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Let $\mathcal{P}_{n}$ be the set of all probability mass functions (PMFs) $(p_{1},p_{2},\ \ldots, p_{n})$ that satisfy $p_{i} > 0$ for $1\leq i\leq n$ . Define the minimum expected length function $\mathcal{L}_{D}:\mathcal{P}_{n}\rightarrow \mathbb{R}$ such that $\mathcal{L}_{D}(P)$ is the minimum expected length of a prefix code, formed out of an alphabet of size D, for the discrete memoryless source having $P$ as its source distribution. It is well-known that the function $\mathcal{L}_{D}$ attains its maximum value at the uniform distribution. Further, when $n$ is of the form $D^{m}$ , with $m$ being a positive integer, PMFs other than the uniform distribution at which $\mathcal{L}_{D}$ attains its maximum value are known. However, a complete characterization of all such PMFs at which the minimum expected length function attains its maximum value has not been done so far. This is done in this paper.

A prefix code X is said to satisfy the (d, k) runlength- limited (RLL) constraint if all the possible concatenations of the codewords of X satisfy the (d, k) RLL constraint. In this paper, the problem of constructing a minimum expected length prefix code satisfying the (d, k) RLL constraint is studied for certain (d, k) pairs. The question of maximality, with maximality defined relative to the RLL constraint, of these optimal prefix codes is also taken up and answered for some cases.

Cardiovascular disease is the most prevalent age-related illness worldwide, causing approximately 15 million deaths every year. Hypertension is central in determining cardiovascular risk and is a strong predictive indicator of morbidity and mortality; however, there remains an unmet clinical need for disease-modifying and prophylactic interventions. Enhanced sympathetic activity is a well-established contributor to the pathophysiology of hypertension, however the cellular and molecular changes that increase sympathetic neurotransmission are not known. The aim of this study was to identify key changes in the transcriptome in normotensive and spontaneously hypertensive rats. We validated 15 of our top-scoring genes using qRT-PCR, and network and enrichment analyses suggest that glutamatergic signalling plays a key role in modulating Ca2+ balance within these ganglia. Additionally, phosphodiesterase activity was found to be altered in stellates obtained from the hypertensive rat, suggesting that impaired cyclic nucleotide signalling may contribute to disturbed Ca2+ homeostasis and sympathetic hyperactivity in hypertension. We have also confirmed the presence of these transcripts in human donor stellate samples, suggesting that key genes coupled to neurotransmission are conserved. The data described here may provide novel targets for future interventions aimed at treating sympathetic hyperactivity associated with cardiovascular disease and other dysautonomias.

BackgroundStudies analyzing optimal voltage thresholds for scar detection with electroanatomic mapping frequently lack a gold standard for comparison.ObjectiveThe purpose of this study was to use a porcine infarct model with ex vivo magnetic resonance imaging (MRI) integration to characterize the relationship between interelectrode spacing and bipolar voltage thresholds and examine the influence of 3-dimensional scar on unipolar voltages.MethodsThirty-two combined endocardial-epicardial electroanatomic maps were created in 8 postinfarct porcine subjects (bipolar 2-mm, 5-mm, and 8-mm interelectrode spacing and unipolar) for comparison with ex vivo MRI. Two thresholds were compared: (1) 95% normal distribution and (2) best fit to MRI. Direct electrogram analysis was performed in regions across from MRI-defined scar and adjacent to scar border zone.ResultsA linear increase in optimal thresholds was observed with wider bipole spacing. The 95% thresholds for scar were lower than MRI-matched thresholds with moderate sensitivity for nontransmural scar (54% endo, 63% epi). Unipolar endocardial scar area exceeded MRI-defined scar, resulting in mismatched false scar in 5 of 8 (63%). Endocardial and epicardial unipolar voltages were lower than normal in regions adjacent and across from scar.ConclusionVariations in interelectrode spacing necessitate tailored bipolar voltage thresholds to optimize scar detection. Statistical 95% thresholds appear to be conservative and not fully sensitive for the detection of scar defined by high-resolution ex vivo MRI. In the presence of endocardial scar, unipolar mapping to quantitatively characterize epicardial scar may be overly sensitive due to 3-dimensional spatial averaging.

The autonomic nervous system regulates all aspects of normal cardiac function, and is recognized to play a critical role in the pathophysiology of many cardiovascular diseases. As such, the value of neuroscience‐based cardiovascular therapeutics is increasingly evident. This White Paper reviews the current state of understanding of human cardiac neuroanatomy, neurophysiology, pathophysiology in specific disease conditions, autonomic testing, risk stratification, and neuromodulatory strategies to mitigate the progression of cardiovascular diseases.

We present a case of a 67-year-old patient with nonischemic cardiomyopathy and recurrent sustained ventricular tachycardia of epicardial origin referred for ablation. Due to two previous episodes of cardiac tamponade secondary to implantable cardioverter-defibrillator lead perforation at the time of device implant, the patient had significant pericardial adhesions making epicardial access and ablation challenging.

Online Social Networking (OSN) applications such as Facebook's communication and Zynga's gaming platforms service hundreds of millions of users. To understand and model such relationships, social network graphs are extracted from running OSN applications and subsequently processed using social and complex network analysis tools. In this paper, we focus on the application domain of Online Social Games (OSGs) and deploy a formalism for extracting graphs from large datasets. Our formalism covers notions such as game participation, adversarial relationships, match outcomes, and allows to filter out “weak” links based on one or more threshold values. Using two novel large-scale OSG datasets, we investigate a range of threshold values and their influence on the resulting OSG graph properties. We discuss how an analysis of multiple graphs - obtained through different extraction rules - could be used in an algorithm to improve matchmaking for players.

Methods and Results: Transseptal endocardial and percutaneous epicardial mapping were performed in a porcine model (n = 7). Two opposing 4-mm electrophysiological catheters were positioned endocardially and epicardially. A circular mapping catheter (CMC) was positioned at the ostium of the common inferior pulmonary vein (CIPV) recording left atrial (LA)-PV potentials. Endocardial and epicardial effective refractory periods (ERPs) at two basic cycle lengths (CLs) of 600 and 400 ms were recorded from four anatomic locations (CIPV, LA appendage, right superior PV, and LA posterior wall). Atrial repetitive response (ARR) induction was also tested from endocardial and epicardial sites. Overall, 254 ERP measurements (mean 36.3 per animal) and 84 induction attempts (mean 12 per animal) were performed. The ERP was significantly shorter in the epicardium compared to the endocardium at basic CL of 400 ms (P = 0.006) but not at CL of 600 ms (P = 0.2). In addition, only the epicardium demonstrated ERP shortening when the CL of the basic drive was shortened (P = 0.03). ARR could be induced more often from the epicardium (P = 0.002) and fibrillatory activity with epicardial/endocardial dissociation was recorded (n = 3). Also, the earliest PV activation site on the CMC was noted to be different in 16.5% of cases during epicardial and endocardial pacing. Conclusion: The electrophysiological characteristics of the atrial epicardium are different from the endocardium with a shorter ERP and more frequent ARR induction by programed stimulation. (PACE 2011; 37-46).

Aims Cardiac resynchronization therapy (CRT) is associated with reverse left ventricular (LV) remodelling. However, the effects of CRT-induced mechanical remodelling on electrical remodelling, and the occurrence of ventricular arrhythmias have not been clearly established. We studied the relationship between mechanical remodelling, electrical remodelling, and the occurrence of appropriate implantable cardioverter-defibrillator (ICD) therapy 1 year after CRT. Methods and results We analysed data from 45 patients who underwent ICD-CRT implantation at our centre. Significant LV reverse remodelling was defined by a minimum 10% decrease in the LV end-diastolic diameter (LVEDd) at 1 year of follow-up. Electrocardiographic indices of dispersion of repolarization [ QTc, Tpeak-Tend (Tp-e) and their dispersion] were measured immediately and 1 year post-CRT implantation. The occurrence of appropriate ICD therapy was noted for each patient. Patients with (n = 21) and without (n = 24) significant LV reverse remodelling had similar baseline characteristics. At 1 year of follow-up, patients with mechanical reverse LV remodelling exhibited a significant decrease in QTc (505 +/- 42 vs. 485 +/- 52 ms, P < 0.05) and Tp-e (107 +/- 26 vs. 92 +/- 22 ms, P < 0.0001). However, patients without mechanical LV reverse remodelling exhibited a significant increase in QT dispersion (29 +/- 43 vs. 98 +/- 47 ms, P = 0.002) and Tp-e dispersion (22 +/- 21 vs. 54 +/- 36 ms, P = 0.0001). Finally patients with mechanical LV reverse remodelling experienced a lower rate of ICD therapy (P = 0.0025) after a mean follow-up of 19 months. Conclusion Reverse LV mechanical remodelling is associated with reversal of electrical remodelling and a lower rate of appropriate ICD therapy following CRT.

BACKGROUND Catheter ablation of the left atrium ( LA) is associated with potential collateral injury to surrounding structures, especially the esophagus and the right phrenic nerve (PN). OBJECTIVES The purpose of this study was to evaluate the efficacy and feasibility of intrapericardial balloon placement (IPBP) for the protection of collateral structures adjacent to the LA. METHODS Electroanatomic mapping was performed in porcine hearts using a transseptal endocardial approach in eight swine weighing 40-50 kg. An intrapericardial balloon was inflated in the oblique sinus, via percutaneous epicardial access, to displace the esophagus. Similarly, with the balloon positioned in the transverse sinus, IPBP was used to displace the right PN. Esophageal temperature was monitored while endocardial radiofrequency (RF) energy was delivered to the distal inferior PV. RESULTS In all cases, balloon placement was successful with no significant effects on hemodynamic function. Balloon inflation increased the distance between the esophagus and posterior LA by 12.3 +/- 4.0 mm. IPBP significantly attenuated increases in luminal esophageal temperature during endocardial RF application (6.1 +/- 2.4 degrees C vs. 1.2 +/- 1.1 degrees C; P

BACKGROUND Many patients with appropriate indications fait to respond to cardiac resynchronization therapy (CRT). OBJECTIVE The purpose of our study was to determine the relationship between CRT response and preimplantation apical wall motion abnormality. METHODS We analyzed data from 83 patients with ischemic cardiomyopathy who underwent CRT. All patients had New York Heart Association class III or IV symptoms despite maximal medical therapy, Left ventricular ejection fraction (LVEF) = 130 ms or

Background: Atrial fibrillation (AF) is commonly associated with heart failure. The benefit of cardiac resynchronization therapy (CRT) on atrial remodeling has been demonstrated. However, biventricular pacing did not reduce the global incidence of AF. We evaluated the relationship between CRT response and AF duration. Methods: We retrospectively analyzed data from 96 patients (59 +/- 15 years; 78% male) who underwent CRT. All patients had class III-IV New York Heart Association (NYHA) symptoms despite maximal medical therapy, left ventricular ejection fraction (LVEF) 130 ms, and sinus rhythm before implantation. CRT response in patients who survived at six months of follow-up was defined as: (1) no hospitalization for heart failure and (2) improvement of one or more grades in the NYHA classification. Results: CRT responders (n = 54) and non-responders (n = 42) had similar baseline characteristics, including the incidence of persistent AF within six months before implantation. Six months after implantation, when compared to baseline, CRT responders exhibited a significant decrease in left atrial size (47.5 +/- 7.1 mm vs 44.6 +/- 7.7 mm, P < 0.01) and in the incidence of persistent AF (17% vs 2%, P = 0.02). At six months, CRT responders demonstrated shorter mean AF duration (7.5 +/- 43.3 hours vs 48.8 +/- 129.0 hours, P = 0.03) and lower incidence of persistent AF (2% vs 19%, P = 0.004) compared to nonresponders. Conclusion: CRT response is associated with a reversal of atrial remodeling and a shorter AF duration.

BACKGROUND The impact of cardiac resynchronization therapy (CRT) on dispersion of repolarization is controversial. The benefit of CRT on sudden cardiac death has been demonstrated only after 3 years follow-up. OBJECTIVE The purpose of this study was to explore the immediate effect of CRT on dispersion of repolarization and to define the value of dispersion of repolarization parameters as predictors of appropriate implantable cardioverter-defibrillator (ICD) therapy. METHODS Data from 100 patients who underwent CRT-ICD placement were analyzed retrospectively. Patients had symptoms of New York Heart Association functional class III or IV heart failure, left ventricular ejection fraction 130 ms or QRS

Objectives This study sought to characterize left atrial (LA) sinus rhythm electrogram (EGM) patterns and their relationship to parasympathetic responses during atrial fibrillation (AF) ablation. Background The mechanistic basis of fractionated LA EGMs in patients with paroxysmal AF is not well understood. Methods We analyzed 1,662 LA ablation sites from 30 patients who underwent catheter ablation for paroxysmal AF. Preablation EGM characteristics (number of deflections, amplitude, and duration) were measured in sinus rhythm. Parasympathetic responses during radiofrequency application (increase of atrial-His interval by 10 ms or decrease of sinus rate by >= 20%) were assessed at all sites. We also prospectively studied the effect of adenosine, a pharmacological agent mimicking acetylcholine signaling in myocytes, on LA EGMs. Finally, we performed mathematical simulations of atrial tissue to delineate possible mechanisms of fractionated EGMs in sinus rhythm. Results A specific pattern of pre-ablation sinus rhythm EGM (deflections >= 4, amplitude >= 0.7 mV, and duration >= 40 ms) was strongly associated with parasympathetic responses (sensitivity 72%, specificity 91%). The sites associated with these responses were found to be located mainly in the posterior wall of the LA. Adenosine administration and mathematical simulation of the effect of acetylcholine were able to reproduce a similar EGM pattern. Conclusions Parasympathetic activation during AF ablation is associated with the presence of pre-ablation high-amplitude fractionated EGMs in sinus rhythm. Local acetylcholine release could potentially explain this phenomenon.

Nearly 1/3 of patients with heart failure (HF) fail to respond to cardiac resynchronization therapy (CRT). The purpose of this study was to evaluate the value of preimplantation brain natriuretic peptide (BNP) in predicting the clinical response to CRT. We retrospectively analyzed 164 patients who underwent CRT. Patients with New York Heart Association functional class III or IV HF symptoms despite maximal medical therapy, who were not on inotropic medications, had left ventricular ejection fraction 130 ms were included in the study. CRT response in patients who survived at 6-month follow-up was defined as no HF hospitalization and improvement of >= 1 grades in the New York Heart Association classification. BNP assays were performed before implantation and at 6-month follow-up. Patients had ischemic (47%) or nonischemic (53%) cardiopathy. Responders (n = 107) and nonresponders (n = 57) had similar baseline characteristics. Cardiac death and hospitalization for HF occurred in 5 (4.7%) and 18 (31.6%) patients, respectively. CRT responders compared with nonresponders exhibited higher preimplantation BNP levels (800 +/- 823 vs 335 +/- 348 pg/ml, p = 0.0002) and a significant reduction in the QRS duration after implantation (-6 +/- 34 vs +7 +/- 32 ms, p = 0.048). The preimplantation BNP was the only independent predictor of the CRT response (p = 0.001). A BNP value >= 447 pg/ml demonstrated a sensitivity of 62% and specificity of 79% in identifying CRT response. In a subgroup of 41 patients who underwent Doppler tissue imaging analysis, the preimplantation BNP was higher in patients presenting with intraventricular dyssynchrony (845 +/- 779 vs 248 +/- 290 pg/ml, p = 0.04). In conclusion, the preimplantation BNP value independently predicts CRT response and was superior to QRS duration reduction in identifying CRT responders. (c) 2007 Elsevier Inc. All rights reserved.