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37: 19 Pre-Class Assignment - Least Squares Fit (Regression) - Mathematics


37: 19 Pre-Class Assignment - Least Squares Fit (Regression) - Mathematics

37: 19 Pre-Class Assignment - Least Squares Fit (Regression) - Mathematics

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Electrification of personal transportation is widely regarded as an effective solution to relieve. more Electrification of personal transportation is widely regarded as an effective solution to relieve some increasingly serious crises facing our society today and in the near future, such as energy security, climate change and air quality. Depending on the type of power sources, electric vehicles (EVs) may be categorized into hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs), and battery electric vehicles (BEVs). While HEVs and PHEVs may better satisfy people’s travel need nowadays, especially for long-distance trips, it is generally believed that BEVs will most probably dominate the EV market, after charging infrastructures are sufficiently expanded and charging time is reduced to a satisfactorily short level. Partially for this reason, an increasing number of EV-related scientific studies have focused on BEVs in recent years.

The last decade observed a fast climb of the market penetration level of EVs in many economies, especially in China, the United States and the European Union. The increasing global market share leads to a series of new engineering, economic, environmental and institutional problems and concerns we have not dealt with in our past transportation systems development and management experience, such as electricity-charging infrastructure planning for EVs, EV-based travel and charging demand analysis, EVs’ energy consumption and cost analysis, EVs’ market penetration forecasting, air quality and environment improvements due to EV adoption, and so on. These new problems and concerns intrigued numerous attention from the research community and general public. Moreover, with the continuous advances in EV technologies and increasing willingness of consumers purchasing and utilizing EVs, the mechanism, means and magnitude of these impacts on transportation systems as well as their evolution have developed to a highly complex and unprecedented level that we might have underestimated before, if we still made judgments by fully relying on our existing knowledge.

In additional to electric cars, electrification of transportation is also reflected by the increasing penetration of electric bicycles, which now are widely adopted in many large cities with high population density, especially in Asian and European countries. Their influences on urban travel behaviors and transportation planning are not fully investigated yet and worth being further discovered.


METHODS

Model transients were studied in the Ramirez-Nattel-Courtemanche (RNC) model of the canine atrial AP (28). The RNC model is composed of 23 coupled first-order ordinary differential equations and accounts for intracellular concentrations of potassium ([K + ]i), sodium ([Na + ]i), calcium ([Ca 2+ ]i), and chloride ([Cl − ]i).

The rate of change in the transmembrane potential (V) is given by

All simulations were performed with I in picoamps, V in millivolts, and Cm = 100 pF. A fixed time step of 5 and 20 μs was used in the presence and absence of stimulation, respectively. For reasons discussed in Stimulus Current Assignment (see results ), all simulations were performed with the stimulus current attributed to potassium unless stated otherwise. All simulations were performed using double-precision arithmetic on Unix PC workstations.


Non-Rigid Point Matching: Algorithms, Extensions and Applications

Abstract <strong>Non</strong>-<strong>Rigid</strong> <strong>Point</strong> <strong>Matching</strong>: <strong>Algorithms</strong>, <strong>Extensions</strong> <strong>and</strong> <strong>Applications</strong> Haili Chui Yale University 2001 A new algorithm has been developed in this thesis for the non-rigid point matching problem. Designed as an integrated framework, the algorithm jointly estimates a one-to-one correspondence <strong>and</strong> a non-rigid transformation between two sets of points. The resulting algorithm is called “robust point matching (RPM) algorithm” because of its capability to tolerate noise <strong>and</strong> to reject possible outliers existed within the data points. The algorithm is built upon the heuristic of “fuzzy correspondence”, which allows for multiple partial cor- respondences between points. With the help of the deterministic annealing technique, this new heuristic enables the algorithm to overcome many local minima that can be encountered in the matching process. Devised as a general point matching framework, the algorithm can be easily extended to accommodate differ- ent speci£c requirements in many registration applications. Firstly, the modular design of the transformation module enables convenient incorporation of different non-rigid splines. Secondly, the point matching algorithm can be easily extended into a symmetric joint clustering-matching framework. It will be shown that by introducing a super point-set, the joint cluster-matching extension can be applied to estimate an average shape point-set from multiple point shape sets. The algorithm is applied to the registration of 3D brain anatomical structures. We proposed in this work a joint feature registration framework, which is mainly based on the joint clustering-matching extension of the robust point matching. The proposed framework provides an effective <strong>and</strong> uni£ed way to utilize spatial relationship existed between different brain structural features to improve the brain anatomical registration/normalization. For the £rst time, a carefully designed synthetic study is carried out to investigate <strong>and</strong> compare different anatomical features’ abilities to achieve such an registration/normalization. Other applications of the robust non-rigid point matching algorithm, such as key-frame animation <strong>and</strong> human face matching, will also be demonstrated in this work.


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