On integer programming models for the maximum 2-club problem and its robust generalizations in sparse graphs

We consider the maximum 2-club problem, which aims at finding an induced subgraph of maximum cardinality with the diameter at most two. Such subgraphs arise from a popular diameter-based clique relaxation concept, as a subgraph is a clique if and only if its diameter is one. In a 2-club every pair of non-adjacent vertices has a common neighbor; this “2-hop” property naturally arises in a variety of applications. In this paper, by exploiting a somewhat different interpretation of the problem, we provide two new mixed-integer programming (MIP) models for finding maximum 2-clubs. Our MIPs provide much tighter linear programming (LP) relaxations for sufficiently sparse graphs and have fewer constraints than the standard integer programming (IP) model at the expense of having slightly more continuous variables. We also consider feasibility versions of our MIPs that verify whether there exists a 2-club of some specified size. Then we incorporate them into a simple-to-implement “feasibility-check” algorithm that iteratively solves one of the feasibility MIPs for each possible 2-club size within some known lower and upper bounds. The upper bound is obtained from an LP relaxation of our new MIPs and is shown to be sharp. Furthermore, we show how to extend our approaches for solving some “robust” (attack- and failure-tolerant) generalizations of the maximum 2-club problem. Finally, we perform an extensive computational study with randomly generated and real-life graphs to support our theoretical results and to provide some empirical observations and insights

Identification of critical paralog groups with indispensable roles in the regulation of signaling flow

Extensive cross-talk between signaling pathways is required to integrate the myriad of extracellular signal combinations at the cellular level. Gene duplication events may lead to the emergence of novel functions, leaving groups of similar genes - termed paralogs - in the genome. To distinguish critical paralog groups (CPGs) from other paralogs in human signaling networks, we developed a signaling network-based method using cross-talk annotation and tissue-specific signaling flow analysis. 75 CPGs were found with higher degree, betweenness centrality, closeness, and ‘bowtieness’ when compared to other paralogs or other proteins in the signaling network. CPGs had higher diversity in all these measures, with more varied biological functions and more specific post-transcriptional regulation than non-critical paralog groups (non-CPG). Using TGF-beta, Notch and MAPK pathways as examples, SMAD2/3, NOTCH1/2/3 and MEK3/6-p38 CPGs were found to regulate the signaling flow of their respective pathways. Additionally, CPGs showed a higher mutation rate in both inherited diseases and cancer, and were enriched in drug targets. In conclusion, the results revealed two distinct types of paralog groups in the signaling network: CPGs and non-CPGs. Thus highlighting the importance of CPGs as compared to non-CPGs in drug discovery and disease pathogenesis

Two-dimensional Sparse Antenna Array of a Passive Coherent Radar using a Parametric Algorithm of Signal Processing via the Section Method

Introduction. A two-dimensional configuration of the receiving antenna array (AA) is used to measure the angular coordinates of radar targets – azimuth and elevation. A transformation of one-dimensional uniform AA into a flat two-dimensional AA with a fixed number of antenna elements (AEs) and constant aperture size leads to a nonuniform arrangement of AE in the AA rows. As a result, the AA becomes sparse, which negatively affects the quality of the AA three-dimensional antenna pattern (AP). The section method based on the modified parametric Burg algorithm is a promising and relevant method for constructing directional characteristics. This method can be recommended for spatial processing of reflected signals in a passive coherent radar with a two-dimensional sparse receiving AA.Aim. To analyze the azimuthal and elevation sections of three-dimensional APs obtained using a modified Burg method for spatial processing of reflected signals in a passive coherent radar, the AEs of which are located horizontally and vertically with a step that is a multiple of the half the wavelength λ of the used illumination signal carrier oscillation.Materials and methods. The construction of directional characteristics was implemented via computer simulation in the MATLAB environment with the effect of uncorrelated additive complex normal noise on the receiving channels in each AE as an interference.Results. The possibility and conditions for the application of the modified parametric Burg method in the problems of single signal detecting and angular resolution of equal-power signals in a passive coherent radar, which includes a two-dimensional sparse AA, were determined. The obtained Burg method directional characteristics were compared with the directional characteristics obtained using conventional algorithms based on the discrete Fourier transform. The use of the Burg method allowed the AP side lobe level to be reduced to a practically acceptable level of -12 ... -17 dB at a signal to noise ratio 6 dB. In addition, the Rayleigh resolution of signals in the AA was significantly improved.Conclusion. The presented modified Burg method is suitable for signal processing in two-dimensional sparse AA, subject to restrictions on the AE placing method and the AA aperture size. This allows the Burg method to be recommended for use in passive coherent radars

Verifying Measurements of Surface Current Velocities by X-Band Coherent Radar Using Drifter Data

Introduction. Conventional contact measurements of hydrographic parameters frequently fail to provide the necessary accuracy of data in the field of water area monitoring. This problem can be solved using coherent radars enabling direct measurements of surface current velocities.Aim. To establish the accuracy of surface current velocities measured by a Doppler radar using drifter data.Materials and methods. In June 2022, coastal operational oceanography studies were conducted at the hydrophysical test site of the Institute of Oceanology of the Russian Academy of Sciences in the Black Sea near Gelendzhik. Measurements were carried out using a coherent X-band radar installed on the Ashamba research vessel simultaneously with drifter experiments using Lagrangian drifters of the near-surface layer with an underwater 0.5 m sail. Coordinates were transmitted via mobile communication. The drifter data on the current velocity and direction were used to verify radar measurements. Measurements were taken onboard of the research vessel at a low speed and different distances from the shore, near the drifters. The tracks of the vessel and drifters were recorded simultaneously. Processing of the radar data involved obtaining Doppler spectra of signals to estimate the dynamic processes on the sea surface, including the current velocity.Results. Radial components of the near-surface current velocity were calculated. Then, the current velocity values obtained based on the drifter and radar data were compared.Conclusion. The present work makes a contribution to the advancement of methods for measuring surface currents from the board of a moving ship by Doppler radars. The obtained results confirm the suitability of the radar hardware and software and signal processing algorithms for measuring currents. The radar measurement data were found agree well with drifter data in the velocity range from 15 cm/s

КОРОТКОВОЛНОВАЯ РАДИОЛОКАЦИЯ В СИСТЕМЕ МОНИТОРИНГА ПРИБРЕЖНЫХ АКВАТОРИЙ

Introduction. The modern approach for ensuring marine activities of necessary quality related to the assessment of current information on the state of the ocean environment in Russia is clearly insufficient. The development of operational methods and instruments of observation, as well as the assessment of the state of the ocean and its forecast naturally determine such an approach. Therefore, the development of the concept, tools and methods of obtaining data is an urgent task of the operational Oceanography formation.Objective. The objective of the paper is to con-sider the concept of ocean surface monitoring using short-wave surface wave radar.Methods and materials. The paper presents a number of specific Oceanologic examples that require operational monitoring of the state of coastal waters of the oceans and individual regions. Also, it describes observational systems used in other countries. The paper pays special attention for the development of radar sensing of surface waters, carried out in our country occasionally. The resonant nature of the reflections gives the opportunity to obtain maps of high-precision measurements of surface currents and wave characteristics on the long-range area in real time. The paper notes difficulties of the experiments implementation and the results interpretation, shows the insistent issues for the establishment of the ocean surface operational monitoring, and gives the approaches for solvation of the existing problems. The paper formulates the main task of the world ocean parameters forecast for ensuring of the sea transport safety from natural and anthropogenic threats, as well as formulates the problems solution of effective nature management.Results. The paper shows that the optimal means of natural data acquisition is the creation of an observation network of coastal HF radars, which enables to assess surface currents and wave characteristics, as well as to solve the problem of monitoring. It is Important to develop an adequate coastal model and correlate its parameters with experimental data. The adaptive modeling and monitoring by modern technical means can overcome inadequacy of physical models to specific natural conditions can.Conclusion. By assimilation in hydrodynamic and wave models, these data become applicable in spatial mapping of hydrophysical inhomogeneities of the water layer, sound velocity, and underwater acoustic noise.Введение. Современный подход к обеспечению необходимого качества морской деятельности, связанный с оценкой текущей информации о состоянии океанической среды в России, явно недостаточен. Указанный подход определяется развитием оперативных методов и инструментария наблюдения, а также оценкой состояния океана и его прогноза. Поэтому развитие концепции, инструментария и разработка методов получения данных является актуальной задачей становления оперативной океанографии.Цель работы. Рассмотрение концепции мониторинга морской поверхности с использованием коротковолновой радиолокации поверхностной волны.Методы и материалы. Представлен ряд конкретных океанологических примеров, требующих оперативного мониторинга состояния прибрежных вод мирового океана и отдельных регионов. Описаны наблюдательные системы, используемые в других странах. Особое внимание уделено развитию радиолокационного зондирования поверхностных вод, проводимого в нашей стране эпизодически. Резонансные отражения позволяют получать карты высокоточных измерений поверхностных течений и характеристик волнения на большой площади в реальном масштабе времени. Отмечены трудности проведения экспериментов и интерпретации результатов, выделены вопросы, требующие особого внимания для создания оперативного мониторинга морской поверхности, и методы их решения. Сформулирована основная задача прогноза параметров мирового океана с целью обеспечения безопасности морского транспорта от природных и антропогенных угроз, а также решения задач эффективного природопользования.Результаты. Показано, что оптимальным средством получения натурных данных служит создание наблюдательной сети из прибрежных коротковолновых радиолокаторов, позволяющей оценивать поверхностные течения и характеристики волнения, а также в целом решать задачу мониторинга. Отмечено, что важным элементом является разработка адекватной прибрежной модели и соотнесение ее параметров с экспериментальными данными. Неадекватность физических моделей конкретным природным условиям преодолевается адаптивным моделированием и мониторингом с помощью современных технических средств.Заключение. Ассимилируясь в моделях гидродинамики и волнения, эти данные становятся применимыми при пространственном картировании гидрофизических неоднородностей водного слоя, скорости звука и подводных акустических шумов

О верификации измерений скорости поверхностных течений когерентным радаром СВЧ-диапазона с помощью дрифтеров

Introduction. Conventional contact measurements of hydrographic parameters frequently fail to provide the necessary accuracy of data in the field of water area monitoring. This problem can be solved using coherent radars enabling direct measurements of surface current velocities.Aim. To establish the accuracy of surface current velocities measured by a Doppler radar using drifter data.Materials and methods. In June 2022, coastal operational oceanography studies were conducted at the hydrophysical test site of the Institute of Oceanology of the Russian Academy of Sciences in the Black Sea near Gelendzhik. Measurements were carried out using a coherent X-band radar installed on the Ashamba research vessel simultaneously with drifter experiments using Lagrangian drifters of the near-surface layer with an underwater 0.5 m sail. Coordinates were transmitted via mobile communication. The drifter data on the current velocity and direction were used to verify radar measurements. Measurements were taken onboard of the research vessel at a low speed and different distances from the shore, near the drifters. The tracks of the vessel and drifters were recorded simultaneously. Processing of the radar data involved obtaining Doppler spectra of signals to estimate the dynamic processes on the sea surface, including the current velocity.Results. Radial components of the near-surface current velocity were calculated. Then, the current velocity values obtained based on the drifter and radar data were compared.Conclusion. The present work makes a contribution to the advancement of methods for measuring surface currents from the board of a moving ship by Doppler radars. The obtained results confirm the suitability of the radar hardware and software and signal processing algorithms for measuring currents. The radar measurement data were found agree well with drifter data in the velocity range from 15 cm/s.Введение. Традиционные контактные средства измерений гидрографических параметров зачастую не обеспечивают необходимую оперативность получаемых данных для решения задач мониторинга акваторий. Перспективным направлением является применение когерентных радаров, позволяющих непосредственно измерять скорости поверхностных течений.Цель работы. Оценка достоверности результатов измерений приповерхностной скорости течения доплеровским радаром сравнением с данными дрифтеров.Материалы и методы. В июне 2022 г. был проведен эксперимент по прибрежной оперативной океанографии в Черном море на акватории гидрофизического полигона "Геленджик" Южного отделения Института океанологии РАН с использованием доплеровского радара. Скорость течения измерялась когерентизированным навигационным радиолокатором сантиметрового диапазона с цифровой обработкой, установленным на научноисследовательском судне "Ашамба", одновременно с дрифтерными экспериментами с использованием лагранжевых дрифтеров приповерхностного слоя с подводным парусом высотой 0.5 м, с передачей координат по мобильной связи. Данные дрифтеров о скорости и направлении течения использовались для верификации радарных измерений. Измерения проводились с борта научно-исследовательского судна на малом ходу на различном расстоянии от берега, вблизи дрифтеров. В процессе измерений осуществлялась запись треков судна и дрифтеров. Обработка данных радиолокатора основана на исследовании спектральных характеристик отраженного сигнала, позволяющих оценивать динамические процессы на морской поверхности.Результаты. По результатам обработки доплеровских спектров были получены радиальные составляющие скорости приповерхностных течений, далее было выполнено сопоставление скорости течений по данным дрифтеров и данным радиолокации.Заключение. Настоящая работа является определенным шагом в усовершенствовании методов измерений поверхностных течений с борта движущегося судна доплеровским радаром. Результаты верификации подтверждают пригодность аппаратно-программной части радара и алгоритмов обработки сигнала для измерения течений. Данные радиолокационных измерений хорошо согласуются с данными дрифтеров в диапазоне скоростей от 15 см/с

Critical node detection with connectivity based on bounded path lengths

For a given graph representing a transparent optical network, a given weight associated to each node pair and a given positive integer c, the Critical Node Detection problem variant addressed here is the determination of the set of c nodes that, if removed from the graph, minimizes the total weight of the node pairs that remain connected. In the context of transparent optical networks, a node pair is considered connected only if the surviving network provides it with a shortest path not higher than a given positive value T representing the optical transparent reach of the network. Moreover, the length of a path depends both on the length of its links and on its number of intermediate nodes. A path-based Integer Linear Programming model is presented together with a row generation approach to solve it. We present computational results for a real-world network topology with 50 nodes and 88 links and for c=2 up to 6. The optimal results are compared with node centrality based heuristics showing that such approaches provide solutions which are far from optimal.publishe