Thouless-Anderson-Palmer equation for analog neural network with temporally fluctuating white synaptic noise

Effects of synaptic noise on the retrieval process of associative memory neural networks are studied from the viewpoint of neurobiological and biophysical understanding of information processing in the brain. We investigate the statistical mechanical properties of stochastic analog neural networks with temporally fluctuating synaptic noise, which is assumed to be white noise. Such networks, in general, defy the use of the replica method, since they have no energy concept. The self-consistent signal-to-noise analysis (SCSNA), which is an alternative to the replica method for deriving a set of order parameter equations, requires no energy concept and thus becomes available in studying networks without energy functions. Applying the SCSNA to stochastic network requires the knowledge of the Thouless-Anderson-Palmer (TAP) equation which defines the deterministic networks equivalent to the original stochastic ones. The study of the TAP equation which is of particular interest for the case without energy concept is very few, while it is closely related to the SCSNA in the case with energy concept. This paper aims to derive the TAP equation for networks with synaptic noise together with a set of order parameter equations by a hybrid use of the cavity method and the SCSNA.Comment: 13 pages, 3 figure

慢性肺血栓性肺高血圧症患者における２Dスペックルトラッキングによる右室基部フリーストレインの有用性

藤田保健衛生大

Phase transitions driven by L\'evy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including nonequilibrium ones may appear. A Brownian motion is a special case of L\'evy motion and the stochastic process based on the latter is an alternative choice for studying cooperative phenomena in various fields. Recently, fractional Fokker-Planck equations associated with L\'evy noise have attracted much attention and behaviors of systems with double-well potential subjected to L\'evy noise have been studied intensively. However, most of such studies have resorted to numerical computation. We construct an {\it analytically solvable model} to study the occurrence of phase transitions driven by L\'evy stable noise.Comment: submitted to EP

Who Uses Free Trade Agreements?

It is noted that utilization of ASEAN Free Trade Agreements (FTAs) is low by international standards. In order to clarify the reasons for such low utilization, this paper investigates what kinds of Japanese affiliates in ASEAN are more likely to use FTAs in their exporting, by employing unique affiliate-level data. Our findings are as follows. First, the larger the affiliate is, or the more diversified the origins of its procurements, the more likely it is to utilize an FTA scheme in its exporting. Second, affiliates that export actively to countries with higher general tariffs are more likely to use FTAs. Third, there are clear differences in FTA utilization depending affiliates, locations and sectors.