DAHA approach to iterated torus links

We extend the construction of the DAHA-Jones polynomials for any reduced root systems and DAHA-superpolynomials in type A from the iterated torus knots (our previous paper) to links, including arbitrary algebraic links. Such a passage essentially corresponds to the usage of the products of Macdonald polynomials and is directly connected to the so-called splice diagrams. The specialization t=q of our superpolynomials conjecturally results in the HOMFLY-PT polynomials. The relation of our construction to the stable Khovanov-Rozansky polynomials and the so-called ORS-polynomials of the corresponding plane curve singularities is expected for algebraic links in the uncolored case. These 2 connections are less certain, since the Khovanov-Rozansky theory for links is not sufficiently developed and the ORS polynomials are quite involved. However we provide some confirmations. For Hopf links, our construction produces the DAHA-vertex, similar to the refined topological vertex, which is an important part of our paper.Comment: v3: Further editing, essentially a somewhat extended version of our article in Contemporary Mathematic

Integrative concept of homeostasis: translating physiology into medicine

To truly understand living systems they must be viewed as a whole. In order to achieve this and to come to some law to which living systems obey, data obtained on cells, tissues and organs should be integrated. Because there are no such laws yet, there is usually a long path for physiological findings obtained by reductionist approaches to be translated into medical practice. The concept and accompanying equations of homeostasis presented here are aimed to develop biological laws and to bridge this gap between physiology and medicine. The concept of homeostasis takes into account energy input and output, enlisting all relevant contributors. In homeostasis, input should equal the output. What I suggest here is that if the system is out of homeostasis, the homeostasis may be regained by changing any of the input or output components in an adequate manner, not only the one that has changed first. The proposed equation should enable for new lab findings regarding any pathophysiological conditions to find a more direct use in medicine. It should also ease ‘decision making’ in medicine and make therapy development and treatment outcome more straightforward and predictable. Finally, to recognize the basic laws of living systems enables for evolutionary adaptations and processes to be understood better