Relationship between Batch Size and Number of Steps Needed for Nonconvex Optimization of Stochastic Gradient Descent using Armijo Line Search

Stochastic gradient descent (SGD) is the simplest deep learning optimizer with which to train deep neural networks. While SGD can use various learning rates, such as constant or diminishing rates, the previous numerical results showed that SGD performs better than other deep learning optimizers using when it uses learning rates given by line search methods. In this paper, we perform a convergence analysis on SGD with a learning rate given by an Armijo line search for nonconvex optimization. The analysis indicates that the upper bound of the expectation of the squared norm of the full gradient becomes small when the number of steps and the batch size are large. Next, we show that, for SGD with the Armijo-line-search learning rate, the number of steps needed for nonconvex optimization is a monotone decreasing convex function of the batch size; that is, the number of steps needed for nonconvex optimization decreases as the batch size increases. Furthermore, we show that the stochastic first-order oracle (SFO) complexity, which is the stochastic gradient computation cost, is a convex function of the batch size; that is, there exists a critical batch size that minimizes the SFO complexity. Finally, we provide numerical results that support our theoretical results. The numerical results indicate that the number of steps needed for training deep neural networks decreases as the batch size increases and that there exist the critical batch sizes that can be estimated from the theoretical results

Nanocomposite of silk fibroin nanofiber and montmorillonite: Fabrication and morphology

The purpose of our research is creating a new nanocomposite material. Generally silk fibroin (SF) is regarded as a promising base material for biomedical uses. The incorporation of montmorillonite (MMT) into SF fibers would improve physical properties of the SF fibers. We investigated a new method of combining electospun SF with MMT. Specifically, electrospun silk nanofibers were treated with methanol and dipped in a MMT suspension. We could obtain a nanosheet composite of silk nanofibers and MMT. Their ultrastructures were successfully visualized by high resolution transmission electron microscopy. This compound was comprised of individual silk nanofibers surrounded by thin layers of MMT, each with a thickness of about 1.2 nm. This structure was confirmed by elemental analysis. We also performed IR, NMR and X-ray diffraction analyses in conjunction with morphological data. Conclusively we obtained a new composite of silk nanofiber and MMT, which has never been reported. Using this unique nanocomposite biological tests of its application for a scaffold for tissue engineering are under way.ArticleINTERNATIONAL JOURNAL OF BIOLOGICAL MACROMOLECULES. 57:124-128 (2013)journal articl

Quantification of Local Morphodynamics and Local GTPase Activity by Edge Evolution Tracking

Advances in time-lapse fluorescence microscopy have enabled us to directly observe dynamic cellular phenomena. Although the techniques themselves have promoted the understanding of dynamic cellular functions, the vast number of images acquired has generated a need for automated processing tools to extract statistical information. A problem underlying the analysis of time-lapse cell images is the lack of rigorous methods to extract morphodynamic properties. Here, we propose an algorithm called edge evolution tracking (EET) to quantify the relationship between local morphological changes and local fluorescence intensities around a cell edge using time-lapse microscopy images. This algorithm enables us to trace the local edge extension and contraction by defining subdivided edges and their corresponding positions in successive frames. Thus, this algorithm enables the investigation of cross-correlations between local morphological changes and local intensity of fluorescent signals by considering the time shifts. By applying EET to fluorescence resonance energy transfer images of the Rho-family GTPases Rac1, Cdc42, and RhoA, we examined the cross-correlation between the local area difference and GTPase activity. The calculated correlations changed with time-shifts as expected, but surprisingly, the peak of the correlation coefficients appeared with a 6–8 min time shift of morphological changes and preceded the Rac1 or Cdc42 activities. Our method enables the quantification of the dynamics of local morphological change and local protein activity and statistical investigation of the relationship between them by considering time shifts in the relationship. Thus, this algorithm extends the value of time-lapse imaging data to better understand dynamics of cellular function

Efectos de la edad y el sexo sobre la memoria espacial de ratas Wistar en el laberinto radial de 8 brazos

Trabajo de InvestigaciónEl presente estudio tuvo como objetivo evaluar el desempeño de 24 ratas Wistar en una tarea de memoria espacial, según las características de sexo y edad (ratas jóvenes y ratas adultas). Para este fin, se llevó a cabo una fase inicial de habituación de 10 minuto diarios en el laberinto radial de Olton, y una fase de entrenamiento de una tarea de memoria espacial durante 27 sesiones.INTRODUCCIÓN Y ASPECTOS GENERALES 1. RESUMEN 2. JUSTIFICACIÓN 3. MARCO TEÓRICO 4. MÉTODO 5. RESULTADOS 6. DISCUSIÓN Y CONCLUSIONES BIBLIOGRAFÍA ANEXOSPregradoPsicólog

Aprepitant plus granisetron and dexamethasone for prevention of chemotherapy-induced nausea and vomiting in patients with gastric cancer treated with S-1 plus cisplatin

Background: We aimed to evaluate the efficacy of a new combination antiemetic therapy comprising aprepitant, granisetron, and dexamethasone in gastric cancer patients undergoing chemotherapy with cisplatin and S-1. Methods: Gastric cancer patients scheduled to receive their first course of chemotherapy with cisplatin (60 mg/m2) and S-1 (80 mg/m2) were treated with a new combination antiemetic therapy aprepitant, granisetron, and dexamethasone on day 1; aprepitant and dexamethasone on days 2 and 3; and dexamethasone on day 4. The patients reported vomiting, nausea, use of rescue therapy, and change in the amount of diet intake, and completed the Functional Living Index-Emesis (FLIE) questionnaire. The primary endpoint was complete response (CR; no emesis and use of no rescue antiemetics) during the overall study phase (0-120 h after cisplatin administration). The secondary endpoints included complete protection (CP; CR plus no significant nausea); change in the amount of diet intake; and the impact of chemotherapy-induced nausea and vomiting (CINV) on daily life during the overall, acute (0-24 h), and delayed (24-120 h) phases. Results: Fifty-three patients were included. CR was achieved in 88.7, 98.1, and 88.7 % of patients in the overall, acute, and delayed phases, respectively. The corresponding rates of CP were 67.9, 96.2, and 67.9 %. Approximately half of the patients had some degree of anorexia. FLIE results indicated that 79.5 % of patients reported "minimal or no impact of CINV on daily life". Conclusions: Addition of aprepitant to standard antiemetic therapy was effective in gastric cancer patients undergoing treatment with cisplatin and S-1. © 2013 Springer Japan

Novel and Conserved Protein Macoilin Is Required for Diverse Neuronal Functions in Caenorhabditis elegans

Neural signals are processed in nervous systems of animals responding to variable environmental stimuli. This study shows that a novel and highly conserved protein, macoilin (MACO-1), plays an essential role in diverse neural functions in Caenorhabditis elegans. maco-1 mutants showed abnormal behaviors, including defective locomotion, thermotaxis, and chemotaxis. Expression of human macoilin in the C. elegans nervous system weakly rescued the abnormal thermotactic phenotype of the maco-1 mutants, suggesting that macoilin is functionally conserved across species. Abnormal thermotaxis may have been caused by impaired locomotion of maco-1 mutants. However, calcium imaging of AFD thermosensory neurons and AIY postsynaptic interneurons of maco-1 mutants suggest that macoilin is required for appropriate responses of AFD and AIY neurons to thermal stimuli. Studies on localization of MACO-1 showed that C. elegans and human macoilins are localized mainly to the rough endoplasmic reticulum. Our results suggest that macoilin is required for various neural events, such as the regulation of neuronal activity

Late Proterozoic juvenile arc metatonalite and adakitic granitoids in the Sør Rondane Mountains, East Antarctica

第3回極域科学シンポジウム/第32回極域地学シンポジウム 11月30日（金） 国立極地研究所 ３階ラウン

Rho ファミリー テイブンシリョウ GTP ケツゴウ タンパクシツ ト サイボウ ケイタイ セイギョ ニ カンスル テイリョウテキナ ケンキュウ

博士(Doctor)理学(Science)奈良先端科学技術大学院大学博第810号甲第810号博士(理学)奈良先端科学技術大学院大

Curvature tensors and Singer invariants of four-dimensional homogeneous spaces

summary:We show that the Singer invariant of a four-dimensional homogeneous space is at most $1$