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

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

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.

/pdf/central-sensitization-implications-for-the-diagnosis-and-18p4x3px9q.pdf

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

The cross-layer design of future communication systems jointly optimizes multiple network layers with the goal of boosting the system wide performance. This trend brings together the physical and the medium access layers. For the joint optimization of these two lowest layers, it is necessary to understand and relate their terms and concepts. In this paper, we study the interplay between four terms, namely channel state information from link-level, scheduling and user distribution from system level, and different performance measures from both levels. The envisaged scenario is the cellular downlink transmission.

On the interplay between scheduling, user distribution, CSI, and performance measures in cellular downlink

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior inverse-Wishart distributions. The nonconvex problem of jointly estimating the signal of interest and the covariance matrices is tackled by a computationally efficient fixed-point iteration as well as an approximate variational Bayes solution. The statistical performance of estimators is compared numerically to state-of-the-art estimators from the literature and shown to perform favorably.

Estimation for the Linear Model With Uncertain Covariance Matrices

We investigate energy-efficient communications for time-division multiple access (TDMA) multiple-input multiple-output (MIMO) cognitive radio (CR) networks operating in underlay mode. In particular, we consider the joint optimization over both the time resource and the transmit precoding matrices to minimize the overall energy consumption of a single cell secondary network with multiple secondary users (SUs), while ensuring their quality of service (QoS). The corresponding mathematical formulations turn out to be non-convex, and thus of high complexity to solve in general. We give a comprehensive treatment of this problem, considering both the cases of perfect channel state information (CSI) and statistical CSI of the channels from the SUs to the primary receiver. We tackle the non-convexity by applying a proper optimization decomposition that allows the overall problem to be efficiently solved. In particular, we show that when the SUs only have statistical CSI, the optimal solution can be found in polynomial time. Moreover, if we consider additional integer constraints on the time variable which is usually a requirement in practical wireless system, the overall problem becomes a mixed-integer non-convex optimization which is more complicated. By exploring the special structure of this particular problem, we show that the optimal integer time solution can be obtained in polynomial time with a simple greedy algorithm. When the SUs have perfect CSI, the decomposition based algorithm is guaranteed to find the optimal solution when the secondary system is under-utilized . Simulation results show that the energy-optimal transmission scheme adapts to the traffic load of the secondary system to create a win-win situation where the SUs are able to decrease the energy consumption and the PUs experience less interference from the secondary system. The effect is particularly pronounced when the secondary system is under-utilized.

Energy Efficient Transmissions in Cognitive MIMO Systems With Multiple Data Streams

Physical wireless transceivers suffer from a variety of impairments that distort the transmitted and received signals. Their degrading impact is particularly evident in modern systems with multiuser transmission, high transmit power, and low-cost devices, but their existence is routinely ignored in the optimization literature for multicell transmission. This paper provides a detailed analysis of coordinated beamforming in the multicell downlink. We solve two optimization problems under a transceiver impairment model and derive the structure of the optimal solutions. We show numerically that these solutions greatly reduce the impact of impairments, compared with beamforming developed for ideal transceivers. Although the so-called multiplexing gain is zero under transceiver impairments, we show that the gain of multiplexing can be large at practical SNRs.

Optimal Coordinated Beamforming in the Multicell Downlink with Transceiver Impairments

In the search of improved capacity and performance in wireless communication systems, antenna arrays have emerged as a promising technique. In these applications, as well as radar and other sensor array applications , it is important to have a good model of the propagation channel. This thesis deals with one such model an environment where the signal of each source is scattered by a large number of reeections close to the source as an example to study some techniques that can be used in more realistic environments. Two main problems are studied, estimation of parameters characterizing the channel and estimation of the signal transmitted at each source, the so-called Signal Copy problem. Since the optimal solutions require high computational power, several algorithms with suboptimal performance but low complexity are presented. For the particular choice of model, an approximation of each spatially scattered source by two point sources is shown to perform well. For the signal copy problem, the rate of change of the channel has large impact on the theoretical treatment, but makes almost no diierence on the results. It is shown that in the search of high signal to interference and noise ratio as well as low probability of outage, it is no loss to assume that the channel variations are rapid. A new low complexity algorithm is presented for estimation of Direction of Arrival (DOA) and spread angle of scattered sources. The main computational step is performed using a standard DOA estimation algorithm for point sources, such as root-MUSIC or MODE. The estimates are shown to be consistent and the asymptotic variance of the estimation errors is derived. As an alternative for future algorithm development, the idea of subspace tting is extended to estimation of parameters in full rank data models. All results are exempliied and veriied with numerical simulations. Acknowledgments Leaving an interesting and safe job in Karlstad for a new life as a Ph.D. student in Stockholm, was certainly a big step and a hard decision. Now 2 1 2 years later, I certainly do not regret my choice. I would like to express my gratitude to my supervisor Professor Bjjrn Ottersten for giving me the opportunity to spend these years at KTH and for all his encouragement , ideas, proof reading and advice. I want to thank all my colleagues at the department for the nice atmosphere and all discussions at the lunch table and …

Mats Bengtsson

Papers

On the interplay between scheduling, user distribution, CSI, and performance measures in cellular downlink

Estimation for the Linear Model With Uncertain Covariance Matrices

Energy Efficient Transmissions in Cognitive MIMO Systems With Multiple Data Streams

Optimal Coordinated Beamforming in the Multicell Downlink with Transceiver Impairments

Sensor array processing for scattered sources