Inflationary power spectra with quantum holonomy corrections

In this paper we study slow-roll inflation with holonomy corrections from loop quantum cosmology. Both tensor and scalar power spectra of primordial perturbations are computed up to the first order in slow-roll parameters and $V/\rho_{c}$, where $V$ is a potential of the scalar field and $\rho_{c}$ is a critical energy density (expected to be of the order of the Planck energy density). Possible normalizations of modes at short scales are discussed. In case the normalization is performed with use of the Wronskian condition applied to adiabatic vacuum, the tensor and scalar spectral indices are not quantum corrected in the leading order. However, by choosing an alternative method of normalization one can obtain quantum corrections in the leading order. Furthermore, we show that the holonomy-corrected equation of motion for tensor modes can be derived from an effective background metric. This allows us to prove that the Wronskian normalization condition for the tensor modes preserves the classical form.Comment: 21 page

Discovery and recognition of motion primitives in human activities

We present a novel framework for the automatic discovery and recognition of motion primitives in videos of human activities. Given the 3D pose of a human in a video, human motion primitives are discovered by optimizing the `motion flux', a quantity which captures the motion variation of a group of skeletal joints. A normalization of the primitives is proposed in order to make them invariant with respect to a subject anatomical variations and data sampling rate. The discovered primitives are unknown and unlabeled and are unsupervisedly collected into classes via a hierarchical non-parametric Bayes mixture model. Once classes are determined and labeled they are further analyzed for establishing models for recognizing discovered primitives. Each primitive model is defined by a set of learned parameters. Given new video data and given the estimated pose of the subject appearing on the video, the motion is segmented into primitives, which are recognized with a probability given according to the parameters of the learned models. Using our framework we build a publicly available dataset of human motion primitives, using sequences taken from well-known motion capture datasets. We expect that our framework, by providing an objective way for discovering and categorizing human motion, will be a useful tool in numerous research fields including video analysis, human inspired motion generation, learning by demonstration, intuitive human-robot interaction, and human behavior analysis

Neural correlates of contrast normalization in the Drosophila visual system

The fruit fly Drosophila melanogaster has long become a paramount model organism for research in life sciences. As a result of the fly’s high temporal resolution and its reliable optomotor response - a reflex that helps it compensate for movements of the environment, - Drosophila lends itself exceptionally well to the study of vision and, in particular, the mechanism of motion detection. In the wild, Drosophila is active throughout the day, with especially high levels of activity at dawn and dusk, the periods of time when the visuals of the environment are changing rapidly. The fruit flies can also be found in a variety of habitats, from the expanse of an open field to the inside of a cluttered kitchen. Altogether, Drosophila encounters a variety of visual statistics it must employ to robustly respond to the outside world and succeed in finding food, escaping predators, and carrying out courtship behavior. In my thesis, I focused on the effects of visual contrast, i.e., differences in brightness in the environment, on the fly’s motion vision. I studied the impact of the surround contrast on the filtering properties of the visual interneurons within the motion detection circuit, including the first direction-selective T4 and T5 cells and their main inputs, and how the fly compensates for the changes in contrast to faithfully match the direction and speed of its movement to the external motion under various contrast conditions. Firstly, in Manuscript 1, we established the existence of contrast normalization in the early visual system of Drosophila and demonstrated its suppressive effect on the response amplitude at higher contrasts. We determined where contrast normalization first arises in the optic lobe and identified the main inputs into the T4 and T5 cells that exhibit contrast normalizing properties. We comprehensively characterized the normalization process: namely, it is fast, not dependent on the direction of motion, its effect comes from outside the receptive field of a cell and increases in strength with the size of the visual surround. Additionally, we demonstrated that the normalization relies on neuronal feedback and showed that adding a contrast normalization stage to the existing models of motion detection improves their robustness, matching their performance to the results obtained in behavioral experiments. In Manuscript 2, we further investigated the effects of contrast normalization on the main inputs to T4 and T5 cells, now focusing on its effect on the filtering properties of the cells. We demonstrated that spatially or temporally dynamic surrounds elicit contrast normalization, while static ones do not. We further showed that, in addition to the suppressive effect on the amplitude, contrast normalization speeds up the kinetics of the response and confirmed that this effect is not due to signal saturation and involves a change in the filtering properties of the cell. In summary, we elucidated the role of contrast normalization in the motion detection circuit in the early visual system of Drosophila, comprehensively described the characteristics of the normalization process, and outlined its effects on the filtering properties of the cells. We also emphasized the potential role of shunting inhibition and narrowed down the search for the main candidates in the contrast normalization mechanism, paving the way for future studies to further delve into the contrast normalization circuit and implementation mechanism

Green's function of fully anharmonic lattice vibration

Motivated by the discovery of superconductivity in beta-pyrochlore oxides, we study property of rattling motion coupled with conduction electrons. We derive the general expression of the Green's function of fully anharmonic lattice vibration within the accuracy of the second order perturbation of electron-ion interaction by introducing self-energy, vertex-correction, and normalization factor for each transition. Using the expression, we discuss the characteristic properties of the spectral function in the entire range from weakly anharmonic potential to double-well case, and calculate NMR relaxation rate due to the two phonon Raman process