Statistical Mechanics of Time Domain Ensemble Learning

Conventional ensemble learning combines students in the space domain. On the other hand, in this paper we combine students in the time domain and call it time domain ensemble learning. In this paper, we analyze the generalization performance of time domain ensemble learning in the framework of online learning using a statistical mechanical method. We treat a model in which both the teacher and the student are linear perceptrons with noises. Time domain ensemble learning is twice as effective as conventional space domain ensemble learning.Comment: 10 pages, 10 figure

On-line Learning of an Unlearnable True Teacher through Mobile Ensemble Teachers

On-line learning of a hierarchical learning model is studied by a method from statistical mechanics. In our model a student of a simple perceptron learns from not a true teacher directly, but ensemble teachers who learn from the true teacher with a perceptron learning rule. Since the true teacher and the ensemble teachers are expressed as non-monotonic perceptron and simple ones, respectively, the ensemble teachers go around the unlearnable true teacher with the distance between them fixed in an asymptotic steady state. The generalization performance of the student is shown to exceed that of the ensemble teachers in a transient state, as was shown in similar ensemble-teachers models. Further, it is found that moving the ensemble teachers even in the steady state, in contrast to the fixed ensemble teachers, is efficient for the performance of the student.Comment: 18 pages, 8 figure

Statistical Mechanics of Nonlinear On-line Learning for Ensemble Teachers

We analyze the generalization performance of a student in a model composed of nonlinear perceptrons: a true teacher, ensemble teachers, and the student. We calculate the generalization error of the student analytically or numerically using statistical mechanics in the framework of on-line learning. We treat two well-known learning rules: Hebbian learning and perceptron learning. As a result, it is proven that the nonlinear model shows qualitatively different behaviors from the linear model. Moreover, it is clarified that Hebbian learning and perceptron learning show qualitatively different behaviors from each other. In Hebbian learning, we can analytically obtain the solutions. In this case, the generalization error monotonically decreases. The steady value of the generalization error is independent of the learning rate. The larger the number of teachers is and the more variety the ensemble teachers have, the smaller the generalization error is. In perceptron learning, we have to numerically obtain the solutions. In this case, the dynamical behaviors of the generalization error are non-monotonic. The smaller the learning rate is, the larger the number of teachers is; and the more variety the ensemble teachers have, the smaller the minimum value of the generalization error is.Comment: 13 pages, 9 figure

Effect of oxygen and nitrogen interactions on friction of single-crystal silicon carbide

Friction studies were conducted with single-crystal silicon carbide contacting silicon carbide and titanium after having been exposed to oxygen and nitrogen in various forms. After they had been sputter cleaned, the surfaces were (1) exposed to gaseous oxygen and nitrogen (adsorption), (2) ion bombarded with oxygen and nitrogen, or (3) reacted with oxygen (SiC only). Auger emission spectroscopy was used to determine the presence of oxygen and nitrogen. The results indicate that the surfaces of silicon carbide with reacted and ion-bombarded oxygen ions give higher coefficients of friction than do argon sputter-cleaned surfaces. The effects of oxygen on friction may be related to the relative chemical, thermodynamic properties of silicon, carbon, and titanium for oxygen. The adsorbed films of oxygen, nitrogen, and mixed gases of oxygen and nitrogen on sputter-cleaned, oxygen-ion bombarded, and oxygen-reacted surfaces generally reduce friction. Adsorption to silicon carbide is relatively weak

Occurrence of spherical ceramic debris in indentation and sliding contact

Indenting experiments were conducted with the silicon carbide (0001) surface in contact with a spherical diamond indenter in air. Sliding friction experiments were also conducted with silicon carbide in contact with iron and iron-based binary alloys at room temperature and 800 C. Fracture pits with a spherical particle and spherical wear debris were observed as a result of indenting and sliding. Spherical debris may be produced by a mechanism that involves a spherical-shaped fracture along the circular or spherical stress trajectories under the inelastic deformation zone

Surface chemistry and wear behavior of single-crystal silicon carbide sliding against iron at temperatures to 1500 C in vacuum

X-ray photoelectron and Auger electron spectroscopy analyses and morphological studies of wear and metal transfer were conducted with a single-crystal silicon carbide 0001 surface in contact with iron at various temperatures to 1500 C in a vacuum of 10 to the minus 8th power pascal. The results indicate that below 800 C, carbide-carbon and silicon are primarily seen on the silicon carbide surface. Above 800 C the graphite increases rapidly with increase in temperature. The outermost surficial layer, which consists mostly of graphite and little silicon at temperatures above 1200 C is about 2 nm thick. A thicker layer, which consists of a mixture of graphite, carbide, and silicon is approximately 100 nm thick. The closer the surface sliding temperature is to 800 C, the more the metal transfer produced. Above 800 C, there was a transfer of rough, discontinuous, and thin iron debris instead of smooth, continuous and thin iron film which was observed to transfer below 800 C. Two kinds of fracture pits were observed on the silicon carbide surface: (1) a pit with a spherical asperity; and (2) multiangular shaped pits

Anisotropic friction, deformation, and fracture of single-crystal silicon carbide at room temperature

Anisotropic friction, deformation, and fracture studies were conducted with /0001/, /10(-1)0/, and /11(-2)0/ silicon carbide surfaces in sliding contact with diamond. The experiments were conducted with loads of 0.1, 0.2, and 0.3 N at a sliding velocity of 3 mm/min in mineral oil or in dry argon at room temperature. The 1010 direction on the basal /0001/ plane exhibits the lowest coefficient of friction and the greatest resistance to abrasion for silicon carbide. Anisotropic friction and deformation of the /0001/, /10(-1)0/, and /11(-2)0/ silicon carbide surfaces are primarily controlled by the slip system /10(-1)0/ 11(-2)0. The anisotropic fracture during sliding on the basal plane is due to surface cracking along /10(-1)0/ and subsurface cracking along /0001/. The fracture during sliding on the /11(-2)0/ or /10(-1)0/ surfaces is due to surface cracking along /0001/ and /11(-2)0/ or /10(-1)-1 and to subsurface cracking along /10(-1)0/

Properties of ferrites important to their friction and wear behavior

Environmental, chemical and crystallographical effects on the fundamental nature on friction and wear of the ferrites in contact with metals, magnetic tapes and themselves are reviewed. The removal of adsorbed films from the surfaces of ferrites results in very strong interfacial adhesion and high friction in ferrite to metal and ferrite to magnetic tape contacts. The metal ferrite bond at the interface is primarily a chemical bond between the metal atoms and the large oxygen anions in the ferrite surface, and the strength of these bonds is related to the oxygen to metal bond strength in the metal oxide. The more active the metal, the higher is the coefficient of friction. Not only under adhesive conditions, but also under abrasive conditions the friction and wear properties of ferrites are related to the crystallographic orientation. With ferrite to ferrite contact the mating of highest atomic density (most closely packed) direction on matched crystallographic planes, that is, 110 directions on /110/planes, results in the lowest coefficient of friction

Adhesion and friction of iron-base binary alloys in contact with silicon carbide in vacuum

Single pass sliding friction experiments were conducted with various iron base binary alloys (alloying elements were Ti, Cr, Mn, Ni, Rh, and W) in contact with a single crystal silicon carbide /0001/ surface in vacuum. Results indicate that atomic size and concentration of alloying elements play an important role in controlling adhesion and friction properties of iron base binary alloys. The coefficient of friction generally increases with an increase in solute concentration. The coefficient of friction increases linearly as the solute to iron atomic radius ratio increases or decreases from unity. The chemical activity of the alloying elements was also an important parameter in controlling adhesion and friction of alloys, as these latter properties are highly dependent upon the d bond character of the elements

Surface chemistry, friction and wear of Ni-Zn and Mn-Zn ferrites in contact with metals

X-ray photoelectron and Auger electron spectroscopy analysis were used in sliding friction experiments. These experiments were conducted with hot-pressed polycrystalline Ni-Zn and Mn-Zn ferrites, and single-crystal Mn-Zn ferrite in contact with various transition metals at room temperature in both vacuum and argon. The results indicate that Ni2O3 and Fe3O4 were present on the Ni-Zn ferrite surface in addition to the nominal bulk constituents, while MnO2 and Fe3O4 were present on the Mn-Zn ferrite surface in addition to the nominal bulk constituents. The coefficients of friction for the ferrites in contact with metals were related to the relative chemical activity of these metals. The more active the metal, the higher is the coefficient of friction. The coefficients of friction for the ferrites were correlated with the free energy of formation of the lowest metal oxide. The interfacial bond can be regarded as a chemical bond between the metal atoms and the oxygen anions in the ferrite surfaces. The adsorption of oxygen on clean metal and ferrite does strengthen the metal-ferrite contact and increase the friction. The ferrites exhibit local cracking and fracture with sliding under adhesive conditions. All the metals transferred to he surfaces of the ferrites in sliding