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

Ultrafast pump-probe dynamics in ZnSe-based semiconductor quantum-wells

Pump-probe experiments are used as a controllable way to investigate the properties of photoexcited semiconductors, in particular, the absorption saturation. We present an experiment-theory comparison for ZnSe quantum wells, investigating the energy renormalization and bleaching of the excitonic resonances. Experiments were performed with spin-selective excitation and above-bandgap pumping. The model, based on the semiconductor Bloch equations in the screened Hartree-Fock approximation, takes various scattering processes into account phenomenologically. Comparing numerical results with available experimental data, we explain the experimental results and find that the electron spin-flip occurs on a time scale of 30 ps.Comment: 10 pages, 9 figures. Key words: nonlinear and ultrafast optics, modeling of femtosecond pump-probe experiments, electron spin-flip tim

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

Influence of Coulomb and Phonon Interaction on the Exciton Formation Dynamics in Semiconductor Heterostructures

A microscopic theory is developed to analyze the dynamics of exciton formation out of incoherent carriers in semiconductor heterostructures. The carrier Coulomb and phonon interaction is included consistently. A cluster expansion method is used to systematically truncate the hierarchy problem. By including all correlations up to the four-point (i.e. two-particle) level, the fundamental fermionic substructure of excitons is fully included. The analysis shows that the exciton formation is an intricate process where Coulomb correlations rapidly build up on a picosecond time scale while phonon dynamics leads to true exciton formation on a slow nanosecond time scale.Comment: 18 pages, 7 figure

Cerebellar Pathology Does Not Impair Performance on Identification or Categorization Tasks

In comparison to the basal ganglia, prefrontal cortex, and medial temporal lobes, the cerebellum has been absent from recent research on the neural substrates of categorization and identification, two prominent tasks in the learning and memory literature. To investigate the contribution of the cerebellum to these tasks, we tested patients with cerebellar pathology (seven with bilateral degeneration, six with unilateral lesions, and two with midline damage) on rule-based and information-integration categorization tasks and an identification task. In rule-based tasks, it is assumed that participants learn the categories through an explicit reasoning process. In information-integration tasks, optimal performance requires the integration of information from multiple stimulus dimensions, and participants are typically unaware of the decision strategy. The identification task, in contrast, required participants to learn arbitrary, color-word associations. The cerebellar patients performed similar to matched controls on all three tasks and performance did not vary with the extent of cerebellar pathology. Although the interpretation of these null results requires caution, these data contribute to the current debate on cerebellar contributions to cognition by providing boundary conditions on understanding the neural substrates of categorization and identification, and help define the functional domain of the cerebellum in learning and memory

Bose-Einstein statistics in thermalization and photoluminescence of quantum well excitons

Quasi-equilibrium relaxational thermodynamics is developed to understand LA-phonon-assisted thermalization of Bose-Einstein distributed excitons in quantum wells. We study the quantum-statistical effects in the relaxational dynamics of the effective temperature of excitons $T = T(t)$. When $T$ is less than the degeneracy temperature $T_0$, well-developed Bose-Einstein statistics of quantum well excitons leads to nonexponential and density-dependent thermalization. At low bath temperatures $T_b \to 0$ the thermalization of quantum-statistically degenerate excitons effectively slows down and $T(t) \propto 1 / \ln t$. We also analyze the optical decay of Bose-Einstein distributed excitons in perfect quantum wells and show how nonclassical statistics influences the effective lifetime $\tau_{opt}$. In particular, $\tau_{opt}$ of a strongly degenerate gas of excitons is given by $2 \tau_R$, where $\tau_R$ is the intrinsic radiative lifetime of quasi-two-dimensional excitons. Kinetics of resonant photoluminescence of quantum well excitons during their thermalization is studied within the thermodynamic approach and taking into account Bose-Einstein statistics. We find density-dependent photoluminescence dynamics of statistically degenerate excitons. Numerical modeling of the thermalization and photoluminescence kinetics of quasi-two-dimensional excitons are given for GaAs/AlGaAs quantum wells.Comment: 19 pages, 9 figures. Phys. Rev. B (accepted for publication

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

Genomic-Bioinformatic Analysis of Transcripts Enriched in the Third-Stage Larva of the Parasitic Nematode Ascaris suum

Differential transcription in Ascaris suum was investigated using a genomic-bioinformatic approach. A cDNA archive enriched for molecules in the infective third-stage larva (L3) of A. suum was constructed by suppressive-subtractive hybridization (SSH), and a subset of cDNAs from 3075 clones subjected to microarray analysis using cDNA probes derived from RNA from different developmental stages of A. suum. The cDNAs (n = 498) shown by microarray analysis to be enriched in the L3 were sequenced and subjected to bioinformatic analyses using a semi-automated pipeline (ESTExplorer). Using gene ontology (GO), 235 of these molecules were assigned to ‘biological process’ (n = 68), ‘cellular component’ (n = 50), or ‘molecular function’ (n = 117). Of the 91 clusters assembled, 56 molecules (61.5%) had homologues/orthologues in the free-living nematodes Caenorhabditis elegans and C. briggsae and/or other organisms, whereas 35 (38.5%) had no significant similarity to any sequences available in current gene databases. Transcripts encoding protein kinases, protein phosphatases (and their precursors), and enolases were abundantly represented in the L3 of A. suum, as were molecules involved in cellular processes, such as ubiquitination and proteasome function, gene transcription, protein–protein interactions, and function. In silico analyses inferred the C. elegans orthologues/homologues (n = 50) to be involved in apoptosis and insulin signaling (2%), ATP synthesis (2%), carbon metabolism (6%), fatty acid biosynthesis (2%), gap junction (2%), glucose metabolism (6%), or porphyrin metabolism (2%), although 34 (68%) of them could not be mapped to a specific metabolic pathway. Small numbers of these 50 molecules were predicted to be secreted (10%), anchored (2%), and/or transmembrane (12%) proteins. Functionally, 17 (34%) of them were predicted to be associated with (non-wild-type) RNAi phenotypes in C. elegans, the majority being embryonic lethality (Emb) (13 types; 58.8%), larval arrest (Lva) (23.5%) and larval lethality (Lvl) (47%). A genetic interaction network was predicted for these 17 C. elegans orthologues, revealing highly significant interactions for nine molecules associated with embryonic and larval development (66.9%), information storage and processing (5.1%), cellular processing and signaling (15.2%), metabolism (6.1%), and unknown function (6.7%). The potential roles of these molecules in development are discussed in relation to the known roles of their homologues/orthologues in C. elegans and some other nematodes. The results of the present study provide a basis for future functional genomic studies to elucidate molecular aspects governing larval developmental processes in A. suum and/or the transition to parasitism

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

Physical Activity, Sedentary Time and Physical Capability in Early Old Age: British Birth Cohort Study

Purpose To investigate the associations of time spent sedentary, in moderate-to-vigorous-intensity physical activity (MVPA) and physical activity energy expenditure (PAEE) with physical capability measures at age 60-64 years. Methods Time spent sedentary and in MVPA and, PAEE were assessed using individually calibrated combined heart rate and movement sensing among 1727 participants from the MRC National Survey of Health and Development in England, Scotland and Wales as part of a detailed clinical assessment undertaken in 2006-2010. Multivariable linear regression models were used to examine the cross-sectional associations between standardised measures of each of these behavioural variables with grip strength, chair rise and timed up-&-go (TUG) speed and standing balance time. Results Greater time spent in MVPA was associated with higher levels of physical capability; adjusted mean differences in each capability measure per 1standard deviation increase in MVPA time were: grip strength (0.477 kg, 95% confidence interval (CI): 0.015 to 0.939), chair rise speed (0.429 stands/min, 95% CI: 0.093 to 0.764), standing balance time (0.028 s, 95% CI: 0.003 to 0.053) and TUG speed (0.019 m/s, 95% CI: 0.011 to 0.026). In contrast, time spent sedentary was associated with lower grip strength (-0.540 kg, 95% CI: -1.013 to -0.066) and TUG speed (-0.011 m/s, 95% CI: -0.019 to -0.004). Associations for PAEE were similar to those for MVPA. Conclusion Higher levels of MVPA and overall physical activity (PAEE) are associated with greater levels of physical capability whereas time spent sedentary is associated with lower levels of capability. Future intervention studies in older adults should focus on both the promotion of physical activity and reduction in time spent sedentary