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We study the pinning transition in a (1+1)-dimensional lattice model of a fluctuating interface interacting with a corrugated impenetrable wall. The interface is modeled as an N-step directed one-dimensional random walk on the half-line x≥0. Its interaction with the wall is described by a quenched, site-dependent, short-ranged random potential uj (j=1,…,N), distributed according to Q(uj) and localized at x=0. By computing the first two disorder-averaged moments of the partition function, ⟨GN⟩ and ⟨GN2⟩, and by analyzing the analytic structure of the resulting expressions, we derive an explicit criterion for the coincidence or distinction of the pinning transitions in annealed and quenched systems. We show that, although the transition points of the annealed and quenched systems are always different in the thermodynamic limit, for finite systems there exists a “gray zone” in which this difference is hardly detectable. Our results may help reconcile conflicting views on whether quenched disorder is marginally relevant.

A bstract Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems, such as Heisenberg spin chains, has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis. We focus on the Heisenberg time scale, which approximately corresponds to the ramp–plateau transition for the Krylov complexity in systems with a large but finite number degrees of freedom. Two frameworks are under consideration: i) the system with growing Lanczos coefficients and an artificial cut-off, and ii) the system with the finite Hilbert space. In both cases via numerical analysis, we observe the transition from Gaussian to KPZ-like scaling, or equivalently, the diffusion-superdiffusion transition at the critical Euclidean time t E ∗ = c cr K , for the Krylov chain of finite length K , and c cr = O (1). In particular, we find a scaling ~ K 1/3 for fluctuations in the one-point correlation function and a dynamical scaling ~ K −2/3 associated with the return probability (Loschmidt echo) corresponding to autocorrelators in physical space. In the first case, the transition is of the 3rd order and can be considered as an example of dynamical quantum phase transition (DQPT), while in the second, it is a crossover. For case ii), utilizing the relationship between the spectrum of tridiagonal matrices at the spectral edge and the spectrum of the stochastic Airy operator, we demonstrate analytically the origin of the KPZ scaling for the particular Krylov chain using the results of the probability theory. We argue that there is interesting outcome of our study for the double scaling limit of matrix models. For the case of topological gravity, the white noise term of order O (1/ N ) is identified, which should be taken into account in the controversial issue of ensemble averaging in 2D/1D holography.

A bstract We propose the holographic description of the Lifshitz tail typical for one-particle spectral density of bounded disordered system in D = 1 space. To this aim the “polymer representation” of the Jackiw-Teitelboim (JT) 2D dilaton gravity at a finite cutoff is used and the corresponding partition function is considered as the weighted sum over paths of fixed length in an external magnetic field. We identify the regime of small loops, responsible for emergence of a Lifshitz tail in the Gaussian disorder, and relate the strength of disorder to the boundary value of the dilaton. The geometry corresponding to the Poisson disorder in the boundary theory involves random paths fluctuating in the vicinity of the hard impenetrable cut-off disc in a 2D plane. It is shown that the ensemble of “stretched” paths evading the disc possesses the Kardar-Parisi-Zhang (KPZ) scaling for fluctuations, which is the key property that ensures the dual description of the Lifshitz tail in the spectral density for the Poisson disorder.

We study correlations between the structure and properties of a free association network of the English language, and solutions of psycholinguistic Remote Association Tests (RATs). We show that average hardness of individual RATs is largely determined by relative positions of test words (stimuli and response) on the free association network. We argue that the solution of RATs can be interpreted as a first passage search problem on a network whose vertices are words and links are associations between words. We propose different heuristic search algorithms and demonstrate that in “easily-solving” RATs (those that are solved in 15 seconds by more than 64% subjects) the solution is governed by “strong” network links (i.e. strong associations) directly connecting stimuli and response, and thus the efficient strategy consist in activating such strong links. In turn, the most efficient mechanism of solving medium and hard RATs consists of preferentially following sequence of “moderately weak” associations.

The flows generated by the iterative dynamics of triangle reflections are analyzed. These flows are interpreted as the adiabatic dynamics of probe particles within the fundamental domain of the modular group. Two specific cases of lattices are considered: (a) those generated by reflections of equilateral triangles, and (b) those generated by reflections of rectangular isosceles triangles. We demonstrate that the stationary points of the flows for equilateral and isosceles triangles correspond to the “Golden” and the “Silver” ratios, respectively.

We study, by extensive numerical simulations, the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder-frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour ∼t4/3, t being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position X along the x-axis, for which we unveil a previously unknown behaviour. Indeed, our analysis evidences that in absence of the lattice gas particles the latter probability distribution has a Gaussian central part ∼ exp ( − u 2 ) , where u = X/t2/3, and exhibits slower-than-Gaussian tails ∼ exp ( − u 4 3 ) for sufficiently large t and u. Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models.

Regulation of gene expression is integral to the development and survival of all organisms. Transcription begins with the assembly of a pre-initiation complex at the gene promoter 1 , followed by initiation of RNA synthesis and the transition to productive elongation 2 , 3 , 4 . In many cases, recruitment of RNA polymerase II (Pol II) to a promoter is necessary and sufficient for activation of genes. However, there are a few notable exceptions to this paradigm, including heat shock genes and several proto-oncogenes, whose expression is attenuated by regulated stalling of polymerase elongation within the promoter-proximal region 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 . To determine the importance of polymerase stalling for transcription regulation, we carried out a genome-wide search for Drosophila melanogaster genes with Pol II stalled within the promoter-proximal region. Our data show that stalling is widespread, occurring at hundreds of genes that respond to stimuli and developmental signals. This finding indicates a role for regulation of polymerase elongation in the transcriptional responses to dynamic environmental and developmental cues.

Responses of cells to stimuli are increasingly discovered to involve the binding of sequence-specific transcription factors outside of known target genes. We wanted to determine to what extent the genome-wide binding and function of a transcription factor are shaped by the cell type versus the stimulus. To do so, we induced the Heat Shock Response pathway in two different cancer cell lines with two different stimuli and related the binding of its master regulator HSF1 to nascent RNA and chromatin accessibility. Here, we show that HSF1 binding patterns retain their identity between basal conditions and under different magnitudes of activation, so that common HSF1 binding is globally associated with distinct transcription outcomes. HSF1-induced increase in DNA accessibility was modest in scale, but occurred predominantly at remote genomic sites. Apart from regulating transcription at existing elements including promoters and enhancers, HSF1 binding amplified during responses to stimuli may engage inactive chromatin. The authors compare the heat shock response between different cell lines and stimuli and reveal the genome-wide binding of its master transcription factor HSF1 as a platform for context-specific transcription activation.

The kinetics and magnitude of cytokine gene expression are tightly regulated to elicit a balanced response to pathogens and result from integrated changes in transcription and mRNA stability. Yet, how a single microbial stimulus induces peak transcription of some genes (TNFα) within minutes whereas others (IP-10) require hours remains unclear. Here, we dissect activation of several lipopolysaccharide (LPS)-inducible genes in macrophages, an essential cell type mediating inflammatory response in mammals. We show that a key difference between the genes is the step of the transcription cycle at which they are regulated. Specifically, at TNFα, RNA Polymerase II initiates transcription in resting macrophages, but stalls near the promoter until LPS triggers rapid and transient release of the negative elongation factor (NELF) complex and productive elongation. In contrast, no NELF or polymerase is detectible near the IP-10 promoter before induction, and LPS-dependent polymerase recruitment is rate limiting for transcription. We further demonstrate that this strategy is shared by other immune mediators and is independent of the inducer and signaling pathway responsible for gene activation. Finally, as a striking example of evolutionary conservation, the Drosophila homolog of the TNFα gene, eiger, displayed all of the hallmarks of NELF-dependent polymerase stalling. We propose that polymerase stalling ensures the coordinated, timely activation the inflammatory gene expression program from Drosophila to mammals.

Lyme disease is caused by infection with the bacterium Borrelia burgdorferi (Bb), which is transmitted to humans by deer ticks. The infection manifests usually as a rash and minor systemic symptoms; however, the bacteria can spread to other tissues, causing joint pain, carditis, and neurological symptoms. Lyme neuroborreliosis presents itself in several ways, such as Bell's palsy, meningitis, and encephalitis. The molecular basis for neuroborreliosis is poorly understood. Analysis of the changes in the expression levels of messenger RNAs and non-coding RNAs, including microRNAs, following Bb infection could therefore provide vital information on the pathogenesis and clinical symptoms of neuroborreliosis. To this end, we used cultured primary human astrocytes, key responders to CNS infection and important components of the blood-brain barrier, as a model system to study RNA and microRNA changes in the CNS caused by Bb. Using whole transcriptome RNA-seq, we found significant changes in 38 microRNAs and 275 mRNAs at 24 and 48 hours following Bb infection. Several of the RNA changes affect pathways involved in immune response, development, chromatin assembly (including histones) and cell adhesion. Further, several of the microRNA predicted target mRNAs were also differentially regulated. Overall, our results indicate that exposure to Bb causes significant changes to the transcriptome and microRNA profile of astrocytes, which has implications in the pathogenesis, and hence potential treatment strategies to combat this disease.