After a brief introduction that overviews quantum phase transitions and quantum criticality at finite temperatures, we begin Chapter 1 by introducing an exactly solved model with multiple critical lines - transverse field Ising model with added 3-spin interaction. We focus on the phase diagram and discuss several features associated with critical lines. Then we explicitly show how to calculate the spin-spin correlation function and dynamical structure factor S(k, ω) in terms of a Pfaffian. Next, we present the zero-temperature dynamical structure factor at various critical lines in the pure and disordered systems. Finally, this chapter concludes with a discussion about further research on similar models with quantum critical lines or quantum critical surfaces.In Chapter 2, we emphasize the finite temperature behavior of the same model as in the previous chapter by first showing any necessary modifications when the temperature is nonzero. Then we illustrate the finite temperature properties of the model in various aspects. We show how specific heat is computed and its temperature dependence at several critical points. In addition, we identify several crossovers (quantum critical to quantum disordered or renormalized classical) by classifying different temperature dependencies of the correlation length and thus constructing a quantum critical fan along one of the critical lines. In Chapter 3, we start with an introduction to show what measurement-induced entanglement transition is and its current status. Next, we discuss our model and its setup. Topological entanglement entropy and mutual information have been calculated to construct the phase diagram. We discover the system ends in different phases by applying non-commutative measurement gates at each time step on a line of qubits. Moreover, we obtain various critical exponents through finite-size scaling.

This study investigates uses of manner demonstratives zheyang and nayang in spontaneous conversation in Chinese (Mandarin). Following Interactional Linguistics, I hold the view that uses of manner demonstratives are shaped by the immediate interactional needs in ongoing conversations. This study uses video-recorded conversations as empirical data to examine uses of the manner demonstratives: (i) deictic use and nonverbal expressions, (ii)anaphoric use in the subject position, and (iii) discourse/interactional uses as inferential connectives, discourse boundary markers, and receipt tokens.

First, my analyses on deictic manner demonstratives, together with nonverbal expressions (i.e., hand gestures, body demonstrations, eye gaze and visible display) show (i) the range of the manner demonstratives’ references includes movements, situations/events, and the manner, quality and/or degree of a referent; and (ii) most of the nonverbal expressions are treated as a part of the verbal conversation that the speakers had planned to produce as the verbal expressions. Second, anaphoric manner demonstratives function as overt subjects to (i) express an emphasis or contrast on the co-referent, or (ii) introduce the speakers’ assessments. When used for emphasis, the manner demonstratives co-refer the same referents with a refined granularity by indicating them as motions, ways/methods or events, instead of individual entities. When used for assessments, manner demonstratives serve as anaphors referring to co-referents as events on which the speakers are given knowledge access in the conversation for follow-up comments.

Discourse/Interactional uses of the manner demonstratives deal with their uses as discourse markers. First, when used as inferential causal connectives, the manner demonstratives are used for speakers to claim the causal relationship between two events based on their subjective inferences. Second, it is also found for the first time that both the proximal and the distal manner demonstratives can be used as completion markers. The completion marking use occurs when speakers (i) declare unilaterally a turn as the end of a topical discussion, and (ii) await responses from other potential next speakers. The distal manner demonstratives are marked completion markers used for discourse that are perceived as temporally or mentally distant from the speakers. The last use observed is the manner demonstratives marking the current turns as collaborative finishes for previous turns. Last, based on only a few occurrences observed, zheyang(zi) used as neutral receipt tokens express the current speakers’ receipt of information but withhold their agreement (or disagreement).

This study joins the existing body of usage-based studies, in particular Interactional Linguistics, and emphasize using video-recorded conversation as empirical data to examine language use and language structures emerge from a situated context, how language is used to respond to ongoing conversations, as well as how these uses are triggered by interactional needs in terms of turn management and sequencing.

A supersaturated design is a design whose run size is not enough for estimating all the main effects. It is commonly used in screening experiment, where the goal is to identify sparse and dominant active effects with low cost. In this paper, we study a variable selection method via Dantzig selector, proposed by Candes and Tao (2007), to screen active effects. A graphical procedure and an automated procedure are suggested to accompany with the method. Simulation studies show that this method is effective over the existing data analysis methods in the literature.

A supersaturated design is a design whose run size is not enough for estimating all the main effects. It is commonly used in screening experiment, where the goal is to identify sparse and dominant active effects with low cost. In this paper, we study a variable selection method via Dantzig selector, proposed by Candes and Tao (2007), to screen active effects. A graphical procedure and an automated procedure are suggested to accompany with the method. Simulation studies show that this method is effective over the existing data analysis methods in the literature.