scholarly journals Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 228
Author(s):  
Rasoul Shafipour ◽  
Gonzalo Mateos
Keyword(s):  
Inverse Problem ◽  
Covariance Matrix ◽  
A Priori ◽  
Dynamic Network ◽  
Streaming Data ◽  
Optimal Time ◽  
Time Varying ◽  
Graph Learning ◽  
Topology Inference ◽  
Diffusion Dynamics

We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

General decay synchronization of complex multi-links time-varying dynamic network

2019 ◽  
Vol 67 ◽  
pp. 108-123 ◽  
Author(s):  
Mingwen Zheng ◽  
Lixiang Li ◽  
Haipeng Peng ◽  
Jinghua Xiao ◽  
Yixian Yang ◽  
...  
Keyword(s):  
Dynamic Network ◽  
General Decay ◽  
Time Varying

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

scholarly journals Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 85
Author(s):  
Andreas Rauh ◽  
Julia Kersten
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
A Priori ◽  
Real Life ◽  
Reachability Analysis ◽  
Interval Methods ◽  
Space Representation ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Similarity Transformations

Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.

Assembly method in GIS INTEGRO and its usage for solving of gravitational inverse problem

2021 ◽  
pp. 36-47
Author(s):  
Sergey Mitsyn ◽  
Egor Bolshakov
Keyword(s):  
Inverse Problem ◽  
A Priori ◽  
Regional Scale ◽  
Original Formulation ◽  
Model Evolution ◽  
Assembly Method ◽  
Practice Methods

Various methods based on growing bodies are lately gaining attention in a context of inverse gravity problem that we call a family of “assembly methods”. A variant of method was adopted for GIS INTEGRO in original formulation that is fit for the problem of multiple bodies incorporated in an environment of varying density, in absolute densities (not density contrasts) that are however have to be a priori specified. Such formulation allowed the implementation of the method that is suitable for territory modeling in the regional scale. To workaround method’s instability a number of changes are proposed that consist of introduction of priority on atomic modifications, modification queue and assessment of model evolution instead of just the final result. The developed software allows processing of large grids (tens of millions of tiling elements) even on 5–8 year old desktops. Based on method approbation experience some insights and practice methods are presented. An application example is presented as part of work on modeling of Enisei-Khatanga regional depression territory.

scholarly journals Fisuras de contracción en pavimentos de hormigón y el aserrado de juntas

2013 ◽  
Vol 3 (2) ◽  
pp. 111-121
Author(s):  
M. F. Barreda ◽  
M. J. Naber ◽  
I. Quispe Sallo ◽  
J. D. Sota
Keyword(s):  
A Priori ◽  
Ultrasonic Pulse ◽  
Optimal Time ◽  
Hardened Concrete ◽  
Concrete Pavements ◽  
Maintenance Costs ◽  
Shrinkage Cracks ◽  
Contraction Joints ◽  
First Results ◽  
The Right

RESUMENLos cambios volumétricos por variaciones de temperatura y contenido de humedad en el hormigón endurecido de los pavimentos, que por sus restricciones impiden su deformación, causan tensiones de tracción, provocando fisuras aleatorias. La presencia de fisuras de contracción en los pavimentos de hormigón, reducen su vida útil y generan costos de mantenimiento importantes. Es necesario definir a priori la ubicación de las fisuras aserrando el pavimento. Las zonas aserradas crean planos de debilidad donde se forman las fisuras, siendo crítico el momento oportuno para realizar el aserrado de las juntas de contracción en los pavimentos. El período óptimo para efectuar el aserrado se denomina ventana de aserrado. El objetivo de este trabajo es (poner objetivo). Entre los resultados obtenidos se puede decir que (dar resultados). Los estudios son parte de un Proyecto de I+D.Palabras Clave: contracción; hormigón; pavimentos; juntas; fisuras.ABSTRACTIn the hardened concrete of pavements, with limited deformation, volumetric changes due to variations in temperature and humidity cause tensile stresses, with subsequent cracks random. The presence of shrinkage cracks in concrete pavements, reduces its service life and generates substantial maintenance costs. It is necessary to define a priori the location of cracks, by sawing the pavement. Sawn areas create planes of weakness where cracks form, being critical the right time to saw the contraction joints in pavements. The optimal time to perform the sawing is called sawing window. In this paper the first results about concrete pavements are recorded, establishing sawing times, comparing cylindrical compressive strength, maturity of concrete and ultrasonic pulse values. The studies are part of a R & D project.Keywords: contraction; concrete; pavements; joints; cracks.

scholarly journals Dynamic Optimization of a Subcritical Steam Power Plant under Time-Varying Power Load

2018 ◽  
Author(s):  
Chen Chen ◽  
George M. Bollas
Keyword(s):  
Power Plant ◽  
Dynamic Optimization ◽  
Electricity Market ◽  
Optimization Problems ◽  
Optimal Time ◽  
Time Varying ◽  
Power Demand ◽  
Test Bed ◽  
Simulation And Optimization ◽  
Power Load

The increasing variability in power plant load, in response to a wildly uncertain electricity market and the need to to mitigate CO2 emissions, lead power plant operators to explore advanced options for efficiency optimization. Model-based, system-scale dynamic simulation and optimization are useful tools in this effort, and the subject of the work presented here. In prior work, a dynamic model validated against steady-state data from a 605 MW subcritical power plant was presented. This power plant model is used as a test-bed for dynamic simulations, in which the coal load is regulated to satisfy a varying power demand. Plant-level control regulates plant load to match an anticipated trajectory of the power demand. The efficiency of the power plant operating at varying load is optimized through a supervisory control architecture that performs set point optimization on the regulatory controllers. Dynamic optimization problems are formulated to search for optimal time-varying input trajectories that satisfy operability and safety constraints during the transition between plant states. An improvement in time-averaged efficiency of up to 1.8% points is shown feasible with corresponding savings in coal consumption of 184.8 tons/day and carbon footprint decrease of 0.035 kg/kWh.

scholarly journals Optimum Flows in Directed Bipartite Dynamic Network. The Static Approach

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Combinatorial Optimization ◽  
Network Flow ◽  
Dynamic Network ◽  
Time Varying ◽  
Flow Models ◽  
Dynamic Network Flow ◽  
Static Approach ◽  
Network Flow Models ◽  
Discrete Values ◽  
Time Expanded Network

The theory of flows is one of the most important parts of Combinatorial Optimization and it has various applications. In this paper we study optimum (maximum or minimum) flows in directed bipartite dynamic network and is an extension of article [9]. In practical situations, it is easy to see many time-varying optimum problems. In these instances, to account properly for the evolution of the underlying system overtime, we need to use dynamic network flow models. When the time is considered as a variable discrete values, these problems can be solved by constructing an equivalent, static time expanded network. This is a static approach.

scholarly journals The Neuroelectromagnetic Inverse Problem and the Zero Dipole Localization Error

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Rolando Grave de Peralta ◽  
Olaf Hauk ◽  
Sara L. Gonzalez
Keyword(s):  
Inverse Problem ◽  
Unique Solution ◽  
A Priori ◽  
Inverse Solution ◽  
Localization Error ◽  
A Priori Information ◽  
Dipole Localization ◽  
Inverse Solutions ◽  
Priori Information ◽  
Additional Constraints

A tomography of neural sources could be constructed from EEG/MEG recordings once the neuroelectromagnetic inverse problem (NIP) is solved. Unfortunately the NIP lacks a unique solution and therefore additional constraints are needed to achieve uniqueness. Researchers are then confronted with the dilemma of choosing one solution on the basis of the advantages publicized by their authors. This study aims to help researchers to better guide their choices by clarifying what is hidden behind inverse solutions oversold by their apparently optimal properties to localize single sources. Here, we introduce an inverse solution (ANA) attaining perfect localization of single sources to illustrate how spurious sources emerge and destroy the reconstruction of simultaneously active sources. Although ANA is probably the simplest and robust alternative for data generated by a single dominant source plus noise, the main contribution of this manuscript is to show that zero localization error of single sources is a trivial and largely uninformative property unable to predict the performance of an inverse solution in presence of simultaneously active sources. We recommend as the most logical strategy for solving the NIP the incorporation of sound additional a priori information about neural generators that supplements the information contained in the data.

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