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In the present study, active fractions of the methanolic extract of Xanthium strumarium (XS) showing potent cytotoxicity were determined using microculture tetrazolium (MTT) and sulforhodamine B (SRB) assays in selected cancer cell lines. The active fractions viz., chloroform soluble fraction of root (CEXSR), hexane soluble fraction of leaf (HEXSL), hexane soluble fraction of fruits (HEXSF) and chloroform soluble fraction of fruits (CEXSF) of XS were tested in transplantable animal tumor models for their antitumor potential. Dalton's ascitic lymphoma (DLA) cells were used to induce solid and liquid (ascites) tumor in mice. The tumor bearing animals were treated with active fractions at two dose levels (100 and 200 mg/kg). The antitumor activities of the active fractions in tumor bearing animals were monitored with parameters such as body weight and increase in life-span as well as biochemical and hematological modalities (in the case of liquid tumor). Tumor incidence and tumor volume were the parameters monitored in the case of the solid tumor model. The results were analyzed by one-way ANOVA followed by Tukey's post hoc test. The extracts were found to increase the life-span of tumor bearing animals and restore the altered hematological and biochemical parameters significantly.

We have investigated the effect of loss of cell polarity at the individual cell level on the global pattern formation of squamous cell carcinoma. Simple models of cancer growth are able to reproduce qualitatively the sequence of observed abnormalities of metaplasia, dysplasia and carcinoma in situ and invasive carcinoma. The models are based on loss of cell polarity alone by cancerous cells, coupled to an otherwise normal growth rate and epithelial behavior. The models show that, as the probability of a wrong plane of cell division is increased, a transition from normal, well stratified epithelium, to an invasive, fractal, dendritic pattern is observed. This transition shows a sequence of morphologies in the following order as a function of loss of polarity: first an apparently normal but already diseased tissue, then metaplasic followed by a dysplasic tissue, and eventually carcinoma first in situ, then invasive. The model also suggests a killing mechanism of most severe cancer clones towards weaker ones.

A drying droplet changes its morphological pattern depending upon complex pattern forming system. To control the distribution of solute particles in a droplet during drying is an important aspect in many scientific and industrial purposes. In this work, with the help of optical microscopy, we study characteristic patterns generated in dried drops of colloidal copper sulphate (CuSO${}_4\cdot$5H₂O) solution on surface of glass. At lower concentration of salt solution the growth pattern follows a monofractal structure whereas at higher concentration, the self-assembled pattern gradually gets disappeared. Calculating the fractal dimension (FD) of the generated patterns by box counting method with help of imageJ, it is observed that the patterns resemble DLA structure through a specific range of concentration of the salt solution.

We study the aggregation process on the geometric graph. The geometric graph is composed by sites randomly distributed in space and connected locally. Similar to the regular lattice, the network possesses local connection, but the randomness in the spatial distribution of sites is considered. We show that the correlations within the aggregate patterns fall off with distance with a fractional power law. The numerical simulation results indicate that the aggregate patterns on the geometric graph are fractal. The fractals are robust against the randomness in the structure. A remarkable new feature of the aggregate patterns due to the geometric graph is that the fractal dimension can be adjusted by changing the connection degree of the geometric graph.

This paper introduces a modified DLA model, based on a fractional diffusion mechanism, as a novel approach to modeling fractal growth. The specific memory performance of fractional operators can be reflected macroscopically in aggregated patterns eventually. The influence of the model’s order on the structure and behavior of its pattern is further quantitatively described by anisotropy index and fractal dimension. Some simulations are provided to illustrate the correctness and effectiveness of the main results.

A model of particle-cluster aggregation on the rewired small-world network is studied. In this model, particles can adjoin to the end of the rewired long-range edges. The rewired long-range edge is controlled by two parameters, the reconnecting probability and distance controlling parameter. The simulation results indicate that, with the increasing of the length and the number of rewired long-range edges, the patterns become diffuse and the fractal dimensions of the aggregates decrease. The range of the value of dimension and the feature of patterns obtained in the model are consistent with the amyloid deposits.