We give a complete classification and present new exotic phenomena of the meromorphic structure of ζ-functions associated to general selfadjoint extensions of Laplace-type operators over conic manifolds. We show that the meromorphic extensions of these ζ-functions have, in general, countably many logarithmic branch cuts on the nonpositive real axis and unusual locations of poles with arbitraril...

SUDDEN THROMBOSIS of an aneurysnm of the abdominal aorta is an extremely rare complication. More commonly, abdominal aortic aneurysms rupture and bleed either retroperitoneally, into the free peritoneal cavity, or into adjacent bowel or mesentery. By contrast, the commonest complications of popliteal aneurysms are acute occlusion due to thrombosis of the aneurysm and peripheral embolic occlusio...

Modeling a complex phenomenon such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, a problem or some theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes mo...

We introduce a three-dimensional, computationally feasible, mesoscopic model for snow-crystal growth, based on diffusion of vapor, anisotropic attachment, and a boundary layer. Several case studies are presented that faithfully replicate most observed snow-crystal morphology, an unusual achievement for a mathematical model. In particular, many of the most striking physical specimens feature bot...

We investigate the Schelling model of social segregation, formulated as an intrinsically nonequilibrium system, in which the agents occupy districts (or patches) rather than sites on a grid. We show that this allows the equations governing the dynamical behavior of the model to be derived. Analysis of these equations reveals a jamming transition in the regime of low-vacancy density, and inclusi...

This polymer is characterized by relatively high gas permeability, (Р(О2)=800 Barrer, Р(СО2)=4350 Barrer). It is interesting that for the series of gaseous alkanes С1-С4 permeability increases when the size of the penetrant increases and reaches the value Р(С4Н10)=17500 Barrer (at 1 atm). It is also noteworthy that this polymer keeps high permselectivity in separation of the mixture butane/meth...

Received: 29 September 2005 Revised: 30 September 2005 Accepted: 30 September 2005 Introduction In this short paper I want to do something unusual (as I think Claudio would want me to). I want to celebrate Claudio’s life, his particular way of being, and simultaneously challenge us to use this reflection to think more carefully about the phenomena we study: the world of particular information s...

In optical experiments one-sided reflectionless (ORL) and coherent perfect absorption (CPA) are unusual scattering properties yet fascinating for their fundamental aspects and for their practical interest. Although these two concepts have so far remained separated from each other, we prove that the two phenomena are indeed strictly connected. We show that a CPA-ORL connection exists between pai...

We consider insulating states of spin-one bosons in optical lattices in the presence of a weak magnetic field. For the states with more than one atom per lattice site we find a series of quantum phase transitions between states with fixed magnetization and a canted nematic phase. In the presence of a global confining potential, this unusual phase diagram leads to several novel phenomena, includ...

In 2008 P. Nurse advocated the pursuit of biological phenomena through information processing. Along these lines, we aim to explain some of the salient characteristics of the mapping between amino acid sequences to protein folds through an information theoretic lens. To this end, we propose a protein folding channel that maps protein sequences into two-dimensional self-avoiding walks (also call...