Minimal Width for Universal Property of Deep RNN

A recurrent neural network (RNN) is a widely used deep-learning network for dealing with sequential data. Imitating a dynamical system, an infinite-width RNN can approximate any open dynamical system in a compact domain. In general, deep networks with bounded widths are more effective than wide networks in practice; however, the universal approximation theorem for deep narrow structures has yet to be extensively studied. In this study, we prove the universality of deep narrow RNNs and show that the upper bound of the minimum width for universality can be independent of the length of the data. Specifically, we show that a deep RNN with ReLU activation can approximate any continuous function or $L^p$ function with the widths $d_x+d_y+2$ and $\max\{d_x+1,d_y\}$, respectively, where the target function maps a finite sequence of vectors in $\mathbb{R}^{d_x}$ to a finite sequence of vectors in $\mathbb{R}^{d_y}$. We also compute the additional width required if the activation function is $\tanh$ or more. In addition, we prove the universality of other recurrent networks, such as bidirectional RNNs. Bridging a multi-layer perceptron and an RNN, our theory and proof technique can be an initial step toward further research on deep RNNs

Role of G{alpha}12 and G{alpha}13 as Novel Switches for the Activity of Nrf2, a Key Antioxidative Transcription Factor

G{alpha}12 and G{alpha}13 function as molecular regulators responding to extracellular stimuli. NF-E2-related factor 2 (Nrf2) is involved in a protective adaptive response to oxidative stress. This study investigated the regulation of Nrf2 by G{alpha}12 and G{alpha}13. A deficiency of G{alpha}12, but not of G{alpha}13, enhanced Nrf2 activity and target gene transactivation in embryo fibroblasts. In mice, G{alpha}12 knockout activated Nrf2 and thereby facilitated heme catabolism to bilirubin and its glucuronosyl conjugations. An oligonucleotide microarray demonstrated the transactivation of Nrf2 target genes by G{alpha}12 gene knockout. G{alpha}12 deficiency reduced Jun N-terminal protein kinase (JNK)-dependent Nrf2 ubiquitination required for proteasomal degradation, and so did G{alpha}13 deficiency. The absence of G{alpha}12, but not of G{alpha}13, increased protein kinase C {delta} (PKC {delta}) activation and the PKC {delta}-mediated serine phosphorylation of Nrf2. G{alpha}13 gene knockout or knockdown abrogated the Nrf2 phosphorylation induced by G{alpha}12 deficiency, suggesting that relief from G{alpha}12 repression leads to the G{alpha}13-mediated activation of Nrf2. Constitutive activation of G{alpha}13 promoted Nrf2 activity and target gene induction via Rho-mediated PKC {delta} activation, corroborating positive regulation by G{alpha}13. In summary, G{alpha}12 and G{alpha}13 transmit a JNK-dependent signal for Nrf2 ubiquitination, whereas G{alpha}13 regulates Rho-PKC {delta}-mediated Nrf2 phosphorylation, which is negatively balanced by G{alpha}12

Splenectomy is associated with an aggressive tumor growth pattern and altered host immunity in an orthotopic syngeneic murine pancreatic cancer model.

The purpose of this study was to investigate whether splenectomy influences the tumor growth and metastatic pattern in an orthotopic syngeneic murine pancreatic cancer model. Murine pancreatic cancer cells (PAN02) were subcutaneously injected into the flanks of nude mice. A small tumor fragment (3 mm2), harvested from a subcutaneous tumor. was orthotopically implanted in the tail of the pancreas of C57/BL6 mice without splenectomy (control group, n=15) or with simultaneous splenectomy (splenectomy group, n=15). Tumor growth and metastatic patterns were analyzed by laparotomy at 21 days after surgery. No tumor growth was found in 5 mice (33.3%) of the control group and 1 mouse (6.7%) of the splenectomy group (p=0.169). Tumor volume was significantly larger in splenectomy group (p=0.013). Peritoneal seeding was more frequently observed in the splenectomy group (11 (73.3%) vs. 4 (26.7%), p=0.011). There were no differences in the number of liver and kidney metastasis between the two groups. The ratios of tumor-infiltrating CD4+ to FoxP3+ and CD8+ to FoxP3+ were significantly higher in the control group compared to the splenectomy group (8.2 ± 9.3 vs. 2.4 ± 1.5, p=0.046; 2.5 ± 1.4 vs. 1.5 ± 0.4, p=0.031, respectively). Splenectomy enhanced tumor growth and peritoneal seeding in an orthotopic syngeneic murine pancreatic cancer mouse model. The ramification of these results are discussed for pancreatic cancer treatment

Properties of Magnesia Composites According to Replacement Ratio of Perlite

Recently, passive and zero-energy construction has increased in Korea due to the government`s continuous application of budget-conscious policies for establishments. Accordingly, construction materials are being advanced, and the required performance standards for insulation materials are increasing. However, problems such as fire vulnerability and degradation of physical properties for organic and inorganic insulation materials are shown, so it is necessary to solve this problem. The objective of this research is to examine the properties of the composites by analyzing the flexural breaking load, impact resistance, density, VOCs concentration reduction rate, and fine dust concentration reduction rate of the composites manufactured based on the perlite substitution rate of the magnesia composites. The flexural breaking load test of the composites was assessed according to ‘KS F 3504’, a gypsum board standard and the impact resistance was assessed according to ‘KS F 4715’. The performance evaluation of adsorption performance of air pollutants of the VOCs and fine dust in the context of the small chamber technique suggested by Hanbat University. The results of this study are as follows: The flexural breaking load according to the perlite replacement rate tended to decrease as the perlite replacement rate increased. It is determined that the flexural breaking load is reduced by generating a large amount of pores inside due to the perlite porous structure characteristics. In the case of impact resistance, the impact resistance tended to increase as the perlite displacement rate increased. It is determined that the volume of the binder in the board is reduced, and pores inside the board are generated due to perlite, which is a porous material, thereby reducing the overall bonding force of the board. In the case of VOCs and fine dust concentrations, the VOCs and fine dust concentration reduction rates tended to increase as the perlite replacement rate increased. In the case of the perlite displace rate of 30%, the VOCs concentration decreased by 82.6%, and the fine dust concentration decreased by 87.9%. It has been established that the porous properties of perlite used to create a huge number of pores in the hardened body cause the concentration to be lowered physically through adsorption. This study\u27s findings are thought to be fundamental information for securing the engineering properties and air pollution absorption of magnesia composites blended with perlite

Tailorable, 3D microfabrication for photonic applications: Two-polymer microtransfer molding

For photonic devices, extending beyond the planar regime to the third dimension can allow a higher degree of integration and novel functionalities for applications such as photonic crystals and integrated optical circuits. Although conventional photolithography can achieve both high quality and structural control, it is still costly and slow for threedimensional (3D) fabrication. Moreover, as diverse functional polymers emerge, there is potential to develop new techniques for quick and economical fabrication of 3D structures. We present a 3D microfabrication technique based on the soft lithographic technique, called two-polymer microtransfer molding (2P-µTM) to accomplish low cost, high structural fidelity and tailorable 3D microfabrication for polymers. Using 2P-µTM, highly layered polymeric microstructures are achievable by stacking planar structures layer by layer. For increased processing control, the surface chemistry of the polymers is characterized as a function of changing ultraviolet dosage to optimize yield in layer transfer. We discuss the application of the 2P-µTM to build polymer templates for woodpile photonic crystals, and demonstrate methods for converting the polymer templates to dielectric and metallic photonic crystal structures. Finally, we will show that 2P-µTM is promising for fabricating 3D polymeric optical waveguides

The Globular Cluster System of M60 (NGC 4649). I. CFHT MOS Spectroscopy and Database

We present the measurement of radial velocities for globular clusters in M60, giant elliptical galaxy in the Virgo cluster. Target globular cluster candidates were selected using the Washington photometry based on the deep 16\arcmin \times 16\arcmin images taken at the KPNO 4m and using the $VI$ photometry derived from the HST/WFPC2 archive images. The spectra of the target objects were obtained using the Multi-Object Spectrograph (MOS) at the Canada-France-Hawaii Telescope (CFHT). We have measured the radial velocity for 111 objects in the field of M60: 93 globular clusters (72 blue globular clusters with $1.0\le(C-T_1)<1.7$ and 21 red globular clusters with $1.7\le(C-T_1)<2.4$), 11 foreground stars, 6 small galaxies, and the nucleus of M60. The measured velocities of the 93 globular clusters range from $\sim 500$ km s$^{-1}$ to $\sim 1600$ km s$^{-1}$, with a mean value of $1070_{-25}^{+27}$ km s$^{-1}$, which is in good agreement with the velocity of the nucleus of M60 ($v_{\rm gal}=1056$ km s$^{-1}$). Combining our results with data in the literature, we present a master catalog of radial velocities for 121 globular clusters in M60. The velocity dispersion of the globular clusters in the master catalog is found to be $234_{-14}^{+13}$ km s$^{-1}$ for the entire sample, $223_{-16}^{+13}$ km s$^{-1}$ for 83 blue globular clusters, and $258_{-31}^{+21}$ km s$^{-1}$ for 38 red globular clusters.Comment: 29 pages, 8 figures. To appear in Ap

Fabrication of layer-by-layer photonic crystals using two polymer microtransfer molding

A method of manufacturing photonic band gap structures operable in the optical spectrum has been presented. The method comprises the steps of filling a plurality of grooves of an elastomeric mold with a UV curable first polymer, each groove in parallel with each other and partially curing the first polymer. A second polymer is coated on the first polymer. A substrate or a multi-layer polymer structure is placed on the filled mold and the resulting structure is exposed to UV light (i.e., is UV cured). The mold is peeled away from the first and second polymers such that a layer of polymer rods is formed on the substrate/multi-layer polymer structure. The process is repeated until a desired number of layers have been formed. The multi-layer structure can be used to create ceramic and metallic photonic band gaps by infiltration, electro-deposition, and/or metal coating

A Human Embryo of Carnegie Stage 12

A human embryo obtained from a salpinx removed for the treatment of tubal gestation was serially sectioned and observed. On gross examination, the embryo showed three prominent pharyngeal arches, but not the cervical sinus. The upper arm bud had just begun to appear with a slight elevation in the skin ectoderm. Both the anterior and posterior neuropores had already been closed. The heart was at the cardiac loop stage. The respiratory diverticulum, the dorsal pancreas and the beginning of the omental bursa had appeared. In the pharyngeal region, the adenohypophyseal pocket and the thyroid anlage were observed. The optic evagination showed no regional differentiation yet. From the above findings, we concluded that this embryo belonged to Carnegie stage 12