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The higher order neural network using for pattern recognition and optimization is studied in this paper and the results in two different aspects have been obtained. < 1 > Theoretically , the capacity formula of the Hopfield Neural Network with the second order weights has been obtained. Compared with the first order network, the capacity of the second order network is about three times greater than that of the first order one and the cost to reach such a efficiency is to add higher order weights . The simulated experiments according to the theory by digital computer are satisfied. < 2 > Theoretically , the method of how to solve the optimization problems, whose energy functions are more general than Lyapunov function , has been put forward at the end of this paper. ABSTRACTThe higher order neural network using for pattern recognition and optimization is studied in this paper and the results in two different aspects have been obtained. < 1 > Theoretically, the capacity formula of the Hopfield Neural Network with the second order weights has been obtained. Compared with the first order network, the capacity of the second order network is about three times greater than that of the first order one and the cost to reach such a efficiency is to add higher order weights .The simulated experiments according to the theory by digital computer are satisfied. < 2 > Theoretically , the method of how to solve the optimization problems , whose energy functions are more general than Lyapunov function , has been put forward at the end of this paper.

The mechanism of Late Cretaceous crustal thickening and exhumation of the southern Lhasa terrane is critical for understanding the tectonic evolution of the Tibetan Plateau. High-pressure metamorphic rocks from the lower crust are good candidates for addressing this issue. In this study, we focus on Late Cretaceous, high-pressure, garnet-bearing amphibolites from the Nyingchi Complex of the Eastern Himalayan Syntaxis and present an integrated study of geochronology, petrography, mineral chemistry, and thermodynamic modeling. Petrographic data determine three metamorphic stages (M1−M3). The M1 stage is characterized by a peak mineral assemblage of garnet + hornblende + albite + rutile + muscovite + quartz, which is followed by a post-peak (M2) assemblage of garnet + hornblende + plagioclase + epidote + biotite + rutile + quartz. The late retrograde stage (M3) is defined by hornblende + plagioclase symplectites surrounding garnet porphyroblasts. Mineral chemistry, with thermodynamic modeling, constrains the P-T conditions of the M1−M3 stages to 14−19 kbar/660−720 °C, 8−10 kbar/650−660 °C, and &lt;7 kbar/&lt;600 °C, respectively. Metamorphic zircons yield a concordant age at 90 Ma, which indicates the formation of garnet-bearing amphibolites. These results indicate a P-T-t path involving near-isothermal decompression for garnet-bearing amphibolites, which suggests that the Nyingchi Complex underwent peak-pressure metamorphism (M1) at 90 Ma, followed by rapid exhumation to the depth of 32−26 km along the subduction channel. Moreover, the garnet-bearing amphibolites are considered to be the product of high-pressure metamorphism of mafic crust at the base of the Gangdese belt. Hence, the crust of the Gangdese belt experienced significant crustal thickening of up to 60 km at 90 Ma.