We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in R with arbitrary dimension H. Each IFS defines a probability distribution on R , so that the fractal inverse problem can b...

background: mesenchymal stem cells (mscs) can be expanded and differentiated into many mature cell types including smooth muscle cells (smcs). in addition to growth factor, cyclic stretch contributes to differentiation of stem cells. mechanical stimuli are critical to morphological changes, development, regeneration, differentiation and pathology of mesenchymal tissues. the aim of this study is...

the soil water retention curve (swrc) is a basic characteristic of the determination of soil hydraulic properties, including unsaturated hydraulic conductivity. measurement of this curve is essential to research, thus scientists have focused on indirect methods such as pedotransfer functions and empirical relationships to estimate swrc easily. since there is a close relationship between swrc an...

We investigate the detailed dynamics of a truncated αω dynamo model with a dynamic α effect. We find the presence of multiple attractors, including two chaotic attractors with a fractal basin boundary which merge to form a single attractor as the control parameter is increased. By considering phase portraits and the scaling of averaged times of transitions between the two attractors, we demonst...

The wavelet transform modulus maxima (WTMM) used in the singularity analysis of one fractal function is extended to study the fractal correlation of two multifractal functions. The technique is developed in the framework of joint partition function analysis (JPFA) proposed by Meneveau et al. [1] and is shown to be equally effective. In addition, we show that another leading approach developed f...

We consider for an anyon gas its thermodynamic properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension h. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states. ...