Schr\"odinger operator on homogeneous metric trees: spectrum in gaps

The paper studies the spectral properties of the Schr\"odinger operator $A_{gV} = A_0 + gV$ on a homogeneous rooted metric tree, with a decaying real-valued potential $V$ and a coupling constant $g\ge 0$. The spectrum of the free Laplacian $A_0 = -\Delta$ has a band-gap structure with a single eigenvalue of infinite multiplicity in the middle of each finite gap. The perturbation $gV$ gives rise to extra eigenvalues in the gaps. These eigenvalues are monotone functions of $g$ if the potential $V$ has a fixed sign. Assuming that the latter condition is satisfied and that $V$ is symmetric, i.e. depends on the distance to the root of the tree, we carry out a detailed asymptotic analysis of the counting function of the discrete eigenvalues in the limit $g\to\infty$. Depending on the sign and decay of $V$, this asymptotics is either of the Weyl type or is completely determined by the behaviour of $V$ at infinity.Comment: AMS LaTex file, 47 page

Transition absorption as a mechanism of surface photoelectron emission from metals

Transition absorption of electromagnetic field energy by an electron passing through a boundary between two media with different dielectric permittivities is considered both classically and quantum mechanically. It is shown that transition absorption can make a substantial contribution to the process of electron photoemission from metals due to the surface photoelectric effect.Comment: 4 pages, 3 figure

Исследование углекислого газа и метана в глобальном и региональном (Сибирь) масштабах: обзор

Статья на рус. яз. с.

Social flocculation in plant–animal worms

Individual animals can often move more safely or more efficiently as members of a group. This can be as simple as safety in numbers or as sophisticated as aerodynamic or hydrodynamic cooperation. Here, we show that individual plant–animal worms (Symsagittifera roscoffensis) can move to safety more quickly through flocculation. Flocs form in response to turbulence that might otherwise carry these beach-dwelling worms out to sea. They allow the worms to descend much more quickly to the safety of the substrate than single worms could swim. Descent speed increases with floc size such that larger flocs can catch up with smaller ones and engulf them to become even larger and faster. To our knowledge, this is the first demonstration of social flocculation in a wild, multicellular organism. It is also remarkable that such effective flocculation occurs where the components are comparatively large multicellular organisms organized as entangled ensembles

Maladaptation and the paradox of robustness in evolution

Background. Organisms use a variety of mechanisms to protect themselves against perturbations. For example, repair mechanisms fix damage, feedback loops keep homeostatic systems at their setpoints, and biochemical filters distinguish signal from noise. Such buffering mechanisms are often discussed in terms of robustness, which may be measured by reduced sensitivity of performance to perturbations. Methodology/Principal Findings. I use a mathematical model to analyze the evolutionary dynamics of robustness in order to understand aspects of organismal design by natural selection. I focus on two characters: one character performs an adaptive task; the other character buffers the performance of the first character against perturbations. Increased perturbations favor enhanced buffering and robustness, which in turn decreases sensitivity and reduces the intensity of natural selection on the adaptive character. Reduced selective pressure on the adaptive character often leads to a less costly, lower performance trait. Conclusions/Significance. The paradox of robustness arises from evolutionary dynamics: enhanced robustness causes an evolutionary reduction in the adaptive performance of the target character, leading to a degree of maladaptation compared to what could be achieved by natural selection in the absence of robustness mechanisms. Over evolutionary time, buffering traits may become layered on top of each other, while the underlying adaptive traits become replaced by cheaper, lower performance components. The paradox of robustness has widespread implications for understanding organismal design

Optimization of therapy on the basis of mathematical model individualized in real time

In article methods for synthesis and therapy optimization are offered