Mitochondrial DNA Profiling by Fractal Lacunarity to Characterize the Senescent Phenotype as Normal Aging or Pathological Aging

Biocomplexity, chaos, and fractality can explain the heterogeneity of aging individuals by regarding longevity as a "secondary product" of the evolution of a dynamic nonlinear system. Genetic-environmental interactions drive the individual senescent phenotype toward normal, pathological, or successful aging. Mitochondrial dysfunctions and mitochondrial DNA (mtDNA) mutations represent a possible mechanism shared by disease(s) and the aging process. This study aims to characterize the senescent phenotype and discriminate between normal (nA) and pathological (pA) aging by mtDNA mutation profiling. MtDNA sequences from hospitalized and non-hospitalized subjects (age-range: 65-89 years) were analyzed and compared to the revised Cambridge Reference Sequence (rCRS). Fractal properties of mtDNA sequences were displayed by chaos game representation (CGR) method, previously modified to deal with heteroplasmy. Fractal lacunarity analysis was applied to characterize the senescent phenotype on the basis of mtDNA sequence mutations. Lacunarity parameter beta, from our hyperbola model function, was statistically different (p < 0.01) between the nA and pA groups. Parameter beta cut-off value at 1.26 x 10(-3) identifies 78% nA and 80% pA subjects. This also agrees with the presence of MT-CO gene variants, peculiar to nA (C9546m, 83%) and pA (T9900w, 80%) mtDNA, respectively. Fractal lacunarity can discriminate the senescent phenotype evolving as normal or pathological aging by individual mtDNA mutation profile

Fingerprint Orientation Refinement Through Iterative Smoothing

We propose a new gradient-based method for the extraction of the orientation field associated to a fingerprint, and a regularisation procedure to improve the orientation field computed from noisy fingerprint images. The regularisation algorithm is based on three new integral operators, introduced and discussed in this paper. A pre-processing technique is also proposed to achieve better performances of the algorithm. The results of a numerical experiment are reported to give an evidence of the efficiency of the proposed algorithm

Biocomplexity and Fractality in the Search of Biomarkers of Aging and Pathology: Focus on Mitochondrial DNA and Alzheimer's Disease

Alzheimer's disease (AD) represents one major health concern for our growing elderly population. It accounts for increasing impairment of cognitive capacity followed by loss of executive function in late stage. AD pathogenesis is multifaceted and difficult to pinpoint, and understanding AD etiology will be critical to effectively diagnose and treat the disease. An interesting hypothesis concerning AD development postulates a cause-effect relationship between accumulation of mitochondrial DNA (mtDNA) mutations and neurodegenerative changes associated with this pathology. Here we propose a computerized method for an easy and fast mtDNA mutations-based characterization of AD. The method has been built taking into account the complexity of living being and fractal properties of many anatomic and physiologic structures, including mtDNA. Dealing with mtDNA mutations as gaps in the nucleotide sequence, fractal lacunarity appears a suitable tool to differentiate between aging and AD. Therefore, Chaos Game Representation method has been used to display DNA fractal properties after adapting the algorithm to visualize also heteroplasmic mutations. Parameter β from our fractal lacunarity method, based on hyperbola model function, has been measured to quantitatively characterize AD on the basis of mtDNA mutations. Results from this pilot study to develop the method show that fractal lacunarity parameter β of mtDNA is statistically different in AD patients when compared to age-matched controls. Fractal lacunarity analysis represents a useful tool to analyze mtDNA mutations. Lacunarity parameter β is able to characterize individual mutation profile of mitochondrial genome and appears a promising index to discriminate between AD and aging

A mathematical model to infer underground thermal characteristics for the design of borehole heat exchangers

Geothermal exchangers are exploited as tools for the indirect analysis of the thermal properties of the underground material. Two simple inverse problems based on different heat transfer models are proposed: the first one is based on the cylindrical model of heat transfer and yields the thermal parameters of the borehole, the second one is based on a forced convective model and yields the soil thermal profile. We test our approach on sets of data collected by direct numerical simulation and from a real experiment

An inverse medium problem for the heat equation

In the article we consider the two-dimensional heat equation in a circular domain where the thermal diffusivity is a piecewise constant function in the radial directon and is a constant function in the angular direction. In particular we consider the problem of computation of a perturbation in this stratified medium having some information/knowledge about the temperature on the boundary of the domain due to heat flux applied to the same boundary. A linearized version of this inverse problem is considered and a linear integral equation is used for the numerical solution of the inverse problem. Some numerical examples are reported

The solution of linear systems by using the Sherman-Morrison formula

We consider the problem of solving the linear system Ax = b, where A is the coefficient matrix, b is the known right hand side vector and x is the solution vector to be determined. Let us suppose that A is a nonsingular square matrix, so that the linear system Ax = b is uniquely solvable. The well known Sherman–Morrison formula, that gives the inverse of a rank-one perturbation of a matrix from the knowledge of the unperturbed inverse matrix, is used to compute the numerical solution of arbitrary linear systems, in fact it can be repetitively applied to invert an arbitrary matrix.We describe some interesting properties of the method proposed. Finally we show some numerical results obtained with the method proposed

A numerical method for a direct obstacle scattering problem

We consider a direct scattering problem for an impenetrable obstacle. This problem is solved numerically with the operator expansion method, that can be seen as a perturbative method with respect to the boundary of the considered obstacle. This method requires the solution of various linear systems having the same coefficient matrix. The main result of this paper is the efficient solution of such linear systems with a numerical linear algebra algorithm based on the well-known Sherman–Morrison formula