We consider a system of two identical Morris-Lecar neurons coupled via electrical coupling. We focus our study on the effects that the coupling strength, γ , and the coupling time delay, τ , cause on the dynamics of the system. For small γ we use the phase model reduction technique to analyze the system behavior. We determine the stable states of the system with respect to γ and τ using the appropriate phase models, and we estimate the regions of validity of the phase models in the γ , τ plane using both analytical and numerical analysis. Next we examine asymptotic of the arbitrary conductance-based neuronal model for γ → +∞ and γ → −∞. The theory of nearly linear systems developed in [30] is extended in the special case of matrices with non-positive eigenvalues. The asymptotic analysis for γ > 0 shows that with appropriate choice of γ the voltages of the neurons can be made arbitrarily close in finite time and will remain that close for all subsequent time, while the asymptotic analysis for γ < 0 suggests the method of estimation of the boundary between “weak” and “strong” coupling.

Quantum entanglement is employed as a resource throughout quantum information science. However, before entanglement can be put to intelligent use, the issues of its production and detection must be considered. This thesis proposes four schemes for producing the bound entangled Smolin state. Three of these schemes produce the Smolin state by means of general quantum gates acting on different initial states - an all-zero state, a GHZ-state and two combined Bell states. The fourth scheme is based on one-qubit operations acting on two-photon states produced by SPDC. Furthermore, a maximum overlap entanglement witness detecting entanglement in the Smolin state is derived. This witness is measurable in three measurement settings with the maximal noise tolerance p=2/3. Lastly, simplified entanglement witnesses for the 4-, 6- and 8-qubit unitary invariant states are derived. These witnesses are measurable in three measurement settings with noise tolerances p=0.1802..., p=0.1502... and p=0.0751..., respectively.

Since last two decades researches have been working on developing systems that can assistsdrivers in the best way possible and make driving safe. Computer vision has played a crucialpart in design of these systems. With the introduction of vision techniques variousautonomous and robust real-time traffic automation systems have been designed such asTraffic monitoring, Traffic related parameter estimation and intelligent vehicles. Among theseautomatic detection and recognition of road signs has became an interesting research topic.The system can assist drivers about signs they don’t recognize before passing them.Aim of this research project is to present an Intelligent Road Sign Recognition System basedon state-of-the-art technique, the Support Vector Machine. The project is an extension to thework done at ITS research Platform at Dalarna University [25]. Focus of this research work ison the recognition of road signs under analysis. When classifying an image its location, sizeand orientation in the image plane are its irrelevant features and one way to get rid of thisambiguity is to extract those features which are invariant under the above mentionedtransformation. These invariant features are then used in Support Vector Machine forclassification. Support Vector Machine is a supervised learning machine that solves problemin higher dimension with the help of Kernel functions and is best know for classificationproblems.

We consider a system of two identical Morris-Lecar neurons coupled via electrical coupling. We focus our study on the effects that the coupling strength, γ , and the coupling time delay, τ , cause on the dynamics of the system. For small γ we use the phase model reduction technique to analyze the system behavior. We determine the stable states of the system with respect to γ and τ using the appropriate phase models, and we estimate the regions of validity of the phase models in the γ , τ plane using both analytical and numerical analysis. Next we examine asymptotic of the arbitrary conductance-based neuronal model for γ → +∞ and γ → −∞. The theory of nearly linear systems developed in [30] is extended in the special case of matrices with non-positive eigenvalues. The asymptotic analysis for γ > 0 shows that with appropriate choice of γ the voltages of the neurons can be made arbitrarily close in finite time and will remain that close for all subsequent time, while the asymptotic analysis for γ < 0 suggests the method of estimation of the boundary between “weak” and “strong” coupling.

An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric n-tuple V. The structure of a free semigroup algebra contains a great deal of information about V. Thus it is natural to study this algebra in order to study V. A free semigroup algebra is said to be analytic if it is isomorphic to the noncommutative analytic Toeplitz algebra, which is a higher-dimensional generalization of the classical algebra of bounded analytic functions on the complex unit disk. This notion of analyticity is of central importance in the general theory of free semigroup algebras. A vector x in H is said to be wandering for an isometric n-tuple V if the set of words in the entries of V map x to an orthonormal set. As in the classical case, the analytic structure of the noncommutative analytic Toeplitz algebra is determined by the existence of wandering vectors for the generators of the algebra. In the first part of this thesis, we prove the following dichotomy: either an isometric n-tuple V has a wandering vector, or the free semigroup algebra it generates is a von Neumann algebra. This implies the existence of wandering vectors for every analytic free semigroup algebra. As a consequence, it follows that every free semigroup algebra is reflexive, in the sense that it is completely determined by its invariant subspace lattice. In the second part of this thesis we prove a decomposition for an isometric tuple of operators which generalizes the classical Lebesgue-von Neumann-Wold decomposition of an isometry into the direct sum of a unilateral shift, an absolutely continuous unitary and a singular unitary. The key result is an operator-algebraic characterization of an absolutely continuous isometric tuple in terms of analyticity. We show that, as in the classical case, this decomposition determines the weakly closed algebra and the von Neumann algebra generated by the tuple.

Spatial processing that exploits the diversity provided by smart antenna arrays, in which the adaptive beamformer is employed, is another alternative to increase the efficiency of wireless system capacity and performance without allocating additional frequency spectrum. An array beamformer is a processor used in conjunction with an array of sensors to provide a versatile form of spatial filtering; it can be designed to form main lobe in direction corresponding to the desired source and nulling the interferences from others direction. They are two types of adaptive array beamformer structures, viz., broadband and narrowband array structures. To deal with the wideband desired signal or interferences the broadband array beamformer is preferred. For broadband interferences suppression, many adaptive array beamforming algorithms, based on the linearly constrained have been extensively used. In this thesis, the beamspace approach for designing the broadband antenna array beamformer, with frequency invariant character, is devised and implemented with the sliding window linearly constrained RLS (SW-LC-RLS) algorithm, to deal with the broadband moving jammers (or interferences) suppression. Also, to combat the pointing error effect of desired user¡¦s look direction, the derivative constraint is adopted for devising the derivative SW-LC-RLS beamforming algorithm for broadband moving jammers suppression. Computer simulation results confirmed that the proposed scheme is more robust against the moving jammers over the conventional algorithms. It can be applied to the existing wideband wireless communications systems to achieve desired performance for supporting high data rate communication services.

For many undersea research application scenarios, instruments need to be deployed for more than one month which is the basic time interval for many phenomena. With limited power supply and memory, management strategies are crucial for the success of data collection. For acoustic recording of undersea activities, in general,either preprogrammed duty cycle is configured to log partial time series,or spectrogram of signal is derived and stored,to utilize the available memory storage efficiently.To overcome this limitation, we come up with an algorithm to classify different and store only the sound data of interest. Features like characteristic frequencies, large amplitude of selected frequencies or intensity threshold are used to identify or classify different patterns. On main limitation for this type of approaches is that the algorithm is generally range-dependent, as a result, also sound-level-dependent. This type of algorithms will be less robust to the change of the environment.One the other hand, one interesting observation is that when human beings look at the spectrogram, they will immediately tell the difference between two patterns. Even though no knowledge about the nature of the source, human beings still can discern the tiny dissimilarity and group them accordingly. This suggests that the recognition and classification can be done in spectrogram as a recognition problem. In this work, we propose to modify Principal Component Analysis by generating feature points from moment invariant and sound Level variance, to classify sounds of interest in the ocean. Among all different sound sources in the ocean, we focus on three categories of our interest, i.e., rain, ship and whale and dolphin. The sound data were recorded with the Passive Acoustic Listener developed by Nystuen, Applied Physics Lab, University of Washington. Among all the data, we manually identify twenty frames for each cases, and use them as the base training set. Feed several unknown clips for classification experiments, we suggest that both point-based feature extraction are effective ways to describe whistle vocalizations and believe that this algorithm would be useful for extracting features from noisy recordings of the callings of a wide variety of species.

In this thesis the direction of arrival estimation of wideband signals using frequency invariant beamforming method is examined. The difficulty with the direction of arrival estimation of wideband signals is that it is not possible to obtain a single covariance matrix valid for the whole frequency spectrum of the signal. There are various methods proposed in the literature to overcome this difficulty. The common aim of all the methods is to obtain a composite covariance matrix for the overall band of the signal. In this thesis, we concentrate on a method in [12]. This method is based on a beamforming technique that provides frequency invariant beams in the band of interest. Therefore there is no need for frequency decomposition as it is done with the other wideband methods. A comparison of the frequency invariant beamforming method with coherent signal subspace methods and narrow band methods is also given.

In this paper, the gap metric is introduced to study the robustness of the stability of feedback systems. A relation between the gap metric and coprime fractions is also investigated. It is shown that the stability radius of the controller in the gap metric is equal to the stability margin of the controller. In the loop-shaping design procedure in the £h-gap metric, it is practically hard to formulate an ideal controller. Finally, this paper studied the conservatism of the gap metric, and proposed some properties that can help for control design and analysis.

A mixture experiment is an experiment in which the q-ingredients {xi,i=1,...,q} are nonnegative and subject to the simplex restriction sum_{i=1}^q x_i=1 on the (q-1)-dimensional probability simplex S^{q-1}. In this work, we investigate the robust D-optimal designs for mixture experiments with consideration on uncertainties in the Scheffe's linear, quadratic and cubic model without 3-way effects. The D-optimal designs for each of the Scheffe's models are used to find the robust D-optimal designs. With uncertianties on the Scheffe's linear and quadratic models, the optimal convex combination of the two model's D-optimal designs can be proved to be a robust D-optimal design. For the case of the Scheffe's linear and cubic model without 3-way effects, we have some numerical results about the robust D-optimal designs, as well as that for Scheffe's linear, quadratic and cubic model without 3-way effects. Ultimately, we discuss the efficiency of a maxmin type criterion D_r under given the robust D-optimal designs for the Scheffe's linear and quadratic models.