Intuitively, in four-dimensional gauge theories one counts instantons, and in twodimensional string theory one counts holomorphic curves. These correspond to the instanton counting and curve counting in the title. There is no obvious connection between them, but a remarkable physical idea called geometric engineering [9, 10, 11] dictates that they are indeed related. More precisely, the generat...

The TopCount Microplate Scintillation and Luminescence Counter has been widely used in biopharmaceutical assays involving both radionuclide and luminescence measurement. A new feature allows the use of TopCount for measuring a high energy beta emitter such as P by Cerenkov counting, a well-known measurement technique that has the main advantage of not requiring the addition of scintillation coc...

Obesity has spread worldwide and become a common health problem in modern society. One typical feature of obesity is the excessive accumulation of fat in adipocytes, which occurs through the following two physiological phenomena: hyperplasia (increase in quantity) and hypertrophy (increase in size) of adipocytes. In clinical and scientific research, the accurate quantification of the number and...

The notions of “labelled set” and “numerosity” are introduced to generalize the counting process of finite sets. The resulting numbers, called numerosities, are then used to develop nonstandard analysis. The existence of a numerosity function is equivalent to the existence of a selective ultrafilter, hence it is independent of the axioms of ZFC.

A similarity measure based on the number of coincident bits in multichannel images is presented. The similarity criterion incorporated in the image registration algorithm uses a coincident bit counting (CBC) method to obtain the number of matching bits between the frames of interest. The CBC method not only performs favorably compared with traditional techniques, but also renders simpler implem...

The counting process of cell colonies is always a long and laborious process that is dependent on the judgment and ability of the operator. The judgment of the operator in counting can vary in relation to fatigue. Moreover, since this activity is time consuming it can limit the usable number of dishes for each experiment. For these purposes, it is necessary that an automatic system of cell colo...

Model counting is the classical problem of computing the number of solutions of a given propositional formula. It vastly generalizes the NP-complete problem of propositional satisfiability, and hence is both highly useful and extremely expensive to solve in practice. We present a new approach to model counting that is based on adding a carefully chosen number of so-called streamlining constrain...

Palmer [1] has the advantage of being simple to implement and have good performances compared to the other similarity measures [2]. Nevertheless, the Wu and Palmer measure present the following disadvantage: in some situations, the similarity of two elements of an IS-A ontology contained in the neighborhood exceeds the similarity value of two elements contained in the same hierarchy. This situa...

In 2007, researchers at Boston’s Massachusetts General Hospital (MGH) Cancer Center showed that a microfluidic device, the CTC-Chip, could separate and count rare circulating tumor cells (CTCs) in wholeblood samples (Nature 2007;450:1235–9). Last year, the team developed the CTCiChip, a refined version of its predecessor, and confirmed its utility in catching viable CTCs. This device can profil...

These notes are intended as an easy-to-read supplement to some of the background material presented in my talks on enumerative geometry. In particular, the numbers n3 and n4 of plane rational cubics through eight points and of plane rational quartics through eleven points are determined via the classical approach of counting curves. The computation of the latter number also illustrates my topol...