Search results for “limits”

Why the definition of a filtered category insists on non-emptiness: the empty colimit fails to commute with the empty limit, and that is the only failure.

A pilot study mapping ion-induced charge collection against bandgap and carrier mobility, and what it revealed about the cost of getting the time integration wrong

Cold atomic ensembles are among the most versatile tools in modern physics research. They play a key role in advancing next-generation frequency standards, qubit architectures, and quantum sensing technologies. Many experiments demand prolonged spatial confinement of atoms to facilitate extended interactions with electromagnetic fields, achievable through electric, magnetic, gravitational, or optical trapping mechanisms.

A cornerstone of atomic trapping is the magneto-optical trap (MOT), which relies on six counterpropagating laser beams and a pair of anti-Helmholtz coils to produce a radially symmetric quadrupole magnetic field with a central zero point.

Alternatively, optical dipole traps exploit the electric dipole interaction with a tightly focused, fardetuned high-power laser beam, offering weaker confinement than MOTs—typically below 1 mK. Unlike MOTs, these traps permit extremely weak optical excitation, circumventing limitations imposed by radiation pressure. Additionally, their trapping mechanism is largely insensitive to ground-state magnetic sublevels (neglecting tensor polarizability effects), enabling versatile configurations such as optical lattices.

Figure 1: Image of atoms trapped in the MOT. The atomic cloud is at the center of the image. The cloud dimensions are approximately 1 mm.

ble of confining Rb 87 atomic clouds at temperatures near 175 µ K. For dipole trapping, we adopted a farred-detuned (1012 nm) laser system, chosen for its dual functionality: we plan to use it both as a trapping beam and as one component in two-photon Rydberg excitation schemes. A further advantage of this configuration is its potential to confine Rydberg atoms while meeting the magic wavelength condition for ground-to-Rydberg transitions.

Magic-wavelength optical dipole traps offer particularly powerful advantages for cold atom manipulation. At this specific wavelength, the light shift for two atomic states becomes identical, effectively decoupling the internal atomic dynamics from the external motional states. This enables long coherence times for quantum operations while maintaining strong spatial confinement. Furthermore, such traps allow state-insensitive confinement, which is crucial for precision measurements and quantum information processing. The magic wavelength condition also facilitates efficient Rydberg excitation by providing identical trapping potentials for both ground and Rydberg states, minimizing decoherence during excitation processes.

We characterized the dipole trap intended for atom transfer, achieving a maximum depth of 3 mK under our experimental conditions—surpassing the Doppler cooling limit and ensuring efficient atomic confinement.

Topic modelling is an area of text mining that has been actively developed in the last 15 years. A probabilistic topic model extracts a set of hidden topics from a collection of text documents. It defines each topic by a probability distribution over words and describes each document with a probability distribution over topics. In applications, there are often many requirements, such as, for example, problem-specific knowledge and additional data, to be taken into account. Therefore, it is natural for topic modelling to be considered a multiobjective optimization problem. However, historically, Bayesian learning became the most popular approach for topic modelling. In the Bayesian paradigm, all requirements are formalized in terms of a probabilistic generative process. This approach is not always convenient due to some limitations and technical difficulties. In this work, we develop a non-Bayesian multiobjective approach called the Additive Regularization of Topic Models (ARTM). It is based on regularized Maximum Likelihood Estimation (MLE), and we show that many of the well-known Bayesian topic models can be re-formulated in a much simpler way using the regularization point of view. We review some of the most important types of topic models: multimodal, multilingual, temporal, hierarchical, graph-based, and short-text. The ARTM framework enables easy combination of different types of models to create new models with the desired properties for applications. This modular “lego-style” technology for topic modelling is implemented in the open-source library BigARTM.

A wide class of natural language processing tasks is solved using markup.At the moment, the vast majority of models and datasets rely on a simple markup structure containing only fragments and labels.Moreover, simple classification metrics such as F1, Precision, Recall are used to evaluate the model's accuracy.The problem with such metrics is that they do not take into account all aspects of the markup structure and that they are applicable only under the assumption of the existence of an ideal markup.This paper proposes a more general and universal markup structure that allows solving complex problems and builds a methodology for multi-criteria evaluation of text markup models based on inconsistent expert markup.After that, the application of the constructed method is considered to assess the quality of the model obtained within the winning algorithm of the "READ//ABLE" competition, which focused on building an effective essay markup system.The results demonstrate that the new markup structure and evaluation approach provides a more comprehensive and accurate assessment of model performance, addressing the limitations of traditional metrics by accounting for complex markup scenarios and expert inconsistencies.

Modern AI systems often comprise multiple learnable components that can be naturally organized as graphs. A central challenge is the end-to-end training of such systems without restrictive architectural or training assumptions. Such tasks fit the theory and approaches of the collaborative Multi-Agent Reinforcement Learning (MARL) field. We introduce Reinforcement Networks, a general framework for MARL that organizes agents as vertices in a directed acyclic graph (DAG). This structure extends hierarchical RL to arbitrary DAGs, enabling flexible credit assignment and scalable coordination while avoiding strict topologies, fully centralized training, and other limitations of current approaches. We formalize training and inference methods for the Reinforcement Networks framework and connect it to the LevelEnv concept to support reproducible construction, training, and evaluation. We demonstrate the effectiveness of our approach on several collaborative MARL setups by developing several Reinforcement Networks models that achieve improved performance over standard MARL baselines. Beyond empirical gains, Reinforcement Networks unify hierarchical, modular, and graph-structured views of MARL, opening a principled path toward designing and training complex multi-agent systems. We conclude with theoretical and practical directions - richer graph morphologies, compositional curricula, and graph-aware exploration. That positions Reinforcement Networks as a foundation for a new line of research in scalable, structured MARL.

Nowadays optical frequency transfer has become an essential component for numerous quantum technology applications. There is a gradual increase in demand for such systems due to the rapid development of quantum technologies themselves, e. g. optical frequency transmission became crucial for high-precision timekeeping and communication systems relying on the frequency stability of quantum clocks that offer unparalleled accuracy, making ideal for metrology, navigation, and testing fundamental physical theories. Moreover, optical frequency transmission has already found popularity in such up-to-date topics as quantum communication and quantum cryptography.

For over 6 years, our laboratory has been developing various systems for the transmission of stabilized frequency signals. In 2017, we started with the elaboration of a phase noise compensation system in a 5-meter long optical fiber frequency transmission line and afterwards extended the line to 2.8 kilometers. Taking advantage of the result we also connected three of our laboratories with fiber optic cables with phase noise compensation systems to facilitate the process of comparing developed frequency standards. With an awareness of the fiber optic links applicability limitations (such as insufficient mobility and flexibility) we developed a 5-meter long free-space optical link with the same phase-noise compensation system in 2020 and increased its length to 17 meters with the addition of a precision pointing system in 2021.

Finally, in 2023, we introduced a 215-cm free-space optical transmission link with a flexible pointing system that enables dynamically stable tracking of moving objects: potentially drones or even satellites. The test scheme of this transfer system with defined upgrades is presented in Figure 1.

Phase noise compensation system for both fiber and free-space optical links The transmission link introduces phase noise into the signal. To compensate for corresponding frequency shifts, a laser beam used for transmission is split into two parts. The first part passes through a reference arm of an interferometer, while the second is transmitted to the receiver via an acousto-optic modulator (AOM1) and partly reflected back. The returned signal contains doubled link noise and is heterodyned with the reference beam. The resulting beat signal is used in a phase-locked loop that controls the frequency shift introduced by AOM1 and compensates the link noise.

Pointing system for free-space optical link To compensate for small high-frequency beam direction fluctuations, a precise (fast) pointing system was used, which includes a position-sensitive quadrant photodetector managing a mirror with two-coordinate galvanic control. To expand the pointing range, we implement a coarse (slow) pointing system by attaching the optical plate to an alt-azimuth telescope mount. The servo signal of the fast system is used to correct the angular velocity of the dynamic tripod rotation around two axes.

In the near future, we plan to extend the free-space link length and test the system in actual environments when pointing at a moving UAV. In addition, we plan to focus on processing the received noise signal in order to use it to obtain information about atmospheric parameters.

We strongly believe that the development of optical transmission systems is extremely useful for the expansion of quantum technologies.

Two methods for solving a SLAE — Cramer's rule via determinants and the universal Gaussian elimination method, with examples.