General bounds on holographic complexity

We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under the Complexity=Volume proposal, this constitutes a positive holographic complexity theorem. The result features a number of parallels with the positive energy theorem, including the assumption of an energy condition that excludes false vacuum decay (the AdS weak energy condition). Our proof is rigorously established in broad generality in four bulk dimensions, and we provide strong evidence in favor of a generalization to arbitrary dimensions. Our techniques also yield a holographic proof of Lloyd’s bound for a class of bulk spacetimes. We further establish a partial rigidity result for wormholes: wormholes with a given throat size are more complex than AdS-Schwarzschild with the same throat size.

Random matrix theory for complexity growth and black hole interiors

We study a precise and computationally tractable notion of operator complexity in holographic quantum theories, including the ensemble dual of Jackiw-Teitelboim gravity and two-dimensional holographic conformal field theories. This is a refined, “microcanonical” version of K-complexity that applies to theories with infinite or continuous spectra (including quantum field theories), and in the holographic theories we study exhibits exponential growth for a scrambling time, followed by linear growth until saturation at a time exponential in the entropy — a behavior that is characteristic of chaos. We show that the linear growth regime implies a universal random matrix description of the operator dynamics after scrambling. Our main tool for establishing this connection is a “complexity renormalization group” framework we develop that allows us to study the effective operator dynamics for different timescales by “integrating out” large K-complexities. In the dual gravity setting, we comment on the empirical match between our version of K-complexity and the maximal volume proposal, and speculate on a connection between the universal random matrix theory dynamics of operator growth after scrambling and the spatial translation symmetry of smooth black hole interiors.

314 Automated left atrial volume measurement by two-dimensional speckle-tracking echocardiograpy. Feasibility, accuracy, and reproducibility

Aims A by-product of left atrial (LA) strain analysis is the automated measurement of LA maximal volume (LAVmax), which may decrease the time of echocardiography reporting, and increase the reproducibility of the LAVmax measurement. However, the automated measurement of LAVmax by two-dimensional speckle-tracking analysis (2DSTE) has never been validated. Accordingly, we sought to: (i) assess the feasibility of automated LAVmax measurement by 2DSTE; (ii) compare the automated LAVmax by 2DSTE with conventional two-dimensional (2DE) biplane and three-dimensional echocardiography (3DE) measurements; and (iii) evaluate the accuracy and reproducibility of the three echocardiography techniques. Methods and results LAVmax (34–197 ml) were obtained from 198/210 (feasibility 94%) consecutive patients with various cardiac diseases (median age 67 years, 126 men) by 2DSTE, 2DE, and 3DE. 2DE and 2DSTE measurements resulted in similar LAVmax values (bias = 1.5 ml, limits of agreement, LOA ± 7.5 ml), and slightly underestimated 3DE LAVmax (biases = −5 ml, LOA ± 17 ml, and −6 ml, LOA ± 16 ml, respectively). LAVmax by 2DSTE and 2DE were strongly correlated to those obtained by cardiac magnetic resonance (CMR) (r = 0.946, and r = 0.935, respectively; P < 0.001). However, LAVmax obtained by 2DSTE (bias = −9.5 ml, LOA ± 16 ml) and 2DE (bias = −8 ml, LOA ± 17 ml) were significantly smaller than those measured by CMR. Conversely, 3DE LAVmax were similar to CMR (bias = −2 ml, LOA ± 10 ml). Excellent intra- and inter-observer intraclass correlations were found for 3DE (0.995 and 0.995), 2DE (0.990 and 0.988), and 2DSTE (0.990 and 0.989). Conclusions Automated LAVmax measurement by 2DSTE is highly feasible, highly reproducible, and provided similar values to conventional 2DE calculations in consecutive patients with a wide range of LAVmax.

319 Right heart chambers geometry and function in patients with the atrial and the ventricular phenotypes of functional tricuspid regurgitation

Aims Atrial functional tricuspid regurgitation (A-FTR) is a recently defined phenotype of FTR associated with persistent/permanent atrial fibrillation. Differently from the classical ventricular form of FTR (V-FTR), patients with A-FTR might present with severely dilated right atrium (RA) and tricuspid annulus (TA), and with preserved right ventricular (RV) size and systolic function. However, the geometry and function of the RV, RA, and TA in patients with A-FTR and V-FTR remain to be systematically evaluated. Accordingly, we sought to: (i) study the geometry and function of the RV, RA, and TA in A-FTR by two- and three-dimensional transthoracic echocardiography and (ii) compare them with those found in V-FTR. Methods and results We prospectively analysed 113 (44 men, age 68 ± 18 years) FTR patients (A-FTR = 55 and V-FTR = 58) that were compared to two groups of age- and sex-matched controls to develop the respective Z-scores. Severity of FTR was similar in A-FTR and V-FTR patients. Z-scores of RV size were significantly larger, and those of RV function were significantly lower in V-FTR than in A-FTR (P < 0.001 for all). The RA was significantly enlarged in both A-FTR and V-FTR compared to controls (P < 0.001, Z-scores > 2), with similar RA maximal volume (RAVmax) between A-FTR and V-FTR (P = 0.2). Whereas, the RA minimal volumes (RAVmin) were significantly larger in A-FTR than in V-FTR (P = 0.001). Conclusions Despite similar degrees of FTR, and RAVmax size, A-FTR patients show a larger RAVmin, and smaller TA areas than V-FTR patients. Conversely, V-FTR patients show dilated, more elliptic, and dysfunctional RV than A-FTR patients.

Decentralized issues in bitcoin blockchain and Nakamoto monetary rule

The paper is devoted to studying the bitcoin blockchain as a new global phenomenon in monetary economics, which requires comprehending from the economic theory view - a self-regulating system of decentralized emission without participation of a central monetary authority. Mathematical modelling is the instrument of this studying. The author has analyzed the Bitcoin system parameters that determine dynamics of a self-regulating emission mechanism. This mechanism operates in a peer-to-peer computer network and provides a smooth increasing of the "money supply" with a gradually decreasing rate of growth. The limit of this growth is determined by maximal volume 21 million BTC. Self-regulation is implemented through negative feedback between changes of control parameters (the target interval for the hash function values and the Bitcoin Difficulty level) and the speed of mining process. Control parameters depend on the real speed deviations from the target value. This mechanism provides a stable mining speed and determines annual rate of emission. The author suggests a spline-function for describing the annual rate of the cryptocurrency emission in accordance with the Proof-of-Work protocol in the Bitcoin blockchain algorithm. This spline-function gives possibility to find a monetary rule for annual rate of emission. The author in the paper proposes to call this monetary rule by the name of the Bitcoin system inventor - Nakamoto Monetary Rule. The Nakamoto Monetary Rule could be seen as the first example of a programmable monetary rule of the decentralized emission algorithm on the basis of blockchain technology. Central banks could use a similar approach, with the necessary modifications, to develop their programmable monetary rules for Central Bank Digital Currencies (CBDCs) emission based on DLT or blockchain technology

Assessment of Dysphonia in Children with Pompe Disease Using Auditory-Perceptual and Acoustic/Physiologic Methods

Bulbar and respiratory weakness occur commonly in children with Pompe disease and frequently lead to dysarthria. However, changes in vocal quality associated with this motor speech disorder are poorly described. The goal of this study was to characterize the vocal function of children with Pompe disease using auditory-perceptual and physiologic/acoustic methods. High-quality voice recordings were collected from 21 children with Pompe disease. The Grade, Roughness, Breathiness, Asthenia, and Strain (GRBAS) scale was used to assess voice quality and ratings were compared to physiologic/acoustic measurements collected during sustained phonation tasks, reading of a standard passage, and repetition of a short phrase at maximal volume. Based on ratings of grade, dysphonia was present in 90% of participants and was most commonly rated as mild or moderate in severity. Duration of sustained phonation tasks was reduced and shimmer was increased in comparison to published reference values for children without dysphonia. Specific measures of loudness were found to have statistically significant relationships with perceptual ratings of grade, breathiness, asthenia, and strain. Our data suggest that dysphonia is common in children with Pompe disease and primarily reflects impairments in respiratory and laryngeal function; however, the primary cause of dysphonia remains unclear. Future studies should seek to quantify the relative contribution of deficits in individual speech subsystems on voice quality and motor speech performance more broadly.

Left Ventricular Diastolic Function Studied with Magnetic Resonance Imaging: A Systematic Review of Techniques and Relation to Established Measures of Diastolic Function

Purpose: In recent years, cardiac magnetic resonance (CMR) has been used to assess LV diastolic function. In this systematic review, studies were identified where CMR parameters had been evaluated in healthy and/or patient groups with proven diastolic dysfunction or known to develop heart failure with preserved ejection fraction. We aimed at describing the parameters most often used, thresholds where possible, and correlation to echocardiographic and invasive measurements. Methods and results: A systematic literature review was performed using the databases of PubMed, Embase, and Cochrane. In total, 3808 articles were screened, and 102 studies were included. Four main CMR techniques were identified: tagging; time/volume curves; mitral inflow quantification with velocity-encoded phase-contrast sequences; and feature tracking. Techniques were described and estimates were presented in tables. From published studies, peak change of torsion shear angle versus volume changes in early diastole (−dφ′/dV′) (from tagging analysis), early peak filling rate indexed to LV end-diastolic volume <2.1 s−1 (from LV time-volume curve analysis), enlarged LA maximal volume >52 mL/m2, lowered LA total (<40%), and lowered LA passive emptying fractions (<16%) seem to be reliable measures of LV diastolic dysfunction. Feature tracking, especially of the atrium, shows promise but is still a novel technique. Conclusion: CMR techniques of LV untwisting and early filling and LA measures of poor emptying are promising for the diagnosis of LV filling impairment, but further research in long-term follow-up studies is needed to assess the ability for the parameters to predict patient related outcomes.

Comparison of the early cardiac electromechanical remodeling following transcatheter and surgical secundum atrial septal defect closure in adults

Background Secundum atrial septal defect (ASD) closure leads to electrical and mechanical remodeling that occurs early after shunt disappearance. The relationship between electromechanical remodeling using electrocardiogram (ECG) and cardiac magnetic resonance (CMR) after percutaneous and surgical closure has not yet been recorded in prospective studies. Objective We thought to study right atrium (RA) and right ventricle (RV) changes by CMR 3 months after transcatheter and surgical closure and their comparison with electrical remodeling by ECG. Results We prospectively evaluated 30 consecutive adult patients with isolated secundum ASD who were referred for (transcatheter and surgical) ASD closure. There was significant reduction in all of the electrical parameters within the same group as compared to the baseline values, except P wave dispersion (Pd). (P max was 97.33 ± 16.67 (pre closure) to 76 ± 15.49 (post closure) in the device group and 97.33 ± 12.79 (preclosure) to 73.33 ± 16.32 (post closure) in the surgical group, QRS complex was 104 ± 18.82 (preclosure) to 80 ± 18.51 (post closure) in the device group and 106.67 ± 14.47 (preclosure) to 86.67 ± 17.99 (post closure) in the surgical group. QTc maximum was 478.53 ± 36.79 (preclosure) to 412.53 ± 38.03 (post closure) in the device group and 470.53 ± 65.70 (preclosure) to 405.93 ± 63.08 (post closure) in the surgical group, and QTc dispersion was 70.33 ± 24.04 (preclosure) to 60.26 ± 28.56 (post closure) in the device group and 80.73 ± 30.38 (preclosure) to 60.27 ± 28.57 (post closure) in the surgical group).There was no significant difference between two groups indicating that transcatheter and surgical closure had led to equivalent value of electrical remodeling. In CMR study, we measured RA maximal volume and right ventricle end diastolic volume (RVEDV), RA maximal volume decreased significantly as compared to the base line values post closure in both groups (P value < 0.001). The reduction in RA max volume was more in the transcatheter closure group; however, this difference was not statistically significant when compared with the surgical arm (P value = 0.5).RVEDV decreased significantly in both groups as compared to the baseline values (P value < 0.001). Transcatheter closure resulted in more significant reduction in the RVEDV than the surgical closure (P value = 0.03). Conclusion Our study showed early significant electromechanical reverse remodeling in most of the study parameters from the baseline values after ASD closure. We found no significant differences in all of the electrical and RA mechanical remodeling parameters with significantly better mechanical remodeling of RV in the device group.