Hitchin Fibrations on Two-Dimensional Moduli Spaces of Irregular Higgs Bundles with One Singular Fiber

We analyze and completely describe the four cases when the Hitchin fibration on a $2$-dimensional moduli space of irregular Higgs bundles over $\mathbb{C}P^{1}$ has a single singular fiber. The case when the fiber at infinity is of type $I_0^*$ is further analyzed, and we give constructions of all the possible configurations of singular curves inelliptic fibrations having this type of singular fiber at infinity

Combinatorial Heegaard Floer homology and sign assignments

We provide an intergral lift of the combinatorial definition of Heegaard Floer homology for nice diagrams, and show that the proof of independence using convenient diagrams adapts to this setting.Comment: 51 pages, 32 figure

How much is involved in DB publishing?

XML has been intensive investigated lately, with the sentence, that "XML is (has been) the standard form for data publishing", especially in data base area.That is, there are assumptions, that the newly published data take mostly the form of XML documents, particularly when databases are involved. This presumption seems to be the reason of the heavy investment applied for researching the topics of handling, querying and comprising XML documents. We check these assumptions by investigating the documents accessible on the Internet, possible going under the surface, into the "deep Web". The investigation involves analyzing large scientific databases, but the commercial data stored in the "deep Web" will be handled also.We used the technique of randomly generated IP addresses for investigating the "deep Web", i.e. the part of the Internet not indexed by the search engines. For the part of the Web that is accessed (indexed) by the large search engines we used the random walk technique to collect uniformly distributed samplings. We found, that XML has not(yet) been the standard of Web publishing, but it is strongly represented on the Web. We add a simple new evaluation method to the known uniformly sampling processes.These investigations can be repeated in the future in order to get a dynamic picture of the growing rate of the number of the XML documents present on the Web

Is Quantum Mechanics Compatible with a Deterministic Universe? Two Interpretations of Quantum Probabilities

Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the Aspect-type EPR experiment. It will be shown that the quantum mechanical probabilities appearing in this experiment can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies in the Aspect experiment that quantum theory is incompatible with a deterministic universe.Comment: REVISED VERSION! ONLY SMALL CHANGES IN THE TEXT! compressed and uuencoded postscript, a uuencoded version of a demo program file (epr.exe for DOS) is attached as a "Figure