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Polyatomic molecules provide complex internal structures that are ideal for applications in quantum information science, quantum simulation, and precision searches for physics beyond the Standard Model. A key feature of polyatomic molecules is the presence of parity-doublet states. These structures, which generically arise from the rotational and vibrational degrees of freedom afforded by polyatomic molecules, are a powerful feature to pursue these diverse quantum science applications. Linear triatomic molecules contain $\ell$-type parity doublet states, which are predicted to exhibit robust coherence properties. We optically trap CaOH molecules, prepare them in $\ell$-type parity-doublet states, and realize a bare qubit coherence time of $T_2^* = 0.8(2)$ s. We suppress differential Stark shifts by employing molecular spectroscopy to cancel ambient electric fields, and characterize parity-dependent trap shifts, which are found to limit the coherence time. The parity-doublet coherence times achieved in this work are a defining milestone for the use of polyatomic molecules in quantum science.

Suppose $\widehatθ_n$ is a strongly consistent estimator for $θ_0$ in some i.i.d. situation. Let $N_\varepsilon$ and $Q_\varepsilon$ be respectively the last $n$ and the total number of $n$ for which $\widehatθ_n$ is at least $\varepsilon$ away from $θ_0$. The limit distributions for ${\varepsilon}^2 N_\varepsilon$ and ${\varepsilon}^2 Q_\varepsilon$ as $\varepsilon$ goes to zero are obtained under natural and weak conditions. The theory covers both parametric and nonparametric cases, multi-dimensional parameters, and general distance functions. Our results are of probabilistic interest, and, on the statistical side, suggest ways in which competing estimators can be compared. In particular several new optimality properties for the maximum likelihood estimator sequence in parametric families are established. Another use of our results is ways of constructing sequential fixed-volume or shrinking-volume confidence sets, as well as sequential tests with power 1. The paper also includes limit distribution results for the last $n$ and the number of $n$ for which the supremum distance $\|F_n-F\|\ge\varepsilon$, where $F_n$ is the empirical distribution function. Yet other results are reac

Using the results of Ding, Lee, Peres [3], we develop formulas to compute the hitting times and cover times for random walks on groups. We developed an explicit formula for hitting times in terms of the irreducible representations of the group. We also have a way of computing cover times in terms of these hitting times. This computation is based on a quantity we indentified, which we call the volume growth function. And we believe that it is the right object to study in order to understand the cover time.

Let $E$ be a flat Lorentzian space of signature $(2,1)$. A Margulis space-time is a noncompact complete flat Lorentzian $3$-manifold $E/Γ$, where the holonomy group $Γ$ is a free group of rank $g\geq 2$ acting freely and properly discontinuously by isometries. We consider the case where $Γ$ contains a parabolic element. We show that sufficiently small deformations of $Γ$ still act properly discontinuously on $E$ provided their linear parts are Fuchsian; moreover, the number of conjugacy classes of parabolic elements may increase or decrease under deformation. Our proof combines our previous compactification of $E/Γ$ relative to parabolic holonomy elements with a partial generalization of the work of Carrière. However, this result depends only on the parts on parabolic actions of our earlier work. We believe that the shortness of the proof of this openness result is of independent interest.

The paper studies thin times which are random times whose graph is contained in a countable union of the graphs of stopping times with respect to a reference filtration $\mathbb F$. We show that a generic random time can be decomposed into thin and thick parts, where the second is a random time avoiding all $\mathbb F$-stopping times. Then, for a given random time $τ$, we introduce ${\mathbb F}^τ$, the smallest right-continuous filtration containing $\mathbb F$ and making $τ$ a stopping time, and we show that, for a thin time $τ$, each $\mathbb F$-martingale is an ${\mathbb F}^τ$-semimartingale, i.e., the hypothesis $({\mathcal H}^\prime)$ for $(\mathbb F, {\mathbb F}^τ)$ holds. We present applications to honest times, which can be seen as last passage times, showing classes of filtrations which can only support thin honest times, or can accommodate thick honest times as well.

How to compute the probability distribution of a detection time, i.e., of the time which a detector registers as the arrival time of a quantum particle, is a long-debated problem. In this regard, Bohmian mechanics provides in a straightforward way the distribution of the time at which the particle actually does arrive at a given surface in 3-space in the absence of detectors. However, as we discuss here, since the presence of detectors can change the evolution of the wave function and thus the particle trajectories, it cannot be taken for granted that the arrival time of the Bohmian trajectories in the absence of detectors agrees with the one in the presence of detectors, and even less with the detection time. In particular, we explain why certain distributions that Das and Dürr [arXiv:1802.07141] presented as the distribution of the detection time in a case with spin, based on assuming that all three times mentioned coincide, is actually not what Bohmian mechanics predicts.

Two concepts of random stopping times in continuous time have been defined in the literature, mixed stopping times and randomized stopping times. We show that under weak conditions these two concepts are equivalent, and, in fact, that all types of random stopping times are equivalent. We exhibit the significance of the equivalence relation between stopping times using stopping problems and stopping games. As a by-product we extend Kuhn's Theorem to stopping games in continuous time.

We study the problem of preemptive scheduling n jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. We show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.

Based on the Langevin description of the Continuous Time Random Walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly decaying persistent power-law correlations between the waiting times as two generic examples and obtain the corresponding mean squared displacements as functions of time. In the case of exponential-type correlations the (sub)diffusion at short times is slower than in the absence of correlations. At long times the behavior of the mean squared displacement is the same as in uncorrelated CTRW. For power-law correlations we find subdiffusion characterized by the same exponent at all times, which appears to be smaller than the one in uncorrelated CTRW. Interestingly, in the limiting case of an extremely long power-law correlations, the (sub)diffusion exponent does not tend to zero, but is bounded from below by the subdiffusion exponent corresponding to a short time behavior in the case of exponential correlations.

Let ${\mathscr F}(N\times \mathbb{R})$ be the set of all closed $H$-hypersurfaces $M\subset N\times \mathbb{R}$, where $N$ is a simply connected complete Riemannian $n$-manifold with sectional curvature $K_{N}\leq -κ^{2}<0$. We show that ${\Hm}(N\times \mathbb{R})=\inf_{M\in {\mathscr F}(N\times \mathbb{R})}\{| H_{M}| \}\geq (n-1)κ/n $.

In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain non-explosion and metric-entropy conditions are satisfied, then the associated stochastic processes and their local times also converge. The metric-entropy condition can be checked by applying volume estimates of balls. Whilst similar results have been proved previously, the approach of this article is more widely applicable. Indeed, we recover various known conclusions for scaling limits of some deterministic self-similar fractal graphs, critical Galton-Watson trees, the critical Erdős-Rényi random graph and the configuration model (in the latter two cases, we prove for the first time the convergence of the models with respect to the resistance metric and also, for the configuration model, we overcome an error in the existing proof of local time convergence). Moreover, we derive new ones for scaling limits of uniform spanning trees and random recursive fractals. The metric-entropy condition also implies convergence of associated Gaussian processes.

Over the past two decades, numerous studies have demonstrated how less predictable (i.e., higher surprisal) words take more time to read. In general, these studies have implicitly assumed the reading process is purely responsive: Readers observe a new word and allocate time to process it as required. We argue that prior results are also compatible with a reading process that is at least partially anticipatory: Readers could make predictions about a future word and allocate time to process it based on their expectation. In this work, we operationalize this anticipation as a word's contextual entropy. We assess the effect of anticipation on reading by comparing how well surprisal and contextual entropy predict reading times on four naturalistic reading datasets: two self-paced and two eye-tracking. Experimentally, across datasets and analyses, we find substantial evidence for effects of contextual entropy over surprisal on a word's reading time (RT): in fact, entropy is sometimes better than surprisal in predicting a word's RT. Spillover effects, however, are generally not captured by entropy, but only by surprisal. Further, we hypothesize four cognitive mechanisms through which cont

We consider an extension of the standard G/G/1 queue, described by the equation $W\stackrel{\mathcal{D}}{=}\max\{0, B-A+YW\}$, where $\mathbb{P}[Y=1]=p$ and $\mathbb{P}[Y=-1]=1-p$. For $p=1$ this model reduces to the classical Lindley equation for the waiting time in the G/G/1 queue, whereas for $p=0$ it describes the waiting time of the server in an alternating service model. For all other values of $p$ this model describes a FCFS queue in which the service times and interarrival times depend linearly and randomly on the waiting times. We derive the distribution of $W$ when $A$ is generally distributed and $B$ follows a phase-type distribution, and when $A$ is exponentially distributed and $B$ deterministic.

Extending the approach of the paper [Mathieu, P. (1997) Hitting times and spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437 -- 465], we prove that the Poincare inequality for a (possibly non-symmetric) Markov process yields the exponential integrability of the hitting times of this process. For symmetric elliptic diffusions, this provides a criterion for the Poincare inequality in the terms of hitting times.

There exists a simple, didactically useful one-to-one relationship between stopping times and adapted càglàd (LCRL) processes that are non-increasing and take the values 0 and 1 only. As a consequence, stopping times are always hitting times.

Ignition of Jet-A/air mixtures was studied behind reflected shock waves. Heating of shock tube at temperature of 150 C was used to prepare a homogeneous fuel mixture. Ignition delay times were measured from OH emission at 309 nm and from absorption of He-Ne laser radiation at 3.3922 micrometers. The conditions behind shock waves were calculated by one-dimensional shock wave theory from initial conditions T1, P1, mixture composition and incident shock wave velocity. The ignition delay times were obtained at two fixed pressures 10, 20 atm for lean, stoichiometric and rich mixtures (ER=0.5, 1, 2) at an overall temperature range of 1040-1380 K.

We prove the existence of automorphisms of $\mathbb C^k$, $k\ge 2$, having an invariant, non-recurrent Fatou component biholomorphic to $\mathbb C \times (\mathbb C^\ast)^{k-1}$ which is attracting, in the sense that all the orbits converge to a fixed point on the boundary of the component. Such a Fatou component also avoids $k$ analytic discs intersecting transversally at the fixed point. As a corollary, we obtain a Runge copy of $\mathbb C \times (\mathbb C^\ast)^{k-1}$ in $\mathbb C^k$.