Searching of gapped repeats and subrepetitions in a word

A gapped repeat is a factor of the form $uvu$ where $u$ and $v$ are nonempty words. The period of the gapped repeat is defined as $|u|+|v|$. The gapped repeat is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its period. The gapped repeat is called $\alpha$-gapped if its period is not greater than $\alpha |v|$. A $\delta$-subrepetition is a factor which exponent is less than 2 but is not less than $1+\delta$ (the exponent of the factor is the quotient of the length and the minimal period of the factor). The $\delta$-subrepetition is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its minimal period. We reveal a close relation between maximal gapped repeats and maximal subrepetitions. Moreover, we show that in a word of length $n$ the number of maximal $\alpha$-gapped repeats is bounded by $O(\alpha^2n)$ and the number of maximal $\delta$-subrepetitions is bounded by $O(n/\delta^2)$. Using the obtained upper bounds, we propose algorithms for finding all maximal $\alpha$-gapped repeats and all maximal $\delta$-subrepetitions in a word of length $n$. The algorithm for finding all maximal $\alpha$-gapped repeats has $O(\alpha^2n)$ time complexity for the case of constant alphabet size and $O(n\log n + \alpha^2n)$ time complexity for the general case. For finding all maximal $\delta$-subrepetitions we propose two algorithms. The first algorithm has $O(\frac{n\log\log n}{\delta^2})$ time complexity for the case of constant alphabet size and $O(n\log n +\frac{n\log\log n}{\delta^2})$ time complexity for the general case. The second algorithm has $O(n\log n+\frac{n}{\delta^2}\log \frac{1}{\delta})$ expected time complexity

Daily Service Activity of Inner Guard Officer in the Russian Empire in the Middle of 19th Century

The aims of this article are: (1) delineation of the categories of “casual” and “normal” based on the results of the study of archival materials documenting the daily activities of the Internal guard troops, particularly their disciplinary and legal violations; (2) identification of the characteristics of the daily activities of the internal troops of the Russian Empire in the following areas: staffing the army, maintenance of public order, officers’ interpersonal relations. To achieve the said goals, the methods of historical research are used: systemic and narrative. The author claims that minor breaches of the discipline and regulations by military personnel of Separate corps of Internal guards were everyday in nature, but the recurrence did not legalize them, that is they did non become the norm of behaviour. The activity of the Inner guard in ensuring public order, restriction of access of citizens to drinking establishments could bring losses to the owners of such establishments. It is noteworthy that abuse of authority by an officer of the Inner guard (Lieutenant Strizhevsky) in the implementation of such actions was suppressed only by military and civil authorities at the level of the governorate. The everyday nature of the practice of evasion of the population from military service through the conclusion of an unintended legal agreements with the officers who carried out the recruitment were noted. The interaction between the commanders of the internal troops of awareness on the personal qualities of military personnel, transferring from unit to unit, was identified

Daily Official Activities of V. F. von der Launitz, Last Commander of Separate Corps of Internal Guard

The article is devoted to the last commander of a Separate corps of the Internal guard (SCIG) of the Russian Empire, Lieutenant General Vasily Fedorovich von der Launitz. The relevance of the topic is determined by the need to understand the historical experience of management decisions on the reorganization of the SCIG in the transformation of internal troops and the creation of Rosgvardia in Russia. A brief biography of V. F. von der Launitz is given. On the basis of the archival material first introduced into circulation, the content of the daily work of the commander of the SCIG is considered, which determines the novelty of the study. With the help of analysis of archival documents and scientific literature the main activities of V. F von der Launitz as commander of the SCIG are identified. The role of V. F von der Launitz in the decision to disband SCIG in the course of D. A. Milyutin’s military transformations is considered. It is concluded that V. F von der Launitz made every effort to ensure order and discipline in the corps entrusted to him, and its disbandment was induced by the general logic of the Milyutin’s reforms and cannot be blamed on the commander of the SCIG. It is reasonably assumed that a number of Milyutin’s reform decisions, including the abolition of the SCIG, were determined by his personal experience of service as chief of staff of a Separate Caucasian corps

Scratch-Healing Behavior of Ice by Local Sublimation and Condensation

[Image: see text] We show that the surface of ice is scratch healing: micrometer-deep scratches in the ice surface spontaneously disappear by thermal relaxation on the time scale of roughly an hour. Following the dynamics and comparing it to different mass transfer mechanisms, we find that sublimation from and condensation onto the ice surface is the dominant scratch-healing mechanism. The scratch-healing kinetics shows a strong temperature dependence, following an Arrhenius behavior with an activation energy of ΔE = 58.6 ± 4.6 kJ/mol, agreeing with the proposed sublimation mechanism and at odds with surface diffusion or fluid flow or evaporation–condensation from a quasi-liquid layer

Longest Common Extensions in Sublinear Space

The longest common extension problem (LCE problem) is to construct a data structure for an input string $T$ of length $n$ that supports LCE$(i,j)$ queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions $i$ and $j$ in $T$. This classic problem has a well-known solution that uses $O(n)$ space and $O(1)$ query time. In this paper we show that for any trade-off parameter $1 \leq \tau \leq n$, the problem can be solved in $O(\frac{n}{\tau})$ space and $O(\tau)$ query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.Comment: An extended abstract of this paper has been accepted to CPM 201

Spherical structures on torus knots and links

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formul{\ae} are presented.Comment: 17 pages, 5 figures; typo

Counterintelligence Activities of Gendarmerie Railway Police before and during World War I

The article analyzes the role of the gendarmerie railway police in the system of counterintelligence agencies in the Russian Empire before and during World War I. Based on documentary materials, the goals of enemy espionage on railways are revealed. Measures taken by the gendarmerie to restrict photography of railway infrastructure are examined. Through analysis of secret correspondence between gendarmerie leaders and railway department heads, categories of individuals most actively recruited by German and Austro-Hungarian intelligence for espionage are identified: prisoners of war, foreign nationals not involved in combat, and children. The organization of surveillance of foreign officials’ railway transport movements within the Russian Empire is also explored. The conclusion is drawn that the gendarmerie railway police’s ability to carry out counterintelligence tasks was complicated by their simultaneous duties as general and political police, as well as the scale of the infrastructure they were tasked with protecting

Gendarmerie Railway Police of Russian Empire in Early 20th Century: Working with Political Agents

The study examines the historical experience of interaction between the gendarmerie railway police of the Russian Empire and covert informants in political organizations. It explores the establishment of intelligence work on railways, the monitoring of its effectiveness, the verification of the reliability of secret agents, and the identification of provocateurs and blackmailers among them. The materials for analysis are extracted from previously unpublished secret and top-secret case files of the gendarmerie police departments of the railways. The authors provide their own definition of intelligence work. It is emphasized that priority was given to recruiting informants who had a financial interest in collaborating with the police. The study demonstrates that the value of information obtained by secret agents was the main criterion for evaluating the effectiveness of financial resources allocated to intelligence work. The authors highlight the need for caution in establishing relationships between railway gendarmes and informants due to the possibility of assassination attempts against handlers or the provision of misinformation. The study concludes that assigning the duty of recruiting political agents and obtaining information through them was justified by the need to suppress revolutionary movements, but inertia in acquiring informants and the scale of crises in the empire prevented the achievement of the set goal

Resonance vector mode locking

A mode locked fibre laser as a source of ultra-stable pulse train has revolutionised a wide range of fundamental and applied research areas by offering high peak powers, high repetition rates, femtosecond range pulse widths and a narrow linewidth. However, further progress in linewidth narrowing seems to be limited by the complexity of the carrier-envelope phase control. Here for the first time we demonstrate experimentally and theoretically a new mechanism of resonance vector self-mode locking where tuning in-cavity birefringence leads to excitation of the longitudinal modes sidebands accompanied by the resonance phase locking of sidebands with the adjacent longitudinal modes. An additional resonance with acoustic phonons provides the repetition rate tunability and linewidth narrowing down to Hz range that drastically reduces the complexity of the carrier-envelope phase control and so will open the way to advance lasers in the context of applications in metrology, spectroscopy, microwave photonics, astronomy, and telecommunications