<p>We show topological priors play an important role in solving the inverse problem of shape reconstruction. We classify the applications into 1D, 2D, and 3D cases:</p><p>In 1D, we show that the persistent extrema of the curvature function of a closed curve are useful for shape simplication. In 2D, we study how to label a scene into multiple tiers to approximate the actual scene layout. We use the number of extrema as a topological prior to bound the complexity of the shape of tiers and study 2D labeling under symmetry shape priors. In 3D, we recover the detailed 3D root shape using multiple 2D images. Three novel ideas are presented. First, we propose the use of harmonic images for background subtraction. Second, we develop the regularized visual hull to preserve the details of an example image in reconstruction. Third, we enforce the topological connectedness by an ecient algorithm that is inspired by the recent development of persistent homology.</p><p>Computational efficiency is emphasized throughout the thesis. We show that 1D topological persistence can be computed in O(n) time on a closed curve of n nodes. For 2D tiered labeling, we give an approximation algorithm to compute it in O(nK) time for K tiers on an image of n pixels. For 3D root reconstruction, we accelerate the computation using oct-trees and minimal spanning trees. With these ingredients, it takes only a few seconds to reconstruct a detailed root shape from 40 images of resolution 1600*1200 on a laptop.</p> / Dissertation

Optical packet switching (OPS) is the most prominent candidate transport solution that can seamlessly integrate electrical and optical layers by transferring certain switching functionality from electronics to optics, thus alleviating unnecessarily slow and expensive optical-electrical-optical conversions and signal processing at the switching node. Optical Label Switching (OLS) is an important aspect of the optical packet switched network that enables very low-latency forwarding of ultra-high bit-rate, protocol-independent packets entirely in the optical domain. The objective of the proposed research is to develop novel, efficient techniques to realize several key enabling technologies such as optical label generation and encoding, optical label swapping, all-optical buffering, and spectral efficient transmission system for optical label switched based OPS networks. A novel scheme of generating optical label at the ingress node using optical carrier suppression and separation (OCSS) technique is proposed. This scheme does not suffer from any unavoidable interference, limited extinction ratio or strict synchronization requirements between payload and label as observed by the currently available other label generation methods. One of the primary challenges to realize optical label swapping at the core node of scalable OLS network is the insertion of new optical labels without any wavelength conversion for same wavelength packet routing. A novel mechanism to realize same wavelength packet switching without using any conventional wavelength converter in the OLS network carrying differential phase-shift keying (DPSK) modulated payload and on-off keying (OOK) modulated optical label is demonstrated. Also a new dense wavelength division multiplexing (DWDM) optical buffer architecture using optical fiber delay lines that can provide wavelength selective reconfigurable variable delays is proposed. Optical packet switching provides automated, reconfigurable, and faster provision of both wavelength and bandwidth with finer granularity in the optical layer. However, a newer, cost-effective, and spectrally efficient optical transmission technology is essential to support the explosive bandwidth demand expected by the future optical packet switched networks. To meet this challenge, a spectrally efficient solution for transporting 40 Gbps per channel data over 50 GHz spaced DWDM system is developed by exploiting optical carrier suppression and separation technique and optical duobinary modulation.

We propose that the industry structure in Taiwan broadband market is a two-sided market. In this framework, the networks need to be completely interconnected in order to ensure unhindered (or smoothly) information flow. Based on a two-sided market model, we analyze the IP peering mechanism for Taiwan Internet market. We show that the IP peering access charges should be a very low constant amount to reflect the unique Taiwan broadband industry structure. Furthermore, in attracting more Internet content providers (ICP) and end users to provide more content services and Internet applications, the Internet service providers (ISP) should provide free broadband services to ICPs. Though these results are contradictory with the ¡§user-pays¡¨ principle, it ensures more profitable for ISPs and ICPs. Most importantly, the impacts on the whole social welfare are improved. Last, we examine a more efficacious framework for ensuring network neutrality is Efficient Component Pricing Rule (ECPR) in a vertically-integrated monopoly market, as in Taiwan Broadband industry.

Stationarity is an essential property to portfolio return in the past statistical arbitrage strategy, this article uses Neo-75 rule, momentum effect, properties as independent and identically distribution and stationarity in error term, in one asset and in the very short holding period. The result in out sample period owning positive cumulative return. The finding suggests individual investors use this strategy in higher efficiency market to avoid invalidation in our model. This article surveyed CAC40, DJI, HangSeng, NASDAQ, Nikkei225, Shanghai and TWII indices. All the excess returns in out sample periods indicate they are exclude weak form of efficient market.

Nowadays, Internet plays an indispensable role in human lives. People use Internet to search information, transmit data, download ?le, and so on. The data transformed to the composed digital signal by ¡¦0¡¦ and ¡¦1¡¦ are transmitted on Internet . However, Internet is open and unreliable, data may be stolen from the other people if they are not encrypted. In order to ensure the security and secret of data, the cryptosystem is very important. RSA is a famous public-key cryptosystem, and it has easy concept and high security. It needs a lot of modular exponentiations while encryption or decryption. The key length of RSA is always larger than 1024 bits to ensure the high security. In order to achieve real time transmission, we have to speed up the RSA cryptosystem. Therefore, it must be implemented on hardware. In RSA cryptosystem, modular exponentiation is the only operation. Modular exponentiation is based on modular multiplications. Montgomery¡¦s Algorithm used simple additions and shifts to implement the complex modular multiplication. Because the key length is usually larger than 1024 bits, some signals have a lot of fan-outs in hardware architecture. Therefore, the signals have to connect buffers to achieve enough driving ability. But, it may lead to longer delay time and more power consumption. So, Tenca et al. proposed a Multiple Word Montgomery Algorithm to improve the problem of fan-out. Recently, Huang et al. proposed an algorithm which can reduce data dependency of Tenca¡¦s algorithm. This research is based on the architecture of Huang¡¦s algorithm and detects the redundant operations. Then, we block the unnecessary signals to reduce the switch activities. Besides, we use low power shift register to reduce the power consumption of shift register. Experimental results show that our design is useful on decreasing power consumption.

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In this thesis, We propose two power saving strategy in wireless sensor networks with multi-packet reception and slotted ALOHA is as a systematic model. We concentrate on the case in which the packet arrival process is Bernoulli and the maximum queue is 1.This thesis first simulate results and to compare with the analytical results of pervious thesis. Traditional slotted ALOHA only have transmit and idle state. In this thesis, add a sleep state to decrease the energy consumption, and according to different strategy propose two different methods. This two methods decide to the sleep time and the retransmission probability to achieve the energy-efficient. At last we will use the simulation result to show the performance of our power saving strategy.

In this thesis, we develop two exact algorithms and a heuristic procedure for Multiobjective Combinatorial Optimization Problems (MOCO). Our exact algorithms guarantee to generate all nondominated solutions of any MOCO problem. We test the performance of the algorithms on randomly generated problems including the Multiobjective Knapsack Problem, Multi-objective Shortest Path Problem and Multi-objective Spanning Tree Problem. Although we showed the algorithms work much better than the previous ones, we also proposed a fast heuristic method to approximate efficient frontier since it will also be applicable for real-sized problems. Our heuristic approach is based on fitting a surface to approximate the efficient frontier. We experiment our heuristic on randomly generated problems to test how well the heuristic procedure approximates the efficient frontier. Our results showed the heuristic method works well.

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