Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay

Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results

How to Describe Images in a More Funny Way? Towards a Modular Approach to Cross-Modal Sarcasm Generation

Sarcasm generation has been investigated in previous studies by considering it as a text-to-text generation problem, i.e., generating a sarcastic sentence for an input sentence. In this paper, we study a new problem of cross-modal sarcasm generation (CMSG), i.e., generating a sarcastic description for a given image. CMSG is challenging as models need to satisfy the characteristics of sarcasm, as well as the correlation between different modalities. In addition, there should be some inconsistency between the two modalities, which requires imagination. Moreover, high-quality training data is insufficient. To address these problems, we take a step toward generating sarcastic descriptions from images without paired training data and propose an Extraction-Generation-Ranking based Modular method (EGRM) for cross-model sarcasm generation. Specifically, EGRM first extracts diverse information from an image at different levels and uses the obtained image tags, sentimental descriptive caption, and commonsense-based consequence to generate candidate sarcastic texts. Then, a comprehensive ranking algorithm, which considers image-text relation, sarcasticness, and grammaticality, is proposed to select a final text from the candidate texts. Human evaluation at five criteria on a total of 1200 generated image-text pairs from eight systems and auxiliary automatic evaluation show the superiority of our method