A Study on Teaching the Method of Lagrange Multipliers in the Era of Digital Transformation (라그랑주 승수법의 교수·학습에 대한 소고: 라그랑주 승수법을 활용한 주성분 분석 사례)
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- Communications of Mathematical Education
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- v.37 no.1
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- pp.65-84
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- 2023
The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.
Alvin Toffler mentioned that it is important for future society to keep pace with synchronization and that time deviations can hinder social development. As we experience the new normal era of untact, we have experienced an increase in non-face-to-face contact and accelerated digital transformation. Amid these rapid changes, we can maintain the need for synchronization or change in space. Therefore, we would like to study what kind of settlements people create and choose. We looked at the metaverse as an object that could indirectly find out about this, and used the content called "Animal Crossing" to collect data related to the spatial form of the metaverse. Sampling utilized a judgment sampling method during non-probability sampling to alleviate differences due to the progress of the game. The collected data was classified according to floor plan and location type and briefly organized through descriptive statistics. After matching each facility by use, data was constructed by setting coordinates for each cluster and listing them. This data was interpreted graphically on the coordinate plane for each cluster, and Euclidean analysis was performed to analyze the relationships between clusters and residential choice using a Euclidean matrix. As a result of the analysis, it could be interpreted that efficiency was pursued by arranging similar functions in close proximity. Nevertheless, when choosing a residence, it was interpreted that the intention was to create a community through arrangement adjacent to residents rather than efficiency or convenience. Due to the differences between the metaverse and the real world, it is expected that there will be limitations in equating it with reality. However, through the space expressed in the virtual world by people who are far away from the constraints of reality, we can indirectly know the wishes that we have not been able to express due to our lack of awareness.
Human and monogastric animals can not synthesize 10 out of the 20 amino asids and therefor need to obtain these from their diet. The plant seed is a major source of dietary protein. It is particular important in their study to increase nutritional quality of the seed storage proteins. The low contents of lysine, asparagine and threonenein various cereal seeds and of cystein and methionine. In legume seeds is due to the low proportions of these amino acids in the major storage proteins, we have tried to apply the three strategies; (1) mutagenesis and selection of specific amino acid analogue resistance, (2) cloning and expression study of lysine biosynthesis related gene, (3) transfomation of lysine rich soybean glycinin gene. The 5-methyltryptophan (5MT) resistant cell lines, SAR1, SAR2 and SAR3 were selected from anther derived callus of rice (Oryza sativa L. "Sasanishiki"). Among these selected cell lines, two (SAR1 and SAR3) were able to grow stably at 200 mg/L of 5MT. Analysis of the freed amino acids in callus shows that 5MT resistant cells (SAR3) accumulated free tryptophan at least up to 50 times higher than those that of the higher than of SAS. These results indicated that the 5MT resistant cell lines are useful in studies of amino acid biosynthesis. Tr75, a rice (Oryza sativa L., var. Sasanishiki) mutant resistant to 5MT was segregated from the progenies of its initial mutant line, TR1. The 5MT resistant of TR75 was inherited in the M8 generations as a single dominant nuclear gene. The content of free amino acids in the TR75 homozygous seeds increased approximately 1.5 to 2.0 fold compared to wild-type seeds. Especially, the contents of tryptophan, phenylalanine and aspartic acid were 5.0, 5.3 and 2.7 times higher than those of wild-type seeds, respectively. The content of lysine is significantly low in rice. The lysine is synthesized by a complex pathway that is predominantly regulated by feedback inhibition of several enzymes including asparginase, aspatate kinase, dihydrodipicolinat synthase, etc. For understanding the regulation mechanism of lysine synthesis in rice, we try to clone the lysine biosynthetic metabolism related gene, DHPS and asparaginase, from rice. We have isolated a rice DHPS genomic clone which contains an ORF of 1044 nucleotides (347 amino acids, Mr. 38, 381 daltons), an intron of 587 nucleotides and 5'and 3'-flanking regions by screening of rice genomic DNA library. Deduced amino acid sequence of mature peptide domain of GDHPS clone is highly conserved in monocot and dicot plants whereas that of transit peptide domain is extremely different depending on plant specie. Southern blot analysis indicated that GDHPS is located two copy gene in rice genome. The transcripts of a rice GDHPS were expressed in leaves and roots but not detected in callus tissues. The transcription level of GDHPS is much higher in leaves indicating enormous chloroplast development than roots. Genomic DNA clones for asparaginase genes were screened from the rice genomic library by using plaque hybridization technique. Twelve different genomic clones were isolated from first and second screening, and 8 of 12 clones were analyzed by restriction patterns and identified by Southern Blotting, Restriction enzyme digestion patterns and Southern blot analysis of 8 clones show the different pattern for asparaginase gene. Genomic Southern blot analysis from rice were done. It is estimated that rice has at least 2-3 copy of asparaginase gene. One of 8 positive clones was subcloned into the pBluescript SK(+) vector, and was constructed the physical map. For transformation of lysine rich storage protein into tobacco, soybean glycinin genes are transformed into tobacco. To examine whether glycinin could be stably accumulated in endosperm tissue, the glycinin cDNA was transcriptionally fused to an endosperm-specific promotor of the rice storage protein glutelin gene and then introduced into tobacco genomic via Agrobacterium-mediated transformation. Consequently the glycinin gene was expressed in a seed-and developmentally-specific manner in transgenic tobacco seeds. Glycinin were targeted to vacuole-derived protein bodies in the endosperm tissue and highly accumulated in the matrix region of many transgenic plant (1-4% of total seed proteins). Synthesized glycinin was processed into mature form, and assembled into a hexamer in a similar manner as the glycinin in soybean seed. Modified glycinin, in which 4 contiguous methionine residues were inserted at the variable regions corresponding to the C - teminal regions of the acidic and basic polypeptides, were also found to be accumulated similarly as in the normal glycinin. There was no apparent difference in the expression level, processing and targeting to protein bodies, or accumulation level between normal and modified glycinin. glycinin.
Recently, with the development of deep learning technology, research on unstructured data analysis is being actively conducted, and it is showing remarkable results in various fields such as classification, summary, and generation. Among various text analysis fields, text classification is the most widely used technology in academia and industry. Text classification includes binary class classification with one label among two classes, multi-class classification with one label among several classes, and multi-label classification with multiple labels among several classes. In particular, multi-label classification requires a different training method from binary class classification and multi-class classification because of the characteristic of having multiple labels. In addition, since the number of labels to be predicted increases as the number of labels and classes increases, there is a limitation in that performance improvement is difficult due to an increase in prediction difficulty. To overcome these limitations, (i) compressing the initially given high-dimensional label space into a low-dimensional latent label space, (ii) after performing training to predict the compressed label, (iii) restoring the predicted label to the high-dimensional original label space, research on label embedding is being actively conducted. Typical label embedding techniques include Principal Label Space Transformation (PLST), Multi-Label Classification via Boolean Matrix Decomposition (MLC-BMaD), and Bayesian Multi-Label Compressed Sensing (BML-CS). However, since these techniques consider only the linear relationship between labels or compress the labels by random transformation, it is difficult to understand the non-linear relationship between labels, so there is a limitation in that it is not possible to create a latent label space sufficiently containing the information of the original label. Recently, there have been increasing attempts to improve performance by applying deep learning technology to label embedding. Label embedding using an autoencoder, a deep learning model that is effective for data compression and restoration, is representative. However, the traditional autoencoder-based label embedding has a limitation in that a large amount of information loss occurs when compressing a high-dimensional label space having a myriad of classes into a low-dimensional latent label space. This can be found in the gradient loss problem that occurs in the backpropagation process of learning. To solve this problem, skip connection was devised, and by adding the input of the layer to the output to prevent gradient loss during backpropagation, efficient learning is possible even when the layer is deep. Skip connection is mainly used for image feature extraction in convolutional neural networks, but studies using skip connection in autoencoder or label embedding process are still lacking. Therefore, in this study, we propose an autoencoder-based label embedding methodology in which skip connections are added to each of the encoder and decoder to form a low-dimensional latent label space that reflects the information of the high-dimensional label space well. In addition, the proposed methodology was applied to actual paper keywords to derive the high-dimensional keyword label space and the low-dimensional latent label space. Using this, we conducted an experiment to predict the compressed keyword vector existing in the latent label space from the paper abstract and to evaluate the multi-label classification by restoring the predicted keyword vector back to the original label space. As a result, the accuracy, precision, recall, and F1 score used as performance indicators showed far superior performance in multi-label classification based on the proposed methodology compared to traditional multi-label classification methods. This can be seen that the low-dimensional latent label space derived through the proposed methodology well reflected the information of the high-dimensional label space, which ultimately led to the improvement of the performance of the multi-label classification itself. In addition, the utility of the proposed methodology was identified by comparing the performance of the proposed methodology according to the domain characteristics and the number of dimensions of the latent label space.
Objectives: The objective of this study was to evaluate the effects of cytotoxicity, skin regeneration, anti-wrinkle, whitening and skin moisturizing of Oncheongeum (OCE).Methods: The cytotoxicity of OCE lyophilized aqueous extracts (yield=13.82%) was observed against human normal fibroblast cells and B16/F10 murine melanoma cells by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium Bromide (MTT) assay, and skin regeneration and anti-wrinkle effects were also evaluated through the assay of collagen type I synthesis compared to the transformation of the growth factor (TGF)-β1, hyaluronidase, collagenase and matrix metalloproteinase (MMP)-1 inhibitory assays compared to oleanolic acid (OA), and elastase inhibitory effects compared to phosphoramidon disodium salt (PP). In addition, OCE’s whitening effects were measured by a tyrosinase inhibitory assay and melanin formation test in B16/F10 murine melanoma cells compared to arbutin, and skin moisturizing effects were observed through a mouse skin water content test, respectively. Results: No OCE treatment-related cytotoxic effects appeared on human normal fibroblasts and B16/F10 murine melanoma cells. OCE concentration-dependently increased the collagen Type I synthesis on human normal fibroblast cells, and also effectively inhibited hyaluronidase, elastase, collagenase and MMP-1 activities. In addition, OCE inhibited melanin production of B16/F10 murine melanoma cells and activity of tyrosinase. And significant and dose-dependent increases of skin water content were detected in OCE-treated mouse skin compared to vehicle control skins. Conclusions: OCE showed favorable and sufficient effects in skin regeneration, anti-wrinkle, whitening and skin moisturizing in this experiment. But more detail mechanisms and studies on the skin protective efficiency of in vivo are needed with the screening of active biological compounds in individual OCE herbs.
The wall shear stress in the vicinity of end-to end anastomoses under steady flow conditions was measured using a flush-mounted hot-film anemometer(FMHFA) probe. The experimental measurements were in good agreement with numerical results except in flow with low Reynolds numbers. The wall shear stress increased proximal to the anastomosis in flow from the Penrose tubing (simulating an artery) to the PTFE: graft. In flow from the PTFE graft to the Penrose tubing, low wall shear stress was observed distal to the anastomosis. Abnormal distributions of wall shear stress in the vicinity of the anastomosis, resulting from the compliance mismatch between the graft and the host artery, might be an important factor of ANFH formation and the graft failure. The present study suggests a correlation between regions of the low wall shear stress and the development of anastomotic neointimal fibrous hyperplasia(ANPH) in end-to-end anastomoses. 30523 T00401030523 ^x Air pressure decay(APD) rate and ultrafiltration rate(UFR) tests were performed on new and saline rinsed dialyzers as well as those roused in patients several times. C-DAK 4000 (Cordis Dow) and CF IS-11 (Baxter Travenol) reused dialyzers obtained from the dialysis clinic were used in the present study. The new dialyzers exhibited a relatively flat APD, whereas saline rinsed and reused dialyzers showed considerable amount of decay. C-DAH dialyzers had a larger APD(11.70
The wall shear stress in the vicinity of end-to end anastomoses under steady flow conditions was measured using a flush-mounted hot-film anemometer(FMHFA) probe. The experimental measurements were in good agreement with numerical results except in flow with low Reynolds numbers. The wall shear stress increased proximal to the anastomosis in flow from the Penrose tubing (simulating an artery) to the PTFE: graft. In flow from the PTFE graft to the Penrose tubing, low wall shear stress was observed distal to the anastomosis. Abnormal distributions of wall shear stress in the vicinity of the anastomosis, resulting from the compliance mismatch between the graft and the host artery, might be an important factor of ANFH formation and the graft failure. The present study suggests a correlation between regions of the low wall shear stress and the development of anastomotic neointimal fibrous hyperplasia(ANPH) in end-to-end anastomoses. 30523 T00401030523 ^x Air pressure decay(APD) rate and ultrafiltration rate(UFR) tests were performed on new and saline rinsed dialyzers as well as those roused in patients several times. C-DAK 4000 (Cordis Dow) and CF IS-11 (Baxter Travenol) reused dialyzers obtained from the dialysis clinic were used in the present study. The new dialyzers exhibited a relatively flat APD, whereas saline rinsed and reused dialyzers showed considerable amount of decay. C-DAH dialyzers had a larger APD(11.70