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.

We consider the uplink of a cellular massive MIMO network. Acquiring channel state information at the base stations (BSs) requires uplink pilot signaling. Since the number of orthogonal pilot sequences is limited by the channel coherence, pilot reuse across cells is necessary to achieve high spectral efficiency. However, finding efficient pilot reuse patterns is non-trivial especially in practical asymmetric BS deployments. We approach this problem using coalitional game theory. Each BS has a few unique pilots and can form coalitions with other BSs to gain access to more pilots. The BSs in a coalition thus benefit from serving more users in their cells, at the expense of higher pilot contamination and interference. Given that a cell's average spectral efficiency depends on the overall pilot reuse pattern, the suitable coalitional game model is in partition form. We develop a low-complexity distributed coalition formation based on individual stability. By incorporating a base station intercommunication budget constraint, we are able to control the overhead in message exchange between the base stations and ensure the algorithm's convergence to a solution of the game called individually stable coalition structure. Simulation results reveal fast algorithmic convergence and substantial performance gains over the baseline schemes with no pilot reuse, full pilot reuse, or random pilot reuse pattern.

Adaptive Pilot Clustering in Heterogeneous Massive MIMO Networks

In this paper we have proposed clock error mitigation from the measurements in the scheduled based self localization system. We propose measurement model with clock errors while following a scheduled transmission among anchor nodes. Further, RLS algorithm is proposed to estimate clock error and to calibrate measurements of self localizing node against relative clock errors of anchor nodes. A full-scale experimental validation is provided based on commercial off-the-shelf UWB radios under IEEE-standardized protocols.

Schedule based self localization of asynchronous wireless nodes with experimental validation

Based on measured MIMO channel impulse responses, this paper investigates and compares low rate channel feedback techniques and their influence on the throughput. The main focus is on codebook based precoding techniques which only require a few bits in the feedback to achieve near optimal performance. Three types of precoding schemes are compared. The first technique uses a combination of both long term and low rate short term CSI at the transmitter, whereas the second technique uses only the low rate short term CSI at the transmitter. These first two techniques have been proposed by Tung et al. The third technique is the closed loop spatial multiplexing mode proposed in LTE Release 8. All these techniques are here evaluated for measured 4×2 MIMO channels. The results indicate the benefits of the proposed techniques (i.e. technique one and two) over the LTE codebook.

Evaluation of low rate channel feedback schemes for MIMO systems

Successive zero-forcing dirty paper coding (SZF-DPC) is a simplified alternative to DPC for MIMO broadcast channels (MIMO BCs). In the SZF-DPC scheme, the noncausally-known interference is canceled by DPC, while the residual interference is suppressed by the ZF technique. Due to the ZF constraints, the precoders are constrained to lie in the null space of a matrix. For the sum rate maximization problem under a sum power constraint, the existing precoder designs naturally rely on the singular value decomposition (SVD). The SVD-based design is optimal but needs high computational complexity. Herein, we propose two low-complexity optimal precoder designs for SZF-DPC, all based on the QR decomposition (QRD), which requires lower complexity than SVD. The first design method is an iterative algorithm to find an orthonormal basis of the null space of a matrix that has a recursive structure. The second proposed method, which will be shown to require the lowest complexity, results from applying a single QRD to the matrix comprising all users' channel matrices. We analytically and numerically show that the two proposed precoder designs are optimal.

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Successive zero-forcing DPC with sum power constraint: Low-complexity optimal designs

Herein, we investigate the mismatch of the Kronecker structure based MIMO channel model. Finding the minimum mismatch is trivial and the result is always 0. The maximization problem, on the other hand, is not convex in general. Therefore we combine semidefinite programming with a grid search, to find a lower bound of the maximum mismatch. Numerical examples show that the bound is tight even for moderate number of points in the grid. The resulting worst case model error, is much larger than the model error previously observed in measurement campaigns, which confirms that the channel correlation matrix can, indeed, be well approximated by the Kronecker product of the correlation matrices at the transmitter and receiver for the measured NLOS indoor scenarios.

Mats Bengtsson

Papers

Adaptive Pilot Clustering in Heterogeneous Massive MIMO Networks

Schedule based self localization of asynchronous wireless nodes with experimental validation

Evaluation of low rate channel feedback schemes for MIMO systems

Successive zero-forcing DPC with sum power constraint: Low-complexity optimal designs

On The Error of Kronecker Structure Based MIMO Channel Model