Decay of superfluid currents in the interacting one-dimensional Bose gas

We examine the superfluid properties of a 1D Bose gas in a ring trap based on the model of Lieb and Liniger. While the 1D Bose gas has nonclassical rotational inertia and exhibits quantization of velocities, the metastability of currents depends sensitively on the strength of interactions in the gas: the stronger the interactions, the faster the current decays. It is shown that the Landau critical velocity is zero in the thermodynamic limit due to the first supercurrent state, which has zero energy and finite probability of excitation. We calculate the energy dissipation rate of ring currents in the presence of weak defects, which should be observable on experimental time scales.Comment: 5 pages, 4 figure

Exponential martingales and changes of measure for counting processes

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes as well as counting processes with stochastic intensities depending on diffusion processes

Robust pricing and hedging of double no-touch options

Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of super- and sub-hedging strategies to establish the bounds, and the use of Skorokhod embedding techniques to show the bounds are the best possible. In addition to establishing rigorous bounds, we consider carefully what is meant by arbitrage in settings where there is no {\it a priori} known probability measure. We discuss two natural extensions of the notion of arbitrage, weak arbitrage and weak free lunch with vanishing risk, which are needed to establish equivalence between the lack of arbitrage and the existence of a market model.Comment: 32 pages, 5 figure

Follow-Up After Hip and Knee Arthroplasty: a Review of the Literature and a Report on a Pilot Project at the Vreden National Medical Research Center of Traumatology and Orthopedics

Background. Today in our country, the follow-up of patients after arthroplasty is carried out in accordance with clinical guidelines, the wording of which is based on monographs from 2006, 2008, and 2014, in addition, clinical guidelines for follow-up do not take into account the results of treatment assessed by the patient himself. The purpose of this study was to examine existing systems and develop a proprietary follow-up system for patients after hip and knee arthroplasty. Results. A review of the literature revealed that follow-up of patients after arthroplasty is an unsolved problem, within which there is low coverage, reluctance or forgetfulness of the asymptomatic patient, the problem of accessibility of medical examinations, and an excessive financial burden on the health care system. Since 2022, fixed recommendations for follow-up after arthroplasty have been used in the clinical practice of our center in discharge epicrisis. Recommendations for the frequency of follow-up were formulated by experts based on a comprehensive review of the literature and their own experience. In the first three months, 221 hip and 235 knee evaluation questionnaires were collected through the proposed mechanism, with a progressive increase in the number of questionnaires based on weekly monitoring data. Conclusion. Unfortunately, the outpatient clinic system is not always able to provide qualitative monitoring of patients after arthroplasty due to various reasons, therefore, in our opinion, the implementation of the mechanism of remote monitoring of patients will allow detecting various complications at the stage of early diagnosis, which will contribute to prompt solution of these problems. The remote monitoring system is also an important source of scientific data

Genome-wide association meta-analysis identifies 48 risk variants and highlights the role of the stria vascularis in hearing loss

Hearing loss is one of the top contributors to years lived with disability and is a risk factor for dementia. Molecular evidence on the cellular origins of hearing loss in humans is growing. Here, we performed a genome-wide association meta-analysis of clinically diagnosed and self-reported hearing impairment on 723,266 individuals and identified 48 significant loci, 10 of which are novel. A large proportion of associations comprised missense variants, half of which lie within known familial hearing loss loci. We used single-cell RNA-sequencing data from mouse cochlea and brain and mapped common-variant genomic results to spindle, root, and basal cells from the stria vascularis, a structure in the cochlea necessary for normal hearing. Our findings indicate the importance of the stria vascularis in the mechanism of hearing impairment, providing future paths for developing targets for therapeutic intervention in hearing loss

Dense random packing with a power-law size distribution: the structure factor, mass-radius relation, and pair distribution function

We consider dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation and pair distribution function of the disk centers. A toy model of dense segments in one dimension (1d) is solved exactly. It is shown theoretically in 1d and numerically in 1d and 2d that such packing exhibits fractal properties. It is found that the exponent of the power-law distribution and the fractal dimension coincide. An approximate relation for the structure factor in arbitrary dimension is derived, which can be used as a fitting formula in small-angle scattering. The findings can be useful for understanding microstructural properties of various systems like ultra-high performance concrete, high-internal-phase ratio emulsions or biological systems.Comment: 8 pages, 8 figure