Random deep neural networks are biased towards simple functions

We prove that the binary classifiers of bit strings generated by random wide deep neural networks with ReLU activation function are biased towards simple functions. The simplicity is captured by the following two properties. For any given input bit string, the average Hamming distance of the closest input bit string with a different classification is at least sqrt(n / (2{\pi} log n)), where n is the length of the string. Moreover, if the bits of the initial string are flipped randomly, the average number of flips required to change the classification grows linearly with n. These results are confirmed by numerical experiments on deep neural networks with two hidden layers, and settle the conjecture stating that random deep neural networks are biased towards simple functions. This conjecture was proposed and numerically explored in [Valle P\'erez et al., ICLR 2019] to explain the unreasonably good generalization properties of deep learning algorithms. The probability distribution of the functions generated by random deep neural networks is a good choice for the prior probability distribution in the PAC-Bayesian generalization bounds. Our results constitute a fundamental step forward in the characterization of this distribution, therefore contributing to the understanding of the generalization properties of deep learning algorithms

Effects Of Molar Ratio Of Iron Catalyst On Synthesis Of Carbon Nanotubes Via Catalytic Chemical Vapor Deposition

Research on the area of the synthesis of carbon nanotubes is fundamental and critical to the entire subject of carbon nanotubes. This dissertation describes an experiment to synthesize carbon nanotubes by the method of catalytic chemical vapor deposition (CCVD). It focuses on the relationship between the as-prepared catalyst and the synthesized carbon nanotubes. The effect of growth parameters for the synthesis of carbon nanotubes was also studied. The Fe-Mo-MgO catalysts with five different molar ratios of iron (Fe) in this composite catalyst were prepared through the impregnation method. The goal of this work was to identify the suitable molar ratio of iron (Fe) in the composite catalyst of Fe-Mo-MgO on which carbon nanotubes (CNTs) can be grown with a higher yield and quality.Scanning electron microscopy (SEM), transmission electron microscopy (TEM), xray diffraction (XRD), and thermogravimetric analysis (TGA) were used to characterize the as-prepared catalysts and as-grown carbon nanotube samples. Among these catalysts with different molar ratio of iron, the main and obvious observation in the synthesis of carbon nanotubes was the yield of synthesized carbon nanotubes. That is, increasing the molar ratio of iron, the yield of produced carbon nanotubes increases strongly, but the quality did not improve. While by decreasing the Fe concentration, both the structural defects and yield were reduced. Therefore, based on the experimental results, the best catalyst was catalyst 3 (Fe: Mo: MgO = 0.5: 0.1: 10) with a moderate molar ratio of iron. This catalyst not only had good yield but also good quality. The different parameters such as flow rate of argon (Ar) as a carrier gas, and temperature to improve the growth condition of CCVD method for the synthesis of CNTs by Fe-Mo-MgO catalyst were examined. It is found that the best flow rate for carrier gas is 100 ml/min. For the flow rate lower or higher than this, there were very few CNTs formed, since the low flow rate of Ar could not carry enough ethanol vapors through the reactor to be deposited on the catalyst. As for the high flow rate of Ar, most of the carbon source exited from the outlet of the reactor and again they could not be deposited on the catalyst, thus few carbon nanotubes were formed. In the synthesis of carbon nanotubes by CCVD method, the temperature plays a key role. The results show that when the temperature is lower than 750°C, few CNTs were formed, and when the temperature is higher than 900°C, more and more amorphous carbons were formed in the CNTs. The best temperature for the growth of carbon nanotubes by these catalysts is between 800°C and 900°C. The results showed that the growth of carbon nanotubes was significantly influenced by the reaction condition due to its sensitivity. The synthesis products were always a mixture of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs)

Load-Deflection Behaviour of Frp Concrete Composite Deck

Nowadays, Fiber Reinforced Polymer (FRP) concrete composite bridge deck system hasbeen introduced because of its light-weight and durability. Strong composition is neededbetween FRP and concrete to acquire the structural composite behavior of FRP concretecomposite deck. FRP has unique properties that, if disregarded, can lead to failure duringoperation. However, when these same unique properties are taken into advantages, they canprovide the engineers with a system superior to traditional metallic materials. This studyinvestigates analytically the deflection behavior of FRP concrete composite deck using shearconnectors under flexural loading. Finite element software (LUSAS) is used to model FRPcomposite deck. For this purpose, LUSAS has introduced some elements. Volume elementsare utilized to model concrete and Glass Fiber Reinforced Polymer (GFRP) section. Meshingelements are necessary in finite element in order to act as a member in modeling. 3D solidcontinuum elements are used to mesh the sample. Five GFRP module having differentthicknesses of 8mm, 9.6mm, 11.2mm, 12.8mm and 16mm are taken to analyze. Results showthat the thicknesses of GFRP module have significant effect on the ultimate load anddeflection of the deck. Once the thickness of GFRP section increased, the deflection at midspan decreased and the ultimate load increased accordingly. Furthermore, results revealed theappropriate interface material between FRP and concrete in finite element modeling. In orderto get an effective interface element, about 40 numerical models have been analyzed. Theresults were compared with experimental study. Inserted data for verified model in LUSASwere demonstrated as an appropriate interface element between FRP and concrete

Anniversaire de la Révolution et Nowrouz

L'analyse sociologique de la célébration de deux fêtes iraniennes, l'anniversaire de la Révolution et Nowrouz (nouvel an), souligne les interactions entre sphère officielle et sphère privée et remet en question l'idée d'une société islamique dirigée par le haut. La dynamique de transformation du rapport à l'islam a favorisé l'ouverture d'espaces autonomes où se déroulent des débats passionnés sur les enjeux de la vie quotidienne