Dimensional Map Research Articles

Constructing a novel n-dimensional chaotic map with application to image encryption

Constructing a novel <i>n</i>-dimensional chaotic map with application to image encryption

Integral filling volume, complexity, and integral simplicial volume of $3$-dimensional mapping tori

We show that the integral filling volume of a Dehn twist f on a closed oriented surface vanishes, i.e., that the integral simplicial volume of the mapping torus with monodromy f^{n} grows sublinearly with respect to n . We deduce a complete characterization of mapping classes on surfaces with vanishing integral filling volume and, building on results by Purcell and Lackenby on the complexity of mapping tori, we show that, in dimension three, complexity and integral simplicial volume are not Lipschitz equivalent.

Baseline Diameter Does Not Predict Growth Rate in a Presurgical Ascending Thoracic Aortic Aneurysm Population.

Patients with ascending thoracic aortic aneurysm are recommended to undergo routine imaging surveillance. Although maximal diameter is the primary metric of disease severity, recent American College of Cardiology/American Heart Association guidelines emphasize the importance of aortic growth in determining surgical candidacy and risk. As diameter increases, it is assumed that aortic growth rate accelerates because of increased wall tension; however, this relationship is poorly studied. We aim to investigate the relationship between ascending thoracic aortic aneurysm diameter and growth rate using vascular deformation mapping, a validated technique for 3-dimensional growth mapping with submillimeter accuracy. We retrospectively identified adult patients with ascending aortic dilation (≥4.0 cm) and serial gated computed tomography angiograms separated by ≥2 years, excluding confirmed heritable thoracic aortic disease. Ascending growth rate was defined as 90th percentile radial wall deformation by vascular deformation mapping. Maximal diameter measurements were derived from the baseline computed tomography angiogram, and aortic length and body size-adjusted indexes were calculated. Among 258 included patients (63.2% men; age of 63 years [interquartile range, 55-69 years]), mean±SD baseline diameter was 46.3±3.6 mm and median growth rate was 0.21 mm/year (interquartile range, 0.13-0.38 mm/year). No correlation was noted between growth rate and baseline diameter (r=0.02, P=0.74) or other aortic size metrics. On multivariate analysis, age was independently predictive of growth rate (β=-0.007, P=0.021), alongside weight (β=0.003, P=0.016) and the presence of moderate or severe aortic valve insufficiency (β=0.146, P=0.049). Maximal aortic diameter is not predictive of aortic growth rate, in this contemporary cohort of patients with sizes under current surgical thresholds (<55 mm).

Ablation Strategies for Repeat Procedures in Atrial Fibrillation Recurrences Despite Durable Pulmonary Vein Isolation: The Prospective Randomized ASTRO AF Multicenter Trial.

Ablation strategies for patients with symptomatic atrial fibrillation and isolated pulmonary veins vary and their effects on arrhythmia recurrence remain unclear. A prospective randomized German multicenter trial sought to compare 2 ablation strategies in this patient cohort. Patients with atrial fibrillation despite durable pulmonary vein isolation were randomly assigned at 7 centers to undergo low-voltage area ablation using 3-dimensional mapping and irrigated radiofrequency current ablation (group A) or empirical left atrial appendage isolation (LAAI) using the cryoballoon followed by staged interventional left atrial appendage closure (group B). The primary end point was freedom from atrial tachyarrhythmias between 91 and 365 days after index ablation. The study was powered for superiority of LAAI compared with low-voltage area. Patients (40% women; mean age, 68.8±8 years) with paroxysmal (32%) or persistent atrial fibrillation (68%) were randomized to undergo low-voltage area ablation (n=79) or cryoballoon-guided LAAI (n=82). After a planned interim analysis, enrollment was halted for futility on January 10, 2023. In the LAAI group, 77 of 82 left atrial appendages were successfully isolated with subsequent left atrial appendage closure in 57 patients. Procedure-related complications occurred in 4 (5%) and 11 (13.5%) patients in group A and B, respectively (P=0.10). The median follow-up was 367 days (interquartile range, 359-378). The Kaplan-Meier point estimate for freedom from atrial tachyarrhythmias was 51.7% (CI, 40.9%-65.4%) for group A and 55.5% (CI, 44.4%-69.2%; P=0.8069) for group B. The current study did not detect superiority of cryoballoon-guided LAAI over low-voltage area ablation in patients with atrial fibrillation despite durable PVI. URL: https://www.clinicaltrials.gov; Unique identifier: NCT04056390.

MSCMNet: Multi-scale Semantic Correlation Mining for Visible-Infrared Person Re-Identification

The main challenge in the Visible-Infrared Person Re-Identification (VI-ReID) task lies in extracting discriminative features from different modalities for matching purposes. While existing studies primarily focus on reducing modal discrepancies, the modality information fails to be thoroughly exploited. To solve this problem, the Multi-scale Semantic Correlation Mining network (MSCMNet) is proposed to comprehensively exploit semantic features at multiple scales. The network fuses shallow-level features into the deep network through dimensionality reduction and mapping, and the fused features are utilized to minimize modality information loss in feature extraction. Firstly, considering the effective utilization of modality information, the Multi-scale Information Correlation Mining Block (MIMB) is designed to fuse features at different scales and explore the semantic correlation of fusion features. Secondly, in order to enrich the semantic information that MIMB can utilize, the Quadruple-stream Feature Extractor (QFE) with non-shared parameters is specifically designed to extract information from different dimensions of the dataset. Finally, the Quadruple Center Triplet Loss (QCT) is further proposed to address the information discrepancy in the comprehensive features. Extensive experiments on the SYSU-MM01, RegDB, and LLCM datasets demonstrate that the proposed MSCMNet achieves the greatest accuracy. We release the source code on https://github.com/Hua-XC/MSCMNet.

Reversible image hiding algorithm based on adaptive embedding mechanism

A reversible blind image hiding algorithm (ReBIHA) with help of an adaptive embedding mechanism and a compressive sensing technology is presented in this paper, of which can effectively hide the secret image through a natural meaningful carrier image. In the first phase, a new key generation model (KeyGM) is built by combining random numbers and the plaintext, followed by a newly designed four dimensional chaotic map (NewCM) with stronger pseudo-randomness. Then, the generated chaotic sequence is taken to produce a measurement matrix for compressive sensing. In the second phase, the plain image is sparsely processed, confused, encrypted and compressed to get measurements. Afterward, these measurements are subjected to diffusion and binary exchange to achieve a middle cipher image (MCI). In the third stage, a meaningful carrier image is randomly selected, and integer wavelet transform (IWT) is applied to it, getting one low-frequency and three high-frequency coefficients. Then, the pixels of MCI are subjected by splitting and symmetrically shifting transformation for three element matrices. Finally, these matrices are respectively embedded into the high-frequency coefficients through an adaptive mechanism to find replaceable elements, and a final carrier image hiding secrets (CiHS) can be achieved after performing an inverse IWT. The experimental results show that the proposed algorithm can avoid the extra transmission of original carrier image. Moreover, peak signal-to-noise ratio (PSNR) of reconstructed image can surpass 32 dB at compression ratio 0.5. Especially, the proposed adaptive embedding mechanism can not only achieve blind extraction of secrets well, but also ensure the visual quality for the original carrier image.

In vivo assessment of catheter-tissue contact using tissue proximity indication and its impact on cardiac lesion formation in pulsed field ablation

BackgroundNo evidence exists regarding whether tissue proximity indication (TPI), an impedance-based contact indicator, can improve in vivo lesion formation and durability during pulsed field ablation (PFA). ObjectiveThis in vivo study investigated the relationship between catheter-tissue contact and lesion formation. MethodsIn 5 porcine subjects, PFA applications were delivered at 35 atrial target sites using the VARIPULSE variable-loop circular catheter with the CARTO 3 mapping system. We compared acute ablative low-voltage zones (LVZs; <0.5 mV), chronic LVZs, and pathologic lesions between no/minimum contact (TPI-negative/flickering TPI-positive status) and consistent tissue contact (consistent TPI-positive status) for typical clinical scenarios and tissue tenting (TPI-positive status with electrodes extensively away from the 3-dimensional mapping surface) for safety margin. Ultrasound imaging also confirmed contact category assessments. ResultsAcute and chronic LVZs were significantly larger with consistent contact compared with no/minimum contact, including pathologic lesion length (36.0 ± 12.5 mm vs 17.4 ± 15.2 mm; P = .002) and maximum width (10.3 ± 2.7 mm vs 5.7 ± 5.1 mm; P = .035); results with tenting (length: 34.6 ± 11.7; width: 11.3 ± 1.9 mm) were comparable to consistent contact. Lesion transmurality was achieved in all lesions with consistent contact or tissue tenting but only in 54.5% with no/minimum contact (P = .001 for each). The TPI-based electrode contact distance, measured as the cumulative length of the multielectrode catheter tip positive for TPI, significantly correlated with lesion length, maximum width, and transmurality. ConclusionConsistent TPI-based contact during PFA was strongly associated with distinct chronic transmural lesions, emphasizing the importance of tissue contact in optimizing circumferential lesion formation with circular PFA catheters.

A novel image encryption method based on the cycle replacement

For the bit-level image encryption algorithms, pixel values and positions can be changed simultaneously. The operation can enhance the security of image encryption but will require the complicated calculations. Therefore, high security and suitable computation for a new algorithm are needed to be considered. In this paper, a novel image encryption algorithm, which combines the bit-level encryption and the pixel-level encryption methods, is proposed based on the cycle replacement. Firstly, a new 2-dimensional (2D) map with a hyperbolic cosine function (2D-Cosh map) is introduced, which has rich and complex dynamics. Based on the chaotic characteristic of the map, an image encryption algorithm is introduced via the substitution of bit of pixels which can scramble the pixels, and change the image pixel positions effectively. Numerical simulation and security analysis are used to demonstrate the effectiveness and feasibility of the algorithm. From which we can see that the correlation coefficients are almost 0, average entropy = 7.9973, average NPCR = 99.6104%, and average UACI = 33.4664%. It is clear that the algorithm is resistant to differential attacks, interference attacks, and can reduce the correlation of adjacent pixels of the encrypted image greatly. Meanwhile, the algorithm has no limit for the size of a color image in the process of the encryption.

Factors controlling peat soil thickness and carbon storage in temperate peatlands based on UAV high-resolution remote sensing

Peatlands store a large amount of carbon. However, peatlands are complex ecosystems, and acquiring reliable estimates of how much carbon is stored underneath the Earth’s surface is inherently challenging, even at small scales. Here, we aim to establish links between the above- and below-ground factors that control soil carbon status, identify the key environmental variables associated with carbon storage, as well as to explore the potential for using Unmanned Aerial Vehicle (UAV) remote sensing for spatial mapping of peatlands. We combine UAVs equipped with Red-Green-Blue (RGB), multispectral, thermal infrared, and light detection and ranging (LiDAR) sensors with ground-penetrating radar (GPR) technology and traditional field surveys to provide a comprehensive, 3-dimensional mapping of a peatland hillslope-floodplain landscape in the Belgian Hautes Fagnes. Our results indicate that both peat thickness and soil organic carbon (SOC) stock (top 1 m) are spatially heterogeneous and that the contributions from the surface topography to peat thickness and SOC stock varied from micro- to macro-scales. Peat thickness was more strongly controlled by macro-topography (R2 = 0.46) than SOC stock, which was more influenced by micro-topography (R2 = 0.21). Current vegetation had little predictive power for explaining their spatial variability. Additionally, the UAV data provided accurate estimates of both peat thickness and SOC stock, with RMSE and R2 values of 0.16 m and 0.85 for the peat thickness, and 59.25 t/ha and 0.85 for the SOC stock. However, similar performance can already be achieved by using only topographical data from the LiDAR sensor (for peat thickness) and a combination of peat thickness and topography (for SOC stock) as predictor variables. Our study bridges the gap between surface observations and the hidden carbon reservoir below. This not only allows us to improve our ability to assess the spatial distribution of SOC stocks, but also contributes to our understanding of the environmental factors associated with SOC storage in these highly heterogeneous landscapes, providing insights for environmental science and climate projections.

Geometrical construction of a chaotic horseshoe-like map on Cantor dust [formula omitted]

Smale’s horseshoe map is one of the most important examples of 2D chaos in dynamical systems. Its chaotic behavior is often illustrated using a two-sided shift map. In this paper, a 3−dimensional horseshoe-like map is defined inspired by the geometrical motivation of the horseshoe map of Smale. Moreover, this construction is expressed on the Cantor dust (C×C×C) via ternary numbers and then the density of the periodic points is proved by using a different technique. To compute these periodic points more rapidly, we also give an algorithm. Finally, it is shown that this version of 3D horseshoe-like map is Devaney chaotic.

Chemography-guided analysis of a reaction path network for ethylene hydrogenation with a model Wilkinson's catalyst.

Visualization and analysis of large chemical reaction networks become rather challenging when conventional graph-based approaches are used. As an alternative, we propose to use the chemical cartography ("chemography") approach, describing the data distribution on a 2-dimensional map. Here, the Generative Topographic Mapping (GTM) algorithm - an advanced chemography approach - has been applied to visualize the reaction path network of a simplified Wilkinson's catalyst-catalyzed hydrogenation containing some 105 structures generated with the help of the Artificial Force Induced Reaction (AFIR) method using either Density Functional Theory or Neural Network Potential (NNP) for potential energy surface calculations. Using new atoms permutation invariant 3D descriptors for structure encoding, we've demonstrated that GTM possesses the abilities to cluster structures that share the same 2D representation, to visualize potential energy surface, to provide an insight on the reaction path exploration as a function of time and to compare reaction path networks obtained with different methods of energy assessment.

Cryogenic Atom Probe Tomograph to Resolve Confined Electrochemical Interfaces

Atom Probe Tomography (APT) is an analysis technique capable of providing a 3-dimensional, element-sensitive map of needle-shaped samples (where the tip radius is about 50 nm) with sub-nanometre resolution [1]. APT analysis is carried out at temperatures in the range of 25-75 K to limit the thermal motion of surface atoms which improves the spatial and mass resolution. As a result, this enables the analysis of frozen liquids, and by extension solid-liquid interfaces, by so-called “cryo-APT”. While this was historically challenging, recent advancements in UHV-cryogenic transfer and sample preparation methods now make it possible for the atomic scale analysis of interfacial species in electrochemical systems [2-4].In this study, we will attempt to explore the effect of nanoscale geometrical confinement on the distribution of interfacial ions for the first time and to resolve the electric double layer, using cryo-APT. We will describe the workflow for cryo-APT sample preparation to study confined solid-liquid interfaces, using nanoporous gold as a template material with a frozen sodium iodide solution inside its pores. APT reconstructions will allow 3-dimensional mapping of aqueous interfacial species, helping to develop our understanding of the structure of the electric double layer under nanoscale geometrical confinement. The attached Figure shows an SEM image of the later stages of cryo-FIB milling of an APT tip of frozen deionised water and 50 mM sodium iodide and a segment of the related APT atom map reconstruction.

Feasibility of transthoracic echocardiographic guidance for multicatheter electrophysiological mapping studies in horses.

Improved characterization of arrhythmias is based on minimally invasive catheterizations. However, these catheterizations have been poorly explored in horses because apart from 3-dimensional (3D) mapping systems, continuous guidance of the catheter's position with adequate detail is difficult using current imaging modalities. Position multiple electrophysiology catheters simultaneously at predetermined strategical positions in the heart using transthoracic echocardiographic guidance. Eight adult healthy horses. Observational study. Two electrophysiological studies were performed: 1 procedure with catheters positioned in the right heart in the standing sedated horse and 1 procedure under general anesthesia with catheters positioned in the left heart. Except for the coronary sinus catheter, each catheter positioning was simultaneously guided by right-parasternal transthoracic echocardiography and 3D electro-anatomical mapping. For each catheter position, a central imaging plane was taken as the starting point, after which the imaging probe was shifted, rotated, and angulated to visualize the catheter over its entire length, including its distal electrode. Catheter positionings in the right heart and left ventricle were successfully guided in the majority of the horses whereas catheter positionings in the left atrium, and especially the pulmonary veins, were challenging to guide echocardiographically. Ultrasound guidance of catheters to specific positions useful for electrophysiological mapping was feasible in the right heart and left ventricle but challenging for the left atrium. This approach creates a perspective for minimally invasive arrhythmia diagnosis without the need for a 3D mapping system. Left parasternal views and intracardiac echocardiography might provide better guidance for left atrial positions.

Interior Regularity for Two-Dimensional Stationary Q-Valued Maps

We prove that 2-dimensional Q-valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are Hölder continuous and that the dimension of their singular set is at most one. In the course of the proof we establish a strong concentration-compactness theorem for equicontinuous maps that are stationary with respect to outer variations only, and which holds in every dimensions.

Quantitative investigation of acute lesions created by ethanol infusion into the vein of Marshall

BackgroundEthanol infusion into the vein of Marshall (EIVOM) has been performed as an adjunctive atrial fibrillation therapy. However, the time course change, quantitative lesion investigation, and effects on epicardial fat pads and fractionated atrial electrograms created by EIVOM have never been investigated. ObjectiveThis study aimed to perform a quantitative analysis of lesions created by EIVOM. MethodsWe created voltage maps using a 3-dimensional mapping system immediately before and 30 minutes and 60 minutes after performing EIVOM to study the time course change in the lesions. We compared differences in the average contact force value required for successful conduction block in the Marshall vein area of patients with and without EIVOM. We also investigated effects of EIVOM on the area of complex fractionated atrial electrograms before and after EIVOM. We measured the total epicardial fat pad volume before and after EIVOM by computed tomography. ResultsVoltage was significantly reduced after EIVOM, and there were significant differences in voltage reduction between the control status and 30 minutes and 60 minutes after EIVOM (P < .05). The average contact force value was significantly lower with vs without EIVOM (P < .05). The total epicardial fat volume and complex fractionated atrial electrogram area also significantly decreased after EIVOM (P < .05). ConclusionEIVOM provided significant therapeutic effects on the left atrial tissue perpetuating atrial fibrillation, which was demonstrated by a quantitative analysis.

Longitudinal reduction in fluoroscopy with continued use of 3-dimensional electroanatomic mapping systems in catheter ablation of supraventricular tachycardia – then and now

BackgroundCatheter ablation is a first-line treatment for symptomatic, recurrent supraventricular tachycardia (SVT). This study aims to demonstrate if 3D-electroanatomic mapping (EAM) during SVT ablation reduces fluoroscopy time (FT) and determine if further reductions in FT are observed longitudinally. MethodsAll cases of SVT ablation between May 2011–May 2022 at a single tertiary centre were prospectively recruited. FT between the cohorts with and without EAM were compared. Within the EAM subset, the trend of FT across the years was analysed. ResultsThere were 1758 cases included, 563 without EAM, 1195 with EAM. EAM was associated with a longer procedure time (mean + 8.8 min, p = 0.001), but with mean reductions in FT and dose area product (DAP) by 19.6 min and 18 621 mGy*cm2 respectively (p < 0.001). There was comparable efficacy without any increase in complication rates. Over time (2011–2022), further reduction in FT of 0.9 min year on year was observed (p = 0.001). Between 2011 and 2017, there was a significant reduction in FT of 1.1 min year on year (p = 0.019), which was not observed from 2017 onwards (p = 0.061). The greatest reduction in FT was after the first year of adoption. ConclusionEAM in SVT ablation reduces fluoroscopy use. FT was initially observed to reduce further over time before plateauing, likely due to increased operator experience. While there is increased interest in zero fluoroscopy SVT ablation, complementary use of fluoroscopy may still be necessary in complex cases.

Uniqueness of weak solutions of the Plateau flow

In this paper, we study the uniqueness of weak solutions of the heat flow of half-harmonic maps, which was first introduced by Wettstein as a half-Laplacian heat flow and recently studied by Struwe using more classical techniques. On top of its similarity with the two dimensional harmonic map flow, this geometric gradient flow is of interest due to its links with free boundary minimal surfaces and the Plateau problem, leading Struwe to propose the name Plateau flow, which we adopt throughout. We obtain uniqueness of weak solutions of this flow under a natural condition on the energy, which answers positively a question raised by Struwe.

Feasibility study on atrial fibrillation ablation with pulsed field ablation and concomitant occlusion of the left atrial appendage.

Atrial fibrillation (AF) ablation and left atrial appendage occlusion (LAAO) are increasingly performed as individual procedures. Pulsed field ablation (PFA) has significantly reduced procedure duration and may be advantageous for the combined approach. We have launched a programme for simultaneous AF ablation using PFA and LAAO for patients qualifying for both treatments and excluding those with a complex anatomy. We compare procedure duration and fluoroscopy time against individual procedures (either AF ablation or LAAO alone), all performed by the same operators and using consistent technologies. We performed the combined procedure in 10 patients (50% males; median age 70 years) and excluded 2 patients (17%) because of a complex left atrial appendage anatomy. No death, stroke, or major bleeding events, including pericardial effusion, occurred. For single-procedure comparison, 207 AF ablation procedures and 61 LAAO procedures were available. The total median procedure duration was 79 min (range 60-125) for the combined procedure, 71 min (25-241) for individual AF ablation (51 min without and 78 min with 3-dimensional electroanatomic mapping), and 47 min (15-162) for individual LAAO. The respective fluoroscopy times were 21 (15-26), 15 (5-44), and 10 (3-50) min. For the combined procedure, femoral vein access to last PFA application lasted 49 min (34-93) and LAAO added 20 min (15-37). Simultaneous PFA-based AF ablation and LAAO in carefully selected patients is feasible and safe and can be executed within a short overall procedure duration.

Exploiting 2D-SDMCHM and matching embedding driven by flag-shaped hexagon prediction for visually meaningful medical image cryptosystem

With the proliferation of advanced medical technologies and smart wearable devices, a considerable volume of patient data and medical images is being generated and stored, leading to an escalating concern over patient privacy violations and manipulation. Therefore, safeguarding the secrecy and integrity of medical images is paramount for preserving patient privacy and ensuring accurate medical diagnostics. To tackle this challenge, this paper introduces a novel approach, the Visually Meaningful Medical Image Cryptosystem (VMMIC), leveraging a 2-Dimensional Sinusoidal Discrete Memristor Coupled Hyperchaotic Map (2D-SDMCHM) to protect the privacy of medical images. The innovation of this study is primarily reflected in three aspects: Firstly, a novel Discrete Memristor (DM) model is proposed, upon which a new 2D-SDMCHM is constructed. Comparative analysis showcases its superior chaos robustness, as evidenced by evaluations through bifurcation diagrams, phase trajectories, Lyapunov exponents, and Shannon entropy. Secondly, we introduce a measurement matrix optimization algorithm based on Optimal Matrix Arrangement (OMA) for Compressive Sensing (CS), aimed at minimizing the coherence of the measurement matrix, thereby enhancing reconstruction accuracy. Lastly, a Matching Embedding Method Driven by Flag-Shaped Hexagon Prediction (MEMFHP) is introduced to ensure lossless concealment of confidential information. Experimental findings and comparative evaluations affirm the VMMIC's capability to meet high standards of reconstruction quality, steganography, and efficiency in handling medical images, while also demonstrating robustness against various attacks. Consequently, the proposed VMMIC holds significant promise for practical implementation in engineering applications.

Revealing the Correlation Between Lyapunov Exponent and Modulus of an n-Dimensional Nondegenerate Hyperchaotic Map

For their good randomness and long iteration periods, chaotic maps have been widely used in cryptography. Recently, we have revealed the correlation between Lyapunov exponent and sequence randomness of multidimensional chaotic maps based on modular operation. Since the modular operation can realize the boundedness of chaotic state points, it is important to further reveal the deterministic correlation between Lyapunov exponent and modulus. First, we constructed an [Formula: see text]-dimensional nondegenerate hyperchaotic map model with the desired Lyapunov exponents. Then, we gave the existence and uniqueness proof of quadrature rectangle decomposition theorem and revealed the correlation between Lyapunov exponent and modulus. The novelty lies in that (1) in order to realize the irreversibility of the iterative processes of chaotic maps, we constructed a chaotic map based on modular exponentiation, and its inverse function is the discrete logarithm problem; and (2) we reveal for the first time the correlation between Lyapunov exponent and modulus, and give the lower bound of the modulus of the nondegenerate chaotic map. In addition, to verify the effectiveness of the scheme, we constructed four-dimensional and five-dimensional chaotic maps, respectively, and analyzed their dynamical behaviors, and the results revealed that there exist linear or nonlinear correlation between Lyapunov exponent and modulus.