Gene transcription is a complex multistep biochemical process, which can create memory between individual reaction events. On the other hand, many inducible genes, when activated by external cues, are often coregulated by several competitive pathways with crosstalk. This raises an unexplored question: how do molecular memory and crosstalk together affect gene expressions? To address this question, we introduce a queuing model of stochastic transcription, where two crossing signaling pathways are used to direct gene activation in response to external signals and memory functions to model multistep reaction processes involved in transcription. We first establish, based on the total probability principle, the chemical master equation for this queuing model, and then we derive, based on the binomial moment approach, exact expressions for statistical quantities (including distributions) of mRNA, which provide insights into the roles of crosstalk and memory in controlling the mRNA level and noise. We find that molecular memory of gene activation decreases the mRNA level but increases the mRNA noise, and double activation pathways always reduce the mRNA noise in contrast to a single pathway. In addition, we find that molecular memory can make the mRNA bimodality disappear.

Dynamics of dislocations and defects are investigated in 2D dusty plasma experiments with two counterpropagating flows. It is experimentally demonstrated that the Orowan equation is able to accurately determine the plastic strain rate from the motion of dislocations, well agreeing with the shear rate defined from the drift velocity gradient. For a higher shear rate, the studied system is in the liquidlike flow state, as a result, the determined shear rate from the Orowan equation deviates from its definition. The obtained probability distribution function of dislocations from the experiments clearly shows that the dislocation motion can be divided into the local and gliding ones. All findings above are further verified by the corresponding Langevin dynamical simulations with various levels of shear rates. The dislocation and defect analysis results from these simulations clearly indicate that the defect and dislocation dynamics in the sheared dusty plasmas clearly exhibit two stages as the shear rate increases.

Spinodal decomposition in a near-critical binary fluid is examined for experimental scenarios in which the liquid is quenched abruptly by changing the pressure and the subsequent phase separation occurs with no heat flow from the outside, i.e., adiabatically. Equations of motion for the system volume and effective temperature are derived. It is shown for this case that the nonequilibrium decomposition process is well approximated as one of constant entropy, i.e., as thermodynamically reversible. Quantitative comparison, with no adjustable parameters, is made with the experimental light scattering data of Bailey and Cannell [Phys. Rev. Lett. 70, 2110 (1993)]. It is found that including these adiabatic effects accounts for most of the discrepancies between these experiments and previous isothermal theory. The equilibrium static critical properties of the isothermal theory are also examined, this discussion serving to justify some approximations in the current theory.

We consider closed quantum systems which are driven such that only negligible heating occurs. If driving only affects small parts of the system, it may nonetheless be strong. Our analysis aims at clarifying under which conditions the Jarzynski relation (JR) holds in such setups, if the initial states are microcanonical or even energy eigenstates. We find that the validity of the JR for the microcanonical initial state hinges on an exponential density of states and on stiffness. The latter indicates an independence of the probability density functions (PDFs) of work of the energy of the respective microcanonical initial state. The validity of the JR for initial energy eigenstates is found to additionally require smoothness. The latter indicates an independence of the work PDFs of the specific energy eigenstates within a microcanonical energy shell. As the validity of the JR for pure initial energy eigenstates has no analog in classical systems, we consider it a genuine quantum phenomenon.

The long-term growth rate of populations in varying environments quantifies the evolutionary value of processing the information that biological individuals inherit from their ancestors and acquire from their environment. Previous models were limited to asexual reproduction with inherited information coming from a single parent with no recombination. We present a general extension to sexual reproduction and an analytical solution for a particular but important case, the infinitesimal model of quantitative genetics which assumes traits to be normally distributed. We study with this model the conditions under which sexual reproduction is advantageous and can evolve in the context of autocorrelated or directionally varying environments, mutational biases, spatial heterogeneities, and phenotypic plasticity. Our results generalize and unify previous analyses. We also examine the proposal made by Geodakyan that the presence of two phenotypically distinct sexes permits an optimal adaptation to varying environments. We verify that conditions exists where sexual dimorphism is adaptive but find that its evolutionary value does not generally compensate for the twofold cost of males.

Using molecular dynamics simulation we have investigated the influence of random pinning on the phase diagram and melting scenarios of a two-dimensional system with the Hertz potential for $\alpha =5/2$. It has been shown that random pinning can cardinally change the mechanism of first-order transition between the different crystalline phases (triangular and square) by virtue of generating hexatic and tetratic phases: a triangular crystal to hexatic transition is of the continuous Berezinskii-Kosterlitz-Thouless (BKT) type, a hexatic to tetratic transition is of first order, and finally, there is a continuous BKT-type transition from tetratic to the square crystal.

Understanding electrodes' surface morphology influence on ions' distribution is essential for designing supercapacitors with enhanced energy density characteristics. We develop a model for the structure of electrolytes near the rough surface of electrodes. The model describes an effective electrostatic field's increase and associated intensification of ions' spatial separation at the electrode-electrolyte interface. These adsorption-induced local electric and structure properties result in notably increased values and a sharpened form of the differential capacitance dependence on the applied potential. Such capacitance behavior is observed in many published simulations, and its description is beyond the capabilities of the established flat-electrodes theories. The proposed approach could extend the quantitatively verified models providing a new instrument of the electrode surface-parameter optimization for specific electrolytes.

We simulate the two-dimensional $XY$ model in the flow representation by a worm-type algorithm, up to linear system size $L=4096$, and study the geometric properties of the flow configurations. As the coupling strength $K$ increases, we observe that the system undergoes a percolation transition $K_{\mathrm{perc}}$ from a disordered phase consisting of small clusters into an ordered phase containing a giant percolating cluster. Namely, in the low-temperature phase, there exhibits a long-ranged order regarding the flow connectivity, in contrast to the quasi-long-range order associated with spin properties. Near $K_{\mathrm{perc}}$, the scaling behavior of geometric observables is well described by the standard finite-size scaling ansatz for a second-order phase transition. The estimated percolation threshold $K_{\mathrm{perc}}=1.1053\left(4\right)$ is close to but obviously smaller than the Berezinskii-Kosterlitz-Thouless (BKT) transition point $K_{\mathrm{BKT}}=1.1193\left(10\right)$, which is determined from the magnetic susceptibility and the superfluid density. Various interesting questions arise from these unconventional observations, and their solutions would shed light on a variety of classical and quantum systems of BKT phase transitions.

We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits either of observable nodes. We derive exact expressions of the stationary occupation probability, the average number of resets in the long time, and the mean first-passage time between arbitrary two nonobservable nodes. We show that all the quantities can be expressed in terms of the fundamental matrix $\mathbf{Z}={(\mathbf{I}-\mathbf{Q})}^{-1}$, where $\mathbf{I}$ is the identity matrix and $\mathbf{Q}$ is the transition matrix between nonobservable nodes. Finally, we use ring networks, two-dimensional square lattices, barbell networks, and Cayley trees to demonstrate the advantage of first-passage resetting in global search on such networks.

The eigenstate thermalization hypothesis provides to date the most successful description of thermalization in isolated quantum systems by conjecturing statistical properties of matrix elements of typical operators in the (quasi)energy eigenbasis. Here we study the distribution of matrix elements for a class of operators in dual-unitary quantum circuits in dependence of the frequency associated with the corresponding eigenstates. We provide an exact asymptotic expression for the spectral function, i.e., the second moment of this frequency resolved distribution. The latter is obtained from the decay of dynamical correlations between local operators which can be computed exactly from the elementary building blocks of the dual-unitary circuits. Comparing the asymptotic expression with results obtained by exact diagonalization we find excellent agreement. Small fluctuations at finite system size are explicitly related to dynamical correlations at intermediate times and the deviations from their asymptotical dynamics. Moreover, we confirm the expected Gaussian distribution of the matrix elements by computing higher moments numerically.

We study the position distribution $P(\vec{R},N)$ of a run-and-tumble particle (RTP) in arbitrary dimension $d$, after $N$ runs. We assume that the constant speed $v>0$ of the particle during each running phase is independently drawn from a probability distribution $W\left(v\right)$ and that the direction of the particle is chosen isotropically after each tumbling. The position distribution is clearly isotropic, $P(\vec{R},N)\to P(R,N)$ where $R=|\vec{R}|$. We show that, under certain conditions on $d$ and $W\left(v\right)$ and for large $N$, a condensation transition occurs at some critical value of $R=R_c\sim O\left(N\right)$ located in the large-deviation regime of $P(R,N)$. For $R<R_c$ (subcritical fluid phase), all runs are roughly of the same size in a typical trajectory. In contrast, an RTP trajectory with $R>R_c$ is typically dominated by a “condensate,” i.e., a large single run that subsumes a finite fraction of the total displacement (supercritical condensed phase). Focusing on the family of speed distributions $W\left(v\right)=\alpha {(1-v/v_0)}^{\alpha -1}/v_0$, parametrized by $\alpha >0$, we show that, for large $N, P(R,N)\sim exp[-N{\psi }_{d,\alpha }(R/N)]$, and we compute exactly the rate function ${\psi }_{d,\alpha }\left(z\right)$ for any $d$ and $\alpha$. We show that the transition manifests itself as a singularity of this rate function at $R=R_c$ and that its order depends continuously on $d$ and $\alpha$. We also compute the distribution of the condensate size for $R>R_c$. Finally, we study the model when the total duration $T$ of the RTP, instead of the total number of runs, is fixed. Our analytical predictions are confirmed by numerical simulations, performed using a constrained Markov chain Monte Carlo technique, with precision $\sim {10}^{-100}$.

The theory of stochastic processes provides theoretical tools which can be efficiently used to explore the properties of noise-induced escape kinetics. Since noise-facilitated escape over the potential barrier resembles free climbing, one can use the first-passage time theory in an analysis of rock climbing. We perform the analysis of the mean first-passage time in order to answer the question regarding the optimal, i.e., resulting in the fastest climbing, rope length. It is demonstrated that there is a discrete set of favorable rope lengths assuring the shortest climbing times, as they correspond to local minima of mean first-passage time. Within the set of favorable rope lengths there is the optimal rope giving rise to the shortest climbing time. In particular, more experienced climbers can decrease their climbing time by using longer ropes.

Numerous nanoscale studies that are related to harnessing photon energy focus on quantum effects. Thermodynamics analyses indicate the occurrence of a paradox for the standard model of the photocell with the power generated by a decay process. In order to measure the power accurately, a light-harvesting system connecting to Fermi contacts is proposed. Results show that the interference effect between different transition channels plays a decisive role in enhancing the power output of a photocell. The proposed model may provide a foundation for the future development of photoelectric converters.

Multifractal systems usually have singularity spectra defined on bounded sets of Hölder exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly on statistical moment orders at high-enough orders—a phenomenon referred to as the linearization effect. Motivated by general ideas taken from models of turbulent intermittency and focusing on the case of two-dimensional systems, we investigate the issue within the framework of Gaussian multiplicative chaos. As verified by means of Monte Carlo simulations, it turns out that the linearization effect can be accounted for by Liouville-like random measures defined in terms of upper-bounded scalar fields. The coarse-grained statistical properties of Gaussian multiplicative chaos are furthermore found to be preserved in the linear regime of the scaling exponents. As a related application, we look at the problem of turbulent circulation statistics, and obtain a remarkably accurate evaluation of circulation statistical moments, recently determined with the help of massive numerical simulations.

We introduce harmonic cross-correlation decomposition (HCD) as a tool to detect and visualize features in the frequency structure of multivariate time series. HCD decomposes multivariate time series into spatiotemporal harmonic modes with the leading modes representing dominant oscillatory patterns in the data. HCD is closely related to data-adaptive harmonic decomposition (DAHD) [Chekroun and Kondrashov, Chaos 27, 093110 (2017)] in that it performs an eigendecomposition of a grand matrix containing lagged cross-correlations. As for DAHD, each HCD mode is uniquely associated with a Fourier frequency, which allows for the definition of multidimensional power and phase spectra. Unlike in DAHD, however, HCD does not exhibit a systematic dependency on the ordering of the channels within the grand matrix. Further, HCD phase spectra can be related to the phase relations in the data in an intuitive way. We compare HCD with DAHD and multivariate singular spectrum analysis, a third related correlation-based decomposition, and we give illustrative applications to a simple traveling wave, as well as to simulations of three coupled Stuart-Landau oscillators and to human EEG recordings.

In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts for the interaction between a spin-1/2 (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the $\delta$ function, random (Poisson), and power-law exponent $[p\left(k\right)\propto k^{-\gamma }]$ degree distributions, respectively. To describe paramagnetic (PM)-ferromagrenic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin $z$ component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in $z$ and $x$ directions, respectively. For the regular networks and vanishing external field we demonstrate that these phase transitions generally represent prerequisites for the crossover from a disordered spin state to the ordered one inherent to the FM and/or SR phase. Due to the interplay between the spin interaction and the finite-size effects in networks we elucidate novel features of the SR state in the presence of the PM-FM phase transition. In particular, we show that the critical temperature may be high enough and essentially depends on parameters which characterize statistical properties of the network structure. For the scale-free networks we demonstrate that the network architecture, characterized by the particular value of $\gamma$, plays a key role in the SR phase transition problem. Within the anomalous regime scale-free networks possess a strong effective spin-spin interaction supporting fully ordered FM state, which is practically nonsensitive to variations of the quantum transverse field or moderate classical magnetic field. In a scale-free regime the networks exhibit vanishing of the collective spin component in $z$ direction with increasing $\gamma$ accompanied by establishing spontaneous magnetization in the transverse field. The SR phase transition occurs in the presence of some FM state. We establish the conditions for the network parameters, classical and quantum field features to obtain a quantum phase transition in the spin system when the critical temperature approaches zero.

Development in multicellular organisms is marked by a high degree of spatial organization of the cells attaining distinct fates in the embryo. Recent experiments showing that suppression of intercellular interactions can alter the spatial patterns arising during development suggest that cell fates cannot be determined by the exclusive regulation of differential gene expression by morphogen gradients (the conventional view encapsulated in the French flag model). Using a mathematical model that describes the receptor-ligand interaction between cells in close physical proximity, we show that such intercellular signaling can regulate the process of selective gene expression within each cell, allowing information from the cellular neighborhood to influence the process by which the thresholds of morphogen concentration that dictate cell fates adaptively emerge. This results in local modulations of the positional cues provided by the global field set up by the morphogen, allowing interaction-mediated self-organized pattern formation to complement boundary-organized mechanisms in the context of development.

The dependence of stability on the sequence of a DNA hairpin has been investigated through atomistic simulations. For this, a sequence of 16 bases of a hairpin, which consists of a loop of four bases and a stem of six base pairs, has been considered. We have taken eight different sequences, where the first five base pairs were kept fixed in all sequences, whereas the loop sequence and the identity of the duplex base pair closing the loop have been varied. For these hairpin structures, force-induced melting (unzipping) studies were carried out to investigate the effect of the variables on the stability of hairpin. The temperature at which half of the base pairs are open is termed the melting temperature. We defined the unzipping force $F_h$ (half of the base pairs are open) and showed that it may not provide the effect of closing the base pair or loop sequence on the stability of the DNA hairpin. In order to have a better understanding of the stability of a DNA hairpin, the closing base pair or hairpin loop must be open. This requires complete opening of the stem. We defined a force $F_c$ at which all base pairs of the stem are open, and we showed that the $F_c$ gives better understanding of DNA hairpin stability.

Various feedback mechanisms regulate the expression of different genes to ensure the required protein levels inside a cell. In this paper, we develop a kinetic model for one such mechanism that autoregulates RF2 protein synthesis in E. coli through programmed frameshifting. The model finds that the programmed frameshifting autoregulates RF2 protein synthesis by two independent mechanisms. First, it increases the rate of RF2 synthesis from each mRNA transcript at low RF2 concentration. Second, programmed frameshifting can dramatically increase the lifetime of RF2 transcripts when RF2 protein levels are lower than a threshold. This sharp increase in mRNA lifetime is caused by a first-order phase transition from a low to a high ribosome density on an RF2 transcript. The high ribosome density prevents the transcript's degradation by shielding it from nucleases, which increases its average lifetime and hence RF2 protein levels. Our study identifies this quality control mechanism that regulates the cellular protein levels by breaking the hierarchy of processes involved in gene expression.

The dynamic magnetic susceptibility, $\chi \left(\omega \right)$, of a model ferrofluid at a very low concentration (volume fraction, approximately $0.05\%$), and with a range of dipolar coupling constants ($1\le \lambda \le 8$), is examined using Brownian dynamics simulations. With increasing $\lambda$, the structural motifs in the system change from unclustered particles, through chains, to rings. This gives rise to a nonmonotonic dependence of the static susceptibility $\chi \left(0\right)$ on $\lambda$ and qualitative changes to the frequency spectrum. The behavior of $\chi \left(0\right)$ is already understood, and the simulation results are compared to an existing theory. The single-particle rotational dynamics are characterized by the Brownian time, ${\tau }_B$, which depends on the particle size, carrier-liquid viscosity, and temperature. With $\lambda \le 5.5$, the imaginary part of the spectrum, ${\chi }^{\prime \prime }\left(\omega \right)$, shows a single peak near $\omega \sim {\tau }_B^{-1}$, characteristic of single particles. With $\lambda \ge 5.75$, the spectrum is dominated by the low-frequency response of chains. With $\lambda \ge 7$, new features appear at high frequency, which correspond to intracluster motions of dipoles within chains and rings. The peak frequency corresponding to these intracluster motions can be computed accurately using a simple theory.