Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria

Permanence and Global Attractivity of a Discrete Logistic Model with Impulses

By piecewise Euler method, we construct a discrete logistic equation with impulses. The constructed model is more easily implemented at computer and is a better analogue of the continuous-time dynamic system. The dynamic behaviors of the constructed model are investigated. Sufficient conditions which guarantee the permanence and the global attractivity of positive solutions of the model are obtained. Numerical simulations show the feasibility of the main results

Optimal Distributed Controller Design for Nonlinear Coupled Dynamical Networks

This paper is concerned with the optimal distributed impulsive controller design for globally exponential synchronization of nonlinear dynamical networks with coupling delay. By the Lyapunov-Razumikhin method, a novel criterion is proposed to guarantee the global exponential synchronization of the coupled delayed network with distributed impulsive control in terms of matrix inequalities. The sum of coupling strengths of the distributed impulsive control is minimized to save the control effort. Finally, the effectiveness of the proposed method has been demonstrated by some simulations

Necessary and sufficient condition for the global stability of a delayed discrete-time neuron model

Positron emission tomography (PET) studies acquired in list mode offer the opportunity to provide a cine loop showing the dynamics of 18F- PET uptake, giving a visualization of regional bone remodeling. The focus of this report is a group of patients treated with Taylor spatial frames (TSF). The studies were acquired for a period of 45 minutes and saved in list mode. The list was decoded and subsequently segmented into time intervals of one minute each. For each time interval a sinogram was generated from which volumes of one minute each were reconstructed. Slices projected from these volumes could then be displayed as a dynamic loop superimposed on the corresponding computed tomography (CT) slice in order to visualize the 18F- uptake insitu. It was indicated that this technique has the potential of becoming an additional technique to that of using static volumes and SUV values only. As the list mode data was decoded it also offered a method to evaluate the potential decrease in injected activity by eliminating every Nth event from the list before reconstructing the 45 minute volume. This was done and the indication was that the injected activity and hence the effective dose to the patient can be decreased. However, in this work, this was not proven clinically. The open source STIR software was used to reconstruct volumes from sinograms to enable an unlimited access to reconstructing volumes without disturbing the daily routine at the clinic. The data was acquired on a clinical Siemens Medical Solutions Biograph 64 TruePoint TrueV, PET/CT scanner situated at the Nuclear Medicine Department at the Karolinska University Hospital in Solna. This scanner was not supported by the STIR software, hence the data collected by the Siemens PET/CT scanner was translated so that 3D reconstructions could be computed using the STIR tools. The reconstructions made in STIR resulted in volumes of sufficient visual quality, but not as good as those reconstructed by the scanner itself. Further optimization in STIR was left for future work. According to the physicians who treat these patients, dynamic visualization was of sufficient interest to continue to develop and optimize this method. The cine loops that were presented to the physicians were made from JPEG slices produced from the one minute volumes and put together as GIF files. It was also possible to vary the reconstruction time (from uniformly one minute) as well as the presentation rate in the cine loop, but this was left for future work. Ultimately, the cine loop will be implemented in the locally developed software tool.Positronemissionstomografi (PET) studier som förvärvats i list mode erbjuder möjligheten att göra film slingor som visar dynamiken i 18F- PET upptag. Detta förväntas ge en dynamisk visualisering av var ben nybildas. Fokus i denna rapport är en grupp patienter som behandlats med Taylor spatial frames (TSF). Bilderna i studien förvärvades under en period av 45 minuter och sparades i list mode. List mode data avkodades och delades därefter upp i tidsintervaller på en minut vardera. För varje tidsintervall rekonstruerades ett sinogram för vilka bilder av volymen rekonstruerades. Skivor från dessa volymer kan sedan visas som en dynamisk slinga ovanpå motsvarande datortomografi (CT) skiva för att visualisera 18F- upptaget in situ. Denna teknik visade sig ha potential att bli en ytterligare teknik utöver de statiska volymer och SUV-värden som redan finns tillgängliga. Eftersom listmode data avkodats erbjuds också en metod för att utvärdera en potentiell minskning av den injicerade aktivitet genom att eliminera varje N: te händelse från listan innan volymen på 45 minuter rekonstrueras. Detta utfördes och det visade sig att den injicerade aktiviteten och därmed den effektiva dosen till patienten potentiellt kan minskas men i detta arbete har detta inte bevisats kliniskt. Mjukvaran STIR, som är tillgängligt för allmänheten, användes för att rekonstruera volymer från sinogram för att möjliggöra en obegränsad tillgång till att rekonstruera volymer utan att störa den dagliga rutinen på kliniken. Data förvärvades i en klinisk Siemens Medical Solutions Biograph 64 TruePoint TrueV, PET/CT-skanner som är placerad vid nuklearmedicinska avdelningen vid Karolinska Universitetssjukhuset i Solna. Skannern var inte kompatibel med STIR mjukvaran. Därför översattes det data som samlats in av Siemens PET/CT-skannern så att 3D-rekonstruktioner kan beräknas med hjälp av verktygen i STIR. De rekonstruktioner som gjorts i STIR gav upphov till volymer av tillräcklig visuell kvalitet för denna studie, men var inte lika bra som de som rekonstrueras genom själva skannern. Ytterligare optimering i STIR lämnades för framtida arbete. Enligt de läkare som behandlar dessa patienter var en dynamisk visualisering av tillräckligt intresse att fortsätta utveckla och optimera den här metoden. Film slingor som presenterades för läkarna gjordes från JPEG bilder tagna från skivor av volymer på en minut vardera som producerats och sattes ihop som GIF-filer. Det var också möjligt att variera återuppbyggnadstiden (från jämnt en minut) samt presentationshastigheten i film slingan, men detta lämnades till framtida arbetet. I slutändan kommer film slingan implementeras i ett lokalt utvecklat verktyg.QC 20151102</p

Global Synchronization of Complex Networks with Discrete Time Delays on Time Scales

This paper studies the global synchronization problem for a class of complex networks with discrete time delays. By using the theory of calculus on time scales, the properties of Kronecker product, and Lyapunov method, some sufficient conditions are obtained to ensure the global synchronization of the complex networks with delays on time scales. These sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). The main contribution of the result is that the global synchronization problems with both discrete time and continuous time are unified under the same framework