There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

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Convex Analysisの二,三の進展について

On robust estimation of the location parameter

Nociceptor inputs can trigger a prolonged but reversible increase in the excitability and synaptic efficacy of neurons in central nociceptive pathways, the phenomenon of central sensitization. Central sensitization manifests as pain hypersensitivity, particularly dynamic tactile allodynia, secondary punctate or pressure hyperalgesia, aftersensations, and enhanced temporal summation. It can be readily and rapidly elicited in human volunteers by diverse experimental noxious conditioning stimuli to skin, muscles or viscera, and in addition to producing pain hypersensitivity, results in secondary changes in brain activity that can be detected by electrophysiological or imaging techniques. Studies in clinical cohorts reveal changes in pain sensitivity that have been interpreted as revealing an important contribution of central sensitization to the pain phenotype in patients with fibromyalgia, osteoarthritis, musculoskeletal disorders with generalized pain hypersensitivity, headache, temporomandibular joint disorders, dental pain, neuropathic pain, visceral pain hypersensitivity disorders and post-surgical pain. The comorbidity of those pain hypersensitivity syndromes that present in the absence of inflammation or a neural lesion, their similar pattern of clinical presentation and response to centrally acting analgesics, may reflect a commonality of central sensitization to their pathophysiology. An important question that still needs to be determined is whether there are individuals with a higher inherited propensity for developing central sensitization than others, and if so, whether this conveys an increased risk in both developing conditions with pain hypersensitivity, and their chronification. Diagnostic criteria to establish the presence of central sensitization in patients will greatly assist the phenotyping of patients for choosing treatments that produce analgesia by normalizing hyperexcitable central neural activity. We have certainly come a long way since the first discovery of activity-dependent synaptic plasticity in the spinal cord and the revelation that it occurs and produces pain hypersensitivity in patients. Nevertheless, discovering the genetic and environmental contributors to and objective biomarkers of central sensitization will be highly beneficial, as will additional treatment options to prevent or reduce this prevalent and promiscuous form of pain plasticity.

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Central sensitization: implications for the diagnosis and treatment of pain.

Improving channel information quality at the base station (BS) is crucial for the optimization of frequency division duplexed (FDD) multi-antenna multiuser downlink systems with limited feedback. To this end, this paper proposes to estimate a particular representation of channel state information (CSI) at the BS through channel norm feedback and a newly developed channel phase codebook, where the long-term channel correlation is efficiently exploited to improve performance. In particular, the channel representation is decomposed into a gain-related part and a phase-related part, with each of them estimated separately. More specifically, the gain-related part is estimated from the channel norm and channel correlation matrix, while the phase-related part is determined using a channel phase codebook, constructed with the generalized Lloyd algorithm. Using the estimated channel representation, joint optimization of multiuser precoding and opportunistic scheduling is performed to obtain an SDMA transmit scheme. Computer simulation results confirm the advantage of the proposed scheme over state of the art limited feedback SDMA schemes under correlated channel environment.

Exploiting Long-Term Channel Correlation in Limited Feedback SDMA Through Channel Phase Codebook

In this paper, we study virtual full-duplex (FD) buffer-aided relaying to recover the multiplexing loss of half-duplex (HD) relaying in a network with multiple buffer-aided relays, each of which has multiple antennas, through opportunistic relay selection and beamforming. The main idea of virtual FD buffer-aided relaying is that a source and a relay simultaneously transmit their own information to another relay and a destination, respectively. In this network, inter-relay interference (IRI) is a crucial problem which has to be resolved like self-interference in the FD relaying. In contrast to previous work that neglected the IRI, we propose two buffer-aided relay selection and beam-forming schemes taking the IRI into consideration. Numerical results show that our proposed relay selection scheme with zero-forcing beamforming (ZFB)-based IRI cancellation approaches the average end-to-end capacity of IRI-free upper bound as the numbers of relays and antennas increase.

Virtual full-duplex buffer-aided relaying — Relay selection and beamforming

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as “massive MIMO”. Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.

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Low-complexity channel estimation in large-scale MIMO using polynomial expansion

Downlink beamforming is a key technology for cellular networks. However, computing the transmit beamformer that maximizes the weighted sum rate subject to a power constraint is an NP-hard problem. As a result, iterative algorithms that converge to a local optimum are used in practice. Among them, the weighted minimum mean square error (WMMSE) algorithm has gained popularity, but its computational complexity and consequent latency has motivated the need for lower-complexity approximations at the expense of performance. Motivated by the recent success of deep unfolding in the trade-off between complexity and performance, we propose the novel application of deep unfolding to the WMMSE algorithm for a MISO downlink channel. The main idea consists of mapping a fixed number of iterations of the WMMSE algorithm into trainable neural network layers, whose architecture reflects the structure of the original algorithm. With respect to traditional end-to-end learning, deep unfolding naturally incorporates expert knowledge, with the benefits of immediate and well-grounded architecture selection, fewer trainable parameters, and better explainability. However, the formulation of the WMMSE algorithm, as described in Shi et al., is not amenable to be unfolded due to a matrix inversion, an eigendecomposition, and a bisection search performed at each iteration. Therefore, we present an alternative formulation that circumvents these operations by resorting to projected gradient descent. By means of simulations, we show that, in most of the settings, the unfolded WMMSE outperforms or performs equally to the WMMSE for a fixed number of iterations, with the advantage of a lower computational load.

Deep unfolding of the weighted MMSE beamforming algorithm.

In this paper, the problem of preamble-based channel estimation in OFDM offset QAM (OFDM/OQAM) systems under a deterministic channel assumption is studied. Recent results indicate that full (all tones carrying pilot symbols) preambles with equal pilot symbols are locally optimal, in the sense that they yield a local minimum of the mean square error (MSE) performance metric of the estimated channel frequency response (CFR), subject to a total training energy constraint. We study the problem of finding the globally optimal full preamble. We show that under a channel constancy assumption, the global optimum coincides with the full preamble of equal symbols. The same result holds even if the channel constancy assumption is removed. Numerical simulations are presented to support the derived results.

Mats Bengtsson

Papers

Exploiting Long-Term Channel Correlation in Limited Feedback SDMA Through Channel Phase Codebook

Virtual full-duplex buffer-aided relaying — Relay selection and beamforming

Low-complexity channel estimation in large-scale MIMO using polynomial expansion

Deep unfolding of the weighted MMSE beamforming algorithm.

On preamble-based channel estimation in OFDM/OQAM systems