Center of mass distribution of the Jacobi unitary ensembles:Painleve V, asymptotic expansions

In this paper, we study the probability density function, $\mathbb{P}(c,\alpha,\beta, n)\,dc$, of the center of mass of the finite $n$ Jacobi unitary ensembles with parameters $\alpha\,>-1$ and $\beta >-1$; that is the probability that ${\rm tr}M_n\in(c, c+dc),$ where $M_n$ are $n\times n$ matrices drawn from the unitary Jacobi ensembles. We first compute the exponential moment generating function of the linear statistics $\sum_{j=1}^{n}\,f(x_j):=\sum_{j=1}^{n}x_j,$ denoted by $\mathcal{M}_f(\lambda,\alpha,\beta,n)$. The weight function associated with the Jacobi unitary ensembles reads $x^{\alpha}(1-x)^{\beta},\; x\in [0,1]$. The moment generating function is the $n\times n$ Hankel determinant $D_n(\lambda,\alpha,\beta)$ generated by the time-evolved Jacobi weight, namely, $w(x;\lambda ,\alpha,\beta )=x^{\alpha}(1-x)^{\beta}\,{\rm e}^{-\lambda\:x},\,x\in[0,1],\,\alpha>-1,\,\beta>-1$. We think of $\lambda$ as the time variable in the resulting Toda equations. The non-classical polynomials defined by the monomial expansion, $P_n(x,\lambda)= x^n+ p(n,\lambda)\:x^{n-1}+\dots+P_n(0,\lambda)$, orthogonal with respect to $w(x,\lambda,\alpha,\beta )$ over $[0,1]$ play an important role. Taking the time evolution problem studied in Basor, Chen and Ehrhardt (\cite{BasorChenEhrhardt2010}), with some change of variables, we obtain a certain auxiliary variable $r_n(\lambda),$ defined by integral over $[0,1]$ of the product of the unconventional orthogonal polynomials of degree $n$ and $n-1$ and $w(x,\lambda,\alpha,\beta )/x$. It is shown that r_n(2\imath\/{\rm e}^{z}) satisfies a Chazy $II$ equation. There is another auxiliary variable, denote as $R_n(\lambda),$ defined by an integral over $[0,1]$ of the product of two polynomials of degree $n$ multiplied by $w(x,\lambda)/x.$ Then $Y_n(-\lambda)=1-\lambda/R_n(\lambda)$ satisfies a particular Painlev\'{e} \uppercase\expandafter{\romannumeral 5}: $P_{\rm V}(\alpha^2/2$, $-\beta^2/2, 2n+\alpha+\beta+1,1/2)$.\\ The $\sigma_n$ function defined in terms of the $\lambda\:p(n,-\lambda)$ plus a translation in $\lambda$ is the Jimbo--Miwa--Okamoto $\sigma$-form of Painlev\'{e} \uppercase\expandafter{\romannumeral 5}. In the continuum approximation, treating the collection of eigenvalues as a charged fluid as in the Dyson Coulomb Fluid, gives an approximation for the moment generation function $\mathcal{M}_f(\lambda,\alpha,\beta,n)$ when $n$ is sufficiently large. Furthermore, we deduce a new expression of $\mathcal{M}_f(\lambda,\alpha,\beta,n)$ when $n$ is finite in terms the $\sigma$ function of this the Painlev\'{e} \uppercase\expandafter{\romannumeral 5} An estimate shows that the moment generating function is a function of exponential type and of order $n$. From the Paley-Wiener theorem, one deduces that $\mathbb{P}(c,\alpha,\beta,n)$ has compact support $[0,n]$. This result is easily extended to the $\beta$ ensembles, as long as $w$ the weight is positive and continuous over $[0,1].

Predicting the PSQA results of volumetric modulated arc therapy based on dosiomics features: a multi-center study

Backgroud and objectivesThe implementation of patient-specific quality assurance (PSQA) has become a crucial aspect of the radiation therapy process. Machine learning models have demonstrated their potential as virtual QA tools, accurately predicting the gamma passing rate (GPR) of volumetric modulated arc therapy (VMAT)plans, thereby ensuring safe and efficient treatment for patients. However, there is limited multi-center research dedicated to predicting the GPR. In this study, a dosiomics-based machine learning approach was employed to construct a prediction model for classifying GPR in multiple radiotherapy institutions. Additionally, the model’s performance was compared by evaluating the impact of two distinct feature selection methods.MethodsA retrospective data collection was conducted on 572 VMAT patients across three radiotherapy institutions. Utilizing a three-dimensional dose verification technique grounded in real-time measurements, γ analysis was conducted according to the criteria of 3%/2 mm and 2%/2 mm, employing a dose threshold of 10% along with absolute dose and global normalization mode. Dosiomics features were extracted from the dose files, and distinct subsets of features were selected as inputs for the model using the random forest (RF) and RF combined with SHapley Additive exPlanations (SHAP) methods. The data underwent training using the extreme gradient boosting (XGBoost) algorithm, and the model’s classification performance was assessed through F1-score and area under the curve (AUC) values.ResultsThe model exhibited optimal performance under the 3%/2 mm criteria, utilizing a subset of 20 features and attaining an AUC value of 0.88 and an F1-score of 0.89. Similarly, under the 2%/2 mm criteria, the model demonstrated superior performance with a subset of 10 features, resulting in an AUC value of 0.91 and an F1-score of 0.89. The feature selection methods of RF and RF + SHAP have achieved good model performance by selecting as few features as possible.ConclusionBased on the multi-center PSQA results, it is possible to utilize dosiomics features extracted from dose files to construct a machine learning predictive model. This model demonstrates excellent discriminative abilities, thus promoting the progress of gamma passing rate prognostic models in clinical application and implementation. Furthermore, it holds potential in providing patients with secure and efficient personalized QA management, while also reducing the workload of medical physicists

Protective Effect of Edaravone in Primary Cerebellar Granule Neurons against Iodoacetic Acid-Induced Cell Injury

Edaravone (EDA) is clinically used for treatment of acute ischemic stroke in Japan and China due to its potent free radical-scavenging effect. However, it has yet to be determined whether EDA can attenuate iodoacetic acid- (IAA-) induced neuronal death in vitro. In the present study, we investigated the effect of EDA on damage of IAA-induced primary cerebellar granule neurons (CGNs) and its possible underlying mechanisms. We found that EDA attenuated IAA-induced cell injury in CGNs. Moreover, EDA significantly reduced intracellular reactive oxidative stress production, loss of mitochondrial membrane potential, and caspase 3 activity induced by IAA. Taken together, EDA protected CGNs against IAA-induced neuronal damage, which may be attributed to its antiapoptotic and antioxidative activities

Risk Field of Rock Instability using Microseismic Monitoringdata in Deep Mining

With the gradual depletion of surface resources, rock instability caused by deep high stressand mining disturbance seriously affects safe mining. To create effective risk management, a rockinstability risk field model using microseismic monitoring data is proposed in this study. Rockinstability risk was presented visually in 3D visualization. The in-situ microseismic monitoringdata was collected and analyzed to make calculation of peak ground velocity (PGV), peak groundacceleration (PGA), energy flux, energy and seismic moment. Indicator weights of PGV, PGA, energyflux are confirmed by using the analytic hierarchy process (AHP) to calculate risk severity. The Copulafunction is then used to solve the joint probability distribution function of energy and seismic moment.Then the spatial distribution characteristics of risk can be obtained by data fitting. Subsequently, thethree-dimensional (3D) risk field model was established. Meanwhile, the established risk field isverified by comparing monitoring data without disturbance and the blasting data with disturbance.It is suggested that the proposed risk field method could evaluate the regional risk of rock instabilityreasonably and accurately, which lays a theoretical foundation for the risk prediction and managementof rock instability in deep mining

Risk Field of Rock Instability using Microseismic Monitoringdata in Deep Mining

With the gradual depletion of surface resources, rock instability caused by deep high stressand mining disturbance seriously affects safe mining. To create effective risk management, a rockinstability risk field model using microseismic monitoring data is proposed in this study. Rockinstability risk was presented visually in 3D visualization. The in-situ microseismic monitoringdata was collected and analyzed to make calculation of peak ground velocity (PGV), peak groundacceleration (PGA), energy flux, energy and seismic moment. Indicator weights of PGV, PGA, energyflux are confirmed by using the analytic hierarchy process (AHP) to calculate risk severity. The Copulafunction is then used to solve the joint probability distribution function of energy and seismic moment.Then the spatial distribution characteristics of risk can be obtained by data fitting. Subsequently, thethree-dimensional (3D) risk field model was established. Meanwhile, the established risk field isverified by comparing monitoring data without disturbance and the blasting data with disturbance.It is suggested that the proposed risk field method could evaluate the regional risk of rock instabilityreasonably and accurately, which lays a theoretical foundation for the risk prediction and managementof rock instability in deep mining

A Multi-Objective Ground Motion Selection Approach Matching the Acceleration and Displacement Response Spectra

For seismic resilience-based design (RBD), a selection of recorded time histories for dynamic structural analysis is usually required. In order to make individual structures and communities regain their target functions as promptly as possible, uncertainty of the structural response estimates is in great need of reduction. The ground motion (GM) selection based on a single target response spectrum, such as acceleration or displacement response spectrum, would bias structural response estimates leading significant uncertainty, even though response spectrum variance is taken into account. In addition, resilience of an individual structure is not governed by its own performance, but depends severely on the performance of other systems in the same community. Thus, evaluation of resilience of a community using records matching target spectrum at whole periods would be reasonable because the fundamental periods of systems in the community may be varied. This paper presents a GM selection approach based on a probabilistic framework to find an optimal set of records to match multiple target spectra, including acceleration and displacement response spectra. Two major steps are included in that framework. Generation of multiple sub-spectra from target displacement response spectrum for selecting sets of GMs was proposed as the first step. Likewise, the process as genetic algorithm (GA), evolvement of individuals previously generated, is the second step, rather than using crossover and mutation techniques. A novel technique improving the match between acceleration response spectra of samples and targets is proposed as the second evolvement step. It is proved computationally efficient for the proposed algorithm by comparing with two developed GM selection algorithms. Finally, the proposed algorithm is applied to select GM records according to seismic codes for analysis of four archetype reinforced concrete (RC) frames aiming to evaluate the influence of GM selection considering two design response spectra on structural responses. The implications of design response spectra especially the displacement response spectrum and GM selection algorithm are summarized

Evaluation of Water Resources Carrying Capacity and Its Obstruction Factor Analysis: A Case Study of Hubei Province, China

The carrying capacity of water resources can provide a reference index for regional economic construction and development. Hubei produces 13.2% of China’s hydroelectric energy and 4% of China’s water resources, highlighting that the reservoir group in Hubei province is relatively developed. In the current research on water resources carrying capacity, only the amount of water resources was considered; the benign mutual feeding effect of regional reservoirs on regional water resources carrying capacity was not reflected upon. In order to guide social and economic activities better, this paper proposes the addition of reservoir water storage to the calculation of water resources carrying capacity as a separate indicator. In this paper, the cloud model method was used to calculate the water resources carrying capacity of Hubei province and the Dematel method was used to determine the degree of importance of reservoir water storage. Finally, the degree of obstacles was also considered to discuss the main factors affecting the water resources carrying capacity of Hubei province. In the system discussed in this paper, the degree of influence and the affected degree of reservoir water storage were found to be 1.2915 and 0.5759, respectively. The calculation results showed that Hubei province’s water resources carrying capacity has been increasing every year and the amount of water resources per unit area was the main restricting factor, with the obstacle degree reaching 19.24% of the average annual level

Probabilistic Generalization of a Comprehensive Model for the Deterioration Prediction of RC Structure under Extreme Corrosion Environments

In some extreme corrosion environments, the erosion of chloride ions and carbon dioxide can occur simultaneously, causing deterioration of reinforced concrete (RC) structures. This study presents a probabilistic model for the sustainability prediction of the service life of RC structures, taking into account that combined deterioration. Because of the high computational cost, we also present a series of simplifications to improve the model. Meanwhile, a semi-empirical method is also developed for this combined effect. By probabilistic generalization, this simplified method can swiftly handle the original reliability analysis which needs to be based on large amounts of data. A comparison of results obtained by the models with and without the above simplifications supports the significance of these improvements

Integrated resources planning in microgrids considering interruptible loads and shiftable loads

Abstract Demand response has the potential to bring significant benefits to the optimal sizing of distributed generation (DG) resources for microgrids planning. This paper presents an integrated resources planning model considering the impact of interruptible loads (IL) and shiftable loads (SL) in microgrids, which simultaneously deals with supply side and demand side resources and minimizes the overall planning cost of the microgrid. The proposed model can be applied to offer a quantitative assessment how IL and SL can contribute to microgrid planning. The pure peak clipping model with IL and SL is also provided for comparisons. Moreover, sensitivity analysis of parameters in the model is performed. Numerical results confirm that the proposed model is an effective method for reducing the planning cost of microgrids. It was also found that the major contributing factors of IL and SL have great impact on the economic benefits of the proposed model in low-carbon economy environments