Universality of opinions disappearing in sociophysical models of opinion dynamics: From initial multitude of opinions to ultimate consensus.

Possibility of reaching a consensus in social systems with strong initial fragmentation is one of the most interesting issues in sociophysics. It is also intriguing what the dynamics of such processes is. To address those problems, we performed computer simulations using well-established models of social opinion formation, namely, the voter, Sznajd, and Latané models. We investigated opinion dynamics in cases where the initial number of opinions is very large, equal to the number of actors (the voter and Latané models) or when every second actor has their own opinion (Sznajd model), with some variations on the update schemes, lattice topologies, effective ranges of interaction, and information noise levels. For all considered models, the number of opinions assumed by the actors is finally almost always reduced to only one. However, while the voter and Latané models exhibit a power-law time decrease in the number of opinions, the Sznajd model follows a complex three-stage behavior. We also demonstrated the mean/median time of reaching the consensus scales with system size according to a power law for voter and Sznajd models, while for the Latané model, this increase is even faster. Our results show that in the studied models, the consensus is possible, provided that a long enough and model-dependent time to reach this state is available.

Conformity and Mass Media Influence in the Sznajd Model on Regular Lattices.

The polarization of opinions and difficulties in reaching a consensus are central problems of many modern societies. Understanding the dynamics governing those processes is, therefore, one of the main aims of sociophysics. In this work, the Sznajd model of opinion dynamics is investigated with Monte Carlo simulations performed on four different regular lattices: triangular, honeycomb, and square with von Neumann or Moore neighborhood. The main objective is to discuss the interplay of the probability of convincing (conformity) and mass media (external) influence and to provide the details of the possible phase transitions. The results indicate that, while stronger bonds and openness to discussion and argumentation may help in reaching a consensus, external influence becomes destructive at different levels depending on the lattice.

Thermal properties of structurally balanced systems on classical random graphs.

The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) under the influence of the temperature modeling the social noise level are discussed for interacting actors occupying nodes of classical random graphs. Depending on the graph density D, either a smooth crossover or a first-order phase transition from a balanced to an imbalanced state of the system is observed with an increase in the thermal noise level. The minimal graph density Dmin for which the first-order phase transition can be observed decreases with the system size N as Dmin∝N-0.58(1). For graph densities D>Dmin, the reduced critical temperature Tc⋆=Tc/Tc(D=1) increases with the graph density as Tc⋆∝D1.719(6) independently of the system size N.

Thermal properties of structurally balanced systems on diluted and densified triangulations.

The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) are discussed for various networks of interacting actors under the influence of the temperature modeling the social noise level. For that purpose, two main types of lattices are considered. The first is created by removing some links from a regular triangular lattice to produce a diluted triangular lattice, and the second by adding more links to create an enhanced triangular lattice. In both those cases, the full range of possible graph densities is discussed, limited by the extreme cases of networks which consist of a small number of separated triads and fully connected networks. It is shown that the existence of the balanced state is not possible if the average node degree is too close to the value characterizing the regular triangular lattice. Otherwise, both balanced (or partially balanced) and imbalanced states are possible, depending on the temperature. However, only for graphs which are dense enough a phase transition of the first kind is observed, while less enhanced networks (and all diluted) indicate a smooth crossover between the two states. The crossover temperatures are size independent only for the diluted triangular lattices and depend on the size of the system for the enhanced triangular lattices, as is the case also for the critical temperatures of the phase transition observed in denser enhanced lattices.

Phase-space studies of backscattering diffraction of defective Schrödinger cat states.

The coherent superposition of two well separated Gaussian wavepackets, with defects caused by their imperfect preparation, is considered within the phase-space approach based on the Wigner distribution function. This generic state is called the defective Schrödinger cat state due to this imperfection which significantly modifies the interference term. Propagation of this state in the phase space is described by the Moyal equation which is solved for the case of a dispersive medium with a Gaussian barrier in the above-barrier reflection regime. Formally, this regime constitutes conditions for backscattering diffraction phenomena. Dynamical quantumness and the degree of localization in the phase space of the considered state as a function of its imperfection are the subject of the performed analysis. The obtained results allow concluding that backscattering communication based on the defective Schrödinger cat states appears to be feasible with existing experimental capabilities.

Expulsion from structurally balanced paradise.

We perform simulations of structural balance evolution on a triangular lattice using the heat-bath algorithm. In contrast to similar approaches-but applied to the analysis of complete graphs-the triangular lattice topology successfully prevents the occurrence of even partial Heider balance. Starting with the state of Heider's paradise, it is just a matter of time when the evolution of the system leads to an unbalanced and disordered state. The time of the system relaxation does not depend on the system size. The lack of any signs of a balanced state was not observed in earlier investigated systems dealing with the structural balance.

The Heider balance and the looking-glass self: modelling dynamics of social relations.

We consider the dynamics of interpersonal relations which leads to balanced states in a fully connected network. Here this approach is applied to directed networks with asymmetric relations, and it is generalized to include self-evaluation of actors, according to the 'looking-glass self' theory. A new index of self-acceptance is proposed: the relation of an actor to him/herself is positive, if the majority of his/her positive relations to others are reciprocated. Sets of stable configurations of relations are obtained under the dynamics, where the self-evaluation of some actors is negative. Within each set all configurations have the same structure.

The effect of stent coating on stent deliverability: direct randomised comparison of drug eluting and bare metal stents using the same stent platform.

BACKGROUND: There is certain experimental and clinical evidence indicating that the covering of bare metal stents (BMS) with drug eluting polymers to produce drug eluting stents (DES) results in increased stent stiffness and modifies the mechanical properties of the stent platform. In addition, it has been speculated that the mechanical performance of DES, compared to BMS, may be related to the type of polymer used to cover stents. AIM: We aimed at evaluating the deliverability of DES with a lactate based biodegradable polymer and BMS in patients with stable coronary artery disease in a prospective randomised study. METHODS: One hundred eleven consecutive patients (age: 36-77, mean 58.8 years) scheduled for routine angioplasty due to stable coronary disease were randomised to receive BMS (Chopin II(TM), Balton, Poland) or paclitaxel eluting stent (Chopin Luc(TM), Balton, Poland) using the same metal platform. Only patients scheduled for angioplasty using the direct implantation technique of a single stent were randomised. The exclusion criteria included patients 〉 80 years, multivessel disease and reference diameter of the target vessel 〉 3.5 mm. RESULTS: In the BMS group (n = 55; 35 males and 20 females), the mean diameter of implanted stents was 3.09 ± 0.40 and the mean length was 11.37 ± 2.80, whereas in the DES group (n = 56; 34 males and 22 females) the mean stent sizes were 3.02 ± 0.34 and 17.90 ± 7.38 mm, respectively (p 〉 0.05 for length). The groups did not significantly differ regarding the frequency of stent implantation to particular coronary vessels. The direct stenting technique was attempted and failed, leading to the stents' implantation after predilatation in five patients in the BMS group and six patients in the DES group. Failure of stent implantation and subsequent implantation of another stent type was observed in no BMS patients and in one DES patient (NS). CONCLUSIONS: Although stent covering with lactate based drug eluting polymer may increase its stiffness, it does not affect its deliverability in patients with stable coronary disease.

Functional assessment of patients after percutaneous mitral valvuloplasty with Carillon™ device: a preliminary report.

BACKGROUND: Functional mitral regurgitation (MR) due to dilated cardiomyopathy or coronary artery disease remains a significant clinical problem. These clinical entities lead to left ventricular enlargement, which results in annular dilation and MR. Surgical valvuloplasty is associated with a high perioperative risk. This is the reason why percutaneous techniques for mitral valve repair are under development. One of the most advanced devices for mitral annuloplasty is the Carillon™ system. AIM: Functional assessment of patients who have undergone mitral annuloplasty using the Carillon™ device. METHODS: Fourteen consecutive patients with functional MR who had undergone successful implantation of the Carillon™ device were enrolled. The device was implanted into the venous system of the heart and applied tension to the mitral annulus in order to improve coaptation of the cusps and reduce MR. In implanted patients echocardiographic MR parameters (vena contracta, effective regurgitant orifice area) were assessed before, immediately after the procedure and during 1-month follow-up. Furthermore, the 6-minute walk test (6MWT), Naughton stress test and the NYHA functional class assessment were performed before the procedure and at 1 month. Quality of life was evaluated by the Kansas City Cardiomyopathy Questionnaire. One month after the procedure patients were also asked to compare their health status with their baseline condition. RESULTS: In implanted patients improvement of echocardiographic MR parameters was observed, both immediately after the procedure and during 1 month follow-up. These parameters included vena contracta (0.36 ± 0.03 and 0.31 ± 0.03 vs 0.65 ± ± 0.04 cm, both p < 0.001) as well as effective regurgitant orifice area (0.18 ± 0.02 and 0.20 ± 0.02 vs 0.28 ± 0.04 cm², p < 0.05 and p < 0.005, respectively). One month after the procedure the 6MWT (390 ± 26.25 vs 311.9 ± 15.71 m, p < 0.001), Naughton treadmill exercise test (5.06 ± 0.47 vs 3.49 ± 0.27 min, p < 0.005) and NYHA classification (1.93 ± ± 0.20 vs 2.93 ± 0.07, p < 0.005) were significantly improved. Quality of life improved from 67.93 ± 3.30 at baseline to 88.31 ± 4.02 at 1 month (p < 0.001). All the patients reported some degree of improvement at 1 month compared to baseline. CONCLUSIONS: Implantation of the Carillon™ device in patients with functional MR leads to increased exercise capacity and improvement of selected echocardiographic MR parameters. Randomised trials are needed to assess the clinical value of the technique. Kardiol Pol 2011; 69, 3: 228-233.

Echocardiographic evaluation of percutaneous valve repair in patients with mitral regurgitation using the CARILLON system.

BACKGROUND: Dilated cardiomyopathy is characterised by significant enlargement of cardiac chambers, which can lead to functional mitral regurgitation. Surgery is a widely accepted treatment of secondary mitral regurgitation. Conventional cardiac surgery has a high procedural risk and therefore new techniques for percutaneous repair of mitral valve are being developed. The CARILLON system is one of devices that is implanted into the coronary venous system, which enables tension of the mitral ring in order to improve coaptation of the leaflets. AIM: Echocardiographic analysis of the CARILLON system implantation efficacy evaluated directly and one month after implantation. METHODS: The study in included 9 patients, aged 58.56 +/- 6 years, with severe functional mitral regurgitation, who fulfilled the following echocardiographic criteria: large central jet l 4 cm(2) or l 20% of the left atrium area or wall-impinging eccentric jet reaching the pulmonary veins, vena contracta (VC) l 0.30 cm, effective regurgitant orifice area (ERO) l 0.2 cm(2), regurgitant volume (RV) l 30 ml or regurgitant fraction (RF) > 30%. Exclusion criteria were: concomitant severe tricuspid valve insufficiency, significant organic mitral valve pathology, chronic atrial fibrillation, foreign body in the coronary sinus, or thrombus in the left atrial appendage. The prerequsite for implanting the device was a significant reduction in the mitral regurgitation jet observed by transesophageal echo-cadiography (TEE), seen during the procedure. After one month, a transthoracic echocardiography (TTE) was performed to evaluate mitral regurgitation by analysing the same parameters assessed before implanting CARILLON to the coronary sinus. RESULTS: A significant improvement of VC after the procedure, in comparison to the value before the procedure (0.43 +/- 0.12 vs. 0.66 +/- 0.14 cm, p < 0.05), was observed. This improvement was lower one month after the implantation of the device (0.35 +/- 0.1 cm, p < 0.005). The ratio of the jet area to the left atrial area was reduced from 54.96 +/- 11.18% to 38.57 +/- 9.79% (p < 0.005) and sustained after a month at 36.33 +/- 10.15% (p < 0.005). Other echocardiographic parameters of evaluation of mitral regurgitation tended to improve, however the differences did not reach statistical significance. The ERO in subsequent studies was: 0.25 +/- 0.09 cm(2), 0.23 +/- 0.07 cm(2), and 0.24 +/- 0.07 cm(2), and RV decreased from 33.06 +/- 11.81 ml before the procedure, to 32.33 +/- 7.84 ml one month after the procedure. CONCLUSIONS: The CARILLON system implantation to the coronary venous system in patients with secondary mitral regurgitation can lead to the improvement of selected echocardiographic indices of mitral regurgitation.

Percutaneous valve repair for mitral regurgitation using the Carillon Mitral Contour System. Description of the method and case report.

Mitral regurgitation may result from left ventricular dilatation and cause progression of heart failure. Percutaneous techniques for mitral valve repair are under development. Techniques utilizing a trans-coronary venous approach exploit the anatomical relationship between the mitral annulus and the venous system of the heart. The coronary sinus, great cardiac vein and the origin of the anterior interventricular vein surround the posterior mitral annulus. This enables percutaneous approaches to annuloplasty for mitral regurgitation. Devices can be implanted into the coronary veins that modify the shape and size of the mitral annulus. We present a case of ischaemic mitral regurgitation successfully treated by use of a percutaneous approach, the Carillon Mitral Contour System. Significant reduction of the mitral regurgitation jet was observed. The patient was discharged 4 days after the procedure. During the follow-up visits, the patient showed an improved general condition and increased exercise capacity. Procedural steps are shown in detail and the current status of the coronary sinus based technique is discussed. Percutaneous techniques for mitral valve repair may be an attractive alternative to cardiac surgery in heart failure patients with secondary mitral regurgitation. The Carillon Mitral Contour System is under ongoing clinical evaluation in the AMADEUS trial.