ROBUST KULLBACK-LEIBLER DIVERGENCE AND ITS APPLICATIONS IN UNIVERSAL HYPOTHESIS TESTING AND DEVIATION DETECTION

The Kullback-Leibler (KL) divergence is one of the most fundamental metrics in information theory and statistics and provides various operational interpretations in the context of mathematical communication theory and statistical hypothesis testing. The KL divergence for discrete distributions has the desired continuity property which leads to some fundamental results in universal hypothesis testing. With continuous observations, however, the KL divergence is only lower semi-continuous; difficulties arise when tackling universal hypothesis testing with continuous observations due to the lack of continuity in KL divergence. This dissertation proposes a robust version of the KL divergence for continuous alphabets. Specifically, the KL divergence defined from a distribution to the Levy ball centered at the other distribution is found to be continuous. This robust version of the KL divergence allows one to generalize the result in universal hypothesis testing for discrete alphabets to that for continuous observations. The optimal decision rule is developed whose robust property is provably established for universal hypothesis testing. Another application of the robust KL divergence is in deviation detection: the problem of detecting deviation from a nominal distribution using a sequence of independent and identically distributed observations. An asymptotically -optimal detector is then developed for deviation detection where the Levy metric becomes a very natural distance measure for deviation from the nominal distribution. Lastly, the dissertation considers the following variation of a distributed detection problem: a sensor may overhear other sensors\u27 transmissions and thus may choose to refine its output in the hope of achieving a better detection performance. While this is shown to be possible for the fixed sample size test, asymptotically (in the number of samples) there is no performance gain, as measured by the KL divergence achievable at the fusion center, provided that the observations are conditionally independent. For conditionally dependent observations, however, asymptotic detection performance may indeed be improved when overhearing is utilized

Relation of muscular contractions to mechanical deformation in the human tibia during different locomotive activities

As one of the major hard tissue in humans and most vertebrates, the skeleton, generally referring to bone, provides the essential frame to support the body and to thus permit locomotion. Considering the functional requirements of bones across different species, e.g. from rats to dinosaurs, or during different growth periods, e.g. from embryo to old age, it is not difficult to conceive that bones adapt to the experienced mechanical environment. In fact, mechanically regulated bone modeling and remodeling is one of the major means to maintain regular bone metabolism. The findings on the bone adaptation to the mechanical environment have been well theorized by Julius Wolff in 1890s [1] as ‘Wolff’s law’ and refined later by Harold Frost as ‘mechanostat’ [2-4]. Evidence from numerous animal studies in the past revealed the adaptation process of the bones to the well-defined artificial mechanical environment and suggested certain relationship between the adaptation in relation to the types of loading, e.g. loading amplitude, loading cycle, loading frequency and so on [5-8]. Conversely, bone degradation was generally observed during disuse, e.g. prolonged bed rest [9], or in the microgravity environment during space flight [10]. Indeed, the best way to further our understanding in this adaptation process is to quantitatively study the mechanical loading on bone during daily locomotor activities. However, this is still rather challenging due to technical difficulties. More importantly, the mechanical load on bones can vary greatly across individuals or species, as the variance between the body size, locomotor pattern and speed

A Vertical Channel Model of Molecular Communication based on Alcohol Molecules

The study of Molecular Communication(MC) is more and more prevalence, and channel model of MC plays an important role in the MC System. Since different propagation environment and modulation techniques produce different channel model, most of the research about MC are in horizontal direction,but in nature the communications between nano machines are in short range and some of the information transportation are in the vertical direction, such as transpiration of plants, biological pump in ocean, and blood transportation from heart to brain. Therefore, this paper we propose a vertical channel model which nano-machines communicate with each other in the vertical direction based on pure diffusion. We first propose a vertical molecular communication model, we mainly considered the gravity as the factor, though the channel model is also affected by other main factors, such as the flow of the medium, the distance between the transmitter and the receiver, the delay or sensitivity of the transmitter and the receiver. Secondly, we set up a test-bed for this vertical channel model, in order to verify the difference between the theory result and the experiment data. At last, we use the data we get from the experiment and the non-linear least squares method to get the parameters to make our channel model more accurate.Comment: 5 pages,7 figures, Accepted for presentation at BICT 2015 Special Track on Molecular Communication and Networking (MCN). arXiv admin note: text overlap with arXiv:1311.6208 by other author

Newton-based alternating methods for the ground state of a class of multi-component Bose-Einstein condensates

The computation of the ground states of special multi-component Bose-Einstein condensates (BECs) can be formulated as an energy functional minimization problem with spherical constraints. It leads to a nonconvex quartic-quadratic optimization problem after suitable discretizations. First, we generalize the Newton-based methods for single-component BECs to the alternating minimization scheme for multi-component BECs. Second, the global convergent alternating Newton-Noda iteration (ANNI) is proposed. In particular, we prove the positivity preserving property of ANNI under mild conditions. Finally, our analysis is applied to a class of more general "multi-block" optimization problems with spherical constraints. Numerical experiments are performed to evaluate the performance of proposed methods for different multi-component BECs, including pseudo spin-1/2, anti-ferromagnetic spin-1 and spin-2 BECs. These results support our theory and demonstrate the efficiency of our algorithms