Search results for “reference”

Reference table of the basic indefinite integrals of the elementary functions: power, exponential, logarithmic and trigonometric.

Reference table of the derivatives of the elementary functions: power, exponential, logarithmic, trigonometric and their inverses.

Reference table of indefinite integrals of the exponential function and its products with powers of x.

Reference table of indefinite integrals of the hyperbolic sine, cosine, tangent and cotangent.

Reference table of indefinite integrals of expressions containing the natural logarithm.

Reference table of indefinite integrals of rational functions, including quadratic denominators and partial-fraction forms.

Reference table of indefinite integrals of expressions containing square roots and other radicals.

Reference table of indefinite integrals of products of exponentials with sine and cosine.

Reference table of indefinite integrals of products of powers of x with sine and cosine.

Reference table of indefinite integrals of sine, cosine, tangent and their powers and products.

This paper introduces a new approach to estimating the text document complexity.Common readability indices are based on average length of sentences and words.In contrast to these methods, we propose to count the number of rare words occurring abnormally often in the document.We use the reference corpus of texts and the quantile approach in order to determine what words are rare, and what frequencies are abnormal.We construct a general text complexity model, which can be adjusted for the specific task, and introduce two special models.The experimental design is based on a set of thematically similar pairs of Wikipedia articles, labeled using crowdsourcing.The experiments demonstrate the competitiveness of the proposed approach.

Text trees as a data structure occur in numerous machine learning tasks like hierarchical summarization and automatic mind map generation. One of the main methods of quality evaluation in these tasks is comparison with reference hierarchies created by experts. The method used so far to compare text hierarchies, as shown in this work, poorly accounts for their structure and text semantics relative to phrasing. To address this issue, we propose a new metric on the set of text trees — text tree edit distance (TTED), based on tree edit distance with semantic distance between texts measured using a large language model. To evaluate how the metric reflects different aspects of text tree difference, we introduce special quality coefficients that reflect the sensitivity of a metric to paraphrasing relative to structural and semantic differences of text trees. Using these coefficients, we conduct extensive testing of the proposed metric and its modifications compared to a baseline used in previous works to compare text hierarchies, which shows that TTED indeed captures significant differences between text trees more accurately than the previously used method. We also provide a practical implementation of TTED for further usage.

This paper introduces an approach to measuring the cognitive complexity of texts on various language levels. While standard readability indices are based on the linear combination of primary statistics, our general approach allows us to estimate complexity on morphological, lexical, syntactic, and discursive levels. Each model is defined by the tokens for the specific language level and the complexity function of a single token. We then use the reference collection of moderately complex texts and the quantile-based approach to spot the abnormally rare tokens. The proposed supervised ensemble, based on the ElasticNet model, incorporates models from all language levels. Having collected a labeled dataset through crowdsourcing, consisting of pairs of articles from the Russian Wikipedia, we consider several models and ensembles and compare them to common baselines. Suggested models are flexible due to the freedom in choosing the reference collection. The described experiments confirm the competitiveness of the proposed approach, as the ensembles demonstrate the best target metric value.

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.