When calcium salts are added to an aqueous solution of polysaccharide pectin, ionic cross-links form between pectin chains, giving rise to a gel network in dilute solution. In this work, dynamic light scattering (DLS) is employed to study the microscopic dynamics of the fractal aggregates (flocs) that constitute the gels, while rheological measurements are carried out to study the process of ge...

During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In t...

On the one hand, the large scale structure of matter is arguably scale invariant, and, on the other hand, halos and voids are recognized as prominent features of that structure. To unify both approaches, we propose to model the dark matter distribution as a set of fractal distributions of halos of different kinds. This model relies on the concept of multifractal as the most general scaling dist...

We study with Monte Carlo methods an ensemble of c = −5 gravity graphs, generated by coupling a conformal field theory with central charge c = −5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent γs and the intrinsic fractal dimensions dH . We find γs = −1.5(1) and dH = 3.36(4), in reasonable agreement with theoreti...

The model developed by Springer and Tsai is extended using non-linear volume fraction in place of physical porosity for the effective thermal conductivity of composite materials with the help of local fractal techniques. The expression for non-linear volume fraction is obtained using data available in the literature. Present model is constructed in terms of fiber volume fraction, the fiber-matr...

For the familiar Fibonacci sequence (defined by f1 = f2 = 1, and fn = fn−1 + fn−2 for n > 2), fn increases exponentially with n at a rate given by the golden ratio (1 + √ 5)/2 = 1.61803398 . . . . But for a simple modification with both additions and subtractions — the random Fibonacci sequences defined by t1 = t2 = 1, and for n > 2, tn = ±tn−1 ± tn−2, where each ± sign is independent and eithe...

let $a = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrixwhere $n geq 2$. let $dt(a)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. let $g$ be a connected graph with blocks $b_1, b_2, ldots b_p$ and with$q$-exponential distance matrix $ed_g$. we given an explicitformula for $dt(ed_g)$ which shows that $dt(ed_g)$ is independent of the manner in ...

Motivated by applications in which the data may be formulated as a matrix, we consider algorithms for several common linear algebra problems. These algorithms make more efficient use of computational resources, such as the computation time, random access memory (RAM), and the number of passes over the data, than do previously known algorithms for these problems. In this paper, we devise two alg...

The structural characterization of subtilisin mesoscale clusters, which were previously shown to induce supramolecular order in biocatalytic self-assembly of Fmoc-dipeptides, was carried out by synchrotron small-angle X-ray, dynamic, and static light scattering measurements. Subtilisin molecules self-assemble to form supramolecular structures in phosphate buffer solutions. Structural arrangemen...

The Grundy number of an impartial game G is the size of the unique Nim heap equal to G. We introduce a new variant of Nim, Restricted Nim, which restricts the number of stones a player may remove from a heap in terms of the size of the heap. Certain classes of Restricted Nim are found to produce sequences of Grundy numbers with a self-similar fractal structure. Extending work of C. Kimberling, ...