Encoding classical information in gauge subsystems of quantum codes

In this paper, we show how to construct hybrid quantum-classical codes from subsystem codes by encoding the classical information into the gauge qudits using gauge fixing. Unlike previous work on hybrid codes, we allow for two separate minimum distances, one for the quantum information and one for the classical information. We give an explicit construction of hybrid codes from two classical linear codes using Bacon–Casaccino subsystem codes, as well as several new examples of good hybrid code.

Average minimum distances of periodic point sets – foundational invariants for mapping periodic crystals

The fundamental model of any solid crystalline material (crystal) at the atomic scale is a periodic point set. The strongest natural equivalence of crystals is rigid motion or isometry that preserves all inter-atomic distances. Past comparisons of periodic structures often used manual thresholds, symmetry groups and reduced cells, which are discontinuous under perturbations or thermal vibrations of atoms. This work defines the infinite sequence of continuous isometry invariants (Average Minimum Distances) to progressively capture distances between neighbors. The asymptotic behaviour of the new invariants is theoretically proved in all dimensions for a wide class of sets including non-periodic. The proposed near linear time algorithm identified all different crystals in the world's largest Cambridge Structural Database within a few hours on a modest desktop. The ultra fast speed and proved continuity provide rigorous foundations to continuously parameterise the space of all periodic crystals as a high-dimensional extension of Mendeleev's table of elements.

Supraspinatus-to-Glenoid Contact Occurs During Standardized Overhead Reaching Motion

Background: Rotator cuff tears may result from repeated mechanical deformation of the cuff tendons, and internal impingement of the supraspinatus tendon against the glenoid is one such proposed mechanism of deformation. Purpose: To (1) describe the changing proximity of the supraspinatus tendon to the glenoid during a simulated overhead reaching task and (2) determine the relationship between scapular morphology and this proximity. Additionally, the patterns of supraspinatus-to-glenoid proximity were compared with previously described patterns of supraspinatus-to-coracoacromial arch proximity. Study Design: Descriptive laboratory study. Methods: Shoulder models were created from magnetic resonance images of 20 participants. Standardized kinematics were imposed on the models to simulate functional reaching, and the minimum distances between the supraspinatus tendon and the glenoid and the supraspinatus footprint and the glenoid were calculated every 5° between 0° and 150° of humerothoracic elevation. The angle at which contact between the supraspinatus and the glenoid occurred was documented. Additionally, the relationship between glenoid morphology (version and inclination) and the contact angle was evaluated. Descriptive statistics were calculated for the minimum distances, and glenoid morphology was assessed using Pearson correlation coefficients and simple linear regressions. Results: The minimum distances between the tendon and the glenoid and between the footprint and the glenoid decreased as elevation increased. Contact between the tendon and the glenoid occurred in all participant models at a mean elevation of 123° ± 10°. Contact between the footprint and the glenoid occurred in 13 of 20 models at a mean of 139° ± 10°. Less glenoid retroversion was associated with lower tendon-to-glenoid contact angles ( r = –0.76; R 2 = 0.58; P < .01). Conclusion: This study found that the supraspinatus tendon progressively approximated the glenoid during simulated overhead reaching. Additionally, all participant models eventually made contact with the glenoid by 150° of humerothoracic elevation, although anatomic factors influenced the precise angle at which contact occurred. Clinical Relevance: Contact between the supraspinatus and the glenoid may occur frequently within the range of elevation required for overhead activities. Therefore, internal impingement may be a prevalent mechanism for rotator cuff deformation that could contribute to cuff pathology.

Testing the classifier adapted to recognize the languages of works based on the Latin alphabet

Using the example of a model collection of 10 texts in five languages (English, German, Spanish, Italian, and French) using Latin graphics, the article establishes the applicability of the γ-classifier for automatic recognition of the language of a work based on the frequency of 26 common Latin alphabetic letters. The mathematical model of the γ-classifier is represented as a triad. Its first component is a digital portrait (DP) of the text - the distribution of the frequency of alphabetic unigrams in the text; the second component is formulas for calculating the distances between the DP texts and the third is a machine learning algorithm that implements the hypothesis of “homogeneity” of works written in one language and “heterogeneity” of works written in different languages. The tuning of the algorithm using a table of paired distances between all products of the model collection consisted in determining an optimal value of the real parameter γ, for which the error of violation of the “homogeneity” hypothesis is minimized. The γ-classifier trained on the texts of the model collection showed a high, 100% accuracy in recognizing the languages of the works. For testing the classifier, an additional six random texts were selected, of which five were in the same languages as the texts of the model collection. By the method of the nearest (in terms of distance) neighbor, all new texts confirmed their homogeneity with the corresponding pairs of monolingual works. The sixth text in Romanian showed its heterogeneity in relation to all elements of the collection. At the same time, it showed closeness in minimum distances, first of all, to two texts in Spanish and then to two works in Italian.

New entanglement-assisted quantum MDS codes

Entanglement-assisted quantum error-correcting codes (EAQECCs) can be obtained from arbitrary classical linear codes based on the entanglement-assisted stabilizer formalism, which greatly promoted the development of quantum coding theory. In this paper, we construct several families of [Formula: see text]-ary entanglement-assisted quantum maximum-distance-separable (EAQMDS) codes of lengths [Formula: see text] with flexible parameters as to the minimum distance [Formula: see text] and the number [Formula: see text] of maximally entangled states. Most of the obtained EAQMDS codes have larger minimum distances than the codes available in the literature.

Assessment of the capabilities of orbital optical devices for obtaining information about space objects

The purpose of the study is to select the optimal conditions for collecting non-coordinate information about a spacecraft by a space optical-electronic means at the time objects pass the vicinity of the points of the minimum distance between their orbits. The quantitative indicator is proposed that characterize the measure of the possibility of obtaining non-coordinate information about space objects with the required level of quality. The arguments of the function characterizing the indicator are the distance between spacecraft; their relative speed; phase angle of illumination of a spacecraft by the Sun in relation to the optical-electronic means; the length of the time interval during which both objects are in the vicinity of the point of a minimum distance between their orbits. The value of the indicator is computed by solving three particular research problems. The first task is to search for neighborhoods that include the minimum distances between the orbits of the controlled spacecraft and optical-electronic means. To solve it, a fast algorithm for calculating the minimum distance between orbits used. Additionally, the drift of the found neighborhoods is taken into account on the time interval up to 60 hours. The second task is to estimate the characteristics of motion and the conditions of optical visibility of a controlled spacecraft in the vicinity of the minimum points of the distance between the orbits of spacecraft. The solution to this problem is carried out by using the SGP4 library of space objects motion forecast. The third task is justification and calculation of an index characterizing the measure of the possibility of obtaining an optical image of a spacecraft for given conditions of optical visibility. To solve the problem, the developed system of fuzzy inference rules and the Mamdani algorithm is used. The presented method is implemented as a program. In the course of a computational experiment, an assessment was made of the possibility of obtaining non-coordinate information on low-orbit and geostationary space objects. The proposed indicator provides an increase in the efficiency of the procedure for collecting non-coordinate information about space objects by choosing the most informative alternatives for monitoring space objects from the available set of possible observations at a given planning interval for collecting information about space objects.

A comparison between Suzuki invariant code and one-point Hermitian code

In this paper we compare the performance of two algebraic geometry codes (Suzuki and Hermitian codes) constructed using maximal algebraic curves over [Formula: see text] with large automorphism groups by choosing specific divisors. We discuss their parameters, compare the rate of these codes as well as their relative minimum distances, and we show that both codes are asymptotically good in terms of the rate which is in contrast to their behavior in terms of the relative minimum distance.

Reducing the risk of collision between ships in a close-quarters situation by simulating collision avoidance actions

‘Close-quarters situation’ is a term used in the International Regulations for Preventing Collisions at Sea. As the term is not precisely defined, this paper analyses the interpretations and definitions of the term by various authors or courts, based on judicial processes and judgments. In the end, the authors suggest their own definition of the term ‘close-quarters situation’. Knowing the minimum distance from another ship and the time to the closest point of approach at which collision may still be avoided by one's own manoeuvre is information that every ship's officer needs to know. In accordance with the proposed definition of the term ‘close-quarters situation’, minimum distances between ships and time to the closest point of approach in which the ship can still take action to avoid a collision by its own manoeuvring are determined by means of simulations on a navigational simulator. A total of 168 simulations were performed with three fine-form vessel sizes and three full-form vessel sizes. Due to the extensive amount of data, the paper presents the results for one vessel only.

OPTIMIZED DETERMINATION OF 3D COORDINATES IN THE SURVEY OF INACCESSIBLE POINTS OF BUILDINGS - EXAMPLE OF APPLICATION IMPLEMENTED IN FREE SOFTWARE

The forward intersection method is already widely used in the geodetic survey of coordinates of inaccessible points, especially when only angle measurements are available, in this case, also called the triangulation method. However, the mathematical solution of the 3D forward intersection with the analytical definition of spatial lines, resolved by the Minimum Distances Method, is still not widespread in the academic and professional environment. This mathematical modeling determines the 3D coordinates of a point located in the middle of the minimum distance between two or more spatial lines, which spatially "intersect" towards the observation point. This solution is more accurate than others presented in the literature because it simultaneously solves the problem of 3D determination of a point by the method of least squares, in addition to providing an estimate of the coordinate precision, which are inherent to the adjustment. This work, therefore, has the objective of explaining the Minimum Distances Method for the spatial intersection of targeted measurements with a Total Station from two or more known observation points for the 3D determination of inaccessible points located in corners of buildings. For the analysis of the method, a Python tool was developed for QGIS that calculates the 3D coordinates and generates the adjustment processing report, being applied with real observations of the Geodetic survey of the SUDENE building, in Recife-PE. The methodology developed in this work proved to be suitable for measurements of large structures, achieving spherical precision better than ±1.0 cm, following the Brazilian standards for urban cadastre.