Complexity of equivalence relations and preorders from computability theory

We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relations $R, S$, a componentwise reducibility is defined by R\le S \iff \ex f \, \forall x, y \, [xRy \lra f(x) Sf(y)]. Here $f$ is taken from a suitable class of effective functions. For us the relations will be on natural numbers, and $f$ must be computable. We show that there is a $\Pi_1$-complete equivalence relation, but no $\Pi k$-complete for $k \ge 2$. We show that $\Sigma k$ preorders arising naturally in the above-mentioned areas are $\Sigma k$-complete. This includes polynomial time $m$-reducibility on exponential time sets, which is $\Sigma 2$, almost inclusion on r.e.\ sets, which is $\Sigma 3$, and Turing reducibility on r.e.\ sets, which is $\Sigma 4$.Comment: To appear in J. Symb. Logi

Use of triple-site ventricular pacing in a patient with severe congestive heart failure and atrial fibrillation.

Cardiac resynchronization therapy (CRT) has become an accepted treatment for selected patients with drug-resistant heart failure. Data for patients in atrial fibrillation (AF) remains limited but suggests benefit in these patients too. We report the case of an 82-year-old patient with heart failure, VVIR permanent pacemaker, and permanent AF who had an upgrade to triple-site CRT implantation with good clinical response. Triple-site ventricular pacing may enhance the chance of response and LV reverse remodeling and should be considered in AF patients undergoing CRT implantation

Letter by Jeilan et al regarding article, Longitudinal strain delay index by speckle tracking imaging: a new marker of response to cardiac resynchronization therapy .

We read with interest the recent article by Lim et al.1 This article demonstrated a strong correlation between a novel longitudinal strain delay index and left ventricular end-systolic volume reduction in both ischemic and nonischemic patients. The principle outlined by the authors is that an increased longitudinal strain delay index requires both dyssynchrony (defined in their article as a discrepancy between the time of end-systolic contraction and the time to peak strain) and residual contractility. Their concept elegantly considers the problem of cardiac resynchronization therapy (CRT) nonresponse in heart failure patients who have myocardial segments with delayed contraction due to scarred or akinetic segments. The index appears to address some of the limitations of time delay indices that do not take account of residual myocardial contractility. Patients with a high longitudinal strain delay index (dyssynchronous and contractile) are more likely to respond to CRT than are patients with a lower index (synchronous, akinetic, or both). In the authors’ model, an absolute discrepancy between the time of end-systolic contraction and the time to peak strain is 2 sided. Broadly speaking, resynchronization therapy works by preexciting the areas of latest activation in the dyssynchronous left ventricle. This traditional understanding of CRT-responsive dyssynchrony would suggest that peak strain in the dyssynchronous target segments should be delayed and occur after aortic valve closure (postsystolic segments).2–3 However, the proposed strain delay index also includes “presystolic segments” (peak strain occurring in segments before aortic valve closure) within an averaging calculation. Intuitively, it is difficult to understand why CRT may address this type of presystolic dyssynchrony. It would be useful to see whether data that eliminate these presystolic, earlier-contracting segments from the analysis or incorporate a measure of the variability of delay (eg, standard deviation) across the 16 segments studied within the data set might affect or improve the index’s performance. Also, the authors did not describe the effect of CRT on this index. Although CRT’s effect was not the remit of their article, it would be interesting to use these data to evaluate the differences in changes (pre- and post-CRT) to the longitudinal strain delay index score among responders and nonresponders

Program Komputer Aplikasi Alat Musik Digital

Program Aplikasi Alat Musik Digital merupakan solusi bermain musik digital dengan mobilitas tinggi dan praktis. Pemain musik tidak perlu membawa alat-alat musik yang besar dan berat. Alat musik seperti drum, piano, dan gitar dapat dimainkan dengan nyaman dan lancar menggunakan aplikasi ini. Tersedia juga fitur recording untuk merekam musik yang dimainkan, sehingga dapat digunakan untuk membuat musik berkelompok atau band

Program Komputer RPG Matematika Aljabar

Game edukasi matematika berjenis RPG dibuat untuk membantu siswa kelas 7 SMP dalam mempelajari dan meningkatkan motivasi mereka terhadap aljabar. Game RPG ini dibuat menggunakan RPG Maker MV

IMS R and D program at Canada customs

Over the last few years, Revenue Canada, in collaboration with Barringer Instruments Limited, has been involved in the development of a field-usable ion mobility spectrometer (IMS) for the detection of drugs of abuse. This work has culminated in the manufacturing and commercialization by Barringer of the Ionscan 350 instruments, now in use by various law enforcement agencies worldwide. Although IMS exhibits a very strong and distinctive response toward some nitrogen containing drugs, e.g., cocaine, like all separation techniques it has inherent limitations, namely moderate resolution and low chemical signal to noise ratio which may affect the reliability of IMS-based drug detectors. A program is in place at the Laboratory and Scientific Services Directorate (LSSD) to investigate the applicability of various digital signal processing (DSP) techniques to IMS output signals. The application of neural network techniques to overlapping IMS peaks is presented

Ganglionic Plexus Ablation During Pulmonary Vein Isolation - Predisposing to Ventricular Arrhythmias?

Catheter ablation is increasingly used to treat patients with atrial fibrillation (AF). Ablation of ganglionic plexi is often performed to reduce vagal innervation and has been shown to confer a better long-term outcome in terms of AF recurrence. We report a case of a patient having AF ablation with a profound vagal response, suggesting ganglionic plexus ablation, who subsequently developed ventricular fibrillation after programmed ventricular stimulation. Reduced vagal modulation is known to predispose to ventricular arrhythmias and vagal denervation following AF ablation may predispose to ventricular arrhythmias and requires further study

Thermal properties of a solid through q-deformed algebra

We address the study of the thermodynamics of a crystalline solid by applying q-deformed algebras. We based part of our study by considering both Einstein and Debye models. We have mainly explored the q-deformed thermal and electric conductivities as a function of the Debye specific heat. The results led to the interpretation of the q-deformation acting as a factor of disorder or impurity modifying the characteristics of a crystalline structure as, for example, in the case of semiconductors.Comment: 8 pages, twocolumn, 12 figures, Latex, version to appear in Physica