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This paper proposes a deep learning-based method for path planning of college students’ morality and faith instruction. Using a questionnaire and sampling inspection, the teaching effect index test and automatic monitoring of morality and faith teaching data are conducted. The feasible teaching strategy index of college students’ morality and faith teaching is based on students’ deep learning needs and expectations for ideological and political teaching in colleges and universities. The actual effect and teaching effect of teaching reform and innovation serve as the basic monitoring coefficient. Using deep learning and dynamic optimization detection methods, a feature clustering model for data collection and deep and surface learning of morality and faith instruction for college students is developed. A deep learning model for teaching morality and faith to college students is developed using a significant feature analysis method. Implement multidimensional spatial path optimization and data fitting. Perform quantitative regression analysis of college students’ critical, creative, and higher-order thinking in the index data of morality and faith teaching strategies. Detect and extract index data on morality and faith teaching strategies for college students. The test results show that this method improves the practicability and originality of morality and faith instruction for college students by optimizing the course planning and index data of feasible teaching strategies.

The planar Thirring model is thought to have a strongly coupled critical point for a single flavor of fermion. We look at the calculation of the bilinear condensate in this critical region, and its characterization via an equation of state. Since the computation is numerically challenging, we investigate the improved Dirac operators. We present findings on different methods of calculation using a rational hybrid Monte-Carlo scheme, and calculations of the bilinear condensate, an equation of state and the associated critical exponents. Overlap and domain wall Dirac operators, and variants therein are considered.

In this paper, the charged acoustic black hole with a cosmological constant has been assumed. We have taken into account the negative cosmological constant as thermodynamic pressure in the extended phase space. Then we derived the thermodynamic quantities and investigated their behavior. We have studied the critical values of temperature and pressure. By calculating the specific heat capacity, we have analyzed the thermal stability of the charged acoustic black hole. Then we studied the heat engine phenomena of the black hole. We discovered the Carnot engine’s efficiency and the brand-new engine phenomenon of the black hole.

There is a discrepancy between the standard view of equilibrium through price adjustment in economics and the observation of large fluctuations in stock markets. We study here a simple model where agents decisions not only depend upon their individual preferences but also upon information obtained from their neighbors in a social network. The model shows that information diffusion coupled to the adjustment process drives the system to criticality with large fluctuations rather than converging smoothly to equilibrium.

Self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of the suggested simulation method is an artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by a random walk on the temperature axis. The walk is biased towards the critical region through a feedback based on instantaneous energy and magnetization cumulants, which are updated at every Monte Carlo step and filtered through a special recursion algorithm. The simulations revealed the invariance of the temperature probability distribution function, once some self-organized critical steady regime is reached, which is called here noncanonical equilibrium. The mean value of this distribution approximates the pseudocritical temperature of canonical equilibrium. In order to suppress finite-size effects, the self-organized approach is extended to multi-lattice systems, where the feedback basis on pairs of instantaneous estimates of the fourth-order magnetization cumulant on two systems of different size. These replica-based simulations resemble, in Monte Carlo lattice systems, some of the invariant statistical distributions of standard self-organized critical systems.

We describe an ensemble of growing scale-free networks in an equilibrium framework, providing insight into why the exponent of empirical scale-free networks in nature is typically robust. In an analogy to thermostatistics, to describe the canonical and microcanonical ensembles, we introduce a functional, whose maximum corresponds to a scale-free configuration. We then identify the equivalents to energy, Zeroth-law, entropy and heat capacity for scale-free networks. Discussing the merging of scale-free networks, we also establish an exact relation to predict their final "equilibrium" degree exponent. All analytic results are complemented with Monte Carlo simulations. Our approach illustrates the possibility to apply the tools of equilibrium statistical physics to study the properties of growing networks, and it also supports the recent arguments on the complementarity between equilibrium and nonequilibrium systems.

We propose that the herding behavior of traders leads not only to speculative bubbles with accelerating over-valuations of financial markets possibly followed by crashes, but also to "anti-bubbles" with decelerating market devaluations following all-time highs. For this, we propose a simple market dynamics model in which the demand decreases slowly with barriers that progressively quench in, leading to a power law decay of the market price characterized by decelerating log-periodic oscillations. We document this behavior of the Japanese Nikkei stock index from 1990 to present and of the gold future prices after 1980, both after their all-time highs. We perform simultaneously parametric and nonparametric analyses that are fully consistent with each other. We extend the parametric approach to the next order of perturbation, comparing the log-periodic fits with one, two and three log-frequencies, the latter providing a prediction for the general trend in the coming years. The nonparametric power spectrum analysis shows the existence of log-periodicity with high statistical significance, with a preferred scale ratio of λ≈3.5 for the Nikkei index and λ≈1.9 for the Gold future prices, comparable to the values obtained for speculative bubbles leading to crashes.

A possible resolution of the incompatibility of quantum mechanics and general relativity is that the relativity principle is emergent. I show that the central paradox of black holes also occurs at a liquid-vapor critical surface of a bose condensate but is resolved there by the phenomenon of quantum criticality. I propose that real black holes are actually phase boundaries of the vacuum analogous to this, and that the Einstein field equations simply fail at the event horizon the way quantum hydrodynamics fails at a critical surface. This can occur without violating classical general relativity anywhere experimentally accessible to external observers. Since the low-energy effects that occur at critical points are universal, it is possible to make concrete experimental predictions about such surfaces without knowing much, if anything about the true underlying equations. Many of these predictions are different from accepted views about black holes — in particular the absence of Hawking radiation and the possible transparency of cosmological black hole surfaces.

Following the direct observation of abrupt changes in the superconducting ground state in doped low dimensional antiferromagnets, we have identified a phase transition where superconductivity is optimal. The experiments indicate the presence of a putative quantum critical point associated with the emergence of a glassy state. This mechanism is argued to be an intrinsic property and as such, largely independent of material quality and the level of disorder.

We discuss an attractor neural network in which only a fraction ρ of nodes is simultaneously updated. In addition, the network has a heterogeneous distribution of connection weights and, depending on the current degree of order, connections are changed at random by a factor Φ on short-time scales. The resulting dynamic attractors may become unstable in a certain range of Φ thus ensuing chaotic itineracy which highly depends on ρ. For intermediate values of ρ, we observe that the number of attractors visited increases with ρ, and that the trajectory may change from regular to chaotic and vice versa as ρ is modified. Statistical analysis of time series shows a power-law spectra under conditions in which the attractors' space is most efficiently explored.

We investigate the critical behavior of a stochastic lattice model describing a predator–prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

Excitable media may be modeled as simple extensions of the Amari–Hopfield network with dynamic attractors. Some nodes chosen at random remain temporarily quiet, and some of the edges are switched off to adjust the network connectivity, while the weights of the other edges vary with activity. We conclude on the optimum wiring topology and describe nonequilibrium phases and criticality at the edge of irregular behavior.

In this paper, we propose to consider living systems as "coherent critical structures," though extended in space and time, their unity being ensured through global causal relations between levels of organization (integration/regulation). This may be seen as a further contribution to the large amount of work already done on the theme of self-organized criticality. More precisely, our main physical paradigm is provided by the analysis of "phase transitions," as this peculiar form of critical state presents interesting aspect of emergence: the formation of extended correlation lengths and coherence structures, the divergence of some observables with respect to the control parameter(s), etc…. However, the "coherent critical structures" which are the main focus of our work cannot be reduced to existing physical approaches, since phase transitions, in physics, are treated as "singular events," corresponding to a specific well-defined value of the control parameter. Whereas our claim is that in the case of living systems, these coherent critical structures are "extended" and organized in such a way that they persist in space and time. The relation of this concept to the theory of autopoiesis, as well as to various forms of teleonomy, often present in biological analyses, will be also discussed.

Here I show that digraphs (directed graphs) are inherent both in the relationships between elements of biological systems and in transitions between different system states. Properties of digraphs therefore underlie many biological phenomena, especially criticality and phase changes. Examples include epidemics, development, vegetation change and evolution. An important source of variety in biological systems is the extreme variability in digraph patterns that occurs when levels of connectivity are critical. Many biological processes, including evolution, appear to exploit this variety via a mechanism in which the connectivity of a system flips back and forth across the critical level.

Log-periodic power laws often occur as signatures of impending criticality of hierarchical systems in the physical sciences. It has been proposed that similar signatures may be apparent in the price evolution of financial markets as bubbles and the associated crashes develop. The features of such market bubbles have been extensively studied over the past 20 years, and models derived from an initial discrete scale invariance assumption have been developed and tested against the wealth of financial data with varying degrees of success. In this paper, the equations that form the basis for the standard log-periodic power law model and its higher extensions are compared to a logistic model derived from the solution of the Schröder equation for the renormalization group with nonlinear scaling function. Results for the S&P 500 and Nikkei 225 indices studied previously in the literature are presented and compared to established models, including a discussion of the apparent frequency shifting observed in the S&P 500 index in the 1980s. In the particular case of the Nikkei 225 anti-bubble between 1990 and 2003, the logistic model appears to provide a better description of the large-scale observed features over the whole 13-year period, particularly near the end of the anti-bubble.

We present a methodology to identify change-points in financial markets where the governing regime shifts from a constant rate-of-return, i.e. normal growth, to a superexponential growth described by a power-law hazard rate. The latter regime corresponds, in our view, to financial bubbles driven by herding behavior of market participants. Assuming that the time series of log-price returns of a financial index can be modeled by arithmetic Brownian motion, with an additional jump process with power-law hazard function to approximate the superexponential growth, we derive a threshold value of the hazard-function control parameter, allowing us to decide in which regime the market is more likely to be at any given time. An analysis of the Standard & Poors 500 index over the last 60 years provides evidence that the methodology has merit in identifying when a period of herding behavior begins, and, perhaps more importantly, when it ends.

Power indices in simple games measure the relevance of a player through her ability in being critical, i.e. essential for a coalition to win. We introduce new indices that measure the power of a player in being decisive through the collaboration of other players. We study the behavior of these criticality indices to compare the power of different players within a single voting situation, and that of the same player with varying weight across different voting situations. In both cases we establish monotonicity results in line with those of Turnovec [1998]. Finally, we examine which properties characterizing the indices of Shapley–Shubik and Banzhaf are shared by these new indices.

This case study is part of a research project based in Spain between 2011 and 2014 on the social institutions and affective processes involved in what is normally referred to as social movement. Our purpose is to study how information circulates in small-world networks in which the dynamics are modeled with a stochastic version of Greenberg–Hasting’s excitable model. This is a three-state model in which a node can be in an excited, passive, or susceptible state. Only in the susceptible state does a node interact with its neighbors in the small-world network, and its interaction depends on the probability of contagion. We introduce an infection probability, which is the only parameter in our implementation of Greenberg–Hasting’s model. The small-world network is characterized by a mean connectivity parameter and by a disorder parameter.

The resulting dynamics are characterized by the average activity in the network. We have found transitions from inactive to active collective regimes, and we can induce this transition by varying. We search for different dynamics within small-world networks of citizens’ organizations by going through the following steps: identifying alliance patterns; looking for robust small-world attributes and how they are constructed; and interpreting the three modes of our model.

We propose that a regulation mechanism based on Hebbian covariance plasticity may cause the brain to operate near criticality. We analyze the effect of such a regulation on the dynamics of a network with excitatory and inhibitory neurons and uniform connectivity within and across the two populations. We show that, under broad conditions, the system converges to a critcal state lying at the common boundary of three regions in parameter space; these correspond to three modes of behavior: high activity, low activity, oscillation.

The present study examines the possible roles of cortical chaos in generating novel actions for achieving specified goals. The proposed neural network model consists of a sensory-forward model responsible for parietal lobe functions, a chaotic network model for premotor functions and prefrontal cortex model responsible for manipulating the initial state of the chaotic network. Experiments using humanoid robot were performed with the model and showed that the action plans for satisfying specific novel goals can be generated by diversely modulating and combining prior-learned behavioral patterns at critical dynamical states. Although this criticality resulted in fragile goal achievements in the physical environment of the robot, the reinforcement of the successful trials was able to provide a substantial gain with respect to the robustness. The discussion leads to the hypothesis that the consolidation of numerous sensory-motor experiences into the memory, meditating diverse imagery in the memory by cortical chaos, and repeated enaction and reinforcement of newly generated effective trials are indispensable for realizing an open-ended development of cognitive behaviors.