Stochastic gradient descent (SGD) is one of the preferred online optimization algorithms. However, one of its major drawbacks is its predisposition to forgetting previous data when optimizing through a data stream, also known as catastrophic interference. In this project, we attempt to mitigate this drawback by proposing a new low-cost approach which incorporates backward queried images with SGD during online training. Under this new approach, we propose that for every new training sample through the data stream, the neural network is optimized using the corresponding backward queried image from the initial dataset. After compiling the accuracy of the proposed method and SGD under a data-stream of 50,000 training cases with 10,000 test cases and comparing our algorithm to SGD, we see substantial improvements in the performance of the neural network with two different MNIST datasets (Fashion and Kuzushiji), classifying the MNIST datasets at a high accuracy for the mean, minimum, lower quartile, median, and upper quartile, while maintaining lower standard deviation in performance, demonstrating that our proposed algorithm can be a potential alternative to online SGD.

The occurrence and behavior of insects is significantly affected by the environment they live in. In this thesis, I dealt with the influence of structure of landscape on nesting preferences of Hymenoptera. For this comparison I had chosen to work with twig-nesting Hymenoptera, for which I have placed artificial nest opportunities into four biotopes – heath, edge of a heath, country lanes between fields and field. The studied location is located south of Znojmo near Podyjí national park. Particularly, I have focused on small carpenter bees of genus Ceratina. My results show that there is a big difference in the species distribution between the habitates of field and heath. The habitats of edge of a heath and country lanes make up a gradient between these two biotopes. The ecosystem of fields was preferred by a sphecid wasp Pemphredon lethifer and Ceratina cyanea. On the other hand, the ecosystem of heath was preferred by Ceratina chalybea, Ceratina nigrolabiata and megachille bee Hoplitis tridentata. I had also found out that in species that are more abundant on heaths, there is higher mortality of offsprings. Heaths were a place of the highest competition between species, as a result of which species with a lower body weight (Ceratina nigrolabiata) have been pushed into narrower twigs by larger species (Ceratina chalybea). I recorded a high number of nests in biparental bee Ceratina nigrolabiata, which were guarded only by mother in fields and country lane habitats. This may indicate that Ceratina nigrolabiata is only facultatively biparental, not strictly biparental as was considered until now.

This project aimed to study the motion which occurred from the end point on the circumference of the outermost circle by moving the center on the circumference of a preceding circle and the center of an innermost circle at origin. According to the study, when angular velocity was changed, it caused the different of loci. Based on the above information, finding the locus of the point on circumference of n-th circle that formed by moving the center of any radius circles on circumference of preceding set of circles was studied to get general equation. A set of circle and locus were created with GSP program. First, set the same radius circles on the X-axis with the first circle at origin, then found the relationship that occurred from the characteristics of locus. The result showed that if the ratios of angular velocity are 1:1:1, 2:2:2, 3:3:3, ..., …, n:n:n or 1:2:3, 2:4:6, 3:6:9, …,nw1:nw2:nw3, the characteristics of locus will be the same, while the others will be different. Finally, the equation of locus was found as follow: (x,y) = { ..........see in abstract...........} when .........see in abstract........... Where ri is the radius of i-th circle, zeta i is an angle between the radius of i-th circle and X-axis, wi is the angular velocity, t is elapsed time and alpha i is a starting angle between the radius of i-th circle and X-axis.

Silica capillaries have been an integral part of the instrumentation used in many areas of analytical chemistry for decades, especially in analytical separations. In most cases, they are used without treatment, occasionally forceless chemical surface treatments are made to suppress or enhance the activity of silanol groups. The aim of this work was to disrupt the inner surface of the capillary, perfectly smooth from manufactory, so that relatively coarse and various structures would be created, and to study their influence on the separation efficiency. The uniqueness of the used solution is based on the use of special properties of water exposed to high temperatures and pressures (supercritical water), which is able to disrupt this chemically inert material because of its aggressivity. In total, over 2000 experiments were carried out in order to define conditions suitable for the formation of various types of surface structures. Due to the high amount of resulting data, our own database application was created, allowing not only to save the picture of the structure and experimental conditions information, but also to clearly sort them out and create image reports according to the specified parameters. Samples representing individual types of structures were then selected from this database and a number of silica capillaries with a configuration suitable for electromigration analyzes were prepared. The creation of a structured surface in the input part of the separation capillary enabled the separation of some classes of substances and biosamples, which cannot be analyzed on standard capillaries with a smooth surface. An example is the complete separation of two strains of Staphyllococcus aureus bacteria (MRSA and MSSA), or the use of the absorbing capabilities of a structured surface to study the interactions of these bacteria with bacteriophages. This ability was also used in the determination of Aspergillus fungus in a sample taken directly from the patient's lungs, where there was achieved a significant increase in the sensitivity of the analysis. Structured capillaries can also be used in the analysis of food samples, i.e., for the separation of β-lactoglobulins A and B in cow's milk, which belong to its main allergens.

研究目的：脂肪肝的盛行率在全世界的現代化國家都在增加。病理醫師在評估脂肪肝的嚴重等級時，常缺乏參考意見以減少差異。許多地區也缺乏病理醫師。本研究旨在建立一個有效評估脂肪肝嚴重程度的病理組織學人工智慧模型。研究過程：本研究經由臺中榮民總醫院人體研究倫理審查委員會審核通過，篩選後取得病理資料庫中適合的肝臟組織切片，由兩位病理醫師獨立為肝組織中脂肪堆積的程度評分。再以病理醫師討論後的共識答案為分級標準，來訓練人工智慧模型。研究結果：在100個樣本的獨立測試中，人工智慧模型和病理專科醫師的評分，有71%完全相同、27%差異只有一個等級、2%差異2個等級、而沒有2個等級以上的差異。結論及應用：我們已初步建立一個可以評估脂肪肝嚴重程度的人工智慧模型。這模型可為將來人工智慧的臨床應用，建立一個良好的基礎。

方形盒盛透明液體，置放在冷源上方，液體發生熱擴散時，溫度由上往下逐漸下降，形成溫度梯度以及折射率梯度。雷射光照射和鉛直線成一定角度的玻棒透鏡，再穿過方形盒的透明液體時，在屏上形成斜直線，經一段時間的熱擴散後，變成曲線；曲線和斜直線的距離(h)，隨著時間(t)以及光線照射的位置(y)改變，作不同y的h-t圖可得知液體的熱擴散率狀況。 冷源的溫度0℃，分別用甘油和乙醇作待測液，得到的h-t圖，符合熱擴散推導出的h隨t改變的方程式；改用水當待測液，得到的h-t圖，就不符合熱擴散推導出的h隨t改變的方程式。改用-5℃的冷源，分別用水和氯化鈉水溶液作待測液，得到的h-t圖，不符合熱擴散推導出的h隨t改變的方程式。 用簡易的設備可以了解折射率梯度，溫度梯度，熱擴散率，以及液體的非線性熱擴散。

本研究主要探討塔粉綠尺蛾食草選擇與其葉內真菌之關係。觀察培養四種植物（烏臼、鵝掌柴、白匏子與島榕）葉內真菌，以真菌生長率、菌絲與孢子形態辨識真菌種類。當我們以烏臼葉內間座殼菌屬（Diaporthe sp.）真菌與不同植物放在一起時，幼蟲取食原為非食草的白匏子葉片，而島榕則有嘗試啃食之現象；此外，飼養過程中我們發現取食烏臼的塔粉綠尺蛾幼蟲糞便較其他種幼蟲易長出真菌，進行幼蟲糞便與消化道真菌培養後，皆有與葉內真菌相似的菌體形態。我們推測烏臼、葉內真菌與塔粉綠尺蛾間的交互作用關係之一可能為：烏臼透過葉內真菌誘使塔粉綠尺蛾雌蛾前往產卵，經幼蟲食用葉片後所排出之糞便以作為葉內真菌傳播的媒介。

本研究利用自製包覆薄膜裝置，在濕粉圓表面包覆雙層海藻酸鈣薄膜(內層1.0%海藻酸鹽+外層0.5%海藻酸鹽)，經自然乾燥製成新型粉圓，可浸泡冷水不會崩解或破裂，且水分完全滲入粉圓內部僅需25分鐘；新型粉圓在泡水25分鐘後，其內部水分含量高達51.67%。新型粉圓要達到100%煮熟率之時間，僅乾粉圓的37.80%、濕粉圓的42.75%，省時效果十分明顯；而所消耗電能，僅乾粉圓的25.57%、濕粉圓的28.81%，節能效果極為顯著。新型粉圓經全質構分析(TPA)之彈性已達到商品化之水準，並經官能品評驗證，受試者對新型粉圓各項目之喜好程度均優於濕粉圓。最後，測試新型粉圓之水活性僅為0.684，其Aw值明顯低於一般微生物生長界限0.8，可在常溫下長時間貯存。

本文主要在探討平面幾何學中的兩個重要結果—三角形中的『Menelaus定理』與『Ceva定理』推廣到任意的『球面n邊形』的相對應結果，對於任意的球面n邊形，我們分別找到了『球面n邊形的Menelaus共線定理』與『球面n邊形的Ceva共點定理』的一般化結果。

Double Parallelogram Lifting Mechanism (DPLM) is a compact and stable lifting mechanism with a large extension range widely adopted in robot designs. Rubber bands and springs are often installed on the DPLM to lighten the motors' load and maintain its height, yet the installation positions are often obtained through trial and error. This project aims at finding the optimal rubber band installation positions for DPLM using modeling and optimization techniques. A mathematical model which describes the forces and moments acting on all the linkages of DPLM was derived based on the conditions for the static equilibrium and verified with a 3D simulation software. A genetic algorithm (GA) was implemented to optimize rubber band installation positions, which managed to find solutions with the overall root-mean-square- error (RMSE) of the net moment less than 2 for 2 to 6 rubber bands. A further statistical analysis of 50000 random rubber band samples showed that installing rubber bands in triangles is the best solution with the overall lowest RMSE. A test was conducted with a prototype of the DPLM and the results were consistent with our model and optimization. This project derived and verified a mathematical model for the DPLM, and found the optimal way and positions to install rubber bands. The results of this project provides a theoretical basis for controlling DPLM with rubber bands, allowing it to be further adopted in industrial robots that require repetitive lifting and lowering such as inspection robots and aerial work platforms.

Wireless transmission products are widely used in our daily life. In this research, we focus on knowing how solid-state tesla coil works in different conditions and finding the best parameters through an easy way. In our work, a commercial electroscope was used as detector for measuring the strength of radio wave created by our simplified tesla coils. In fact, many factors would lead to experimental erorrs such as detectors, selected types of NPN BJT components, applied voltage and measuring position of height. Therefore, all of the factors were under control to make sure of accuracy and precision for our designed measuring method. In our experiment, graphics of radio wave distribution around tesla coils were drew by mathemetic software of GeoGebra. It shows the BJT types of 2n2222 had good performance for wireless transmisstion efficiency. To our surprised, we found the extended wires (called antenna) from the top of tesla coil also had an ability to transfer electromagnetic energy, and had good retention if the extended wires were within the length of main coil’s height. Finally, the shape’s and size’s effect was determined by our testing work. The result shows that pipe’s length, pipe’s diameter and turns ratio of two coils had great influence on tesla coil’s transmission efficiency. It was found that the tesla’s performance would be more efficient if wire was used to make the length twice rather than make the diameter twice. However, the turns ratio of secondary coil to primary coil would change while making the length twice. To avoid that, we fixed the length and decrease the turns of primary coil. At last, we found tesla coil must work at the turns of primary coil higher than two. Furthermore, the frequency of radio wave not only had less relationship with their length or diameter but also had less relationship with types of BJT In our study, our handmade tesla coil was succesfully applied for wireless charging and we find that the induced voltage decrease in propotion to cube root of distance between tesla coil and induced coil.

An isosceles set is a collection of points in which any subset of three points forms an isosceles triangle. We want to find the upper bound for the size of isosceles sets in any n-dimensional Euclidean space. Kido has already completed the study of isosceles sets in 3 and 4-dimensional space. We study the upper bound of spherical two-distance sets, a special type of isosceles sets, to help us find the upper bound of isosceles sets. More specifically, Musin’s Linear Programming technique on spherical two-distance sets could be used to study isosceles sets if a consistent relationship between isosceles sets and two-distance sets can be characterized. We offer a conjecture of this relationship. We also offer non-trivial lower bounds of isosceles sets in dimension 5 with 17 points and dimension 7 with 30 points as examples.