Session Types in a Linearly Typed Multi-Threaded Lambda-Calculus

We present a formalization of session types in a multi-threaded lambda-calculus (MTLC) equipped with a linear type system, establishing for the MTLC both type preservation and global progress. The latter (global progress) implies that the evaluation of a well-typed program in the MTLC can never reach a deadlock. As this formulated MTLC can be readily embedded into ATS, a full-fledged language with a functional programming core that supports both dependent types (of DML-style) and linear types, we obtain a direct implementation of session types in ATS. In addition, we gain immediate support for a form of dependent session types based on this embedding into ATS. Compared to various existing formalizations of session types, we see the one given in this paper is unique in its closeness to concrete implementation. In particular, we report such an implementation ready for practical use that generates Erlang code from well-typed ATS source (making use of session types), thus taking great advantage of the infrastructural support for distributed computing in Erlang.Comment: This is the original version of the paper on supporting programming with dyadic session types in AT

Stochastic P-bifurcation in a tri-stable Van der Pol system with fractional derivative under Gaussian white noise

In this paper, we study the tri-stable stochastic P-bifurcation problem of a generalized Van der Pol system with fractional derivative under Gaussian white noise excitation. Firstly, using the principle for minimal mean square error, we show that the fractional derivative term is equivalent to a linear combination of the damping force and restoring force, so that the original system can be transformed into an equivalent integer order system. Secondly, we obtain the stationary Probability Density Function (PDF) of the system’s amplitude by the stochastic averaging, and using the singularity theory, we find the critical parametric conditions for stochastic P-bifurcation of amplitude of the system, which can make the system switch among the three steady states. Finally, we analyze different types of the stationary PDF curves of the system amplitude qualitatively by choosing parameters corresponding to each region divided by the transition set curves, and the system response can be maintained at the small amplitude near the equilibrium by selecting the appropriate unfolding parameters. We verify the theoretical analysis and calculation of the transition set by showing the consistency of the numerical results obtained by Monte Carlo simulation with the analytical results. The method used in this paper directly guides the design of the fractional order controller to adjust the response of the system

Open Problems, Research Topics, Recent Results on Numerical and Spiking Neural P Systems (The "Curtea de Arge s 2015 Series")

A series of open problems and research topics are formulated, about numer- ical and spiking neural P systems, initially prepared as a working material for a three months research stage of the second and the third co-author in Curtea de Arge s, Roma- nia, in the fall of 2015. Further problems were added during this period, while certain problems were addressed in this time; some details and references are provided for such cases

The structure of CSC-1 reducible conformal metrics on a compact Riemann surface with finite conical singularities

We study the structure of CSC-1 reducible conformal metrics on a compact Riemann surface with finite conical singularities. We prove that any compact Riemann surface with a CSC-1 reducible conformal metric of finite conical singularities can be divided into a finite number of pieces by cutting along geodesics where each piece is isometric to some football. This allows us to study the existence of CSC-1 reducible conformal metrics with finite conical singularities on a compact Riemann surface. As an application, we give an angle condition of the existence of CSC-1 reducible conformal metrics with finite conical singularities on a compact Riemann surface.Comment: 43pages, 13page

Dual-Branch Temperature Scaling Calibration for Long-Tailed Recognition

The calibration for deep neural networks is currently receiving widespread attention and research. Miscalibration usually leads to overconfidence of the model. While, under the condition of long-tailed distribution of data, the problem of miscalibration is more prominent due to the different confidence levels of samples in minority and majority categories, and it will result in more serious overconfidence. To address this problem, some current research have designed diverse temperature coefficients for different categories based on temperature scaling (TS) method. However, in the case of rare samples in minority classes, the temperature coefficient is not generalizable, and there is a large difference between the temperature coefficients of the training set and the validation set. To solve this challenge, this paper proposes a dual-branch temperature scaling calibration model (Dual-TS), which considers the diversities in temperature parameters of different categories and the non-generalizability of temperature parameters for rare samples in minority classes simultaneously. Moreover, we noticed that the traditional calibration evaluation metric, Excepted Calibration Error (ECE), gives a higher weight to low-confidence samples in the minority classes, which leads to inaccurate evaluation of model calibration. Therefore, we also propose Equal Sample Bin Excepted Calibration Error (Esbin-ECE) as a new calibration evaluation metric. Through experiments, we demonstrate that our model yields state-of-the-art in both traditional ECE and Esbin-ECE metrics

Long-tail Augmented Graph Contrastive Learning for Recommendation

Graph Convolutional Networks (GCNs) has demonstrated promising results for recommender systems, as they can effectively leverage high-order relationship. However, these methods usually encounter data sparsity issue in real-world scenarios. To address this issue, GCN-based recommendation methods employ contrastive learning to introduce self-supervised signals. Despite their effectiveness, these methods lack consideration of the significant degree disparity between head and tail nodes. This can lead to non-uniform representation distribution, which is a crucial factor for the performance of contrastive learning methods. To tackle the above issue, we propose a novel Long-tail Augmented Graph Contrastive Learning (LAGCL) method for recommendation. Specifically, we introduce a learnable long-tail augmentation approach to enhance tail nodes by supplementing predicted neighbor information, and generate contrastive views based on the resulting augmented graph. To make the data augmentation schema learnable, we design an auto drop module to generate pseudo-tail nodes from head nodes and a knowledge transfer module to reconstruct the head nodes from pseudo-tail nodes. Additionally, we employ generative adversarial networks to ensure that the distribution of the generated tail/head nodes matches that of the original tail/head nodes. Extensive experiments conducted on three benchmark datasets demonstrate the significant improvement in performance of our model over the state-of-the-arts. Further analyses demonstrate the uniformity of learned representations and the superiority of LAGCL on long-tail performance. Code is publicly available at https://github.com/im0qianqian/LAGCLComment: 17 pages, 6 figures, accepted by ECML/PKDD 2023 (European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases