Lumpability for Uncertain Continuous-Time Markov Chains

The assumption of perfect knowledge of rate parameters in continuous-time Markov chains (CTMCs) is undermined when confronted with reality, where they may be uncertain due to lack of information or because of measurement noise. In this paper we consider uncertain CTMCs, where rates are assumed to vary non-deterministically with time from bounded continuous intervals. This leads to a semantics which associates each state with the reachable set of its probability under all possible choices of the uncertain rates. We develop a notion of lumpability which identifies a partition of states where each block preserves the reachable set of the sum of its probabilities, essentially lifting the well-known CTMC ordinary lumpability to the uncertain setting. We proceed with this analogy with two further contributions: a logical characterization of uncertain CTMC lumping in terms of continuous stochastic logic; and a polynomial time and space algorithm for the minimization of uncertain CTMCs by partition refinement, using the CTMC lumping algorithm as an inner step. As a case study, we show that the minimizations in a substantial number of CTMC models reported in the literature are robust with respect to uncertainties around their original, fixed, rate values

Острый инфаркт миокарда: возможности сочетанного применения милдроната с базисной терапией

Emergency Department and Cardiac Rhythm Disorders, Institute of Cardiology, СhisinauThe effects of Mildronate used along with basic acute myocardial infarction (AMI) therapy on the clinical, electrocardiographic and echocardiographic parameters of AMI patients (pts) were studied. Material and methods. The study enrolled 60 pts with AMI: 35 pts in the study group I, and 25 in the control group II. Besides the basic AMI treatment according to the respective National Protocol, group I subjects received Mildronate 1.0 gr/day by i/v perfusion for the first 7 days, then orally in tablets for the next 6 weeks. Blood pressure, cardiac rhythm, clinical and ECG signs of myocardial ischemia, manifestations of heart failure, ECG and EchoCG changes, and patients’ exercise capacity were evaluated. Results. Ptsin group I less frequently developed ventricular tachyarrhythmia, ventricular extrasistolia, atrial fibrillation, recurrent myocardial ischemia and showed in a smaller proportion in hospital progression for heart failure. Faster changes of the ST segment towards the isoelectric line, a positive evolution of the left ventricle size, improvement of the regional wall kinetics and a better exercise capacity by a 6 minute walk test were determined in pts treated with Mildronate. No adverse reactions during the treatment with Mildronate were observed. Conclusions. Use of Mildronate along with basic acute myocardial infarction treatment showed a positive effect on the echocardiografic post-infarct changes of the left ventricle and a favorable influence on the patient’s clinical situation and their exercise capacity. Исследовали эффекты сочетанного использования Милдроната и комплексной базисной терапии острого инфаркта миокарда (ОИМ) на клинические, электрокардиографические и эхокардиографические параметры больных с ОИМ. Материал и методы. В исследование включили 60 больных с ОИМ: 35 – в основную, I группу и 25 – во II группу, контроля. Лечение ОИМ проводилось согласно соответственному Национальному Протоколу. В то же время больные I группы получали Милдронат по 1 гр/день в виде в/в введения в течение первых 7 дней, затем в таблетках до 6 недель. Изучали показатели артериального давления, частоту и характер сердечного ритма, клинические и ЭКГ признаки ишемии миокарда, проявления сердечной недостаточности, динамику ЭКГ и ЭхоКГ изменений, толерантность к физической нагрузке. Результаты. У пациентов I группы реже наблюдали желудочковые тахиаритмии и экстрасистолию, приступы мерцательной аритмии, эпизоды ишемии миокарда, прогрессирование сердечной недостаточности за время госпитализации. В этой группе отмечали более быструю динамику сегмента ST, положительную эволюцию эхокардиографических показателей и улучшение регионарной сократимости левого желудочка, увеличение толерантности к нагрузке по данным теста ходьбы в течение 6 минут. Терапия Милдронатом переносилась хорошо, побочных реакций не было зафиксировано. Выводы. Использование Милдроната в сочетании с комплексной базисной терапией острого инфаркта миокарда сопровождалось положительным влиянием на постинфарктные эхокардиографические показатели левого желудочка, имело благоприятное воздействие на клиническое состояние больных и на толерантность к нагрузке

Острый инфаркт миокарда: возможности сочетанного применения милдроната с базисной терапией

Emergency Department and Cardiac Rhythm Disorders, Institute of Cardiology, Сhisinau, Congresul III al Medicilor de Familie din Republica Moldova, 17–18 mai, 2012, Chişinău, Republica Moldova, Conferinţa Naţională „Maladii bronhoobstructive la copii”, consacrată profesorului universitar, doctor habilitat Victor Gheţeul, 27 aprilie, Chişinău, Republica MoldovaThe effects of Mildronate used along with basic acute myocardial infarction (AMI) therapy on the clinical, electrocardiographic and echocardiographic parameters of AMI patients (pts) were studied. Material and methods. The study enrolled 60 pts with AMI: 35 pts in the study group I, and 25 in the control group II. Besides the basic AMI treatment according to the respective National Protocol, group I subjects received Mildronate 1.0 gr/day by i/v perfusion for the first 7 days, then orally in tablets for the next 6 weeks. Blood pressure, cardiac rhythm, clinical and ECG signs of myocardial ischemia, manifestations of heart failure, ECG and EchoCG changes, and patients’ exercise capacity were evaluated. Results. Ptsin group I less frequently developed ventricular tachyarrhythmia, ventricular extrasistolia, atrial fibrillation, recurrent myocardial ischemia and showed in a smaller proportion in hospital progression for heart failure. Faster changes of the ST segment towards the isoelectric line, a positive evolution of the left ventricle size, improvement of the regional wall kinetics and a better exercise capacity by a 6 minute walk test were determined in pts treated with Mildronate. No adverse reactions during the treatment with Mildronate were observed. Conclusions. Use of Mildronate along with basic acute myocardial infarction treatment showed a positive effect on the echocardiografic post-infarct changes of the left ventricle and a favorable influence on the patient’s clinical situation and their exercise capacity.Исследовали эффекты сочетанного использования Милдроната и комплексной базисной терапии острого инфаркта миокарда (ОИМ) на клинические, электрокардиографические и эхокардиографические параметры больных с ОИМ. Материал и методы. В исследование включили 60 больных с ОИМ: 35 – в основную, I группу и 25 – во II группу, контроля. Лечение ОИМ проводилось согласно соответственному Национальному Протоколу. В то же время больные I группы получали Милдронат по 1 гр/день в виде в/в введения в течение первых 7 дней, затем в таблетках до 6 недель. Изучали показатели артериального давления, частоту и характер сердечного ритма, клинические и ЭКГ признаки ишемии миокарда, проявления сердечной недостаточности, динамику ЭКГ и ЭхоКГ изменений, толерантность к физической нагрузке. Результаты. У пациентов I группы реже наблюдали желудочковые тахиаритмии и экстрасистолию, приступы мерцательной аритмии, эпизоды ишемии миокарда, прогрессирование сердечной недостаточности за время госпитализации. В этой группе отмечали более быструю динамику сегмента ST, положительную эволюцию эхокардиографических показателей и улучшение регионарной сократимости левого желудочка, увеличение толерантности к нагрузке по данным теста ходьбы в течение 6 минут. Терапия Милдронатом переносилась хорошо, побочных реакций не было зафиксировано. Выводы. Использование Милдроната в сочетании с комплексной базисной терапией острого инфаркта миокарда сопровождалось положительным влиянием на постинфарктные эхокардиографические показатели левого желудочка, имело благоприятное воздействие на клиническое состояние больных и на толерантность к нагрузке

Approximate probabilistic verification of hybrid systems

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability $1$. Based on this, we formulate a sequential hypothesis testing procedure for verifying -approximately- that the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings

Electron-fluctuation interaction in a non-Fermi superconductor

We studied the influence of the amplitude fluctuations of a non-Fermi superconductor on the energy spectrum of the 2D Anderson non-Fermi system. The classical fluctuations give a temperature dependence in the pseudogap induced in the fermionic excitations.Comment: revtex fil

Уровень глюкозы крови при поступлении у больных с острым инфарктом миокарда и без сахарного диабета: прогностическое значение

Department of Emergency and Cardiac Rhythm Disorders, Institute of Cardiology, Chisinau, Congresul III al Medicilor de Familie din Republica Moldova, 17–18 mai, 2012, Chişinău, Republica Moldova, Conferinţa Naţională „Maladii bronhoobstructive la copii”, consacrată profesorului universitar, doctor habilitat Victor Gheţeul, 27 aprilie, Chişinău, Republica MoldovaAims. Hyperglycemia (HG) is common among patients with acute myocardial infarction (AMI) and is associated with high risk of mortality and morbidity. The aim of this study was to investigate the relationship between admission plasma glucose level and AMI outcomes in patients without diabetes (DM). Materials and results. 224 consecutive AMI patients without DM were included in the study. Patients were stratified into 4 groups (Gr) defined by admission plasma glucose: Gr1 – 11 mmol/l. The mean follow-up was 26 ± 6 months. Patients with HG were older and more often female. More frequently, at admission, they presented with atypical symptoms, ventricular arrhythmias, in Killip class > 2, developed more often Q wave AMI (p < 0.05), reduced EF% (p < 0.05), progression of heart failure. HG was associated in nondiabetics with increased in-hospital morbidity and mortality (p < 0.0001). Long-term mortality didn’t differ among the groups, but survival term was lower in subjects with HG on admission. Conclusion. Hiperglycaemia on admission could identify high risk AMI patients and is associated with high risk of mortality and morbidity among subjects without diabetes.Цель исследования: изучение взаимосвязи уровня глюкозы при поступлении (УГП) и исходов острого инфаркта миокарда (ОИМ) у больных без сахарного диабета (СД). Материал и методы. В исследование включили 224 больных ОИМ без СД. В зависимости от УГП больных разделили на 4 группы: I гр. – 11,0 ммол/л. Длительность наблюдения составила 26 ± 6 месяцев. Лица с гипергликемией (ГГ) при поступлении были старше и чаще женского пола. Пациенты с повышенным УГП чаще имели атипичную клинику, явления сердечной недостаточности > 2 класса по Killip, ОИМ с зубцом Q (p < 0,05), сниженную ФВ% (p < 0,05), прогрессирование сердечной недостаточности за время госпитализации. У больных без СД с ГГ при поступлении была отмечена самая высокая внутрибольничная смертность. Смертность при длительном наблюдении не отличалась в изучаемых группах. Выводы. Гипергликемия при поступлении является маркером неблагоприятного прогноза и ассоциируется с высоким риском осложненного течения и смертельного исхода ОИМ у больных без СД

Ginzburg-Landau Expansion in Non-Fermi Liquid Superconductors: Effect of the Mass Renormalization Factor

We reconsider the Ginzburg-Landau expansion for the case of a non-Fermi liquid superconductor. We obtain analytical results for the Ginzburg-Landau functional in the critical region around the superconducting phase transition, T <= T_c, in two special limits of the model, i.e., the spin-charge separation case and the anomalous Fermi liquid case. For both cases, in the presence of a mass renormalization factor, we derived the form and the specific dependence of the coherence length, penetration depth, specific heat jump at the critical point, and the magnetic upper critical field. For both limits the obtained results reduce to the usual BCS results for a two dimensional s-wave superconductor. We compare our results with recent and relevant theoretical work. The results for a d--wave symmetry order parameter do not change qualitatively the results presented in this paper. Only numerical factors appear additionally in our expressions.Comment: accepted for publication in Physical Review

On the sequential massart algorithm for statistical model checking

Several schemes have been provided in Statistical Model Checking (SMC) for the estimation of property occurrence based on predefined confidence and absolute or relative error. Simulations might be however costly if many samples are required and the usual algorithms implemented in statistical model checkers tend to be conservative. Bayesian and rare event techniques can be used to reduce the sample size but they can not be applied without prerequisite or knowledge about the system under scrutiny. Recently, sequential algorithms based on Monte Carlo estimations and Massart bounds have been proposed to reduce the sample size while providing guarantees on error bounds which has been shown to outperform alternative frequentist approaches [15]. In this work, we discuss some features regarding the distribution and the optimisation of these algorithms.No Full Tex