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This paper aims to provide an effective method for pricing forward starting options under the double fractional stochastic volatilities mixed-exponential jump-diffusion model. The value of a forward starting option is expressed in terms of the expectation of the forward characteristic function of log return. To obtain the forward characteristic function, we approximate the pricing model with a semimartingale by introducing two small perturbed parameters. Then, we rewrite the forward characteristic function as a conditional expectation of the proportion characteristic function which is expressed in terms of the solution to a classic PDE. With the affine structure of the approximate model, we obtain the solution to the PDE. Based on the derived forward characteristic function and the Fourier transform technique, we develop a pricing algorithm for forward starting options. For comparison, we also develop a simulation scheme for evaluating forward starting options. The numerical results demonstrate that the proposed pricing algorithm is effective. Exhaustive comparative experiments on eight models show that the effects of fractional Brownian motion, mixed-exponential jump, and the second volatility component on forward starting option prices are significant, and especially, the second fractional volatility is necessary to price accurately forward starting options under the framework of fractional Brownian motion. [ABSTRACT FROM AUTHOR]

Background: Essential genes encode functions that play a vital role in the life activities of organisms, encompassing growth, development, immune system functioning, and cell structure maintenance. Conventional experimental techniques for identifying essential genes are resource-intensive and time-consuming, and the accuracy of current machine learning models needs further enhancement. Therefore, it is crucial to develop a robust computational model to accurately predict essential genes. Results: In this study, we introduce GCNN-SFM, a computational model for identifying essential genes in organisms, based on graph convolutional neural networks (GCNN). GCNN-SFM integrates a graph convolutional layer, a convolutional layer, and a fully connected layer to model and extract features from gene sequences of essential genes. Initially, the gene sequence is transformed into a feature map using coding techniques. Subsequently, a multi-layer GCN is employed to perform graph convolution operations, effectively capturing both local and global features of the gene sequence. Further feature extraction is performed, followed by integrating convolution and fully-connected layers to generate prediction results for essential genes. The gradient descent algorithm is utilized to iteratively update the cross-entropy loss function, thereby enhancing the accuracy of the prediction results. Meanwhile, model parameters are tuned to determine the optimal parameter combination that yields the best prediction performance during training. Conclusions: Experimental evaluation demonstrates that GCNN-SFM surpasses various advanced essential gene prediction models and achieves an average accuracy of 94.53%. This study presents a novel and effective approach for identifying essential genes, which has significant implications for biology and genomics research. [ABSTRACT FROM AUTHOR]

A distributed output feedback model predictive control (MPC) algorithm is proposed for a team of linear discrete‐time subsystems, for which the states are not measurable. The subsystems are coupled by the cost function. A synchronous update strategy is adopted to formulate a tractable optimisation problem in distributed manner. The terminal controller is specified as the form of output feedback. The weight matrix shared by the terminal region and the terminal cost is designed by solving one optimisation problem. Thereby the terminal region is positively invariant with the terminal controller. Furthermore, the compatibility constraint is tailored for each subsystem to confine the deviation between the real outputs and its assumed ones. The recursive feasibility of the resulting optimisation problem is ensured and the stability of the whole system in closed‐loop operation is guaranteed. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm, which can perform faster than the corresponding centralised MPC in spite of a little higher cost. [ABSTRACT FROM AUTHOR]

Empirical studies suggest that asset price fluctuations exhibit "long memory", "volatility smile", "volatility clustering" and asset prices present "jump". To fit the above empirical characteristics of the market, this paper proposes a fractional stochastic volatility jump-diffusion model by combining two fractional stochastic volatilities with mixed-exponential jumps. The characteristic function of the log-return is expressed in terms of the solution of two-dimensional fractional Riccati equations of which closed-form solution does not exist. To obtain the explicit characteristic function, we approximate the pricing model by a semimartingale and convert fractional Riccati equations into a classic PDE. By the multi-dimensional Feynman-Kac theorem and the affine structure of the approximate model, we obtain the solution of the PDE with which the explicit characteristic function and its cumulants are derived. Based on the derived characteristic function and Fourier cosine series expansion, we obtain approximate European options prices. By differential evolution algorithm, we calibrate our approximate model and its two nested models to S&P 500 index options and obtain optimal parameter estimates of these models. Numerical results demonstrate the pricing method is fast and accurate. Empirical results demonstrate our approximate model fits the market best among the three models. [ABSTRACT FROM AUTHOR]

An electronic transition-based bare bones particle swarm optimization (ETBBPSO) algorithm is proposed in this paper. The ETBBPSO is designed to present high precision results for high dimensional single-objective optimization problems. Particles in the ETBBPSO are divided into different orbits. A transition operator is proposed to enhance the global search ability of ETBBPSO. The transition behavior of particles gives the swarm more chance to escape from local minimums. In addition, an orbit merge operator is proposed in this paper. An orbit with low search ability will be merged by an orbit with high search ability. Extensive experiments with CEC2014 and CEC2020 are evaluated with ETBBPSO. Four famous population-based algorithms are also selected in the control group. Experimental results prove that ETBBPSO can present high precision results for high dimensional single-objective optimization problems. [ABSTRACT FROM AUTHOR]

A twinning bare bones particle swarm optimization(TBBPSO) algorithm is proposed in this paper. The TBBPSO is combined by two operators, the twins grouping operator (TGO) and the merger operator (MO). The TGO aims at the reorganization of the particle swarm. Two particles will form as a twin and influence each other in subsequent iterations. In a twin, one particle is designed to do the global search while the other one is designed to do the local search. The MO aims at merging the twins and enhancing the search ability of the main group. Two operators work together to enhance the local minimum escaping ability of proposed methods. In addition, no parameter adjustment is needed in TBBPSO, which means TBBPSO can solve different types of optimization problems without previous information or parameter adjustment. In the benchmark functions test, the CEC2014 benchmark functions are used. Experimental results prove that proposed methods can present high precision results for various types of optimization problems. [ABSTRACT FROM AUTHOR]

Purpose. To investigate the clinical outcomes and possible risk factors associated with rotational stability after the implantation of a V4c toric implantable Collamer lens (TICL) for the correction of moderate to high myopic astigmatism. Methods. A total of 112 eyes of 66 patients with moderate to high myopic astigmatism underwent TICL implantation. All patients were followed up for more than 1 year. The uncorrected and best-corrected visual acuity (UCVA and BCVA), astigmatism and spherical equivalent, intraocular pressure, vault, endothelial cell morphometry, and rotation of the TICL axis were assessed at l day, 1 week, 1 month, 3 months, 6 months, and 12 months postoperatively. Postoperative rotation was defined as the angle between the intended axis and the achieved axis. Regression analysis was used to investigate the possible risk factors for TICL rotation postoperatively. Results. The mean efficacy index and safety index 12 months postoperatively were 1.03 ± 0.09 and 1.05 ± 0.10, respectively. All patients had the same or better visual acuity than preoperatively. The mean astigmatism value decreased from −1.86 ± 0.79 D preoperatively to −0.37 ± 0.35 D. The mean absolute axis deviation of the TICL at the last follow-up was 2.75 ± 2.04° (range, 0°∼11°). The mean manifest refraction spherical equivalent (MRSE) changed from -9.04 ± 2.67 D preoperatively to −0.67 ± 0.51 D postoperatively. The logistic regression demonstrated that the absolute degree of TICL rotation had a significant association with the fixation angle of the TICL and the size of the lens (P = 0.003 , P = 0.026 , resp.). Conclusion. The results of our study support that TICL implantation is safe, effective, and predictable in the treatment of moderate to high myopic astigmatism, with relatively good postoperative rotational stability. [ABSTRACT FROM AUTHOR]

Purpose. To investigate the clinical outcomes and possible risk factors associated with rotational stability after the implantation of a V4c toric implantable Collamer lens (TICL) for the correction of moderate to high myopic astigmatism. Methods. A total of 112 eyes of 66 patients with moderate to high myopic astigmatism underwent TICL implantation. All patients were followed up for more than 1 year. The uncorrected and best-corrected visual acuity (UCVA and BCVA), astigmatism and spherical equivalent, intraocular pressure, vault, endothelial cell morphometry, and rotation of the TICL axis were assessed at l day, 1 week, 1 month, 3 months, 6 months, and 12 months postoperatively. Postoperative rotation was defined as the angle between the intended axis and the achieved axis. Regression analysis was used to investigate the possible risk factors for TICL rotation postoperatively. Results. The mean efficacy index and safety index 12 months postoperatively were 1.03 ± 0.09 and 1.05 ± 0.10, respectively. All patients had the same or better visual acuity than preoperatively. The mean astigmatism value decreased from −1.86 ± 0.79 D preoperatively to −0.37 ± 0.35 D. The mean absolute axis deviation of the TICL at the last follow-up was 2.75 ± 2.04° (range, 0°∼11°). The mean manifest refraction spherical equivalent (MRSE) changed from -9.04 ± 2.67 D preoperatively to −0.67 ± 0.51 D postoperatively. The logistic regression demonstrated that the absolute degree of TICL rotation had a significant association with the fixation angle of the TICL and the size of the lens (P = 0.003 , P = 0.026 , resp.). Conclusion. The results of our study support that TICL implantation is safe, effective, and predictable in the treatment of moderate to high myopic astigmatism, with relatively good postoperative rotational stability. [ABSTRACT FROM AUTHOR]