We utilize the fractal dimension of the perimeter surface of cell sections as a new observable to characterize cells of different types. We propose that it is possible to distinguish cancerous from healthy cells with the aid of this new approach. As a first application we show that it is possible to perform this distinction between patients with hairy-cell lymphocytic leukemia and those with no...

We introduce a new measure for capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term memory), local herding behavior (information dimension) and uncertainty in the process (entropy). The efficiency measure is then taken as a distance from an ideal efficient market situation. Methodology is applied to a portfolio of 41 stock indices. ...

in this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.

Let ∆A(n, d) denote the largest possible average diameter of a bounded cell of a simple arrangement defined by n hyperplanes in dimension d. We have ∆A(n, 2) ≤ 2+ 2 n−1 in the plane, and ∆A(n, 3) ≤ 3+ 4 n−1 in dimension 3. In general, the average diameter of a bounded cell of a simple arrangement is conjectured to be less than the dimension; that is, ∆A(n, d) ≤ d. We propose an hyperplane arran...

we define and studyco-noetherian dimension of rings for which the injective envelopeof simple modules have finite krull-dimension. this  is a moritainvariant dimension that measures how far the ring is from beingco-noetherian. the co-noetherian dimension of certain rings,including commutative rings, are determined. it is shown that the class ${mathcal w}_n$ of rings with co-noetherian dimension...

Two important goals in stem cell research are to control the cell proliferation without differentiation and to direct the differentiation into a specific cell lineage when desired. Here, we demonstrate such paths by controlling only the nanotopography of culture substrates. Altering the dimensions of nanotubular-shaped titanium oxide surface structures independently allowed either augmented hum...

The notion of a cell and that of a cell decomposition has been a central one in the study of certain first-order theories. A cell is a particular kind of definable set. The notion of a cell was first explicitly considered in [8], in the context of the theory of real closed fields. Collins defined a class of cells in this context, and showed that every definable subset of a real closed field is ...

Objective(s): Cell therapy has provided clinical applications to the treatment of motor neuron diseases. The current obstacle in stem cell therapy is to direct differentiation of stem cells into neurons in the neurodegenerative disorders. Biomaterial scaffolds can improve cell differentiation and are widely used in translational medicine and tissue engineering. The aim...

1. Definition of o-minimality and first examples 1 2. Basic real analysis and the monotonicity theorem 4 3. Definable Skolem functions and elimination of imaginaries 8 4. Dimension, part 1 10 5. Cell decomposition 11 6. Dimension, part 2 15 7. Restricted analytic functions and global exponentiation 17 8. NIP and neural networks 20 8.1. Vapnik-Chervonenkis dimension 20 8.2. O-minimal structures ...