Fractional Maps Research Articles

Bidirectional coupling in fractional order maps of incommensurate orders

We study the stability of bidirectionally coupled integer and fractional-order maps. The system is further generalized to the case where both the equations have fractional order difference operators. We derive stability conditions for the synchronized fixed point in both cases. We show that this formalism can be extended to inhomogeneous systems of N coupled map where any map can be of arbitrary fractional order or integer order. We give a solution to a specific case of a system with periodic disorder where alternate maps are of integer and fractional order or different fractional orders.

Incidental ablation of ganglionated plexus during atrial fibrillation ablation.

Cardioneuroablation targeting the autonomic nerves within ganglionated plexus (GP) has been used to treat atrial fibrillation (AF). Incidental cardioneuroablation may be an important mechanism by which pulmonary vein isolation (PVI) is effective. Automated fractionation mapping software can identify regions of fractionation correlating with GP locations. To examine the overlap between standard PVI ablation lesions and fractionated electrograms suggestive of GP. We retrospectively examined AF ablations performed from 2021 to 2023 that included only PVI performed using wide antral circumferential isolation without prospective evaluation of fractionation. Retrospectively, a fractionation map was created (width 10 ms, refractory time 30 ms, roving sensitivity 0.1 mv, and threshold of 2). We evaluated the anatomic overlap between PVI lesions and fractionation in regions associated with GP. Among 52 patients (mean 65 (IQR 46-74) years, 82% male, and 69% paroxysmal AF), sites of fractionation corresponding to GP locations were seen in all cases. PVI ablation incidentally overlapped with fractionation in 50 (96%) patients. On average, 26% of the fractionation corresponding with GP locations were incidentally ablated. The highest proportion of fractionated areas were ablated in the left superior (36%) and right superior (31%) GP regions. More complete incidental ablation of these regions was associated with a greater intraprocedural increase in heart rate (ρ = 0.46, p < 0.001), which was subsequently associated with freedom from AF during 15.9 ± 5.2 months of follow-up. Patients undergoing AF ablation universally have fractionated electrograms corresponding to anticipated sites of GP. Partial ablation of these regions frequently occurs incidentally during PVI.

Fractional tumor burden maps increase the confidence of reading brain MR perfusion

Rationale and objectivesVarious methods exist to perform and post-process perfusion weighted MR imaging in the post-treatment imaging of glioma patients to differentiate tumor progression from tumor-related abnormalities. One of these post-processing methods produces ‘fractional tumor burden’ maps. This multi-reader study investigated the clinical feasibility of fractional tumor burden maps on real world data from radiological follow-up of high-grade astrocytoma patients. MethodsFive readers with background in radiology and varying levels of experience were tasked with assessing 30 astrocytoma and glioblastoma patients during one reader session. First, they were provided with a dataset of conventional MRI sequences, including perfusion MRI with regional cerebral blood volume maps. Then the dataset was expanded with a corresponding fractional tumor burden maps. Diagnostic accuracy, duration of post-processing, duration of the assessment of the fractional tumor burden maps, the diagnostic confidence reported by the readers and their diagnoses were recorded. Final diagnosis was determined by clinical and radiological follow-up and/or histopathological data used as gold standard. ResultsA mean sensitivity of 83.3 % and mean specificity of 55.1 % was obtained without the use of fractional tumor burden maps, whereas their additional of fractional tumor burden maps resulted in a mean sensitivity and specificity of 79.5 % and 54.2 %, respectively. Diagnostic accuracies with and without fractional tumor burden maps were not significantly different (Z = 0.76, p = 0.450). The median time spent post-processing was 313 s, while the median duration of the assessment of the FTB maps was 19 s. Interestingly, reader confidence increased significantly after adding the fractional tumor burden-maps to the assessment (Z = 454, p < 0.01). ConclusionsWhile the use of fractional tumor burden maps does not carry additional value in the radiological follow-up of post-operative high-grade astrocytoma and glioblastoma patients, it does give readers more confidence in their diagnosis.

Identification of Critical Slowing of Conduction Using Unipolar Atrial Voltage and Fractionation Mapping

BackgroundAblation strategies targeting fractionated or low-voltage potentials have been widely used in patients with persistent types of atrial fibrillation (AF). However, recent studies have questioned their role in effectively representing sites of conduction slowing, and thus arrhythmogenic substrates. ObjectivesThe authors studied the relationship between local conduction velocity (CV) and the occurrence of fractionated and/or low-voltage potentials in order to identify areas with critically slowing of conduction. MethodsIntraoperative epicardial mapping was performed during sinus rhythm. Unipolar potentials with an amplitude <1.0 mV were initially classified as low-voltage and potentials with ≥3 deflections as fractionation. A range of thresholds were also explored. Local CV was computed using discrete velocity vectors. ResultsA total of 319 patients were included. Fractionated, low-voltage potentials were rare, accounting for only 0.36% (Q1-Q3: 0.15%-0.78%) of all atrial sites. Local CV at sites with fractionated, low-voltage potentials (46.0 cm/s [Q1-Q3: 22.6-72.7 cm/s]) was lowest compared with sites with either low-voltage, nonfractionated potentials (64.5 cm/s [Q1-Q3: 34.8-99.4 cm/s]) or fractionated, high-voltage potentials (65.9 cm/s [Q1-Q3: 41.7-92.8 cm/s]; P < 0.001). Slow conduction areas (CV <50 cm/s) could be most accurately identified by using a low voltage threshold (<1 mV) and a minimum of 3 deflections (positive predictive value: 54.2%-70.7%), although the overall sensitivity remained low (0.1%-1.9%). ConclusionsSites with fractionated, low-voltage potentials have substantially slower local CV compared with sites with either low-voltage, nonfractionated potentials or fractionated, high-voltage potentials. However, the strong inverse relationship between the positive predictive value and sensitivity of a combined voltage and fractionation threshold for slowed conduction is likely to complicate the use of these signal-based ablation approaches in AF patients.

On New Symmetric Fractional Discrete-Time Systems: Chaos, Complexity, and Control

This paper introduces a new symmetric fractional-order discrete system. The dynamics and symmetry of the suggested model are studied under two initial conditions, mainly a comparison of the commensurate order and incommensurate order maps, which highlights their effect on symmetry-breaking bifurcations. In addition, a theoretical analysis examines the stability of the zero equilibrium point. It proves that the map generates typical nonlinear features, including chaos, which is confirmed numerically: phase attractors are plotted in a two-dimensional (2D) and three-dimensional (3D) space, bifurcation diagrams are drawn with variations in the derivative fractional values and in the system parameters, and we calculate the Maximum Lyapunov Exponents (MLEs) associated with the bifurcation diagram. Additionally, we use the C0 algorithm and entropy approach to measure the complexity of the chaotic symmetric fractional map. Finally, nonlinear 3D controllers are revealed to stabilize the symmetric fractional order map’s states in commensurate and incommensurate cases.

Vertebral bone quality score was associated with paraspinal muscles fat infiltration, but not modic classification in patients with chronic low back pain: a prospective cross-sectional study

BackgroundThe lumbar vertebra and paraspinal muscles play an important role in maintaining the stability of the lumbar spine. Therefore, the aim of this study was to investigate the relationship between paraspinal muscles fat infiltration and vertebral body related changes [vertebral bone quality (VBQ) score and Modic changes (MCs)] in patients with chronic low back pain (CLBP).MethodsPatients with CLBP were prospectively collected in four hospitals and all patients underwent 3.0T magnetic resonance scanning. Basic clinical information was collected, including age, sex, course of disease (COD), and body mass index (BMI). MCs were divided into 3 types based on their signal intensity on T1 and T2-weighted imaging. VBQ was obtained by midsagittal T1-weighted imaging (T1WI) and calculated using the formula: SIL1−4/SICSF. The Proton density fat fraction (PDFF) values and cross-sectional area (CSA) of paraspinal muscles were measured on the fat fraction map from the iterative decomposition of water and fat with the echo asymmetry and least-squares estimation quantitation (IDEAL-IQ) sequences and in/out phase images at the central level of the L4/5 and L5/S1 discs.ResultsThis study included 476 patients with CLBP, including 189 males and 287 females. 69% had no Modic changes and 31% had Modic changes. There was no difference in CSA and PDFF for multifidus(MF) and erector spinae (ES) at both levels between Modic type I and type II, all P values>0.05. Spearman correlation analysis showed that VBQ was weakly negatively correlated with paraspinal muscles CSA (all r values < 0.3 and all p values < 0.05), moderately positive correlation with PDFF of MF at L4/5 level (r values = 0.304, p values<0.001) and weakly positively correlated with PDFF of other muscles (all r values<0.3 and all p values<0.001). Multivariate linear regression analysis showed that age (β = 0.141, p < 0.001), gender (β = 4.285, p < 0.001) and VBQ (β = 1.310, p = 0.001) were related to the total PDFF of muscles. For MCs, binary logistic regression showed that the odds ratio values of age, BMI and COD were 1.092, 1.082 and 1.004, respectively (all p values ＜ 0.05).ConclusionsPDFF of paraspinal muscles was not associated with Modic classification. In addition to age and gender, PDFF of paraspinal muscles is also affected by VBQ. Age and BMI are considered risk factors for the MCs in CLBP patients.

On fractional discrete financial system: Bifurcation, chaos, and control

Abstract The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets. This paper introduces a new three-dimensional (3D) fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders. As such, we evaluate when the equilibrium points are stable or unstable at various fractional orders. We use many numerical methods, phase plots in 2D and 3D projections, bifurcation diagrams and the maximum Lyapunov exponent. These techniques reveal that financial maps exhibit chaotic attractor behavior. This study is grounded on the Caputo-like discrete operator, which is specifically influenced by the variance of the commensurate and incommensurate orders. Furthermore, we confirm the presence and measure the complexity of chaos in financial maps by the 0–1 test and the approximate entropy algorithm. Additionally, we offer nonlinear-type controllers to stabilize the fractional financial map. The numerical results of this study are obtained using MATLAB.

Changes of brain parenchyma free water fraction reflect tissue damage and impaired processing speed in multiple sclerosis.

Free water fraction (FWF) represents the amount of water per unit volume of brain parenchyma, which is not bound to macromolecules. Its excess in multiple sclerosis (MS) is related to increased tissue loss. The use of mcDESPOT (multicomponent driven single pulse observation of T1 and T2), a 3D imaging method which exploits both the T1 and T2 contrasts, allows FWF to be derived in clinically feasible times. However, this method has not been used to quantify changes of FWF and their potential clinical impact in MS. The aim of this study is to investigate the changes in FWF in MS patients and their relationship with tissue damage and cognition, under the hypothesis that FWF is a proxy of clinically meaningful tissue loss. To this aim, we tested the relationship between FWF, MS lesion burden and information processing speed, evaluated via the Symbol Digit Modalities Test (SDMT). In addition to standard sequences, used for T1- and T2-weighted lesion delineation, the mcDESPOT sequence with 1.7 mm isotropic resolution and a diffusion weighted imaging protocol (b = 0, 1200 s/mm2, 40 diffusion directions) were employed at 3 T. The fractional anisotropy map derived from diffusion data was used to define a subject-specific white matter (WM) atlas. Brain parenchyma segmentation returned masks of gray matter (GM) and WM, and normal-appearing WM (NAWM), in addition to the T1 and T2 lesion masks (T1L and T2L, respectively). Ninety-nine relapsing-remitting MS patients (age = 43.3 ± 9.9 years, disease duration 12.3 ± 7.7 years) were studied, together with twenty-five healthy controls (HC, age = 38.8 ± 11.0 years). FWF was higher in GM and NAWM of MS patients, compared to GM and WM of HC (both p < .001). In MS patients, FWF was the highest in the T1L and GM, followed by T2L and NAWM, respectively. FWF increased significantly with T1L and T2L volume (ρ ranging from 0.40 to 0.58, p < .001). FWF in T2L was strongly related to both T1L volume and the volume ratio T1L/T2L (ρ = 0.73, p < .001). MS patients performed worse than HC in the processing speed test (mean ± SD: 54.1 ± 10.3 for MS, 63.8 ± 10.8 for HC). FWF in GM, T2L, perilesional tissue and NAWM increased with SDMT score reduction (ρ = -0.30, -0.29, -0.33 respectively and r = -.30 for T2L, all with p < .005). A regional analysis, conducted to determine which NAWM regions were of particular importance to explain the relationship between FWF and cognitive impairment, revealed that FWF spatial variance was negatively related to SDMT score in the corpus callosum and the superior longitudinal fasciculus, WM structures known to be associated with cognitive impairment, in addition to the left corticospinal tract, the sagittal stratum, the right anterior limb of internal capsule. In conclusion, we found excess free water in brain parenchyma of MS patients, an alteration that involved not only MS lesions, but also the GM and NAWM, impinging on brain function and negatively associated with cognitive processing speed. We suggest that the FWF metric, derived from noninvasive, rapid MRI acquisitions and bearing good biological interpretability, may prove valuable as an MRI biomarker of tissue damage and associated cognitive impairment in MS.

Color image encryption scheme for distributed architecture with SCFP chaotic map

Image protection mechanism in distributed cloud network is an essential component of information security field. In this paper, a novel one-dimensional sine-cosine fractional power chaotic map (SCFP) is proposed. Results of various dynamical system tests illustrate that SCFP exhibits superior chaotic behavior over its infinite positive real parameter range, whose complexity and unpredictability can guarantee the strength of image cryptosystem. Furthermore, a color image encryption scheme tailored for distributed architecture is devised. Firstly, a hybrid cryptographic mechanism is designed to perform diffusion and confusion encryption for image data and ECC public key encryption for intermediate keys. Secondly, the diffusion structure elevates processing units to row-column level, and the diffusion order is dictated by a pseudo-random sequence generated by SCFP. Thirdly, the confusion structure extends the unbiased and efficient Fisher-Yates algorithm into a 2D space, and adopts a design of dual plaintext-related key. Lastly, three techniques namely QOI lossless compression, DE information embedding and threshold secret sharing are integrated to resolve issues of data volume inflation, key synchronization difficulty and poor fault tolerance. Simulation experiments conducted on multiple color images demonstrate that the proposed scheme offers significant ciphertext randomness, sufficiently large key space and strong key sensitivity, which can ensure the integrity of image data and resist various typical cryptographic attacks, and outperforms existing schemes oriented to centralized architecture in terms of security and efficiency.

Presentation of microstructural diffusion components by color schemes in abdominal organs.

Development of a color scheme representation to facilitate the interpretation of tri-exponential DWI data from abdominal organs, where multi-exponential behavior is more pronounced. Multi-exponential analysis of DWI data provides information about the microstructure of the tissue under study. The tri-exponential signal analysis generates numerous parameter images that are difficult to analyze individually. Summarized color images can simplify at-a-glance analysis. A color scheme was developed in which the slow, intermediate, and fast diffusion components were each assigned to a different red, green, and blue color channel. To improve the appearance of the image, histogram equalization, gamma correction, and white balance were used, and the processing parameters were adjusted. Examples of the resulting color maps of the diffusion fractions of healthy and pathological kidney and prostate are shown. The color maps obtained by the presented method show the merged information of the slow, intermediate, and fast diffusion components in a single view. A differentiation of the different fractions becomes clearly visible. Fast diffusion regimes, such as in the renal hilus, can be clearly distinguished from slow fractions, such as in dense tumor tissue. Combining the diffusion information from tri-exponential DWI analysis into a single color image allows for simplified interpretation of the diffusion fractions. In the future, such color images may provide additional information about the microstructural nature of the tissue under study.

Land cover fraction mapping across global biomes with Landsat data, spatially generalized regression models and spectral-temporal metrics

Mapping land cover in highly heterogeneous landscapes is challenging, and classifications have inherent limitations where the spatial resolution of remotely sensed data exceeds the size of small objects. For example, classifications based on 30-m Landsat data do not capture urban or other heterogeneous environments well. This limitation may be overcome by quantifying the subpixel fractions of different land cover types. However, the selection process and transferability of models designed for subpixel land cover mapping across biomes is yet challenging. We asked to what extent (a) locally trained models can be used for sub-pixel land cover fraction estimates in other biomes, and (b) training data from different regions can be combined into spatially generalized models to quantify fractions across global biomes. We applied machine learning regression-based fraction mapping to quantify land cover fractions of 18 regions in five biomes using Landsat data from 2022. We used spectral-temporal metrics to incorporate intra-annual temporal information and compared the performance of local, spatially transferred, and spatially generalized models. Local models performed best when applied to their respective sites (average mean absolute error, MAE, 9–18%), and also well when transferred to other sites within the same biome, but not consistently so for out-of-biome sites. However, spatially generalized models that combined input data from many sites worked very well when analyzing sites in many different biomes, and their MAE values were only slightly higher than those of the respective local models. A weighted training data selection approach, preferring training data with a lower spectral distance to the image data to be predicted, further enhanced the performance of generalized models. Our results suggest that spatially generalized regression-based fraction models can support multi-class sub-pixel fraction estimates based on medium-resolution satellite images globally. Such products would have great value for environmental monitoring in heterogeneous environments and where land cover varies along spatial or temporal gradients.

Feasibility of omega-3 fatty acid fraction mapping using chemical shift encoding-based imaging at 3 T.

The aim of this work is to develop an ω-3 fatty acid fraction mapping method at 3 T based on a chemical shift encoding model, to assess its performance in a phantom and in vitro study, and to further demonstrate its feasibility in vivo. A signal model was heuristically derived based on spectral appearance and theoretical considerations of the corresponding molecular structures to differentiate between ω-3 and non-ω-3 fatty acid substituents in triacylglycerols in addition to the number of double bonds (ndb), the number of methylene-interrupted double bonds (nmidb), and the mean fatty acid chain length (CL). First, the signal model was validated using single-voxel spectroscopy and a time-interleaved multi-echo gradient-echo (TIMGRE) sequence in gas chromatography-mass spectrometry (GC-MS)-calibrated oil phantoms. Second, the TIMGRE-based method was validated in vitro in 21 adipose tissue samples with corresponding GC-MS measurements. Third, an in vivo feasibility study was performed for the TIMGRE-based method in the gluteal region of two healthy volunteers. Phantom and in vitro data was analyzed using a Bland-Altman analysis. Compared with GC-MS, MRS showed in the phantom study significant correlations in estimating the ω-3 fraction (p < 0.001), ndb (p < 0.001), nmidb (p < 0.001), and CL (p = 0.001); MRI showed in the phantom study significant correlations (all p < 0.001) for the ω-3 fraction, ndb, and nmidb, but no correlation for CL. Also in the in vitro study, significant correlations (all p < 0.001) between MRI and GC-MS were observed for the ω-3 fraction, ndb, and nmidb, but not for CL. An exemplary ROI measurement in vivo in the gluteal subcutaneous adipose tissue yielded (mean ± standard deviation) 0.8% ± 1.9% ω-3 fraction. The present study demonstrated strong correlations between gradient-echo imaging-based ω-3 fatty acid fraction mapping and GC-MS in the phantom and in vitro study. Furthermore, feasibility was demonstrated for characterizing adipose tissue in vivo.

Probing the physics of star formation (ProPStar)

Context. Electron fraction and cosmic-ray ionization rates in star-forming regions are important quantities in astrochemical modeling and are critical to the degree of coupling between neutrals, ions, and electrons, which regulates the dynamics of the magnetic field. However, these are difficult quantities to estimate. Aims. We aim to derive the electron fraction and cosmic-ray ionization rate maps of an active star-forming region. Methods. We combined observations of the nearby NGC 1333 star-forming region carried out with the NOEMA interferometer and IRAM 30 m single dish to generate high spatial dynamic range maps of different molecular transitions. We used the DCO+ and H13CO+ ratio (in addition to complementary data) to estimate the electron fraction and produce cosmic-ray ionization rate maps. Results. We derived the first large-area electron fraction and cosmic-ray ionization rate resolved maps in a star-forming region, with typical values of 10−65 and 10−16.5 s−1, respectively. The maps present clear evidence of enhanced values around embedded young stellar objects (YSOs). This provides strong evidence for locally accelerated cosmic rays. We also found a strong enhancement toward the northwest region in the map that might be related either to an interaction with a bubble or to locally generated cosmic rays by YSOs. We used the typical electron fraction and derived a magnetohydrodynamic (MHD) turbulence dissipation scale of 0.054 pc, which could be tested with future observations. Conclusions. We found a higher cosmic-ray ionization rate compared to the canonical value for N(H2) = 1021−1023 cm−2 of 10−17 s−1 in the region, and it is likely generated by the accreting YSOs. The high value of the electron fraction suggests that new disks will form from gas in the ideal-MHD limit. This indicates that local enhancements of ζ(H2), due to YSOs, should be taken into account in the analysis of clustered star formation.

How Does the Fractional Derivative Change the Complexity of the Caputo Standard Fractional Map

The impact of power-law memory on the dynamics of the Caputo standard fractional map is investigated in this paper. The definition of a complexity measure for the Caputo standard fractional map is introduced. This measure evaluates both the average algebraic complexity of a trajectory and the distribution of the trajectories of different types in the phase space of the system. The interplay between the small-scale spatial chaos and the large-scale spatial behavior is observed and measured during the transition of the Caputo standard fractional map from the circle map to the classical standard map. It is demonstrated that the impact of the fractional derivative on the complexity of the fractional system is not straightforward and is predetermined by the physical properties governing the dynamics of that system.

A New Fractional Discrete Memristive Map with Variable Order and Hidden Dynamics

This paper introduces and explores the dynamics of a novel three-dimensional (3D) fractional map with hidden dynamics. The map is constructed through the integration of a discrete sinusoidal memristive into a discrete Duffing map. Moreover, a mathematical operator, namely, a fractional variable-order Caputo-like difference operator, is employed to establish the fractional form of the map with short memory. The numerical simulation results highlight its excellent dynamical behavior, revealing that the addition of the piecewise fractional order makes the memristive-based Duffing map even more chaotic. It is characterized by distinct features, including the absence of an equilibrium point and the presence of multiple hidden chaotic attractors.

Differentiating Low-Grade from High-Grade Intracranial Ependymomas: Comparison of Dynamic Contrast-Enhanced MRI and Diffusion-Weighted Imaging.

The aim of this study was to determine the diagnostic value of fractional plasma volume derived from dynamic contrast-enhanced perfusion MR imaging versus ADC, obtained from DWI in differentiating between grade 2 (low-grade) and grade 3 (high-grade) intracranial ependymomas. A hospital database was created for the period from January 2013 through June 2022, including patients with histologically-proved ependymoma diagnosis with available dynamic contrast-enhanced MR imaging. Both dynamic contrast-enhanced perfusion and DWI were performed on each patient using 1.5T and 3T scanners. Fractional plasma volume maps and ADC maps were calculated. ROIs were defined by a senior neuroradiologist manually by including the enhancing tumor on every section and conforming a VOI to obtain the maximum value of fractional plasma volume (Vpmax) and the minimum value of ADC (ADCmin). A Mann-Whitney U test at a significance level of corrected P = .01 was used to evaluate the differences. Additionally, receiver operating characteristic curve analysis was applied to assess the sensitivity and specificity of Vpmax and ADCmin values. A total of 20 patients with ependymomas (10 grade 2 tumors and 10 grade 3 tumors) were included. Vpmax values for grade 3 ependymomas were significantly higher (P < .002) than those for grade 2. ADCmin values were overall lower in high-grade lesions. However, no statistically significant differences were found (P = .12114). As a dynamic contrast-enhanced perfusion MR imaging metric, fractional plasma volume can be used as an indicator to differentiate grade 2 and grade 3 ependymomas. Dynamic contrast-enhanced perfusion MR imaging plays an important role with high diagnostic value in differentiating low- and high-grade ependymoma.

Detecting land cover and land use transitions and the associated temperature changes in the East Asian monsoon region

AbstractUnprecedented land cover and land use (LCLU) changes can significantly alter the interactions between the land and atmosphere through biogeophysical processes, potentially changing the monsoon systems. Therefore, it is necessary to quantify the LCLU changes and the impacts on the climate in the East Asian monsoon (EAM) region, where significant human‐induced LCLU changes have occurred. This study quantified the LCLU transitions with fractional maps produced using the recently developed categorical LCLU maps from 1982 to 2015. In the five sub‐regions, identified as having undergone significant LCLU transitions, the relationships of the transitions with 2 m temperature were investigated using the ERA5‐Land reanalysis data. The quantified LCLU transitions revealed that, in northeastern China, the dominant trend was forests and grasslands changing into croplands. Moreover, in the marginal areas of Inner Mongolia, the transitions of grasslands to croplands and forests were evident. Croplands were mainly converted to forests in the Sichuan region. In particular, in the Sichuan region, the temperature increased by more than 0.04°C as the forests increased by 1%. In the marginal areas of Inner Mongolia, a 1% decrease in grasslands and a 1% increase in forests, respectively, were associated with a temperature rise of more than 0.03 and 0.04°C. The detected LCLU transitions affect the regional warming as demonstrated by correlation, regression and Granger‐causality analyses and the related biogeophysical processes. Thus, the identified LCLU transitions can change the regional climate and potentially affect the monsoon systems by changing the contrast in heat between land and ocean. This empirical research will not only provide insight into possible changes to climate by LCLU transitions in the EAM region, but it will also yield practical information for implementing land cover policies while considering the geographical characteristics of the region.

Tunable subdiffusion in the Caputo fractional standard map

The Caputo fractional standard map (C-fSM) is a two-dimensional nonlinear map with memory given in action–angle variables (I,θ). It is parameterized by K and α∈(1,2] which control the strength of nonlinearity and the fractional order of the Caputo derivative, respectively. In this work we perform a scaling study of the average squared action I2 along strongly chaotic orbits, i.e. when K≫1. We numerically prove that I2∝nμ with 0≤μ(α)≤1, for large enough discrete times n. That is, we demonstrate that the C-fSM displays subdiffusion for 1<α<2. Specifically, we show that diffusion is suppressed for α→1 since μ(1)=0, while standard diffusion is recovered for α=2 where μ(2)=1. We describe our numerical results with a phenomenological analytical estimation.

Unmixing-based forest recovery indicators for predicting long-term recovery success

Recovery from forest disturbances is a pivotal metric of forest resilience. Forests globally are facing unprecedented levels of both natural and anthropogenic disturbances, yet our understanding of their recovery from these disturbances remains incomplete. Remote sensing is an effective tool for understanding post-disturbance recovery, but existing approaches largely rely on spectral recovery indicators that are difficult to interpret and require long time series after disturbance, which limits their applicability to recent disturbance pulses. We here introduce a novel, ecologically informed set of recovery indicators based on fractional cover maps derived from spectral unmixing analysis of Landsat and Sentinel-2 time series. We estimated annual pre- and post-disturbance tree cover and bare ground fractions over the eastern Alps (∼130,000 km2) for the period from 1990 to 2021. From these fraction time series, we derived recovery intervals defined as the time it takes to reach a pre-defined tree cover threshold after disturbance, referred to as canopy recovery. We found mean recovery intervals between 5.5 and 13.4 years, depending on recovery threshold and disturbance severity. Comparing our results to traditional remote sensing-based approaches of mapping forest recovery, we found that spectral unmixing-based recovery indicators give considerably more realistic recovery intervals than approaches based on spectral indices because they effectively distinguish tree regeneration from other post-disturbance vegetation (e.g., shrubs, grasses). Finally, we were able to accurately predict the long-term forest recovery success based on the information available only three years after disturbance, which underlines the high importance of a short window of reorganization post-disturbance, and highlights the utility of remote sensing to inform post-disturbance forest management (e.g., in identifying areas in need of tree planting). Our study thus provides an important step ahead in the remote sensing-based monitoring of forest recovery and resilience, which is urgently needed in a time of rapid forest change.

Cardiac MRI for clinical dilated cardiomyopathy: Improved diagnostic power via combined T1, T2, and ECV

IntroductionEarly diagnosis of patients with dilated cardiomyopathy (DCM) remains challenging. Cardiac MR can correlate myocardial changes with their pathological basis. There have been some previous studies on the effect of T1 mapping in DCM, but there is limited data on the incremental value of T2 mapping for DCM in routine clinical practice. This study will examine whether the combination of MRI T1 and T2 mapping offers greater advantages in the diagnosis of DCM. MethodsThe study included 28 patients with DCM and 21 healthy controls. CMR evaluation included late gadolinium enhancement (LGE), T1 mapping, extracellular volume (ECV) fraction and T2 mapping. The DCM group was divided into LGE (+) and LGE (−) subgroups. The main modes of LGE are subendocardial, midwall, subepicardial, or transmural. T1 values, T2 values, and ECV in the 16 segments myocardial levels were measured by post-processing software. Student's t-tests or Mann–Whitney U test was used to compare between two groups, and one-way ANOVA or Kruskal–Wallis H test was used to compare between multiple groups, with p values corrected by Bonferroni. The difference was considered statistically significant at P < 0.05. ROC curve analysis was used to compare the area under the curve (AUC) of each index and its combined value, and the cut-off value, sensitivity and specificity were determined by Jordan's index. ResultsMean native myocardial T1, ECV and T2 were significantly higher in the DCM group compared to controls (p ≤ 0.001, respectively). The best cut-off values for T1, T2 and ECV to discriminate DCM from controls were 1184 ms, 40.9 ms and 29.2%, respectively. The AUC of T1, ECV and T2 were 0.87, 0.89, and 0.83, respectively. The combined AUC of the three values was 0.96. ConclusionNative T1 value and ECV overcome some of the limitations of LGE, and the T2 helps to understand the extent of myocardial damage. The combination of T1 and T2 mapping techniques can reveal fibrotic and oedematous changes in the early stages of DCM, providing a more comprehensive assessment of DCM and better guidance for individualised clinical management of patients. Implications for practiceWe suggest that the addition of T2 mapping to the routine CMR examination of patients with suspected DCM, and the combined assessment of T1mapping and T2 mapping can provide complementary information about the disease and improve the early diagnosis of DCM.