Implication of Barrier Fluctuations on the Rate of Weakly Adiabatic Electron Transfer

The problem of escape of a Brownian particle in a cusp-shaped metastable potential is of special importance in nonadiabatic and weakly-adiabatic rate theory for electron transfer (ET) reactions. Especially, for the weakly-adiabatic reactions, the reaction follows an adiabaticity criterion in the presence of a sharp barrier. In contrast to the non-adiabatic case, the ET kinetics can be, however considerably influenced by the medium dynamics. In this paper, the problem of the escape time over a dichotomously fluctuating cusp barrier is discussed with its relevance to the high temperature ET reactions in condensed media.Comment: RevTeX 4, 14 pages, 3 figures. To be printed in IJMP C. References corrected and update

Position-dependent random maps in one and higher dimensions

A random map is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied on each iteration of the process. We study random maps with position dependent probabilities on the interval and on a bounded domain of Rn. Sufficient conditions for the existence of an absolutely continuous invariant measure for a random map with position dependent probabilities on the interval and on a bounded domain of Rn are the main results

SRB measures for certain Markov processes

We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the IFS. Then, when all the constituent maps have common fixed points at 0 and 1, theorems are given to analyze properties of the ergodic invariant measures \delta_0 and \delta_1. In particular, sufficient conditions for \delta_0 and/or \delta_1 to be, or not to be, SRB measures are given. We apply some of our results to asset market games

Absolutely Continuous Invariant measures for non-autonomous dynamical systems

We consider the non autonomous dynamical system $\{\tau_{n}\},$ where $\tau_{n}$ is a continuous map $X\rightarrow X,$ and $X$ is a compact metric space. We assume that $\{\tau_{n}\}$ converges uniformly to $\tau .$ The inheritance of chaotic properties as well as topological entropy by $\tau$ from the sequence $\{\tau_{n}\}$ has been studied in \cite{Can1, Can2, Li,Ste,Zhu}. In \cite{You} the generalization of SRB\ measures to non-autonomous systems has been considered. In this paper we study absolutely continuous invariant measures (acim) for non autonomous systems. After generalizing the Krylov-Bogoliubov Theorem \cite{KB} and Straube's Theorem \cite{Str} to the non autonomous setting, we prove that under certain conditions the limit map $\tau$ of a non autonomous sequence of maps $\{\tau_n\}$ with acims has an acim

Statistical and Deterministic Dynamics of Maps with Memory

We consider a dynamical system to have memory if it remembers the current state as well as the state before that. The dynamics is defined as follows: $x_{n+1}=T_{\alpha }(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha )\cdot x_{n-1}),$ where $\tau$ is a one-dimensional map on $I=[0,1]$ and $0<\alpha <1$ determines how much memory is being used. $T_{\alpha}$ does not define a dynamical system since it maps $U=I\times I$ into $I$. In this note we let $\tau$ to be the symmetric tent map. We shall prove that for $0<\alpha <0.46,$ the orbits of $\{x_{n}\}$ are described statistically by an absolutely continuous invariant measure (acim) in two dimensions. As $\alpha$ approaches $0.5$ from below, that is, as we approach a balance between the memory state and the present state, the support of the acims become thinner until at $\alpha=0.5$, all points have period 3 or eventually possess period 3. For $0.5<\alpha <0.75$, we have a global attractor: for all starting points in $U$ except $(0,0)$, the orbits are attracted to the fixed point $(2/3,2/3).$ At $\alpha=0.75,$ we have slightly more complicated periodic behavior

Two novel C-terminal frameshift mutations in the β-globin gene lead to rapid mRNA decay

BACKGROUND: The thalassemia syndromes are classified according to the globin chain or chains whose production is affected. β-thalassemias are caused by point mutations or, more rarely, deletions or insertions of a few nucleotides in the β-globin gene or its immediate flanking sequences. These mutations interfere with the gene function either at the transcriptional, translational or posttranslational level. METHODS: Two cases of Polish patients with hereditary hemolytic anemia suspected of thalassemia were studied. DNA sequencing and mRNA quantification were performed. Stable human cell lines which express wild-type HBB and mutated versions were used to verify that detected mutation are responsible for mRNA degradation. RESULTS: We identified two different frameshift mutations positioned in the third exon of HBB. Both patients harboring these mutations present the clinical phenotype of thalassemia intermedia and showed dominant pattern of inheritance. In both cases the mutations do not generate premature stop codon. Instead, slightly longer protein with unnatural C-terminus could be produced. Interestingly, although detected mutations are not expected to induce NMD, the mutant version of mRNA is not detectable. Restoring of the open reading frame brought back the RNA to that of the wild-type level. CONCLUSION: Our results show that a lack of natural stop codon due to the frameshift in exon 3 of β-globin gene causes rapid degradation of its mRNA and indicate existence of novel surveillance pathway

Quantum games and interactive tools for quantum technologies outreach and education

We provide an extensive overview of a wide range of quantum games and interactive tools that have been employed by the quantum community in recent years. We present selected tools as described by their developers, including "Hello Quantum, Hello Qiskit, Particle in a Box, Psi and Delta, QPlayLearn, Virtual Lab by Quantum Flytrap, Quantum Odyssey, ScienceAtHome, and the Virtual Quantum Optics Laboratory." In addition, we present events for quantum game development: hackathons, game jams, and semester projects. Furthermore, we discuss the Quantum Technologies Education for Everyone (QUTE4E) pilot project, which illustrates an effective integration of these interactive tools with quantum outreach and education activities. Finally, we aim at providing guidelines for incorporating quantum games and interactive tools in pedagogic materials to make quantum technologies more accessible for a wider population. (C) The Authors. Published by SPIE under a Creative Commons Attribution 4.0 International License.Peer reviewe