Event-based hyperspace analogue to language for query expansion

Bag-of-words approaches to information retrieval (IR) are effective but assume independence between words. The Hyperspace Analogue to Language (HAL) is a cognitively motivated and validated semantic space model that captures statistical dependencies between words by considering their co-occurrences in a surrounding window of text. HAL has been successfully applied to query expansion in IR, but has several limitations, including high processing cost and use of distributional statistics that do not exploit syntax. In this paper, we pursue two methods for incorporating syntactic-semantic information from textual ‘events’ into HAL. We build the HAL space directly from events to investigate whether processing costs can be reduced through more careful definition of word co-occurrence, and improve the quality of the pseudo-relevance feedback by applying event information as a constraint during HAL construction. Both methods significantly improve performance results in comparison with original HAL, and interpolation of HAL and relevance model expansion outperforms either method alone

11-stable fluctuation of the derivative martingale of branching random walk

In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens the results of Buraczewski et. al. [Ann. Probab., 2021] and is the branching random walk counterpart of the main result of Maillard and Pain [Ann. Probab., 2019] for branching Brownian motion.Comment: 42 pages, 0 figure

Asymptotic expansion for additive measure of branching Brownian motion

Let $N(t)$ be the collection of particles alive at time $t$ in a branching Brownian motion in $\mathbb{R}^d$, and for $u\in N(t)$, let $\mathbf{X}_u(t)$ be the position of particle $u$ at time $t$. For $\theta\in \mathbb{R}^d$, we define the additive measures of the branching Brownian motion by$$\mu_t^\theta (\mathrm{d}\mathbf{x}):= e^{-(1+\frac{\Vert\theta\Vert^2}{2})t}\sum_{u\in N(t)} e^{-\theta \cdot \mathbf{X}_u(t)} \delta_{\left(\mathbf{X}_u(t)+\theta t\right)}(\mathrm{d}\mathbf{x}).$$ In this paper, under some conditions on the offspring distribution, we give asymptotic expansions of arbitrary order for $\mu_t^\theta ((\mathbf{a}, \mathbf{b}])$ and $\mu_t^\theta ((-\infty, \mathbf{a}])$ for $\theta\in \mathbb{R}^d$ with $\Vert \theta \Vert <\sqrt{2}$. These expansions sharpen the asymptotic results of Asmussen and Kaplan (1976) and Kang (1999), and are analogs of the expansions in Gao and Liu (2021) and R\'{e}v\'{e}sz, Rosen and Shi (2005) for branching Wiener processes (a particular class of branching random walks) corresponding to $\theta=\mathbf{0}$

Asymptotic expansion for branching killed Brownian motion with drift

Let $Z_t^{(0,\infty)}$ be the point process formed by the positions of all particles alive at time $t$ in a branching Brownian motion with drift and killed upon reaching 0. We study the asymptotic expansions of $Z_t^{(0,\infty)}(A)$ for $A= (a,b)$ and $A=(a,\infty)$ under the assumption that $\sum_{k=1}^\infty k(\log k)^{1+\lambda} p_k <\infty$ for large $\lambda$ in the regime of $\theta \in [0,\sqrt{2})$. These results extend and sharpen the results of Louidor and Saglietti [J. Stat. Phys, 2020] and Kesten [Stochastic Process. Appl., 1978]

Mean square stabilization of discrete-time switching Markov jump linear systems

This paper consider a special class of hybrid system called switching Markov jump linear system. The system transition is governed by two rules. One is Markov chain and the other is a deterministic rule. Furthermore, the transition probability of the Markov chain is not only piecewise but also orchestrated by a deterministic switching rule. In this paper the mean square stability of the systems is studied when the deterministic switching is subject to two different dwell time conditions: having a lower bound and having both lower and high bounds. The main contributions of this paper are two relevant stability theorems for the systems under study. A numerical example is provided to demonstrate the theoretical results

Phase diagram of holographic thermal dense QCD matter with rotation

We study the rotation effects of the hot and dense QCD matter in a non-perturbative regime by the gauge/gravity duality. We use the gravitational model that is designated to match the state-of-the-art lattice data on the thermal properties of (2+1)-flavor QCD and predict the location of the critical endpoint and the first-order phase transition line at large baryon chemical potential without rotation. After introducing the angular velocity via a local Lorentz boost, we investigate the thermodynamic quantities for the system under rotation in a self-consistent way. We find that the critical temperature and baryon chemical potential associated with the QCD phase transition decrease as the angular velocity increases. Moreover, some interesting phenomena are observed near the critical endpoint. We then construct the 3-dimensional phase diagram of the QCD matter in terms of temperature, baryon chemical potential, and angular velocity. As a parallel investigation, we also consider the gravitational model of $SU(3)$ pure gluon system, for which the 2-dimensional phase diagram associated with temperature and angular velocity has been predicted. The corresponding thermodynamic quantities with rotation are investigated.Comment: 22 pages, 24 figure

Dynamic mechanisms of tight gas accumulation and numerical simulation methods: Narrowing the gap between theory and field application

Despite the significant progress made in tight gas exploration and development in recent years, the understanding of the dynamic mechanisms of tight gas accumulation is still limited, and numerical simulation methods are lacking. In fact, the gap between theory and field application has become an obstacle to the development of tight gas exploration and development. This work sheds light on the dynamic mechanisms of hydrocarbon accumulation in tight formations from the aspect of capillary self-sealing theory by embedding calculation of pressure- and temperature-dependent capillary force in a pore network model. The microscale dynamic mechanisms are scaled up to the reservoir level by geological simulation, and the quantitative evaluation of reserves based on real geological sections is realized. From the results, several considerations are made to assist with resource assessment and sweet spot prediction. Firstly, the self-sealing effect of capillary in the micro-nano pore-throat system is at the core of tight sandstone gas accumulation theory; the hydrocarbon-generated expansion force is the driving force, and capillary force comprises the resistance. Furthermore, microscopic capillary force studies can be embedded into a pore network model and scaled up to a geological model using relative permeability curve and capillary force curve. Field application can be achieved by geological numerical simulations at the reservoir scale. Finally, high temperature and high pressure can reduce capillary pressure, which increases gas saturation and reserves.Cited as: Zhao, W., Jia, C., Song, Y., Li, X., Hou, L., Jiang, L. Dynamic mechanisms of tight gas accumulation and numerical simulation methods: Narrowing the gap between theory and field application. Advances in Geo-Energy Research, 2023, 8(3): 146-158. https://doi.org/10.46690/ager.2023.06.0