the detection direction, to achieve high penetration depth, high acquisition speed, and low photodamage, compared with conventional imaging techniques. These advantages allow unprecedented observation of the processes that govern embryogenesis, where the ability to image fast the dynamic three dimensional structure of the developing embryo, over extended periods of time, is critical. We present a selection of applications where two-photon light sheet microscopy is utilized to observe the dynamics of proteins, cells, and tissues, toward an understanding of the construction program of the developing embryos

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

Time-varying Learning and Content Analytics via Sparse Factor Analysis

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education

On the design of NFT-based communication systems with lumped amplification

Nonlinear Fourier transform (NFT) based transmission technique relies on the integrability of the nonlinear Schrodinger equation (NLSE). However, the lossless NLSE is not directly applicable for the description of light evolution in fibre links with lumped amplifications such as Erbium-doped fibre amplifier (EDFA) because of the non-uniform loss and gain evolution. In this case, the path-averaged model is usually applied as an approximation of the true NLSE model including the fibre loss. However, the inaccuracy of the lossless path-average model, even though being small, can also result in a notable performance degradation in NFT-based transmission systems. In this work, we extend the theoretical approach, which was firstly proposed for solitons in EDFA systems, to the case of NFT-based systems to constructively diminish the aforementioned performance penalty. Based on the quantitative analysis of distortions due to the use of path-average model, we optimise the signal launch and detection points to minimise the models mismatch. Without loss of generality, we demonstrate how the approach works for the NFT systems that use continuous NFT spectrum modulation (vanishing signals) and NFT main spectrum modulation (periodic signals). Through numerical modelling we quantify the corresponding improvements in system performance