Fractional Maps Research Articles

Image Encryption Scheme Based on Newly Designed Chaotic Map and Parallel DNA Coding

In this paper, a new one-dimensional fractional chaotic map is proposed and an image encryption scheme based on parallel DNA coding is designed by using the chaotic map. The mathematical model of the new chaotic system combines a sine map and a fraction operation. Compared with some traditional one-dimensional chaotic systems, the new chaotic system has a larger range of chaotic parameters and better chaotic characteristics, which makes it more suitable for applications in information encryption. In addition, an image encryption algorithm based on parallel DNA coding is proposed, which overcomes the shortcoming of common DNA coding-based image encryption algorithms. Parallel computing significantly increases the speed of encryption and decryption algorithms. The initial key of the cryptosystem is designed to be related to the SHA-3 hash value of the plaintext image so that the algorithm can resist a chosen-plaintext attack. Simulation experiments and security analysis results show that the proposed image encryption scheme has good encryption performance and less time overhead, and has strong robustness to noise and data loss attacks, which indicates that the proposed image encryption scheme has good application potential in secure communication applications.

The dynamic and discrete systems of variable fractional order in the sense of the Lozi structure map

<abstract><p>The variable fractional Lozi map (VFLM) and the variable fractional flow map are two separate systems that we propose in this inquiry. We study several key dynamics of these maps. We also investigate the sufficient and necessary requirements for the stability and asymptotic stability of the variable fractional dynamic systems. As a result, we provide VFLM with the necessary criteria to produce stable and asymptotically stable zero solutions. Furthermore, we propose a combination of these maps in control rules intended to stabilize the system. In this analysis, we take the 1D- and 2D-controller laws as givens.</p></abstract>

Brain regions associated with Brunnstrom and functional independence measure scores in patients after a stroke: a tract-based spatial statistics study.

[Purpose] We aimed to assess diffusion tensor fractional anisotropy to outline the brain regions associated with the long-term motor and cognitive functional outcomes of patients with stroke. [Participants and Methods] Eighty patients from our previous study were enrolled. Fractional anisotropy maps were acquired on days 14-21 after stroke onset, and tract-based spatial statistics were applied. Outcomes were scored using the Brunnstrom recovery stage and Functional Independence Measure motor and cognition components. Fractional anisotropy images were assessed in relation to outcome scores using the general linear model. [Results] For both the right (n=37) and left (n=43) hemisphere lesion groups, the corticospinal tract and the anterior thalamic radiation were most strongly associated with the Brunnstrom recovery stage. In contrast, the cognition component involved large regions encompassing the anterior thalamic radiation, superior longitudinal fasciculus, inferior longitudinal fasciculus, uncinate fasciculus, cingulum bundle, forceps major, and forceps minor. The results for the motor component were intermediate between those for the Brunnstrom recovery stage and those for the cognition component. [Conclusion] Motor-related outcomes were associated with fractional anisotropy decreases in the corticospinal tract, whereas cognitive outcomes were related to broad regions of association and commissural fibers. This knowledge will help scheduling appropriate rehabilitative treatments.

Half-harmonic gradient flow: aspects of a non-local geometric PDE

<abstract><p>The goal of this paper is to discuss some of the results in the author's previous papers and expand upon the work there by proving two new results: a global weak existence result as well as a first bubbling analysis for the half-harmonic gradient flow in finite time. In addition, an alternative local existence proof to the one provided in <sup>[<xref ref-type="bibr" rid="b47">47</xref>]</sup> is presented based on a fixed-point argument. This preliminary bubbling analysis leads to two potential outcomes for the possibility of finite-time bubbling until a conjecture by Sire, Wei and Zheng, see <sup>[<xref ref-type="bibr" rid="b40">40</xref>]</sup>, is settled: Either there always exists a global smooth solution to the half-harmonic gradient flow without concentration of energy in finite-time, which still allows for the formation of half-harmonic bubbles as $ t \to +\infty $, or finite-time bubbling may occur in a similar way as for the harmonic gradient flow due to energy concentration in finitely many points. In the first part of the introduction to this paper, we provide a survey of the theory of harmonic and fractional harmonic maps and the associated gradient flows. For clarity's sake, we restrict our attention to the case of spherical target manifolds $ S^{n-1} $, but our discussion extends to the general case after taking care of technicalities associated with arbitrary closed target manifolds $ N $ (cf. <sup>[<xref ref-type="bibr" rid="b48">48</xref>]</sup>).</p></abstract>

PROPERTIES AND 2α̃-FRACTAL WEIGHTED PARAMETRIC INEQUALITIES FOR THE FRACTAL (m,h)-PREINVEX MAPPINGS

The fractal [Formula: see text]-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type ([Formula: see text]) and Fejér–Hermite–Hadamard-type ([Formula: see text]) inequalities concerning [Formula: see text]-preinvexity are popularized. Then, two weighted parameterized [Formula: see text]-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal [Formula: see text]-preinvex mappings as well as [Formula: see text]-Lipschitzian mappings, a range of error estimations are deduced in the fractal domains. Finally, certain fractal inequalities with relation to the weighted formula and random variable are correspondingly presented as applications.

Dynamic analysis of the discrete fractional-order Rulkov neuron map.

Human evolution is carried out by two genetic systems based on DNA and another based on the transmission of information through the functions of the nervous system. In computational neuroscience, mathematical neural models are used to describe the biological function of the brain. Discrete-time neural models have received particular attention due to their simple analysis and low computational costs. From the concept of neuroscience, discrete fractional order neuron models incorporate the memory in a dynamic model. This paper introduces the fractional order discrete Rulkov neuron map. The presented model is analyzed dynamically and also in terms of synchronization ability. First, the Rulkov neuron map is examined in terms of phase plane, bifurcation diagram, and Lyapunov exponent. The biological behaviors of the Rulkov neuron map, such as silence, bursting, and chaotic firing, also exist in its discrete fractional-order version. The bifurcation diagrams of the proposed model are investigated under the effect of the neuron model's parameters and the fractional order. The stability regions of the system are theoretically and numerically obtained, and it is shown that increasing the order of the fractional order decreases the stable areas. Finally, the synchronization behavior of two fractional-order models is investigated. The results represent that the fractional-order systems cannot reach complete synchronization.

A Robust Steganographic Algorithm based on Linear Fractional Transformation and Chaotic Maps

The fundamental objectives of a steganographic technique are to achieve both robustness and high-capacity for the hidden information. This paper proposes a steganographic algorithm that satisfies both of these objectives, based on enhanced chaotic maps. The algorithm consists of two phases. In the first phase, a cryptographic substitution box is constructed using a novel fusion technique based on logistic and sine maps. This technique overcomes existing vulnerabilities of chaotic maps, such as frail chaos, finite precision effects, dynamical degradation, and limited control parameters. In the second phase, a frequency-domain-based embedding scheme is used to transform the secret information into ciphertext by employing the substitution boxes. The statistical strength of the algorithm is assessed through several tests, including measures of homogeneity, correlation, mean squared error, information entropy, contrast, peak signal-to-noise ratio, energy, as well as evaluations of the algorithm's performance under JPEG compression and image degradation. The results of these tests demonstrate the algorithm's robustness against various attacks and provide evidence of its high-capacity for securely embedding secret information with good visual quality.

Assessing Cerebral Oxygen Metabolism Changes in Patients With Preeclampsia Using Voxel-Based Morphometry of Oxygen Extraction Fraction Maps in Magnetic Resonance Imaging.

The objective of this study was to analyze the different brain oxygen metabolism statuses in preeclampsia using magnetic resonance imaging and investigate the factors that affect cerebral oxygen metabolism in preeclampsia. Forty-nine women with preeclampsia (mean age 32.4 years; range, 18-44 years), 22 pregnant healthy controls (PHCs) (mean age 30.7 years; range, 23-40 years), and 40 non-pregnant healthy controls (NPHCs) (mean age 32.5 years; range, 20-42 years) were included in this study. Brain oxygen extraction fraction (OEF) values were computed using quantitative susceptibility mapping (QSM) plus quantitative blood oxygen level-dependent magnitude-based OEF mapping (QSM + quantitative blood oxygen level-dependent imaging or QQ) obtained with a 1.5-T scanner. Voxel-based morphometry (VBM) was used to investigate the differences in OEF values in the brain regions among the groups. Among the three groups, the average OEF values were significantly different in multiple brain areas, including the parahippocampus, multiple gyri of the frontal lobe, calcarine, cuneus, and precuneus (all P-values were less than 0.05, after correcting for multiple comparisons). The average OEF values of the preeclampsia group were higher than those of the PHC and NPHC groups. The bilateral superior frontal gyrus/bilateral medial superior frontal gyrus had the largest size of the aforementioned brain regions, and the OEF values in this area were 24.2 ± 4.6, 21.3 ± 2.4, and 20.6 ± 2.8 in the preeclampsia, PHC, and NPHC groups, respectively. In addition, the OEF values showed no significant differences between NPHC and PHC. Correlation analysis revealed that the OEF values of some brain regions (mainly involving the frontal, occipital, and temporal gyrus) were positively correlated with age, gestational week, body mass index, and mean blood pressure in the preeclampsia group (r = 0.361-0.812). Using whole-brain VBM analysis, we found that patients with preeclampsia had higher OEF values than controls.

Unmixing of Pollution-Associated Sea Snot in the Near Surface After Its Outbreak in the Sea of Marmara Using Hyperspectral PRISMA Data

The mucilage outbreak in the Sea of Marmara in the spring of 2021 has once again emphasized the importance of addressing climate and pollution associated hazards. Although multispectral images have traditionally been used for such purposes, analysis of marine mucilage, with its spectral similarity to marine debris, and its spectral variations due to composition and/or sediment or bacterial aggregation, is a prime candidate to benefit from the advantages of hyperspectral data. The recently launched PRISMA mission provides an important opportunity to this end. This work proposes the use of unmixing on PRISMA datasets in order to analyze the spectral characteristics, the variation due to aggregation, and the spatial distribution, of marine mucilage. The proposed approach provides consistent and relevant information on two different datasets, with the potential to benefit cleaning and understanding efforts for marine mucilage. Additionally, unlike the previous studies with supervised classification, the proposed approach does not require a training step, and the abundance fraction maps obtained using unmixing are easy to interpret and analyze for mucilage aggregation.

Diffusion basis spectrum imaging as an adjunct to conventional MRI leads to earlier diagnosis of high-grade glioma tumor progression versus treatment effect.

Following chemoradiotherapy for high-grade glioma (HGG), it is often challenging to distinguish treatment changes from true tumor progression using conventional MRI. The diffusion basis spectrum imaging (DBSI) hindered fraction is associated with tissue edema or necrosis, which are common treatment-related changes. We hypothesized that DBSI hindered fraction may augment conventional imaging for earlier diagnosis of progression versus treatment effect. Adult patients were prospectively recruited if they had a known histologic diagnosis of HGG and completed standard-of-care chemoradiotherapy. DBSI and conventional MRI data were acquired longitudinally beginning 4 weeks post-radiation. Conventional MRI and DBSI metrics were compared with respect to their ability to diagnose progression versus treatment effect. Twelve HGG patients were enrolled between August 2019 and February 2020, and 9 were ultimately analyzed (5 progression, 4 treatment effect). Within new or enlarging contrast-enhancing regions, DBSI hindered fraction was significantly higher in the treatment effect group compared to progression group (P = .0004). Compared to serial conventional MRI alone, inclusion of DBSI would have led to earlier diagnosis of either progression or treatment effect in 6 (66.7%) patients by a median of 7.7 (interquartile range = 0-20.1) weeks. In the first longitudinal prospective study of DBSI in adult HGG patients, we found that in new or enlarging contrast-enhancing regions following therapy, DBSI hindered fraction is elevated in cases of treatment effect compared to those with progression. Hindered fraction map may be a valuable adjunct to conventional MRI to distinguish tumor progression from treatment effect.

White matter changes measured by multi-component MR Fingerprinting in multiple sclerosis

T2-hyperintense lesions are the key imaging marker of multiple sclerosis (MS). Previous studies have shown that the white matter surrounding such lesions is often also affected by MS. Our aim was to develop a new method to visualize and quantify the extent of white matter tissue changes in MS based on relaxometry properties.We applied a fast, multi-parametric quantitative MRI approach and used a multi-component MR Fingerprinting (MC-MRF) analysis. We assessed the differences in the MRF component representing prolongedrelaxation time between patients with MS and controls and studied the relation between this component’s volume and structural white matter damage identified on FLAIR MRI scans in patients with MS.A total of 48 MS patients at two different sites and 12 healthy controls were scanned with FLAIR and MRF-EPI MRI scans. MRF scans were analyzed with a joint-sparsity multi-component analysis to obtain magnetization fraction maps of different components, representing tissues such as myelin water, white matter, gray matter and cerebrospinal fluid. In the MS patients, an additional component was identified with increased transverse relaxation times compared to the white matter, likely representing changes in free water content. Patients with MS had a higher volume of the long- component in the white matter of the brain compared to healthy controls (B (95%-CI) = 0.004 (0.0006–0.008), p = 0.02). Furthermore, this MRF component had a moderate correlation (correlation coefficient R 0.47) with visible structural white matter changes on the FLAIR scans. Also, the component was found to be more extensive compared to structural white matter changes in 73% of MS patients.In conclusion, our MRF acquisition and analysis captured white matter tissue changes in MS patients compared to controls. In patients these tissue changes were more extensive compared to visually detectable white matter changes on FLAIR scans. Our method provides a novel way to quantify the extent of white matter changes in MS patients, which is underestimated using only conventional clinical MRI scans.

A new two-dimensional fractional discrete rational map: chaos and complexity

In this paper, a new two-dimensional fractional-order discrete rational map with γth-Caputo fractional difference operator is introduced. The study of the presence and stability of the fixed points shows that there are four types of these points; no fixed point, a line of fixed points, one fixed point and two fixed points. In addition, in the context of the commensurate and incommensurate instances, the nonlinear dynamics of the suggested fractional-order discrete map in different cases of fixed points are investigated through several numerical techniques including Lyapunov exponents, phase attractors and bifurcation diagrams. These dynamic behaviors suggest that the fractional-order discrete rational map has both hidden and self-excited attractors, which have rarely been described in the literature. Finally, to validate the presence of chaos, a complexity analysis is carried out using approximation entropy (ApEn) and the C 0-measure.

Some Results on Invariant Measures for 1-dimensional Maps

For many fibred systems the existence of an invariant measure can be proved but considerably less is known about the shape of the density. In this note various examples of invariant densities are discussed: Piecewise fractional linear maps with four branches and maps which are associated to continued fractions with increasing digits. There are ergodic maps with a non-integrable density which do not have an indifferent fixed point and maps such that the set of points which miss the digit $k=1$ has positive Lebesgue measure.

Differential vulnerability of hippocampal microstructure in 5xFAD mouse model of Alzheimer’s Disease: A dMRI study

AbstractBackgroundHippocampal subfields exhibit differential vulnerabilities to Alzheimer’s disease (AD) associated pathologies. These pathological processes extensively attenuate the structural and functional interconnectivities of the subfields. Abnormal accumulation of beta‐amyloid (Aβ) is considered a primary hallmark of AD. Histopathological studies suggest region‐specific accumulation of Aβ in hippocampal subfields. The aim of the current study is to understand the subfield‐specific in‐vivo microstructural changes in hippocampus due to Aβ load in 2.5 months old 5xFAD mouse model of AD.MethodTwo and a half month old male 5xFAD and age‐matched littermate controls were used in this study. DWI and anatomical images were acquired on a horizontal bore 9.4T Biospec micro‐MRI system equipped with a H1 cryogenic surface coil. 2D T2‐weighted anatomical images were acquired using the following parameters: TE/TR=43.67/7500 ms, voxel size=117x117x250 µm3 and number of slices=20. DWIs were acquired using multi‐shot dual‐spin‐echo EPI sequence using following parameters: TE/TR=34.78/3000 ms, voxel size=117x117x250 µm3, number of slices=20, 3 b‐values (650, 1200 and 2500) s/mm2, 5 b0 per shell, 12 diffusion encoding direction for b=650, 60 for b=1200 and 80 for b=2500 s/mm2. T2‐W images were nonlinearly registered to Badhwar hippocampal atlas. Hippocampal subfields (CA1, CA2, CA3, DG and Subiculum) in atlas space were transformed to individual T2W space and then linearly transformed to DWI space. Multi‐compartment microstructural imaging was performed using Cortical‐NODDI. Volume fraction of isotropic water diffusivity (VFISO) and intracellular volume fraction (VFIC) maps were calculated. The regional mean values (VFIC and VFISO) of individual subfields were extracted and used in general linear model for group‐comparisons.ResultThe results of the study suggest group‐level differences between control and 5xFAD mice in cornu ammonis regions. Compared to 5xFAD, VFIC in littermate control mice was significantly higher in CA1 (p<0.05; d=1.47), CA2 (p<0.05; d=1.11) and CA3 (p<0.05; d=1.54). VFISO in DG was significantly lower in littermate control compared to 5xFAD mice (p<0.05; d=1.31).ConclusionThe study demonstrates the importance of utilizing tissue‐specific microstructural imaging in detecting Aβ associated microstructural alterations in multiple hippocampal subfields. This study demonstrates that Aβ alters the hippocampal microstructure. study also suggests on the differential effect of Aβ pathology on hippocampal microstructure.

Initial Correlation Analysis of Diffusion Basis Spectrum Imaging of Alzheimer's Brain and Quantitative Histology

AbstractBackgroundDiffusion Basis Spectrum Imaging (DBSI), a novel MR imaging method, can be utilized as a biomarker in Alzheimer's disease (AD) staging and progression. By distinguishing diffusion effects from other concomitant disorders like axonal injury/loss and demyelination, it is capable of specifically evaluating cellularity and edema in AD brains. To test the hypothesis that DBSI cell fraction and mean cell apparent diffusion coefficient (ADC) correlate with measures of cell density and neuroinflammation, we employed high‐resolution ex vivo DBSI sequences and quantitative digital histology on post‐mortem human AD brain tissue.MethodA 15 × 20 × 6 mm3 sample of middle frontal gyrus (coronal plane) from a formalin‐fixed post‐mortem human AD brain (Knight ADRC) was incubated in phosphate‐buffered saline for 48 hours and then imaged with a Varian 11.7T MRI, using 2D spin‐echo sequence with 20‐direction diffusion encoding (max b = 3900 s/mm2, voxel = 0.25 × 0.25 × 1 mm). After MRI, it was precisely bisected along the plane of imaging, and processed into paraffin. Slide‐mounted 6 µm histologic sections were stained with H&E and DAB immunohistochemistry (IBA‐1 antibody, hematoxylin counterstain) and digitized (20× magnification, Hamamatsu NanoZoomer). Maps of nuclei and microglia density were computed by segmenting nuclei and microglia respectively using Orbit Image Analysis and in‐house MATLAB programs. These histology maps were registered and downsampled to the corresponding DBSI maps. We generated cell fraction maps and mean cell ADC maps from MR images using in‐house DBSI software by computing the fraction and mean ADC of restricted isotropic diffusion (0 – 0.4 ×10‐3 mm2/s in each image voxel, respectively.ResultAmong 71 evenly spaced regions of interest (ROIs, 2 × 2 mm2) drawn across the entire specimen, the mean DBSI cell fraction correlated with nuclei density (R = 0.74, P < 0.001). Additionally, among 42 ROIs drawn in the white matter region, the mean cell ADC in each ROI correlated with microglia density (R = 0.54, P < 0.001).ConclusionOur findings demonstrated the feasibility of DBSI technique in ex vivo AD brain, which could improve our understanding of neuroinflammation in AD pathogenesis, early diagnostics and new disease‐modifying therapies targeting the immune response.

A SUB-PIXEL VISUALIZATION METHOD TO DISPLAY FUZZY PHENOMENA USING RGB COLOR COMPOSITE (CASE STUDY: MANGROVES FOREST)

Natural phenomena boundaries and complexity of features in an urban area due to the low spatial resolution, lead to more pixels of satellite images included in reflectance of multiple land-cover/object components. The sub-pixel information extracting model outputs are fractional cover maps of interested class (end-member), with membership values between zero and one. These maps represented gradient change in only one fuzzy phenomenon boundaries such as vegetation cover. However, in multiple fuzzy class area or complex fuzzy phenomena such as mangrove forests, in the northwest of the Qeshm Island, Hormozgan, Iran, displaying several fractional covers may cause confusion and misunderstanding for the end-user. In this study, an additive color composite and spectral mixture analysis method is utilized for multiple fractional cover representation. The proposed method is implemented on images acquired from Operational Land Imager (OLI) sensor in the Landsat 8 satellite to extract three fractional covers (water, vegetation, and soil). An RGB color composite was used for each type and percentage of fractional cover for given pixel to display fractional cover separately. Based on such RGB color composite represented both quantitative and qualitative information, we used the RGB color solid cube as map legend for better understanding and map interpretation. The result of this study showed that suggested sub-pixel visualization method, gives new vision to the end-user understanding of fuzzy phenomena.

Special Fractional-Order Map and Its Realization

Recent works have focused the analysis of chaotic phenomena in fractional discrete memristor. However, most of the papers have been related to simulated results on the system dynamics rather than on their hardware implementations. This work reports the implementation of a new chaotic fractional memristor map with “hidden attractors”. The fractional memristor map is developed based on a memristive map by using the Grunwald–Letnikov difference operator. The fractional memristor map has flexible fixed points depending on a system’s parameters. We study system dynamics for different values of the fractional orders by using bifurcation diagrams, phase portraits, Lyapunov exponents, and the 0–1 test. We see that the fractional map generates rich dynamical behavior, including coexisting hidden dynamics and initial offset boosting.

Estimating 3D supraspinatus intramuscular fatty infiltration in older adults: a pilot study.

A recent report suggests that semi-quantitative two-dimensional Goutallier grade (2D-GG) correlates poorly with quantitative three-dimensional Dixon fat fraction (3D-Dixon-FF) on magnetic resonance imaging (MRI). To determine whether the finding of poor correlation of supraspinatus 3D-Dixon-FF with 2D-GG is reproducible, and to determine the strength of the correlation of 3D-Dixon-FF with quantitative 2D Dixon fat fraction (2D-Dixon-FF). Ten adults aged ≥60 years were recruited prospectively received shoulder MRI. 2D-Dixon-FF and 3D-Dixon-FF were measured on 6-point Dixon fat fraction maps. 2D-GG was rated on T1-weighted images. The mean age of participants was 70.7 ± 3.7 years. The mean 3D-Dixon-FF was 8.3% ± 5.7%; the mean 2D-Dixon-FF was 7.3% ± 4.4%; and the mean 2D-GG was 0.9 ± 0.7. There was a strong correlation for 3D-Dixon-FF with 2D-Dixon-FF (rho = 0.90; P < 0.001) and with 2D-GG (rho = 0.73; P = 0.017). Excellent inter-observer reliability was found for Dixon fat fraction (intraclass correlation coefficient = 0.946), which was good for Goutallier grade (weighted kappa = 0.634). Supraspinatus 3D-Dixon-FF had a strong correlation with 2D-Dixon-FF and 2D-GG in our study population.

Farm-scale Mapping of Soil Phosphorus and Potassium Fractions Using Geostatistical Technique

Phosphorus (P) and potassium (K) are two major nutrients for agricultural productivity and sustainability. The spatial variability maps of soil phosphorus and potassium content in surfacesoils collected through grid sampling technique were developed using geo-spatial technology for Indian Council of Agricultural Research-Indian Agricultural Research Institute (ICAR-IARI) farm, New Delhi, India. Soil available P content (NaHCO3-P) and P-fractions such as NaOH extractable-P(NaOH-P), citrate-bicarbonate extractable P (CB-P), citrate-bicarbonate-dithionite extractable-P(CBD-P) and HCl extractable-P (HCl-P) through sequential fractionation techniques and K fractions(available-K and non-exchangeable-K) were estimated. In geostatistical technique, exploratory data analysis and semivariogram analysis for P &amp; K fractions were conducted and ordinary kriging was used for spatial interpolation and mapping. On average basis, among the P-fractions, Ca-boundphosphorus (HCl-P) had highest value followed by non-occluded Fe- and Al-bound-P (i.e. NaOH-P)and occluded-P within iron oxide and hydrous oxide (i.e. CBD-P). Soil available K in the farmranged from 43.9 to 839.3 mg kg-1 and non-exchangeable-K content was found to be in high to veryhigh level (820-1921 mg kg-1). Among the P &amp; K fractions, occluded-P and Ca-bound P showed first order polynomial surface trend, which were removed before ordinary kriging interpolation. Semivariogram analysis of soil P- &amp; K-fractions at the IARI farm indicated the effective spatial range dependency. Prediction maps of P- &amp; K- fractions in the semiarid agricultural farm thorough ordinary kriging were found superior to log-normal ordinary kriging. The spatial variability map based fertilizer recommendation and management practices for major cropping systems in the farmarecrucial for precision nutrient management and sustainable agriculture.

Language input in late infancy scaffolds emergent literacy skills and predicts reading related white matter development.

Longitudinal studies provide the unique opportunity to test whether early language provides a scaffolding for the acquisition of the ability to read. This study tests the hypothesis that parental language input during the first 2 years of life predicts emergent literacy skills at 5 years of age, and that white matter development observed early in the 3rd year (at 26 months) may help to account for these effects. We collected naturalistic recordings of parent and child language at 6, 10, 14, 18, and 24 months using the Language ENvironment Analysis system (LENA) in a group of typically developing infants. We then examined the relationship between language measures during infancy and follow-up measures of reading related skills at age 5 years, in the same group of participants (N = 53). A subset of these children also completed diffusion and quantitative MRI scans at age 2 years (N = 20). Within this subgroup, diffusion tractography was used to identify white matter pathways that are considered critical to language and reading development, namely, the arcuate fasciculus (AF), superior and inferior longitudinal fasciculi, and inferior occipital-frontal fasciculus. Quantitative macromolecular proton fraction (MPF) mapping was used to characterize myelin density within these separately defined regions of interest. The longitudinal data were then used to test correlations between early language input and output, white matter measures at age 2 years, and pre-literacy skills at age 5 years. Parental language input, child speech output, and parent-child conversational turns correlated with pre-literacy skills, as well as myelin density estimates within the left arcuate and superior longitudinal fasciculus. Mediation analyses indicated that the left AF accounted for longitudinal relationships between infant home language measures and 5-year letter identification and letter-sound knowledge, suggesting that the left AF myelination at 2 years may serve as a mechanism by which early language experience supports emergent literacy.