Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation

This paper develops numerical methods for finding optimal dividend pay-out and reinsurance policies. A generalized singular control formulation of surplus and discounted payoff function are introduced, where the surplus is modeled by a regime-switching process subject to both regular and singular controls. To approximate the value function and optimal controls, Markov chain approximation techniques are used to construct a discrete-time controlled Markov chain with two components. The proofs of the convergence of the approximation sequence to the surplus process and the value function are given. Examples of proportional and excess-of-loss reinsurance are presented to illustrate the applicability of the numerical methods.Comment: Key words: Singular control, dividend policy, Markov chain approximation, numerical method, reinsurance, regime switchin

An assessment of overexploitation risk faced by cephalopod fisheries in China: A non-equilibrium surplus production model approach

318-325This study analyses catch and effort(CE) data, 2006-2014, of cephalopod fisheriesto access its stock status for better management practices. Data analysis was performed by using two fisheries software, viz., catch and effort data analysis (CEDA) and a stock production model incorporating covariates (ASPIC). In CEDA, initial proportion (IP) = 0.8, Fox model estimated MSY, CV and R2 as 461687 t, 0.226 and 0.663 for log error assumption. The computed values of these parameters for log-normal and gamma error assumptions remained as 529612 t, 0.115, 0.671 and 503394 t, 0.176, 0.657, correspondingly. Estimated MSY values by using error assumptions, i.e., log and log-normal in Schaefer and Pella-Tomlinson models were same, i.e., 452106 t and 536284 t, in that order. However, gamma error assumption produced minimization failure. Fox model estimated the highest value of R2 (0.671). In ASPIC, Fox model assessed MSY, CV and R2 and FMSY as 545100 t, 0.090, 0.785 and 0.222 y-1, in that order. Whereas, Logistic model calculated similar parameters as 558700 t, 0.198 y-1, 0.111 and 0.78, respectively. The results of this preliminary study represent overexploitation of this fishery resource. Thus, effective management strategies with proper implementation are direly needed to conserve this commercially important marine fishery resource for its long-term economic gain. Moreover, supplement research on local fisheries resources by using single fish species data is strongly suggested in order to further strengthen this preliminary research

A hybrid deep learning method for finite-horizon mean-field game problems

This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep learning algorithm. Under the framework of finite-horizon mean-field games, the induced measure and Monte-Carlo algorithm are adopted to establish the iterative mean-field interaction in MCAM and deep learning, respectively. The Markov chain approximation method plays a key role in constructing the iterative algorithm and estimating an initial value of a neural network, whereas stochastic approximation is used to find accurate parameters in a bounded region. The convergence of the hybrid algorithm is proved; two numerical examples are provided to illustrate the results

Surge-varying LOS based path following of under actuated surface vehicles

1048-1055Subject to harsh ocean environment, a novel path following control scheme with accurate guidance and high anti-disturbance ability for under actuated surface vehicles is proposed. The innovative work is as follow: (1) Based on the traditional line-of-sight (LOS), a surge-varying LOS (SVLOS) guidance law is designed to achieve double guidance of speed and heading, which enhances the flexibility and precision of the previous LOS; (2) Unknown disturbances are exactly estimated by an exact disturbance observer (EDO), wherein the limitations of bounded and asymptotic observations can be avoided; (3) The EDO-based robust tracking controllers enable accurate disturbance compensation and guided signal tracking in harsh ocean environment. Rigorous theoretical analysis and significant simulation comparison have been done to demonstrate superiority of the EDO-SVLOS scheme

A Faster kk-means++ Algorithm

K-means++ is an important algorithm to choose initial cluster centers for the k-means clustering algorithm. In this work, we present a new algorithm that can solve the $k$-means++ problem with near optimal running time. Given $n$ data points in $\mathbb{R}^d$, the current state-of-the-art algorithm runs in $\widetilde{O}(k )$ iterations, and each iteration takes $\widetilde{O}(nd k)$ time. The overall running time is thus $\widetilde{O}(n d k^2)$. We propose a new algorithm \textsc{FastKmeans++} that only takes in $\widetilde{O}(nd + nk^2)$ time, in total

Domain-Agnostic Molecular Generation with Self-feedback

The generation of molecules with desired properties has gained tremendous popularity, revolutionizing the way scientists design molecular structures and providing valuable support for chemical and drug design. However, despite the potential of language models in molecule generation, they face numerous challenges such as the generation of syntactically or chemically flawed molecules, narrow domain focus, and limitations in creating diverse and directionally feasible molecules due to a dearth of annotated data or external molecular databases. To this end, we introduce MolGen, a pre-trained molecular language model tailored specifically for molecule generation. MolGen acquires intrinsic structural and grammatical insights by reconstructing over 100 million molecular SELFIES, while facilitating knowledge transfer between different domains through domain-agnostic molecular prefix tuning. Moreover, we present a self-feedback paradigm that inspires the pre-trained model to align with the ultimate goal of producing molecules with desirable properties. Extensive experiments on well-known benchmarks confirm MolGen's optimization capabilities, encompassing penalized logP, QED, and molecular docking properties. Further analysis shows that MolGen can accurately capture molecule distributions, implicitly learn their structural characteristics, and efficiently explore chemical space. The pre-trained model, codes, and datasets are publicly available for future research at https://github.com/zjunlp/MolGen.Comment: Work in progress. Add results of binding affinit

Query Complexity of Active Learning for Function Family With Nearly Orthogonal Basis

Many machine learning algorithms require large numbers of labeled data to deliver state-of-the-art results. In applications such as medical diagnosis and fraud detection, though there is an abundance of unlabeled data, it is costly to label the data by experts, experiments, or simulations. Active learning algorithms aim to reduce the number of required labeled data points while preserving performance. For many convex optimization problems such as linear regression and $p$-norm regression, there are theoretical bounds on the number of required labels to achieve a certain accuracy. We call this the query complexity of active learning. However, today's active learning algorithms require the underlying learned function to have an orthogonal basis. For example, when applying active learning to linear regression, the requirement is the target function is a linear composition of a set of orthogonal linear functions, and active learning can find the coefficients of these linear functions. We present a theoretical result to show that active learning does not need an orthogonal basis but rather only requires a nearly orthogonal basis. We provide the corresponding theoretical proofs for the function family of nearly orthogonal basis, and its applications associated with the algorithmically efficient active learning framework

Chinese Herb and Formulas for Promoting Blood Circulation and Removing Blood Stasis and Antiplatelet Therapies

Atherothrombosis, which directly threatens people's health and lives, is the main cause of morbidity and mortality all over the world. Platelets play a key role in the development of acute coronary syndromes (ACSs) and contribute to cardiovascular events. Oral antiplatelet drugs are a milestone in the therapy of cardiovascular atherothrombotic diseases. In recent years, many reports have shown the possibility that “resistance” to oral anti-platelet drugs and many adverse reactions, such as serious bleeding risk, which provides an impetus for developing new anti-platelet drugs possesses highly efficiency and fewer adverse effects. Study on the blood stasis syndrome and promoting blood circulation and removing blood stasis is the most active field of research of integration of traditional and western medicine in China. Blood-stasis syndrome and platelet activation have close relationship, many Chinese herb and formulas for promoting blood circulation and removing blood stasis possess definite anti-platelet effect. This paper covers the progress of anti-platelet mechanism of Chinese herb and formulas for promoting blood circulation and removing blood stasis and is to be deeply discussed in further research