Fractional Hamilton formalism within Caputo's derivative

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page

Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists in a proof that for corresponding classes of nonholonomic distributions a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and up-dated reference

Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D

Recently, the fractional Bloch-Torrey model has been used to study anomalous diffusion in the human brain. In this paper, we consider three types of space and time fractional Bloch-Torrey equations in two dimensions: Model-1 with the Riesz fractional derivative; Model-2 with the one-dimensional fractional Laplacian operator; and Model-3 with the two-dimensional fractional Laplacian operator. Firstly, we propose a spatially second-order accurate implicit numerical method for Model-1 whereby we discretize the Riesz fractional derivative using a fractional centered difference. We consider a finite domain where the time and space derivatives are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Secondly, we utilize the matrix transfer technique for solving Model-2 and Model-3. Finally, some numerical results are given to show the behaviours of these three models especially on varying domain sizes with zero Dirichlet boundary conditions

Keratin 8 expression in colon cancer associates with low faecal butyrate levels

<p>Abstract</p> <p>Background</p> <p>Butyrate has been implicated in the mechanistic basis of the prevention of colorectal cancer by dietary fibre. Numerous in vitro studies have shown that butyrate regulates cell cycle and cell death. More recently we have shown that butyrate also regulates the integrity of the intermediate filament (IF) cytoskeleton <it>in vitro</it>. These and other data suggest a link between the role of diet and the implication of a central role for the keratin 8 (K8) as guardian of the colorectal epithelium.</p> <p>Methods</p> <p>In this cross-sectional study possible links between butyrate levels, field effects and keratin expression in cancer were addressed directly by analysing how levels of expression of the IF protein K8 in tumours, in adjacent fields and at a distant landmark site may be affected by the level of butyrate in the colon microenvironment. An immunohistochemical scoring protocol for K8 was developed and applied to samples, findings were further tested by immunoblotting.</p> <p>Results</p> <p>Levels of K8 in colorectal tumours are lower in subjects with higher levels of faecal butyrate. Immunoblotting supported this finding.Although there were no significant relationships with butyrate on the non-tumour tissues, there was a consistent trend in all measures of extent or intensity of staining towards a reduction in expression with elevated butyrate, consistent with the inverse association in tumours.</p> <p>Conclusions</p> <p>The data suggest that butyrate may associate with down-regulation of the expression of K8 in the cancerized colon. If further validated these findings may suggest the chemopreventive value of butyrate is limited to early stage carcinogenesis as low K8 expression is associated with a poor prognosis.</p

Can Charisma Be Taught? Tests of Two Interventions

We tested whether we could teach individuals to behave more charismatically, andwhether changes in charisma affected leader outcomes. In Study 1, a mixed-design fieldexperiment, we randomly assigned 34 middle-level managers to a control or anexperimental group. Three months later, we reassessed the managers using theircoworker ratings (Time 1 raters = 343; Time 2 raters = 321). In Study 2, a within-subjectslaboratory experiment, we videotaped 41 MBA participants giving a speech. We thentaught them how to behave more charismatically, and they redelivered the speech6 weeks later. Independent assessors (n = 135) rated the speeches. Results from thestudies indicated that the training had significant effects on ratings of leader charisma(mean D = .62) and that charisma had significant effects on ratings of leaderprototypicality and emergence...............................................................................................................................

Cells activated for wound repair have the potential to direct collective invasion of an epithelium.

Mechanisms regulating how groups of cells are signaled to move collectively from their original site and invade surrounding matrix are poorly understood. Here we develop a clinically relevant ex vivo injury invasion model to determine whether cells involved in directing wound healing have invasive function and whether they can act as leader cells to direct movement of a wounded epithelium through a three-dimensional (3D) extracellular matrix (ECM) environment. Similar to cancer invasion, we found that the injured cells invade into the ECM as cords, involving heterotypical cell-cell interactions. Mesenchymal cells with properties of activated repair cells that typically locate to a wound edge are present in leader positions at the front of ZO-1-rich invading cords of cells, where they extend vimentin intermediate filament-enriched protrusions into the 3D ECM. Injury-induced invasion depends on both vimentin cytoskeletal function and MMP-2/9 matrix remodeling, because inhibiting either of these suppressed invasion. Potential push and pull forces at the tips of the invading cords were revealed by time-lapse imaging, which showed cells actively extending and retracting protrusions into the ECM. This 3D injury invasion model can be used to investigate mechanisms of leader cell-directed invasion and understand how mechanisms of wound healing are hijacked to cause disease

Characterization of PTZ-Induced Seizure Susceptibility in a Down Syndrome Mouse Model That Overexpresses CSTB

Down syndrome (DS) is a complex genetic syndrome characterized by intellectual disability, dysmorphism and variable additional physiological traits. Current research progress has begun to decipher the neural mechanisms underlying cognitive impairment, leading to new therapeutic perspectives. Pentylenetetrazol (PTZ) has recently been found to have positive effects on learning and memory capacities of a DS mouse model and is foreseen to treat DS patients. But PTZ is also known to be a convulsant drug at higher dose and DS persons are more prone to epileptic seizures than the general population. This raises concerns over what long-term effects of treatment might be in the DS population. The cause of increased propensity for epilepsy in the DS population and which Hsa21 gene(s) are implicated remain unknown. Among Hsa21 candidate genes in epilepsy, CSTB, coding for the cystein protease inhibitor cystatin B, is involved in progressive myoclonus epilepsy and ataxia in both mice and human. Thus we aim to evaluate the effect of an increase in Cstb gene dosage on spontaneous epileptic activity and susceptibility to PTZ-induced seizure. To this end we generated a new mouse model trisomic for Cstb by homologous recombination. We verified that increasing copy number of Cstb from Trisomy (Ts) to Tetrasomy (Tt) was driving overexpression of the gene in the brain, we checked transgenic animals for presence of locomotor activity and electroencephalogram (EEG) abnormalities characteristic of myoclonic epilepsy and we tested if those animals were prone to PTZ-induced seizure. Overall, the results of the analysis shows that an increase in Cstb does not induce any spontaneous epileptic activity and neither increase or decrease the propensity of Ts and Tt mice to myoclonic seizures suggesting that Ctsb dosage should not interfere with PTZ-treatment

Cattle Mammary Bioreactor Generated by a Novel Procedure of Transgenic Cloning for Large-Scale Production of Functional Human Lactoferrin

Large-scale production of biopharmaceuticals by current bioreactor techniques is limited by low transgenic efficiency and low expression of foreign proteins. In general, a bacterial artificial chromosome (BAC) harboring most regulatory elements is capable of overcoming the limitations, but transferring BAC into donor cells is difficult. We describe here the use of cattle mammary bioreactor to produce functional recombinant human lactoferrin (rhLF) by a novel procedure of transgenic cloning, which employs microinjection to generate transgenic somatic cells as donor cells. Bovine fibroblast cells were co-microinjected for the first time with a 150-kb BAC carrying the human lactoferrin gene and a marker gene. The resulting transfection efficiency of up to 15.79×10−2 percent was notably higher than that of electroporation and lipofection. Following somatic cell nuclear transfer, we obtained two transgenic cows that secreted rhLF at high levels, 2.5 g/l and 3.4 g/l, respectively. The rhLF had a similar pattern of glycosylation and proteolytic susceptibility as the natural human counterpart. Biochemical analysis revealed that the iron-binding and releasing properties of rhLF were identical to that of native hLF. Importantly, an antibacterial experiment further demonstrated that rhLF was functional. Our results indicate that co-microinjection with a BAC and a marker gene into donor cells for somatic cell cloning indeed improves transgenic efficiency. Moreover, the cattle mammary bioreactors generated with this novel procedure produce functional rhLF on an industrial scale