Mathematical Mechanism on Dynamical System Algorithms of the Ising Model

Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for solving the Ising model. Over the past decades, some continuous approaches or algorithms have been proposed from physical, mathematical or computational views for optimizing the Ising model such as quantum annealing, the coherent Ising machine, simulated annealing, adiabatic Hamiltonian systems, etc.. However, the mathematical principle of these algorithms is far from being understood. In this paper, we reveal the mathematical mechanism of dynamical system algorithms for the Ising model by Morse theory and variational methods. We prove that the dynamical system algorithms can be designed to minimize a continuous function whose local minimum points give all the candidates of the Ising model and the global minimum gives the minimizer of Ising problem. Using this mathematical mechanism, we can easily understand several dynamical system algorithms of the Ising model such as the coherent Ising machine, the Kerr-nonlinear parametric oscillators and the simulated bifurcation algorithm. Furthermore, motivated by the works of C. Conley, we study transit and capture properties of the simulated bifurcation algorithm to explain its convergence by the low energy transit and capture in celestial mechanics. A detailed discussion on $2$-spin and $3$-spin Ising models is presented as application.Comment: 39 pages, 2 figures(including 8 sub-figures

The Combined Poisson INMA( q

A new stationary qth-order integer-valued moving average process with Poisson innovation is introduced based on decision random vector. Some statistical properties of the process are established. Estimators of the parameters of the process are obtained using the method of moments. Some numerical results of the estimators are presented to assess the performance of moment estimators

Losses Can Be Blessings: Routing Self-Supervised Speech Representations Towards Efficient Multilingual and Multitask Speech Processing

Self-supervised learning (SSL) for rich speech representations has achieved empirical success in low-resource Automatic Speech Recognition (ASR) and other speech processing tasks, which can mitigate the necessity of a large amount of transcribed speech and thus has driven a growing demand for on-device ASR and other speech processing. However, advanced speech SSL models have become increasingly large, which contradicts the limited on-device resources. This gap could be more severe in multilingual/multitask scenarios requiring simultaneously recognizing multiple languages or executing multiple speech processing tasks. Additionally, strongly overparameterized speech SSL models tend to suffer from overfitting when being finetuned on low-resource speech corpus. This work aims to enhance the practical usage of speech SSL models towards a win-win in both enhanced efficiency and alleviated overfitting via our proposed S$^3$-Router framework, which for the first time discovers that simply discarding no more than 10\% of model weights via only finetuning model connections of speech SSL models can achieve better accuracy over standard weight finetuning on downstream speech processing tasks. More importantly, S$^3$-Router can serve as an all-in-one technique to enable (1) a new finetuning scheme, (2) an efficient multilingual/multitask solution, (3) a state-of-the-art ASR pruning technique, and (4) a new tool to quantitatively analyze the learned speech representation. We believe S$^3$-Router has provided a new perspective for practical deployment of speech SSL models. Our codes are available at: https://github.com/GATECH-EIC/S3-Router.Comment: Accepted at NeurIPS 202

Dried tea residue can alter the blood metabolism and the composition and functionality of the intestinal microbiota in Hu sheep

Ruminant animals face multiple challenges during the rearing process, including immune disorders and oxidative stress. Green tea by-products have gained widespread attention for their significant immunomodulatory and antioxidant effects, leading to their application in livestock production. In this study, we investigated the effects of Dried Tea Residue (DTR) as a feed additive on the growth performance, blood biochemical indicators, and hindgut microbial structure and function of Hu sheep. Sixteen Hu sheep were randomly divided into two groups and fed with 0 and 100 g/d of DTR, respectively. Data were recorded over a 56-day feeding period. Compared to the control group, there were no significant changes in the production performance of Hu sheep fed with DTR. However, the sheep fed with DTR showed a significant increase in IgA (p < 0.001), IgG (p = 0.005), IgM (p = 0.003), T-SOD (p = 0.013), GSH-Px (p = 0.005), and CAT (p < 0.001) in the blood, along with a significant decrease in albumin (p = 0.019), high density lipoprotein (p = 0.050), and triglyceride (p = 0.021). DTR supplementation enhanced the fiber digestion ability of hindgut microbiota, optimized the microbial community structure, and increased the abundance of carbohydrate-digesting enzymes. Therefore, DTR can be used as a natural feed additive in ruminant animal production to enhance their immune and antioxidant capabilities, thereby improving the health status of ruminant animals

An Observation-Driven Random Parameter INAR(1) Model Based on the Poisson Thinning Operator

This paper presents a first-order integer-valued autoregressive time series model featuring observation-driven parameters that may adhere to a particular random distribution. We derive the ergodicity of the model as well as the theoretical properties of point estimation, interval estimation, and parameter testing. The properties are verified through numerical simulations. Lastly, we demonstrate the application of this model using real-world datasets

A New Overdispersed Integer-Valued Moving Average Model with Dependent Counting Series

A new integer-valued moving average model is introduced. The assumption of independent counting series in the model is relaxed to allow dependence between them, leading to the overdispersion in the model. Statistical properties were established for this new integer-valued moving average model with dependent counting series. The Yule–Walker method was applied to estimate the model parameters. The estimator’s performance was evaluated using simulations, and the overdispersion test of the INMA(1) process was applied to examine the dependence between counting series

Booms and Busts in the Oil Market: Identifying Speculative Bubbles Using a Continuous-Time Dynamic System

The sharp changes in oil prices since 2004 featured a nonlinear data-generating mechanism which displayed bubble-like behavior. A popular view is that such a salient pattern cannot be explained by shifts in economic fundamentals, but was driven by speculative bubbles as a consequence of the increased financialization of oil future markets. Testing this hypothesis, however, is challenging since the fundamental component of the oil price is unobservable. This paper attempts to isolate the contribution of speculative bubbles and fundamentals to the evolution of oil prices by providing a stylized model of commodity pricing. Motivated by our theoretical model, we adopt a continuous-time model with a random and time-varying persistence parameter to empirically investigate the presence of speculative bubbles in daily oil future prices over the period April 1983 to June 2020. We do not find any evidence in favor of speculative bubbles, although we indeed find that oil prices exhibit episodes of unstable behavior after 2004