Axion monodromy inflation, trapping mechanisms and the swampland

We study the effects of particle production on the evolution of the inflaton field in an axion monodromy model with the goal of discovering in which situations the resulting dynamics will be consistent with the swampland constraints. In the presence of a modulated potential the evolving background field (solution of the inflaton homogeneous in space) induces the production of long wavelength inflaton fluctuation modes. However, this either has a negligible effect on the inflaton dynamics (if the field spacing between local minima of the modulated potential is large), or else it traps the inflaton in a local minimum and leads to a graceful exit problem. On the other hand, the production of moduli fields at enhanced symmetry points can lead to a realization of trapped inflation consistent with the swampland constraints, as long as the coupling between the inflaton and the moduli fields is sufficiently large.

Identification of counterfactuals in dynamic discrete choice models

Dynamic discrete choice (DDC) models are not identified nonparametrically, but the non‐identification of models does not necessarily imply the nonidentification of counterfactuals. We derive novel results for the identification of counterfactuals in DDC models, such as non‐additive changes in payoffs or changes to agents' choice sets. In doing so, we propose a general framework that allows the investigation of the identification of a broad class of counterfactuals (covering virtually any counterfactual encountered in applied work). To illustrate the results, we consider a firm entry/exit problem numerically, as well as an empirical model of agricultural land use. In each case, we provide examples of both identified and nonidentified counterfactuals of interest.

Eternal inflation, entropy bounds and the swampland

It has been suggested that low energy effective field theories should satisfy given conditions in order to be successfully embedded into string theory. In the case of a single canonically normalized scalar field this translates into conditions on its potential and the derivatives thereof. In this Letter we revisit small field hilltop models of eternal inflation including stochastic effects and study the compatibility of the swampland constraints with entropy considerations. We show that these stochastic inflation scenarios either violate entropy bounds or the swampland criterion on the slope of the scalar field potential. Furthermore, we illustrate that such models are faced with a graceful exit problem: any patch of space which exits the region of eternal inflation is either not large enough to explain the isotropy of the cosmic microwave background, or has a spectrum of fluctuations with an unacceptably large red tilt.

Statistical Characteristics of the First Passage Time Analysis for the Gene Regulatory Circuit in Bacillus subtilis by Cell Mapping Method

In this paper, we will explore the stochastic exit problem for the gene regulatory circuit in B. subtilis affected by colored noise. The stochastic exit problem studies the state transition in B. subtilis (from competent state to vegetative state in this case) through three different quantities: the probability density function of the first passage time, the mean of first passage time, and the reliability function. To satisfy the Markov nature, we convert the colored noise system into the equivalent white noise system. Then, the stochastic generalized cell mapping method can be used to explore the stochastic exit problem. The results indicate that the intensity of noise and system parameters have the effect on the transition from competent to vegetative state in B. subtilis. In addition, the effectiveness of the stochastic generalized cell mapping method is verified by Monte Carlo simulation.

Weyl transformation: A dynamical degree of freedom in the light of Dirac’s Large Number hypothesis

In Einstein’s Field Equation (EFE), the geometry of the spacetime is connected with the matter distribution. The geometry or the gravitational sector deals with classical macroscopic objects involving gravitational units while the matter sector can be better described by quantum theory involving atomic units. It has been argued by Bisabr [ arXiv:gr-qc/1904.09336 ] that there exists an epoch-dependent conversion factor between these two unit systems present in two different conformal frames, i.e. the conformal factor is epoch-dependent. We argue that the conformal transformation (CT) is a dynamical degree of freedom describing it’s possible relevance in inflation in context to the graceful exit problem, dynamics of the cosmological constant [Formula: see text] and justify the argument in the light of consequences of Dirac’s Large Number hypothesis (LNH).

On hysteresis of ion channels

Ion channel proteins have many conformational (metastable) states and, for this reason, they exhibit hysteresis. This fact is responsible for the non-Markovian stochastic nature of single ion channel recordings. It is suggested in the paper that the stochastic single channel recordings can be modeled as the random outputs of rectangular hysteresis loops driven by stochastic processes. The latter problem can be mathematically treated as an exit problem for stochastic processes or by using the theory of stochastic processes on graphs. It is also demonstrated in the paper that the collective action of sodium and potassium channels responsible for the generation and propagation of action potentials exhibit hysteresis. This demonstration is accomplished by using the inverse problem approach to the nonlinear Hodgkin-Huxley diffusion equation.