A General Geometric Fourier Transform

The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature. We show which constraints are additionally necessary to obtain certain features like linearity or a shift theorem. As a result, we provide guidelines for the target-oriented design of yet unconsidered transforms that fulfill requirements in a specific application context. Furthermore, the standard theorems do not need to be shown in a slightly different form every time a new geometric Fourier transform is developed since they are proved here once and for all.Comment: First presented in Proc. of The 9th Int. Conf. on Clifford Algebras and their Applications, (2011

Restoring Speech Following Total Removal of the Larynx

By speech articulator movement and training a transformation to audio we can restore the power of speech to someone who has lost their larynx. We sense changes in magnetic field caused by movements of small magnets attached to the lips and tongue. The sensor transformation uses recurrent neural networks

ChunkitApp : Investigating the relevant units of online speech processing

Peer reviewe

Direct Speech Reconstruction From Articulatory Sensor Data by Machine Learning

This paper describes a technique that generates speech acoustics from articulator movements. Our motivation is to help people who can no longer speak following laryngectomy, a procedure that is carried out tens of thousands of times per year in the Western world. Our method for sensing articulator movement, permanent magnetic articulography, relies on small, unobtrusive magnets attached to the lips and tongue. Changes in magnetic field caused by magnet movements are sensed and form the input to a process that is trained to estimate speech acoustics. In the experiments reported here this “Direct Synthesis” technique is developed for normal speakers, with glued-on magnets, allowing us to train with parallel sensor and acoustic data. We describe three machine learning techniques for this task, based on Gaussian mixture models, deep neural networks, and recurrent neural networks (RNNs). We evaluate our techniques with objective acoustic distortion measures and subjective listening tests over spoken sentences read from novels (the CMU Arctic corpus). Our results show that the best performing technique is a bidirectional RNN (BiRNN), which employs both past and future contexts to predict the acoustics from the sensor data. BiRNNs are not suitable for synthesis in real time but fixed-lag RNNs give similar results and, because they only look a little way into the future, overcome this problem. Listening tests show that the speech produced by this method has a natural quality that preserves the identity of the speaker. Furthermore, we obtain up to 92% intelligibility on the challenging CMU Arctic material. To our knowledge, these are the best results obtained for a silent-speech system without a restricted vocabulary and with an unobtrusive device that delivers audio in close to real time. This work promises to lead to a technology that truly will give people whose larynx has been removed their voices back

A new method for detection of exciton Bose condensation using stimulated two-photon emission

Stimulated two-photon emission by Bose-condensed excitons accompanied by a coherent two-exciton recombination, i.e., by simultaneous recombination of two excitons with opposite momenta leaving unchanged the occupation numbers of excitonic states with nonzero momenta, is investigated. Raman light scattering accompanied by a similar two-exciton recombination (or generation of two excitons) is also analyzed. The processes under consideration can occur only if a system contains Bose condensate, therefore, their detection can be used as a new method to reveal Bose condensation of excitons. The recoil momentum, which corresponds to a change in the momentum of the electromagnetic field in the processes, is transferred to phonons or impurities. If the recoil momentum is transmitted to optical phonons with frequency $\omega_0^s$, the stimulated two-photon emission with the coherent two-exciton recombination leads to the appearance of a line at $2\Omega'-\omega$, where $\Omega'=\Omega-\omega_0^s$ and $\Omega$ is the light frequency corresponding to the recombination of an exciton with zero momentum. Formulas for the cross sections at finite temperatures are obtained for the processes under consideration. Our estimates indicate that a spectral line, corresponding to the stimulated two-photon emission accompanied by the coherent optical phonon-assisted two-exciton recombination can be experimentally detected in Cu$_2$O.Comment: 28 pages, 3 Postscript figure

Going beyond Visualization. Verbalization as Complementary Medium to Explain Machine Learning Models

In this position paper, we argue that a combination of visualization and verbalization techniques is beneficial for creating broad and versatile insights into the structure and decision-making processes of machine learning models. Explainability of machine learning models is emerging as an important area of research. Hence, insights into the inner workings of a trained model allow users and analysts, alike, to understand the models, develop justifications, and gain trust in the systems they inform. Explanations can be generated through different types of media, such as visualization and verbalization. Both are powerful tools that enable model interpretability. However, while their combination is arguably more powerful than each medium separately, they are currently applied and researched independently. To support our position that the combination of the two techniques is beneficial to explain machine learning models, we describe the design space of such a combination and discuss arising research questions, gaps, and opportunities

Some results on the lattice parameters of quaternionic Gabor frames

Gabor frames play a vital role not only modern harmonic analysis but also in several fields of applied mathematics, for instances, detection of chirps, or image processing. In this work we present a non-trivial generalization of Gabor frames to the quaternionic case and give new density results. The key tool is the two-sided windowed quaternionic Fourier transform (WQFT). As in the complex case, we want to write the WQFT as an inner product between a quaternion-valued signal and shifts and modulates of a real-valued window function. We demonstrate a Heisenberg uncertainty principle and for the results regarding the density, we employ the quaternionic Zak transform to obtain necessary and sufficient conditions to ensure that a quaternionic Gabor system is a quaternionic Gabor frame. We conclude with a proof that the Gabor conjecture do not hold true in the quaternionic case

Myocardial perfusion scintigraphy: the evidence: A consensus conference organised by the British Cardiac Society, the British Nuclear Cardiology Society and the British Nuclear Medicine Society, endorsed by the Royal College of Physicians of London and the Royal College of Radiologists

This review summarises the evidence for the role of myocardial perfusion scintigraphy (MPS) in patients with known or suspected coronary artery disease. It is the product of a consensus conference organised by the British Cardiac Society, the British Nuclear Cardiology Society and the British Nuclear Medicine Society and is endorsed by the Royal College of Physicians of London and the Royal College of Radiologists. It was used to inform the UK National Institute of Clinical Excellence in their appraisal of MPS in patients with chest pain and myocardial infarction. MPS is a well-established, non-invasive imaging technique with a large body of evidence to support its effectiveness in the diagnosis and management of angina and myocardial infarction. It is more accurate than the exercise ECG in detecting myocardial ischaemia and it is the single most powerful technique for predicting future coronary events. The high diagnostic accuracy of MPS allows reliable risk stratification and guides the selection of patients for further interventions, such as revascularisation. This in turn allows more appropriate utilisation of resources, with the potential for both improved clinical outcomes and greater cost-effectiveness. Evidence from modelling and observational studies supports the enhanced cost-effectiveness associated with MPS use. In patients presenting with stable or acute chest pain, strategies of investigation involving MPS are more cost-effective than those not using the technique. MPS also has particular advantages over alternative techniques in the management of a number of patient subgroups, including women, the elderly and those with diabetes, and its use will have a favourable impact on cost-effectiveness in these groups. MPS is already an integral part of many clinical guidelines for the investigation and management of angina and myocardial infarction. However, the technique is underutilised in the UK, as judged by the inappropriately long waiting times and by comparison with the numbers of revascularisations and coronary angiograms performed. Furthermore, MPS activity levels in this country fall far short of those in comparable European countries, with about half as many scans being undertaken per year. Currently, the number of MPS studies performed annually in the UK is 1,200/million population/year. We estimate the real need to be 4,000/million/year. The current average waiting time is 20 weeks and we recommend that clinically appropriate upper limits of waiting time are 6 weeks for routine studies and 1 week for urgent studies

Quantum Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers

We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous semiconductor laser devices. The QMBE are derived from fully quantum mechanical operator dynamics describing the interaction of the light field with the quantum states of the electrons and the holes near the band gap. By taking into account field-field correlations and field-dipole correlations, the QMBE include quantum noise effects which cause spontaneous emission and amplified spontaneous emission. In particular, the source of spontaneous emission is obtained by factorizing the dipole-dipole correlations into a product of electron and hole densities. The QMBE are formulated for general devices, for edge emitting lasers and for vertical cavity surface emitting lasers, providing a starting point for the detailed analysis of spatial coherence in the near field and far field patterns of such laser diodes. Analytical expressions are given for the spectra of gain and spontaneous emission described by the QMBE. These results are applied to the case of a broad area laser, for which the frequency and carrier density dependent spontaneous emission factor beta and the evolution of the far field pattern near threshold are derived.Comment: 22 pages RevTex and 7 figures, submitted to Phys.Rev.A, revisions in abstract and in the discussion of temporal coherenc

Absolute Frequency Measurements of the Hg^+ and Ca Optical Clock Transitions with a Femtosecond Laser

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg^+ and Ca optical standards with respect to the SI second as realized at NIST. We find the transition frequencies to be f_Hg=1 064 721 609 899 143(10) Hz and f_Ca=455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg^+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of |(df_Ca/dt)/f_Ca| < 8 x 10^{-14} yr^{-1}, and |(df_Hg/dt)/f_Hg|< 30 x 10^{-14} yr^{-1}.Comment: 6 pages, including 4 figures. RevTex 4. Submitted to Phys. Rev. Let