Distribution of equilibrium free energies in a thermodynamic system with broken ergodicity

At low temperatures the configurational phase space of a macroscopic complex system (e.g., a spin-glass) of $N\sim 10^{23}$ interacting particles may split into an exponential number $\Omega_s \sim \exp({\rm const} \times N)$ of ergodic sub-spaces (thermodynamic states). Previous theoretical studies assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density, and that the equilibrium free energies follow the distribution of exponential decay. Here we show that these assumptions are not necessarily valid. For some complex systems, the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range, and consequently their equilibrium properties are contributed by {\em excited} thermodynamic states. This work will help improving our understanding of the equilibrium statistical mechanics of spin-glasses and other complex systems.Comment: 7 pages, 2 figure

Differential negative reinforcement of other behavior to increase compliance with wearing an anti-strip suit

Using a changing-criterion design, we replicated and extended a study (Cook, Rapp, & Schulze, 2015) on differential negative reinforcement of other behavior (DNRO). More specifically, educational assistants implemented DNRO to teach a 12-year-old boy with autism spectrum disorder to comply with wearing an anti-strip suit to prevent inappropriate fecal behavior in a school setting. The duration for which the participant wore the suit systematically increased from 2 s at the start of treatment to the entire duration of the school day at the termination of the study. Moreover, these effects were generalized to a new school with novel staff and persisted for more than a year. These findings replicate prior research on DNRO and further support the use of the intervention to increase compliance with wearing protective items, or medical devices, in practical settings

Development of Fungal Calcium Oxalate Crystals Associated with the Basidiocarps of Geastrum Minus (Lycoperdales)

Calcium oxalate crystals were observed on facing peridial surfaces of developing basidiocarps of Geastrum minus. Five crystal forms were characterized by their outward shapes and X-ray diffraction patterns: Form One, small bipyramids (COD); Form Two, crystals with split tips (COD); Form Three, crystals with oriented overgrowths (COD); Form Four, large bipyramids (COD); and Form Five, rosettes of plate-like crystals (COM). Forms One and Two were first to appear after peridia separated in unopened basidiocarps, whereas Forms Three, Four and Five were present on exposed peridia of opened basidiocarps. Based on time of appearance during basidiocarp development and crystallography of each form, we believe Form One gives rise to Forms Two, Three and Four. Form Five may arise from dissolution and recrystallization of pre-existing forms. Farinose or asperate basidiocarps of eight other species of Geastrum showed no crystals, indicating that only G. minus forms crystals. Comparison of the five forms with crystals on old basidiocarps indicates Form Four is predominant. The functional value of the crystals is discussed and they are compared with crystal forms found in human and animal urinary tracts

Application of two-parameter dynamical replica theory to retrieval dynamics of associative memory with non-monotonic neurons

The two-parameter dynamical replica theory (2-DRT) is applied to investigate retrieval properties of non-monotonic associative memory, a model which lacks thermodynamic potential functions. 2-DRT reproduces dynamical properties of the model quite well, including the capacity and basin of attraction. Superretrieval state is also discussed in the framework of 2-DRT. The local stability condition of the superretrieval state is given, which provides a better estimate of the region in which superretrieval is observed experimentally than the self-consistent signal-to-noise analysis (SCSNA) does.Comment: 16 pages, 19 postscript figure

Dynamics of on-line Hebbian learning with structurally unrealizable restricted training sets

We present an exact solution for the dynamics of on-line Hebbian learning in neural networks, with restricted and unrealizable training sets. In contrast to other studies on learning with restricted training sets, unrealizability is here caused by structural mismatch, rather than data noise: the teacher machine is a perceptron with a reversed wedge-type transfer function, while the student machine is a perceptron with a sigmoidal transfer function. We calculate the glassy dynamics of the macroscopic performance measures, training error and generalization error, and the (non-Gaussian) student field distribution. Our results, which find excellent confirmation in numerical simulations, provide a new benchmark test for general formalisms with which to study unrealizable learning processes with restricted training sets.Comment: 7 pages including 3 figures, using IOP latex2e preprint class fil

Dynamical Properties of a Growing Surface on a Random Substrate

The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force $F$ and temperature $T$. A continuous transition is found from high-temperature phase characterized by linear response to a low-temperature phase with nonlinear, temperature dependent response. In the simulated regime of driving force the numerical results are in general agreement with recent dynamic renormalization group predictions.Comment: 10 pages, latex, 3 figures, to appear in Phys. Rev. E (RC