3,217 research outputs found
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
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