Cell lineage tracing is a fundamental digital image processing tool for developmental biologists to probe the roles of cell differentiation, cell adhesion, and cell movement among other biophysical principles, in developmental programs. In this project I create an extension of cell lineage tracingtissue fate mapping or tissue lineage tracing. Tissue lineage tracing is useful for observing bioph...

We analyze ‘Distribution to Distribution regression’ where one is regressing a mapping where both the covariate (inputs) and response (outputs) are distributions. No parameters on the input or output distributions are assumed, nor are any strong assumptions made on the measure from which input distributions are drawn from. We develop an estimator and derive an upper bound for the L2 risk; also,...

human was created from both the natural and spiritual dimensions and has multimodal functions (e.g., cognitive, behavioral, affective, sensation, interpersonal relationship, and etc.). having one-dimensional impression in life would provide anxiety predisposition for man, but then having an integrated and monotheistic view would result in an assimilated psychological discipline for him/her. the...

Dimension is a standard and well-studied measure of complexity of posets. Recent research has provided many new upper bounds on the dimension for various structurally restricted classes of posets. Bounded dimension gives a succinct representation of the poset, admitting constant response time for queries of the form “is x < y?”. This application motivates looking for stronger notions of dimensi...

In this report, we give a brief survey of various results relating the Teaching Dimension and VC-Dimension. The concept of Teaching Dimension was first introduced by Goldman and Kearns, 1995 and Sinohara and Miyano, 1991. In this model, an algorithm tries to learn the hidden concept c from examples, called the teaching set, which uniquely identifies c from the rest of the concepts in the concep...

‎In this essay we introduce and study the notion of dimension for observers via Caratheodory structures and relative probability measures‎. ‎We show that the dimension as a three variables function is an increasing function on observers‎, ‎and decreasing function on the cuts of an observer‎. ‎We find observers with arbitrary non-negative dimensions‎. ‎We show that Caratheodory dimension for obs...

Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are establ...

Different cues present in the cellular environment control basic biological processes. A previously established 3D microwell array was used to study dimensionality-related effects on osteogenic differentiation and plasticity of marrow stromal cells. To enable long-term culture of single cells in the array a novel surface functionalization technique was developed, using the principle of subtract...

There are two kinds of algorithms: those that are ‘better’ with respect to accuracy and those that are ‘faster’. In the past, fractal analysis by means of box-counting including both, binary and greyscale analysis has been focused on the former. In our work, however, we want to aim at the second category: algorithms that are fast and easy to use, without losing view on significance. To this end...