Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density

The classical monomer-dimer model in two-dimensional lattices has been shown to belong to the \emph{``#P-complete''} class, which indicates the problem is computationally ``intractable''. We use exact computational method to investigate the number of ways to arrange dimers on $m \times n$ two-dimensional rectangular lattice strips with fixed dimer density $\rho$. For any dimer density $0 < \rho < 1$, we find a logarithmic correction term in the finite-size correction of the free energy per lattice site. The coefficient of the logarithmic correction term is exactly -1/2. This logarithmic correction term is explained by the newly developed asymptotic theory of Pemantle and Wilson. The sequence of the free energy of lattice strips with cylinder boundary condition converges so fast that very accurate free energy $f_2(\rho)$ for large lattices can be obtained. For example, for a half-filled lattice, $f_2(1/2) = 0.633195588930$, while $f_2(1/4) = 0.4413453753046$ and $f_2(3/4) = 0.64039026$. For $\rho < 0.65$, $f_2(\rho)$ is accurate at least to 10 decimal digits. The function $f_2(\rho)$ reaches the maximum value $f_2(\rho^*) = 0.662798972834$ at $\rho^* = 0.6381231$, with 11 correct digits. This is also the \md constant for two-dimensional rectangular lattices. The asymptotic expressions of free energy near close packing are investigated for finite and infinite lattice widths. For lattices with finite width, dependence on the parity of the lattice width is found. For infinite lattices, the data support the functional form obtained previously through series expansions.Comment: 15 pages, 5 figures, 5 table

Room temperature broadband polariton lasing from a dye‐filled microcavity

A material system is proposed to generate polariton lasing at room temperature over a broad spectral range. The system developed is based on a boron‐dipyrromethene fluorescent dye (BODIPY‐G1) that is dispersed into a polystyrene matrix and used as the active layer of a strongly coupled microcavity. It is shown that the BODIPY‐G1 exciton polaritons undergo nonlinear emission over a broad range of exciton–cavity mode detuning in the green‐yellow portion of the visible spectrum, with polariton lasing achieved over a spectral range spanning 33 nm. The recorded linewidth of ≈0.1 nm corresponds to a condensate coherence lifetime of ≈1 ps. It is proposed that similar effects can be anticipated using a range of molecular dyes in the BODIPY family; a result that paves the way for tunable polariton devices over the visible and near‐infrared spectral region

Non-Hermitian dynamics and nonreciprocity of optically coupled nanoparticles

Non-Hermitian dynamics, as observed in photonic, atomic, electrical, and optomechanical platforms, holds great potential for sensing applications and signal processing. Recently, fully tunable nonreciprocal optical interaction has been demonstrated between levitated nanoparticles. Here, we use this tunability to investigate the collective non-Hermitian dynamics of two nonreciprocally and nonlinearly interacting nanoparticles. We observe parity-time symmetry breaking and, for sufficiently strong coupling, a collective mechanical lasing transition, where the particles move along stable limit cycles. This work opens up a research avenue of nonequilibrium multi-particle collective effects, tailored by the dynamic control of individual sites in a tweezer array

Statistical-mechanical lattice models for protein-DNA binding in chromatin

Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibriums measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.Comment: 19 pages, 7 figures, accepted author manuscript, to appear in J. Phys.: Cond. Mat

Mechanisms of blueshifts in organic polariton condensates

This is the final version. Available from Nature Research via the DOI in this record.The data that support the findings of this study are available in University of Southampton Institutional Repository with the identifier https://doi.org/10.5258/SOTON/D1159.Bose-Einstein condensates of exciton-polaritons in inorganic semiconductor microcavities are known to possess strong interparticle interactions attributed to their excitonic component. The interactions play a crucial role in the nonlinear dynamics of such systems and can be witnessed as the energy blueshifts of polariton states. However, the localised nature of Frenkel excitons in strongly coupled organic microcavities precludes interparticle Coulomb exchange-interactions that change mechanisms of the nonlinearity and blueshifts accordingly. In this report, we unravel the origins of blueshifts in organic polariton condensates. We examine the possible contributions: intracavity optical Kerr-effect, gain-induced frequency-pulling, polariton interactions and effects related to saturation of optical transitions for weakly- and strongly-coupled molecules. We conclude that blueshifts in organic polariton condensates arise from the interplay of the saturation effects and intermolecular energy migration. Our model predicts the commonly observed step-like increase of both the emission energy and degree of linear polarization at the polariton condensation threshold.Russian Scientific Foundation (RSF)Government of the Russian FederationGovernment of the Russian FederationEngineering and Physical Sciences Research Council (EPSRC)ITMO Fellowship Progra

On the origin of blueshifts in organic polariton condensates

We report on the origin of energy-shifts in organic polariton condensates. The localised nature of Frenkel excitons in molecular semiconductors precludes interparticle Coulomb exchange interactions -the latter being the dominant mechanism for blueshifts in inorganic semiconductor microcavities that bear Wannier-Mott excitons. We examine the contribution of optically induced change of the intracavity non-linear refractive index, gain induced frequency-pulling and quenching of the Rabi splitting, as well as the role of polariton-exciton and polariton-polariton scattering in the energy-shift of the polariton mode at condensation threshold in strongly coupled molecular dye microcavities. We conclude that blueshifts in organic polariton condensates arise from the interplay of the saturation of molecular optical transitions and intermolecular energy migration. Our model predicts the commonly observed step-wise increase of both the emission energy and degree of linear polarisation at polariton condensation threshold

Ultrafast optical control of polariton energy in an organic semiconductor microcavity

The manipulation of exciton–polaritons and their condensates is of great interest due to their applications in polariton simulators and high-speed, all-optical logic devices. Until now, methods of trapping and manipulating such condensates are not dynamically reconfigurable or resulted in an undesirable reduction in the exciton–photon coupling strength. Here, a new strategy for the ultrafast control of polariton resonances via transient modification of an optical cavity mode is presented. Multilayer organic semiconductor microcavities that contain two absorbers are constructed: one strongly-coupled to the cavity photon mode and one that is out-of-resonance. By selectively exciting the out-of-resonance absorber using ultrashort laser pulses, the cavity refractive index is modulated, and fully-reversible blueshifts of the lower polariton branch by up to 8 meV in sub-ps timescales with no corresponding reduction in the exciton–photon coupling strength are generated. This work demonstrates the ability to manipulate polariton energy landscapes over ultrafast timescales with important applications in emerging computing technologies

Differences in expression profiles in malingant melanoma patients according to immunotherapy response

One of the most important branch of modern molecular genetics and biomedicine is the search for predictive markers that help choose the most effective way of treatment, drug and also determine its individual dosage. Among the markers, those that can provide the possibility of using a non­invasive, so­called “liquid biopsy” are considered particularly promising. This method allows the condition of the tumor to be assessed by analyzing the body’s natural fluids, such as blood, urine or saliva. Such studies are most convenient in those cases when it is necessary to monitor the effectiveness of therapy in order to record the time of the onset of resistance of tumor cells, the onset of relapse and to move on to the next line of therapy. In the treatment of aggressive and rapidly became metastatic malignant tumors, such as melanoma, the presence of reliable markers that allow quick and accurate determination of treatment tactics is especially important. Nowadays, there is an increasing number of studies devoted to the search for predictive markers of the effectiveness of immunotherapy. Melanoma is one of the most immunogenic tumors and, as a result, has become a model object for research into and introduction of new approaches to immunotherapy. In this study, we compared two groups of patients with metastatic skin melanoma, with different responses to immunotherapy with blockers of immune control points, to identify new predictive expression biomarkers among microRNAs and mRNAs, and to identify the genes responsible for the occurrence of an objective response to therapy. As a result, the study detected several microRNAs with a significant change in expression level within the tumor tissue of patients responding differently to immunotherapy. Differences in the level of expression of their target genes have also been found, that will allow a more detailed analysis of the molecular mechanisms that determine the sensitivity or resistance of malignant melanoma cells to the immunotherapy. Based on the obtained data, we have proposed expression markers (mRNAs and microRNAs) that can be used as predictors of malignant melanoma tumors to immunotherapy