Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05

On q–Analogues of Caputo Derivative and Mittag–Leffler Function

Mathematics Subject Classification: 33D60, 33E12, 26A33

On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions

Mathematics Subject Classification: 33D60, 33D90, 26A33

Structural Connectivity Of The Default Mode Network And Cognition In Alzheimer׳s Disease.

Disconnectivity between the Default Mode Network (DMN) nodes can cause clinical symptoms and cognitive deficits in Alzheimer׳s disease (AD). We aimed to examine the structural connectivity between DMN nodes, to verify the extent in which white matter disconnection affects cognitive performance. MRI data of 76 subjects (25 mild AD, 21 amnestic Mild Cognitive Impairment subjects and 30 controls) were acquired on a 3.0T scanner. ExploreDTI software (fractional Anisotropy threshold=0.25 and the angular threshold=60°) calculated axial, radial, and mean diffusivities, fractional anisotropy and streamline count. AD patients showed lower fractional anisotropy (P=0.01) and streamline count (P=0.029), and higher radial diffusivity (P=0.014) than controls in the cingulum. After correction for white matter atrophy, only fractional anisotropy and radial diffusivity remained significantly lower in AD compared to controls (P=0.003 and P=0.05). In the parahippocampal bundle, AD patients had lower mean and radial diffusivities (P=0.048 and P=0.013) compared to controls, from which only radial diffusivity survived for white matter adjustment (P=0.05). Regression models revealed that cognitive performance is also accounted for by white matter microstructural values. Structural connectivity within the DMN is important to the execution of high-complexity tasks, probably due to its relevant role in the integration of the network.

Constitutively Active Mutant D816VKit Induces Megakayocyte and Mast Cell Differentiation of Early Haemopoietic Cells from Murine Foetal Liver

Mutations of Kit at position D816 have been implicated in mastocytosis, acute myeloid leukaemia and germ cell tumours. Expression of this mutant Kit in cell lines results in factor-independent growth, differentiation and increased survival in vitro and tumourigenicity in vivo. Mutant D816VKit and wild-type Kit were expressed in murine primary haemopoietic cells and grown in stem cell factor (SCF) or the absence of factors. Expression of D816VKit did not lead to transformation as assessed by a colony assay, but resulted in enhanced differentiation of cells when compared to control cells. D816VKit induced an increase in the number of cells differentiating along the megakaryocyte lineage in the absence of factors. SCF had an added effect with an increase in differentiation of mast cells. Expression of wild-type Kit in the presence of SCF also failed to cause transformation and induced differentiation of mast cells and megakaryocytes. We conclude that constitutive expression of D816VKit in primary haemopoietic cells is not a sufficient transforming stimulus but leads to the survival and maturation of cells whose phenotype is influenced by the presence of SCF. (C) 2003 Elsevier Science Ltd. All rights reserved.

Equivalent Neurogenic Potential of Wild-Type and GFP-Labeled Fetal-Derived Neural Progenitor Cells Before and After Transplantation Into the Rodent Hippocampus

Introduction. The hippocampal formation is a specific structure in the brain where neurogenesis occurs throughout adulthood and in which the neuronal cell loss causes various demential states. The main goal of this study was to verify whether fetal neural progenitor cells (NPCs) from transgenic rats expressing green fluorescent protein (GFP) retain the ability to differentiate into neuronal cells and to integrate into the hippocampal circuitry after transplantation. Methods. NPCs were isolated from E14 (gestational age: 14 days postconception) transgenic-Lewis and wild-type Sprague-Dawley rat embryos. Wild-type and transgenic cells were expanded and induced to differentiate into a neuronal lineage in vitro. Immunocytochemical and electrophysiological analysis were performed in both groups. GFP-expressing cells were implanted into the hippocampus and recorded electrophysiologically 3 months thereafter. Immunohistochemical analysis confirmed neuronal differentiation, and the yield of neuronal cells was determined stereologically. Results. NPCs derived from wild-type and transgenic animals are similar regarding their ability to generate neuronal cells in vitro. Neuronal maturity was confirmed by immunocytochemistry and electrophysiology, with demonstration of voltage-gated ionic currents, firing activity, and spontaneous synaptic currents. GFP-NPCs were also able to differentiate into mature neurons after implantation into the hippocampus, where they formed functional synaptic contacts. Conclusions. GFP-transgenic cells represent an important tool in transplantation studies. Herein, we demonstrate their ability to generate functional neurons both in vitro and in vivo conditions. Neurons derived from fetal NPCs were able to integrate into the normal hippocampal circuitry. The high yield of mature neurons generated render these cells important candidates for restorative approaches based on cell therapy.

Pkd1 Haploinsufficiency Increases Renal Damage and Induces Microcyst Formation following Ischemia/Reperfusion

Mutations in PKD1 cause the majority of cases of autosomal dominant polycystic kidney disease (ADPKD). Because polycystin 1 modulates cell proliferation, cell differentiation, and apoptosis, its lower biologic activity observed in ADPKD might influence the degree of injury after renal ischemia/reperfusion. We induced renal ischemia/reperfusion in 10- to 12-wk-old male noncystic Pkd1(+/-) and wild-type mice. Compared with wild-type mice, heterozygous mice had higher fractional excretions of sodium and potassium and higher serum creatinine after 48 h. In addition, in heterozygous mice, also cortical damage, rates of apoptosis, and inflammatory infiltration into the interstitium at time points out to 14 d after injury all increased, as well as cell proliferation at 48 h and 7 d. The mRNA and protein expression of p21 was lower in heterozygous mice than wild-type mice at 48 h. After 6 wk, we observed dilated tubules, microcysts, and increased renal fibrosis in heterozygotes. The early mortality of heterozygotes was significantly higher than that of wild-type mice when we extended the duration of ischemia from 32 to 35 min. In conclusion, ischemia/reperfusion induces a more severe injury in kidneys of Pkd1-haploin-sufficient mice, a process that apparently depends on a relative deficiency of p2l activity, tubular dilation, and microcyst formation. These data suggest the possibility that humans with ADPKD from PKD1 mutations may be at greater risk for damage from renal ischemia/reperfusion injury.

Integration pattern of HIV-1 based lentiviral vector carrying recombinant coagulation factor VIII in Sk-Hep and 293T cells

293T and Sk-Hep-1 cells were transduced with a replication-defective self-inactivating HIV-1 derived vector carrying FVIII cDNA. The genomic DNA was sequenced to reveal LTR/human genome junctions and integration sites. One hundred and thirty-two sequences matched human sequences, with an identity of at least 98%. The integration sites in 293T-FVIIIDB and in Sk-Hep-FVIIIDB cells were preferentially located in gene regions. The integrations in both cell lines were distant from the CpG islands and from the transcription start sites. A comparison between the two cell lines showed that the lentiviral-transduced DNA had the same preferred regions in the two different cell lines.

The evolution of controlled multitasked gene networks: The role of introns and other noncoding RNAs in the development of complex organisms

Eukaryotic phenotypic diversity arises from multitasking of a core proteome of limited size. Multitasking is routine in computers, as well as in other sophisticated information systems, and requires multiple inputs and outputs to control and integrate network activity. Higher eukaryotes have a mosaic gene structure with a dual output, mRNA (protein-coding) sequences and introns, which are released from the pre-mRNA by posttranscriptional processing. Introns have been enormously successful as a class of sequences and comprise up to 95% of the primary transcripts of protein-coding genes in mammals. In addition, many other transcripts (perhaps more than half) do not encode proteins at all, but appear both to be developmentally regulated and to have genetic function. We suggest that these RNAs (eRNAs) have evolved to function as endogenous network control molecules which enable direct gene-gene communication and multitasking of eukaryotic genomes. Analysis of a range of complex genetic phenomena in which RNA is involved or implicated, including co-suppression, transgene silencing, RNA interference, imprinting, methylation, and transvection, suggests that a higher-order regulatory system based on RNA signals operates in the higher eukaryotes and involves chromatin remodeling as well as other RNA-DNA, RNA-RNA, and RNA-protein interactions. The evolution of densely connected gene networks would be expected to result in a relatively stable core proteome due to the multiple reuse of components, implying,that cellular differentiation and phenotypic variation in the higher eukaryotes results primarily from variation in the control architecture. Thus, network integration and multitasking using trans-acting RNA molecules produced in parallel with protein-coding sequences may underpin both the evolution of developmentally sophisticated multicellular organisms and the rapid expansion of phenotypic complexity into uncontested environments such as those initiated in the Cambrian radiation and those seen after major extinction events.

And I say to myself: “What a fractional world!”

This paper discusses several complex systems in the perspective of fractional dynamics. For prototype systems are considered the cases of deoxyribonucleic acid decoding, financial evolution, earthquakes events, global warming trend, and musical rhythms. The application of the Fourier transform and of the power law trendlines leads to an assertive representation of the dynamics and to a simple comparison of their characteristics. Moreover, the gallery of different systems, both natural and man made, demonstrates the richness of phenomena that can be described and studied with the tools of fractional calculus.

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7

On the fractional order control of heat systems

The differentiation of non-integer order has its origin in the seventeenth century, but only in the last two decades appeared the first applications in the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated namely the fractional PID and the Smith predictor. Extensive simulations are presented assessing the performance of the proposed fractional-order algorithms.

Numerical calculation of the left and right fractional derivatives

The calculation of fractional derivatives is an important topic in scientific research. While formal definitions are clear from the mathematical point of view, they pose limitations in applied sciences that have not been yet tackled. This paper addresses the problem of obtaining left and right side derivatives when adopting numerical approximations. The results reveal the relationship between the resulting distinct values for different fractional orders and types of signals.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.