Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In ...contrast to traditional time and image signals, data in these domains are supported by arbitrary graphs. Signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs. This paper studies the concepts of low and high frequencies on graphs, and low-, high- and band-pass graph signals and graph filters. In traditional signal processing, these concepts are easily defined because of a natural frequency ordering that has a physical interpretation. For signals residing on graphs, in general, there is no obvious frequency ordering. We propose a definition of total variation for graph signals that naturally leads to a frequency ordering on graphs and defines low-, high-, and band-pass graph signals and filters. We study the design of graph filters with specified frequency response, and illustrate our approach with applications to sensor malfunction detection and data classification.
The proteins extracellular signal-regulated kinase 1 (ERK1) and ERK2 are the downstream components of a phosphorelay pathway that conveys growth and mitogenic signals largely channelled by the small ...RAS GTPases. By phosphorylating widely diverse substrates, ERK proteins govern a variety of evolutionarily conserved cellular processes in metazoans, the dysregulation of which contributes to the cause of distinct human diseases. The mechanisms underlying the regulation of ERK1 and ERK2, their mode of action and their impact on the development and homeostasis of various organisms have been the focus of much attention for nearly three decades. In this Review, we discuss the current understanding of this important class of kinases. We begin with a brief overview of the structure, regulation, substrate recognition and subcellular localization of ERK1 and ERK2. We then systematically discuss how ERK signalling regulates six fundamental cellular processes in response to extracellular cues. These processes are cell proliferation, cell survival, cell growth, cell metabolism, cell migration and cell differentiation.
An efficient and flexible dictionary structure is proposed for sparse and redundant signal representation. The proposed sparse dictionary is based on a sparsity model of the dictionary atoms over a ...base dictionary, and takes the form D = ¿ A, where ¿ is a fixed base dictionary and A is sparse. The sparse dictionary provides efficient forward and adjoint operators, has a compact representation, and can be effectively trained from given example data. In this, the sparse structure bridges the gap between implicit dictionaries, which have efficient implementations yet lack adaptability, and explicit dictionaries, which are fully adaptable but non-efficient and costly to deploy. In this paper, we discuss the advantages of sparse dictionaries, and present an efficient algorithm for training them. We demonstrate the advantages of the proposed structure for 3-D image denoising.
We address the problem of reconstructing a multiband signal from its sub-Nyquist pointwise samples, when the band locations are unknown. Our approach assumes an existing multi-coset sampling. To ...date, recovery methods for this sampling strategy ensure perfect reconstruction either when the band locations are known, or under strict restrictions on the possible spectral supports. In this paper, only the number of bands and their widths are assumed without any other limitations on the support. We describe how to choose the parameters of the multi-coset sampling so that a unique multiband signal matches the given samples. To recover the signal, the continuous reconstruction is replaced by a single finite-dimensional problem without the need for discretization. The resulting problem is studied within the framework of compressed sensing, and thus can be solved efficiently using known tractable algorithms from this emerging area. We also develop a theoretical lower bound on the average sampling rate required for blind signal reconstruction, which is twice the minimal rate of known-spectrum recovery. Our method ensures perfect reconstruction for a wide class of signals sampled at the minimal rate, and provides a first systematic study of compressed sensing in a truly analog setting. Numerical experiments are presented demonstrating blind sampling and reconstruction with minimal sampling rate.
Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem ...of finding sparse representations must be unstable in the presence of noise. This paper establishes the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system. Considering an ideal underlying signal that has a sufficiently sparse representation, it is assumed that only a noisy version of it can be observed. Assuming further that the overcomplete system is incoherent, it is shown that the optimally sparse approximation to the noisy data differs from the optimally sparse decomposition of the ideal noiseless signal by at most a constant multiple of the noise level. As this optimal-sparsity method requires heavy (combinatorial) computational effort, approximation algorithms are considered. It is shown that similar stability is also available using the basis and the matching pursuit algorithms. Furthermore, it is shown that these methods result in sparse approximation of the noisy data that contains only terms also appearing in the unique sparsest representation of the ideal noiseless sparse signal.
In biomedical signal processing, it is often the case that many sources are mixed into the measured signal. The goal is usually to analyze one or several of them separately. In the case of ...multichannel measurements, several blind source separation techniques are available for decomposing the signal into its components e.g., independent component analysis (ICA). However, only a few techniques have been reported for analyses of single-channel recordings. Examples are single-channel ICA (SCICA) and wavelet-ICA (WICA), which all have certain limitations. In this paper, we propose a new method for a single-channel signal decomposition. This method combines empirical-mode decomposition with ICA. We compare the separation performance of our algorithm with SCICA and WICA through simulations, and we show that our method outperforms the other two, especially for high noise-to-signal ratios. The performance of the new algorithm was also demonstrated in two real-life applications.
In a conventional wireless cellular system, signal processing is performed on a per-cell basis; out-of-cell interference is treated as background noise. This paper considers the benefit of ...coordinating base-stations across multiple cells in a multi-antenna beamforming system, where multiple base-stations may jointly optimize their respective beamformers to improve the overall system performance. Consider a multicell downlink scenario where base-stations are equipped with multiple transmit antennas employing either linear beamforming or nonlinear dirty-paper coding, and where remote users are equipped with a single antenna each, but where multiple remote users may be active simultaneously in each cell. This paper focuses on the design criteria of minimizing either the total weighted transmitted power or the maximum per-antenna power across the base-stations subject to signal-to-interference-and-noise-ratio (SINR) constraints at the remote users. The main contribution of the paper is an efficient algorithm for finding the joint globally optimal beamformers across all base-stations. The proposed algorithm is based on a generalization of uplink-downlink duality to the multicell setting using the Lagrangian duality theory. An important feature is that it naturally leads to a distributed implementation in time-division duplex (TDD) systems. Simulation results suggest that coordinating the beamforming vectors alone already provide appreciable performance improvements as compared to the conventional per-cell optimized network.
The poor prognosis and high mortality for cancer patients are majorly ascribed to tumor metastasis, one of the most complicated pathological processes. Elucidation of molecular mechanisms for ...metastasis is essential for management and prevention of this lethal condition. In the book to be published, we take comprehensive review in regard with the signal mechanisms responsible for triggering a series of phenotypical changes of primary tumor which may lead to final colonization of the tumor in a second home. Specifically, the initial stage of tumor metastasis will be highlighted. The complex tumor microenvironment accumulate a lot of growth factors, inflammatory cytokines and extracellular matrix which may turn into a group of potent metastatic factors. An integrated and sustained signaling induced by these metastatic factors may trigger EMT, migration and invasion of primary tumor into surround tissue. Blokcade of these signal pathways is the most effective approach for prevention of
The quaternion least mean square (QLMS) algorithm is introduced for adaptive filtering of three- and four-dimensional processes, such as those observed in atmospheric modeling (wind, vector fields). ...These processes exhibit complex nonlinear dynamics and coupling between the dimensions, which make their component-wise processing by multiple univariate LMS, bivariate complex LMS (CLMS), or multichannel LMS (MLMS) algorithms inadequate. The QLMS accounts for these problems naturally, as it is derived directly in the quaternion domain. The analysis shows that QLMS operates inherently based on the so called ldquoaugmentedrdquo statistics, that is, both the covariance E { xx H } and pseudocovariance E { xx T } of the tap input vector x are taken into account. In addition, the operation in the quaternion domain facilitates fusion of heterogeneous data sources, for instance, the three vector dimensions of the wind field and air temperature. Simulations on both benchmark and real world data support the approach.
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