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The Kibble-Zurek (KZ) mechanism has been applied to a variety of systems ranging from low temperature Bose-Einstein condensations to grand unification scales in particle physics and cosmology and from classical phase transitions to quantum phase transitions. Here we show that finite-time scaling (FTS) provides a detailed improved understanding of the mechanism. In particular, the finite time scale, which is introduced by the external driving (or quenching) and results in FTS, is the origin of the division of the adiabatic regimes from the impulse regime in the KZ mechanism. The origin of the KZ scaling for the defect density, generated during the driving through a critical point, is not that the correlation length ceases growing in the nonadiabatic impulse regime, but rather, is that it is taken over by the effective finite length scale corresponding to the finite time scale. We also show that FTS accounts well for and improves the scaling ansatz proposed recently by Liu, Polkovnikov, and Sandvik [Phys. Rev. B 89, 054307 (2014)]. Further, we show that their universal power-law scaling form applies only to some observables in cooling but not to heating. Even in cooling, it is invalid either when an appropriate external field is present. However, this finite-time-finite-size scaling calls for caution in application of FTS. Detailed scaling behaviors of the FTS and finite-size scaling, along with their crossover, are explicitly demonstrated, with the dynamic critical exponent z being estimated for two-and three-dimensional Ising models under the usual Metropolis dynamics. These values of z are found to give rise to better data collapses than the extant values do in most cases but take on different values in heating and cooling in both twoand three-dimensional spaces.

Long noncoding RNAs (lncRNAs) play multiple key regulatory roles in various cellular pathways. However, their functions in HIV-1 latent infection remain largely unknown. Here we show that a lncRNA named NRON, which is highly expressed in resting CD4+ T lymphocytes, could be involved in HIV-1 latency by specifically inducing Tat protein degradation. Our results suggest that NRON lncRNA potently suppresses the viral transcription by decreasing the cellular abundance of viral transactivator protein Tat. NRON directly links Tat to the ubiquitin/proteasome components including CUL4B and PSMD11, thus facilitating Tat degradation. Depletion of NRON, especially in combination with a histone deacetylase (HDAC) inhibitor, significantly reactivates the viral production from the HIV-1-latently infected primary CD4+ T lymphocytes. Our data indicate that lncRNAs play a role in HIV-1 latency and their manipulation could be a novel approach for developing latency-reversing agents.

We propose a scaling theory for the universal imaginary-time quantum critical dynamics for both short times and long times. We discover that there exists a universal critical initial slip related to a small initial order parameter M0. In this stage, the order parameter M increases with the imaginary time τ as M ∝ M0τ θ with a universal initial slip exponent θ. For the one-dimensional transverse-field Ising model, we estimate θ to be 0.373, which is markedly distinct from its classical counterpart. Apart from the local order parameter, we also show that the entanglement entropy exhibits universal behavior in the short-time region. As the critical exponents in the early stage and in equilibrium are identical, we apply the short-time dynamics method to determine quantum critical properties. The method is generally applicable in both the Landau-Ginzburg-Wilson paradigm and topological phase transitions.

Phase transitions are of great importance in a diversity of fields. They are usually classified into continuous phase transitions and first-order phase transitions (FOPTs). Whereas the former has a well-developed theoretical framework of the renormalization-group (RG) theory, no general theory has yet been developed for the latter that appear far more frequently. Focusing on the dynamics of a generic FOPT in the phi4 model below its critical point, we show by a field-theoretic RG method that it is governed by an unexpected unstable fixed point of the corresponding phi3 model. Accordingly, it exhibits a distinct scaling and universality behavior with unstable exponents different from the critical ones.

PIWI interacting RNAs (piRNAs) are highly expressed in germline cells and are involved in maintaining genome integrity by silencing transposons. These are also involved in DNA/histone methylation and gene expression regulation in somatic cells of invertebrates. The functions of piRNAs in somatic cells of vertebrates, however, remain elusive. We found that snoRNA-derived and C (C′)/D′ (D)-box conserved piRNAs are abundant in human CD4 primary T-lymphocytes. piRNA (piR30840) significantly downregulated interleukin-4 (IL-4) via sequence complementarity binding to pre-mRNA intron, which subsequently inhibited the development of Th2 T-lymphocytes. Piwil4 and Ago4 are associated with this piRNA, and this complex further interacts with Trf4-Air2-Mtr4 Polyadenylation (TRAMP) complex, which leads to the decay of targeted pre-mRNA through nuclear exosomes. Taken together, we demonstrate a novel piRNA mechanism in regulating gene expression in highly differentiated somatic cells and a possible novel target for allergy therapeutics.

PIWI-interacting RNA (piRNA) silences the transposons in germlines or induces epigenetic modifications in the invertebrates. However, its function in the mammalian somatic cells remains unknown. Here we demonstrate that a piRNA derived from Growth Arrest Specific 5, a tumor-suppressive long non-coding RNA, potently upregulates the transcription of tumor necrosis factor (TNF)-related apoptosis-inducing ligand (TRAIL), a proapoptotic protein, by inducing H3K4 methylation/H3K27 demethylation. Interestingly, the PIWIL1/4 proteins, which bind with this piRNA, directly interact with WDR5, resulting in a site-specific recruitment of the hCOMPASS-like complexes containing at least MLL3 and UTX (KDM6A). We have indicated a novel pathway for piRNAs to specially activate gene expression. Given that MLL3 or UTX are frequently mutated in various tumors, the piRNA/MLL3/UTX complex mediates the induction of TRAIL, and consequently leads to the inhibition of tumor growth.

Finite-time Scaling and its Applications to Continuous Phase Transitions 18www.intechopen.com forms for the magnetization M, the susceptibility χ, and the specific heat C as M(τ, L)=Lχ(τ, L)=L γ/ν f 2 (τL 1/ν ),using the scaling laws or relationswhere α and γ are critical exponents and the f s including those that will appear later are all scaling functions. In terms of the infinite system correlation length ξ ∞ that diverges at T c asthe argument of f s in Equations (3) is proportional to L/ξ ∞ that governs the finite-size behavior; for small L/ξ ∞ , finite-size scaling appears in which L is a relevant length scale, while large L/ξ ∞ is the thermodynamic limit in which equilibrium behavior shows and L is irrelevant. Note that all the critical exponents assume their infinite-lattices values due to the aforemention assumption (Brézin, 1982;Brézin & Zinn-Justin, 1985). Consequently, measuring the observables for a series of L can then determine the corresponding exponent ratios and finally the critical exponents themselves, the pitch of the critical properties, from the pure power laws emerged exactly at T c or τ = 0 at which f s are assumed to be analytic. In fact, for too small systems sizes and temperatures too far away from T c , corrections to scaling (Wegner, 1972) have to be taken into account. Nevertheless, delicate methods have been developed for extracting critical exponents as well as T c (Amit & Martin-Mayor, 2005;Landau & Binder, 2005). A sequence of Monte Carlo updates may be interpreted as a discrete Markov process (Glauber, 1963;Landau & Binder, 2005;Müler-Krumbhaar & Binder, 1973). Consequently, Monte Carlo simulations can also be applied to study time-dependent dynamic behavior, though usually studied is stochastic relaxational dynamics instead of 'true dynamics' in which the dynamics is determined by the equations of motion derived from a Hamiltonian. Yet, the stochastic dynamics for the kinetic Ising model with local spin dynamics as realized in the single-site Metropolis algorithm (Metropolis et al., 1953), for instance, is believed to fall into the same universality class as that governed by the time-dependent Ginzburg-Landau equation (Hohenberg & Halperin, 1977). Dynamic critical phenomena (Cardy, 1996;Ferrell et al., 1967;Folk & Moser, 2006;Halperin & Hohenberg, 1967;Hohenberg & Halperin, 1977;Ma, 1976) are also companying with a divergent correlation time t eq which diverges with the correlation length ξ ∞ aswith a new dynamical critical exponent z dynamic finite-size scaling (Suzuki, 1977) can be obtained by formally incorporating the time argument t in Equation (1), giving rise to which implies a dynamic finite-size scaling form for the correlation timeTherefore, at the criticality,in the asymptotic region of large time, large size, and small τ. This is again a standard method to estimate z, though when the asymptotic region is reached is not easy to determine (Landau & Binder, 2005;Wansleben & Landau, 1991). However, actual simulations can only be performed inevitably in a limited time ...