Log-correlated Random Energy Models with extensive free energy fluctuations: pathologies caused by rare events as signatures of phase transitions

We address systematically an apparent non-physical behavior of the free energy moment generating function for several instances of the logarithmically correlated models: the Fractional Brownian Motion with Hurst index $H = 0$ (fBm0) (and its bridge version), a 1D model appearing in decaying Burgers turbulence with log-correlated initial conditions, and finally, the two-dimensional logREM introduced in [Cao et al., Phys.Rev.Lett.,118,090601] based on the 2D Gaussian free field (GFF) with background charges and directly related to the Liouville field theory. All these models share anomalously large fluctuations of the associated free energy, with a variance proportional to the log of the system size. We argue that a seemingly non-physical vanishing of the moment generating function for some values of parameters is related to the termination point transition (a.k.a pre-freezing). We study the associated universal log corrections in the frozen phase, both for log-REMs and for the standard REM, filling a gap in the literature. For the above mentioned integrable instances of logREMs, we predict the non-trivial free energy cumulants describing non-Gaussian fluctuations on the top of the Gaussian with extensive variance. Some of the predictions are tested numerically.Comment: 17 pages, 4 figure

Preparation of N-doped carbon quantum dots and their applications in the selective sensing of Mercury (II)

This master’s thesis presents a comprehensive study on the optimal design and synthesis of nitrogen-doped carbon quantum dots (N-CQDs) from small molecule carbon and nitrogen precursors and their application as fluorescence sensor for the detection of heavy metal ions. By employing the Box-Behnken design (BBD), the optimal synthetic condition for hydrothermal method was obtained, which led to the achievement of the high quantum yield of 51.7% for N-CQDs. The as-prepared N-CQDs are with brownish-yellow color and showed a bright blue light irradiation. To stabilize the N-CQDs, immobilization of N-CQDs onto a glutaraldehyde cross-linked chitosan was then performed to prepare the N-CQDs@GACTS hydrogel film for the selective sensing of Hg2+ ion. FTIR and XPS analyses revealed that N-CQDs were embedded into the GACTS matrix mainly through weak hydrogen bond or electrostatic attraction. Among the three tested heavy metal ions (Cd²⁺, Hg²⁺ and Pb²⁺), the N-CQDs@GACTS hydrogel film exhibited remarkable sensing sensitivity and selectivity of Hg²⁺. The excellent selectivity could be attributed to a stronger interaction between the hydrogel film and Hg²⁺ ion. Due to the strong oxidizing ability and chelating power, Hg²⁺ can be more readily combined with polar groups on the surface of N-CQDs@GACTS hydrogel to form new complexes by either chelation or electrostatic attraction, which provokes an effective electron transfer for the fluorescence quenching of the N-CQDs@GACTS hydrogel. The prepared N-CQDs@GACTS hydrogel demonstrates enhanced practicality in terms of fast response, sensitivity, selectivity, and economical pricing. It has great potential for practical applications in selectively detecting Hg²⁺ from either drinking water or wastewater

Multi-Interactive-Modality based Modeling for Myopia Pro-Gression of Adolescent Student

Myopia is a common visual disorder that affects millions of people worldwide and its prevalence has been increasing in recent years. Environmental factors, such as reading time, viewing distance, and ambient lighting, have been identified as potential factors in the development of myopia. In this study, we investigated the relationship between three major factors and myopia in 120 adolescents. By collecting environmental images of the adolescents in the learning state as well as retinal fundus images, we proposed an environmental visual load (EVL) model to extract the potential information in these images. Through experimental data analysis, we found that these three major factors are closely related to the severity of myopia, and that the simultaneous exacerbation of these factors sharply increases the myopia of the eye. Our results suggest that interventions targeting these environmental factors may help prevent and manage myopia.Comment: 9 pages, 5 figure

Step-by-step unbalanced force iteration method for cable-strut structure with irregular shape

In the design process of a cable-strut structure, the desired shape is first defined and the prestress can be obtained if the geometry is feasible; otherwise, the geometry must be modified. Thus, the initial step for prestress calculation is to estimate the feasibility of the geometry. In this paper, a method called Unbalanced Force Iteration (UFI) is proposed to remove the unbalanced forces using the equilibrium and stiffness equations. Feasibility of the geometry can be judged by the convergence property of UFI. Self-stress modes can be directly obtained easily through UFI method, if initial geometry is feasible. For structures with infeasible initial geometry, the Step-by-Step UFI, which combines finite element analysis and UFI, is proposed to gradually move the nodes to feasible locations. Three examples of cable domes with feasible geometry and three examples of cable domes with irregular and infeasible initial geometry are presented to verify the ability of UFI and Step-by-Step UFI for designing new irregular and asymmetric cable-strut structures

Stochastic Simulation on System Reliability and Component Probabilistic Importance of Road Network

Because of the combination explosion problem, it is difficult to use probability analytical method to calculate the system reliability of large networks. The paper develops a stochastic simulation (Monte Carlo-based) method to study the system reliability and component probabilistic importance of the road network. The proposed method considers the characteristics of the practical road network as follows: both link (roadway segment) and node (intersection) components are emphasized in the road network; the reliability for a link or node component may be at the in-between state; namely, its reliability value is between 0 and 1. The method is then implemented using the object-oriented programming language C++ and integrated into a RARN-MGG (reliability analysis of road network using Monte Carlo, GIS, and grid) system. Finally, two numerical examples based on a simple road network and a large real road network, respectively, are carried out to characterize the feasibility and to demonstrate the strength of the stochastic simulation method

Decision Making under Cumulative Prospect Theory: An Alternating Direction Method of Multipliers

This paper proposes a novel numerical method for solving the problem of decision making under cumulative prospect theory (CPT), where the goal is to maximize utility subject to practical constraints, assuming only finite realizations of the associated distribution are available. Existing methods for CPT optimization rely on particular assumptions that may not hold in practice. To overcome this limitation, we present the first numerical method with a theoretical guarantee for solving CPT optimization using an alternating direction method of multipliers (ADMM). One of its subproblems involves optimization with the CPT utility subject to a chain constraint, which presents a significant challenge. To address this, we develop two methods for solving this subproblem. The first method uses dynamic programming, while the second method is a modified version of the pooling-adjacent-violators algorithm that incorporates the CPT utility function. Moreover, we prove the theoretical convergence of our proposed ADMM method and the two subproblem-solving methods. Finally, we conduct numerical experiments to validate our proposed approach and demonstrate how CPT's parameters influence investor behavior using real-world data.Comment: 30 page

Multi-objective optimization for prestress design of cable-strut structures

Load bearing capacity of a cable-strut structure is dependent on the level and distribution of prestress. Although a higher prestress level enhances overall stiffness of the structure, this condition may demand larger member sectional areas and material cost. The effect of fabrication and installation error should also be incorporated in the prestress design. This paper presents a new optimization method for prestress design of cable-strut structures. A multi-objective optimization problem is formulated and solved to obtain preferred coefficient vectors of prestress modes with the following four objective functions: (1) minimize average area of members; (2) maximize minimum eigenvalue of stiffness matrix; (3) minimize prestress variance of cables; and (4) minimize maximum eigenvalue of error sensitivity matrix. Pareto optimal solutions are obtained by NSGA-II. Among the Pareto optimal solutions, the most preferred solution is selected using PROMETHEE-II. Two examples are presented to illustrate the proposed process. The results are compared with those by existing methods of optimization with a single objective function. Significance of each objective function is also evaluated by the number of remaining Pareto optimal solutions after removal of the objective function

Causally Invariant Predictor with Shift-Robustness

This paper proposes an invariant causal predictor that is robust to distribution shift across domains and maximally reserves the transferable invariant information. Based on a disentangled causal factorization, we formulate the distribution shift as soft interventions in the system, which covers a wide range of cases for distribution shift as we do not make prior specifications on the causal structure or the intervened variables. Instead of imposing regularizations to constrain the invariance of the predictor, we propose to predict by the intervened conditional expectation based on the do-operator and then prove that it is invariant across domains. More importantly, we prove that the proposed predictor is the robust predictor that minimizes the worst-case quadratic loss among the distributions of all domains. For empirical learning, we propose an intuitive and flexible estimating method based on data regeneration and present a local causal discovery procedure to guide the regeneration step. The key idea is to regenerate data such that the regenerated distribution is compatible with the intervened graph, which allows us to incorporate standard supervised learning methods with the regenerated data. Experimental results on both synthetic and real data demonstrate the efficacy of our predictor in improving the predictive accuracy and robustness across domains

Quantitative Risk Assessment and Management of Hydrogen Leaks from Offshore Rocket Launching Platforms

Liquid hydrogen in cryogenic condition can incidentally leak from offshore rocket launching platforms, leading to catastrophic impacts. Risk assessment and management of hydrogen leaks are required to prevent such accidents. The aim of the paper is to develop a methodology for quantitative risk assessment on hydrogen leak hazards from offshore rocket launching platforms during their filling process. A set of credible leak scenarios are chosen using Latin Hypercube Sampling (LHS) technique. The flows of hydrogen leaks for the selected scenarios are simulated using Computational Fluid Dynamics (CFD) method. A probabilistic model for predicting hydrogen leaks is established based on the computed results, where a long short-term memory (LSTM) network is used. Individual risks are defined as likelihood of explosion and fire due to hydrogen leaks. As an illustrative example, the developed methodology was applied to a hypothetical offshore rocket launching platform, confirming that the hydrogen leak risk level of the platform meets the ALARP (As Low As Reasonably Practicable) criteria. Risk mitigation options are also discussed to reduce the risk level