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Computational protein design (CPD) refers to the use of computational methods to design proteins. Traditional methods relying on energy functions and heuristic algorithms for sequence design are inefficient and do not meet the demands of the big data era in biomolecules, with their accuracy limited by the energy functions and search algorithms. Existing deep learning methods are constrained by the learning capabilities of the networks, failing to extract effective information from sparse protein structures, which limits the accuracy of protein design. To address these shortcomings, we developed an Efficient attention-based Models for Computational Protein Design using amino acid microenvironment (EMOCPD). It aims to predict the category of each amino acid in a protein by analyzing the three-dimensional atomic environment surrounding the amino acids, and optimize the protein based on the predicted high-probability potential amino acid categories. EMOCPD employs a multi-head attention mechanism to focus on important features in the sparse protein microenvironment and utilizes an inverse residual structure to optimize the network architecture. The proposed EMOCPD achieves over 80% accuracy on the training set and 68.33% and 62.32% accuracy on two independent test sets, respectively, surpassing the best comparative methods by over 10%. In protein design, the thermal stability and protein expression of the predicted mutants from EMOCPD show significant improvements compared to the wild type, effectively validating EMOCPD's potential in designing superior proteins. Furthermore, the predictions of EMOCPD are influenced positively, negatively, or have minimal impact based on the content of the 20 amino acids, categorizing amino acids as positive, negative, or neutral. Research findings indicate that EMOCPD is more suitable for designing proteins with lower contents of negative amino acids.

In the field of automated programming, large language models (LLMs) have demonstrated foundational generative capabilities when given detailed task descriptions. However, their current functionalities are primarily limited to function-level development, restricting their effectiveness in complex project environments and specific application scenarios, such as complicated image-processing tasks. This paper presents a multi-agent framework that utilises a hybrid set of LLMs, including GPT-4o and locally deployed open-source models, which collaboratively complete auto-programming tasks. Each agent plays a distinct role in the software development cycle, collectively forming a virtual organisation that works together to produce software products. By establishing a tree-structured thought distribution and development mechanism across project, module, and function levels, this framework offers a cost-effective and efficient solution for code generation. We evaluated our approach using benchmark datasets, and the experimental results demonstrate that VisionCoder significantly outperforms existing methods in image processing auto-programming tasks.

We show that optimal stopping surfaces $(t,y)\mapsto x_*(t,y)$ arising from time-inhomogeneous optimal stopping problems on two-dimensional jump-diffusions $(X,Y)$ are continuous (jointly in time and space) under mild monotonicity and regularity assumptions of local nature., Comment: 18 pages, strengthened discussion of related literature

With the rapid development of neural network architectures and speech processing models, singing voice synthesis with neural networks is becoming the cutting-edge technique of digital music production. In this work, in order to explore how to improve the quality and efficiency of singing voice synthesis, in this work, we use encoder-decoder neural models and a number of vocoders to achieve singing voice synthesis. We conduct experiments to demonstrate that the models can be trained using voice data with pitch information, lyrics and beat information, and the trained models can produce smooth, clear and natural singing voice that is close to real human voice. As the models work in the end-to-end manner, they allow users who are not domain experts to directly produce singing voice by arranging pitches, lyrics and beats., Comment: 27 pages, 4 figures, 5 tables

In this paper we study pricing of American put options on the Black and Scholes market with a stochastic interest rate and finite-time maturity. We prove that the option value is a $C^1$ function of the initial time, interest rate and stock price. By means of Ito calculus we rigorously derive the option value's early exercise premium formula and the associated hedging portfolio. We prove the existence of an optimal exercise boundary splitting the state space into continuation and stopping region. The boundary has a parametrisation as a jointly continuous function of time and stock price, and it is the unique solution to an integral equation which we compute numerically. Our results hold for a large class of interest rate models including CIR and Vasicek models. We show a numerical study of the option price and the optimal exercise boundary for Vasicek model., Comment: Corrections in proofs of Propositions 3.3 and 3.11

We derive a change of variable formula for $C^1$ functions $U:\R_+\times\R^m\to\R$ whose second order spatial derivatives may explode and not be integrable in the neighbourhood of a surface $b:\R_+\times\R^{m-1}\to \R$ that splits the state space into two sets $\cC$ and $\cD$. The formula is tailored for applications in problems of optimal stopping where it is generally very hard to control the second order derivatives of the value function near the optimal stopping boundary. Differently to other existing papers on similar topics we only require that the surface $b$ be monotonic in each variable and we formally obtain the same expression as the classical It\^o's formula., Comment: 26 pages; final version accepted for publication

N-PAT is a new model-checking tool that supports the verification of nested-models, i.e. models whose behaviour depends on the results of verification tasks. In this paper, we describe its operation and discuss mechanisms that are tailored to the efficient verification of nested-models. Further, we motivate the advantages of N-PAT over traditional model-checking tools through a network security case study.

It is well-known that using delta hedging to hedge financial options is not feasible in practice. Traders often rely on discrete-time hedging strategies based on fixed trading times or fixed trading prices (i.e., trades only occur if the underlying asset's price reaches some predetermined values). Motivated by this insight and with the aim of obtaining explicit solutions, we consider the seller of a perpetual American put option who can hedge her portfolio once until the underlying stock price leaves a certain range of values $(a,b)$. We determine optimal trading boundaries as functions of the initial stock holding, and an optimal hedging strategy for a bond/stock portfolio. Optimality here refers to the variance of the hedging error at the (random) time when the stock leaves the interval $(a,b)$. Our study leads to analytical expressions for both the optimal boundaries and the optimal stock holding, which can be evaluated numerically with no effort., Comment: Section 6 added and Section 7 expanded

The B method has facilitated the development of software by specifying the design of software as abstract machines and formally verifying the correctness of the abstract machines. The quality of B abstract machines can significantly impact the quality of final software products. In this paper, we propose a set of criteria for measuring the quality of B abstract machines based on ISO/IEC 25010, which is one of the latest international standards for evaluating software quality in software engineering. These criteria evaluate abstract machines using a number of general-purpose and domain-independent equations and model checking techniques, so that the quality of abstract machines can be quantified as vectors. The proposed criteria are implemented as a B model quality evaluator, and they are explained and justified using a number of examples., Comment: 11 pages, 1 figure, 1 table

Based on the transfer learning, we design a bird species identification model that uses the VGG-16 model (pretrained on ImageNet) for feature extraction, then a classifier consisting of two fully-connected hidden layers and a Softmax layer is attached. We compare the performance of the proposed model with the original VGG16 model. The results show that the former has higher train efficiency, but lower mean average precisions(MAP). To improve the MAP of the proposed model, we investigate the result fusion mode to form multi-channel identification model, the best MAP reaches 0.9998. The number of model parameters is 13110, which is only 0.0082% of the VGG16 model. Also, the size demand of sample is decreased., Comment: 11 pages,11 figures

Connections between nodes of fully connected neural networks are usually represented by weight matrices. In this article, functional transfer matrices are introduced as alternatives to the weight matrices: Instead of using real weights, a functional transfer matrix uses real functions with trainable parameters to represent connections between nodes. Multiple functional transfer matrices are then stacked together with bias vectors and activations to form deep functional transfer neural networks. These neural networks can be trained within the framework of back-propagation, based on a revision of the delta rules and the error transmission rule for functional connections. In experiments, it is demonstrated that the revised rules can be used to train a range of functional connections: 20 different functions are applied to neural networks with up to 10 hidden layers, and most of them gain high test accuracies on the MNIST database. It is also demonstrated that a functional transfer matrix with a memory function can roughly memorise a non-cyclical sequence of 400 digits., Comment: 39 pages, 4 figures, submitted as a journal article

This paper introduces an SLD-resolution technique based on deep learning. This technique enables neural networks to learn from old and successful resolution processes and to use learnt experiences to guide new resolution processes. An implementation of this technique is named SLDR-DL. It includes a Prolog library of deep feedforward neural networks and some essential functions of resolution. In the SLDR-DL framework, users can define logical rules in the form of definite clauses and teach neural networks to use the rules in reasoning processes., Comment: 12 pages, 5 figures

There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used to guide rewriting processes after learning from algebraic reasoning examples produced by humans. To enable the neural network to recognise patterns of algebraic expressions with non-deterministic sizes, reduced partial trees are used to represent the expressions. Also, to represent both top-down and bottom-up information of the expressions, a centralisation technique is used to improve the reduced partial trees. Besides, symbolic association vectors and rule application records are used to improve the rewriting processes. Experimental results reveal that the algebraic reasoning examples can be accurately learnt only if the feedforward neural network has enough hidden layers. Also, the centralisation technique, the symbolic association vectors and the rule application records can reduce error rates of reasoning. In particular, the above approaches have led to 4.6% error rate of reasoning on a dataset of linear equations, differentials and integrals., Comment: 8 pages, 7 figures

We study the entropy production of an open quantum system surrounded by a complex environment consisting of several heat baths at different temperatures. The detailed balance is elaborated in view of the distinguishable channels provided by the couplings to different heat baths, and a refined entropy production rate is derived accordingly. It is demonstrated that the entropy production rates can characterize the quantum statistical property of the baths: the bosonic and fermionic baths display different behaviors in the high-temperature limit while they have the same asymptotic behavior at low temperature., Comment: 5 pages, 4 figures

For the HLS-II bunch current measurement system, in order to obtain the absolute value of bunch current, the calibration factor should be determined by using DCCT. At the HLS storage ring, the stretch effect of bunch length is observed and the change rate is about 19% when the bunch current decays over time and this will affect the performance of bunch current detection. To overcome the bunch stretch influence in the HLS-II bunch current measurement, an evaluation about pickup type and signal processing is carried out. Strip-line pickup and button pickup are selectable, and the theoretical analysis and demonstration experiment are performed to find out an acceptable solution for the bunch current measurement system at HLS-II. The experimental data analysis shows that the normalized calibration factor will change by about 27% when the bunch length change by about 19% if using the button pickup and processing by peak value of bunch signal, the influence will be reduced to less 2% if adopting the strip-line pickup and integral., Comment: 5 pages, 8 figures