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Notes: KETTERING, K., et al.: Enhanced Detection Criteria in Implantable Cardioverter Defibrillators: Sensitivity and Specificity of the Stability Algorithm at Different Heart Rates. Sensitivity and Specificity of the Stability Algorithm at Different Heart Rates. The lack of specificity in the detection of ventricular tachyarrhythmias remains a major clinical problem in the therapy with ICDs. The stability criterion has been shown to be useful in discriminating ventricular tachyarrhythmias characterized by a small variation in cycle lengths from AF with rapid ventricular response presenting a higher degree of variability of RR intervals. But RR variability decreases with increasing heart rate during AF. Therefore, the aim of the study was to determine if the sensitivity and specificity of the STABILITY algorithm for spontaneous tachyarrhythmias is related to ventricular rate. Forty-two patients who had received an ICD (CPI Ventak Mini I, II, III or Ventak AV) were enrolled in the study. Two hundred ninety-eight episodes of AF with rapid ventricular response and 817 episodes of ventricular tachyarrhythmias were analyzed. Sensitivity and specificity in the detection of ventricular tachyarrhythmias were calculated at different heart rates. When a stability value of 30 ms was programmed the result was a sensitivity of 82.7% and a specificity of 91.4% in the detection of slow ventricular tachyarrhythmias (heart rate 〈 150 beats/min). When faster ventricular tachyarrhythmias with rates between 150 and 169 beats/min (170–189 beats/min) were analyzed, a stability value of 30 ms provided a sensitivity of 94.5% (94.7%) and a specificity of 76.5% (54.0%). For arrhythmia episodes ≥ 190 beats/min, the same stability value resulted in a sensitivity of 78.2% and a specificity of 41.0%. Even when other stability values were taken into consideration, no acceptable sensitivity/specificity values could be obtained in this subgroup. RR variability decreases with increasing heart rate during AF while RR variability remains almost constant at different cycle lengths during ventricular tachyarrhythmias. Thus, acceptable performance of the STABILITY algorithm appears to be limited to ventricular rate zones 〈 170 beats/min.

Notes: Summary We are given a random walk S 1, S 2, ... on ℤν, ν≧1, and a strongly correlated stationary random field ξ(x), xεℤν, which is independent of the random walk. We consider the field as observed by a random walker and study partial sums of the form $$W_n = \sum\limits_{j = {\text{ }}1}^n {\xi (S_j )}$$ . It is assumed that the law corresponding to the random walk belongs to the domain of attraction of a non-degenerate stable law of index β, 0〈β≦2. We further suppose that the field ξ satisfies the non-central limit theorem of Dobrushin and Major with a scaling factor $$n^{ - v + \tfrac{1}{2}\alpha k} ,\alpha k 〈 v$$ . Under the assumption αk〈β it is shown that $$n^{ - 1 + \tfrac{1}{2}\alpha k/\beta } {\text{ }}W_{[nt]} $$ converges weakly as n→∞ to a self-similar process {Δ t , t≧0} with stationary increments, and Δ t can be represented as a multiple Wiener-Itô integral of a random function. This extends the noncentral limit theorem of Dobrushin and Major and yields a new example of a self-similar process with stationary increments.

Notes: Summary Suppose Ф is a superstable pair potential on ℝϒ with finite range and three times continuously differentiable and Ω i(t) (i=1,2,⋯; t≧0) are independent ϒ-dimensional standard-Wiener-processes related to a probability space (Ω, $$\mathfrak{F}$$ ), Ω: = (Ω i)i=1,2,⋯ The atoms a iεℝϒ (i = 1,2,⋯) of an element aεℳ, the space of the Radon counting measures on ℝv, may move according to the following equations (G) $$x_i (t;a,\omega ) = a_i + \int\limits_o^t {ds( - \tfrac{1}{2}\sum\limits_{j \pm i} {grad} } \Phi (x_i (s;a,\omega ) - x_j (s;a,\omega ))) + \omega _i (t)$$ $$(\omega \in \Omega ; i = 1,2,...; t\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \geqslant } 0)$$ (ΩεΩ; i = 1,2,⋯; t≧0). Let ∇ the σ-algebra generated by the vague topology on ℳ, Μ a probability measure on (ℳ, ∇). Call a ℳ-valued stochastic process x(t) = x i(t): i = 1,2,⋯ (x i(t)εℝv, t≧0,iεIN) on (ℳ × Ω, ∇, Μ ⊗ Q) a Μ-solution of (G), if x(t) satisfies some measurability conditions and the x i(t; a, Ω) (i= 1, 2,⋯; t ≧0) satisfy the equations (G) for Μ ⊗ Q-almost every (a, Ω). Call a Μ-solution x(t) Μ ⊗ Q-invariant, if Μ ⊗ Q x(t)εB=Μ(B) for all t≧0 and Bε∇Be93. Then for all tempered Gibbs-measures Μ associated to Ф holds: A Μ-solution of (G) exists. There is a Μ ⊗ Q-a.e. unique Μ ⊗ Q-invariant solution of (G). The Μ ⊗ Q-invariant solution x(t) is a reversible markov process. This result is the starting point for more research in a forthcoming paper [4].

Notes: Summary We consider Smoluchowski's model of coagulation in colloids: n particles move in three-dimensional euclidean space according to Brownian motions independently of each other as long as the particles are at a distance greater than R. When two particles come to within a distance R they stick together and form a “double particle”, which itself is in Brownian motion — and so on. In the Boltzmann-Grad-limit n→∞, n R=constant, we prove “propagation of chaos” and derive the kinetic equations for the densities of the k-fold particles.

Notes: Summary We consider the Kadanoff transformation T (depending on a positive parameter p) acting on probability measures Μ on the space {+1, −}ℤd. A measure Μ is called a non-trivial fixed point of T, if it is extremal in the set of T-invariant measures but is not a product measure. We describe the set of trivial fixed points and show that non-trivial fixed points exist provided that d≦2 and p large enough. A strong mixing condition on Μ implies convergence of T nΜ towards a trivial fixed point. In particular this applies to the two-dimensional Ising model except at the critical point. What happens at the critical point still remains unknown.