Temporal and dimensional effects in evolutionary graph theory

The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as N^{(D+1)/D} in D-dimensional hypercubic lattices and as N ln N in fully-connected graphs. It is shown that the surface of the interface between mutants and non-mutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction. Includes supplementary information.Comment: 6 pages, 4 figures Replaced after final round of peer revie

Conductance Phases in Aharonov-Bohm Ring Quantum Dots

The regimes of growing phases (for electron numbers N~0-8) that pass into regions of self-returning phases (for N>8), found recently in quantum dot conductances by the Weizmann group are accounted for by an elementary Green function formalism, appropriate to an equi-spaced ladder structure (with at least three rungs) of electronic levels in the quantum dot. The key features of the theory are physically a dissipation rate that increases linearly with the level number (and tentatively linked to coupling to longitudinal optical phonons) and a set of Fano-like meta-stable levels, which disturb the unitarity, and mathematically the change over of the position of the complex transmission amplitude-zeros from the upper-half in the complex gap-voltage plane to the lower half of that plane. The two regimes are identified with (respectively) the Blaschke-term and the Kramers-Kronig integral term in the theory of complex variables.Comment: 20 pages, 4 figure

On L2L^2 -functions with bounded spectrum

We consider the class $PW(\mathbb R^n)$ of functions in $L^2(\mathbb R^n)$, whose Fourier transform has bounded support. We obtain a description of continuous maps $\varphi : \mathbb R^m\rightarrow\mathbb R^n$ such that $f\circ\varphi\in PW(\mathbb R^m)$ for every function $f\in PW(\mathbb R^n)$. Only injective affine maps $\varphi$ have this property

A systematic review with meta-analysis of studies comparing response to experimentally-evoked pain between obese and non-obese individuals

© 2018 Astita et al. Background: The relationship between obesity and pain remains unclear. The aim of this systematic review was to determine whether response to experimentally-evoked pain differed between obese and non-obese individuals. Studies that compared responses to experimentally-evoked pain between obese and non-obese human participants post-puberty (i.e. >16 years) were sought. Eligible studies published between January 1950 and May 2017 were identified by searching OVID, MEDLINE, EMBASE and Science Direct. Explanation: Methodological quality of included studies was assessed using the ‘QualSyst’ questionnaire. Of 1106 references identified only nine studies (683 participants) were eligible for review. Pressure pain was assessed in five studies and electrical pain in three studies. Two studies investigated thermal pain. Obesity was categorized according to body mass index (BMI) or as weight as a percentage of ideal body weight. Six of the nine included studies were of low methodological quality. There was a lack of extractable data to pool for meta-analysis of studies using thermal or electrical pain. A forest plot of data extracted from four studies on pressure pain threshold found no differences between obese and non-obese groups (overall effect size was Z=0.57, p=0.57). Conclusion: Small sample size was the main limitation in all studies. Participants with obesity were more sensitive to mechanical noxious stimuli than non-obese participants in three of five studies. However, overall, it was not possible to determine whether there are differences in pain sensitivity response to experimental stimuli between obese and non-obese individuals

Corneoscleral laceration and ocular burns caused by electronic cigarette explosions

PURPOSE: To report cases of acute globe rupture and bilateral corneal burns from electronic cigarette (EC) explosions. METHODS: Case series. RESULTS: We describe a series of patients with corneal injury caused by EC explosions. Both patients suffered bilateral corneal burns and decreased visual acuity, and one patient sustained a unilateral corneoscleral laceration with prolapsed iris tissue and hyphema. A review of the scientific literature revealed no prior reported cases of ocular injury secondary to EC explosions; however, multiple media and government agency articles describe fires and explosions involving ECs, including at least 4 with ocular injuries. CONCLUSIONS: Given these cases and the number of recent media reports, ECs pose a significant public health risk. Users should be warned regarding the possibility of severe injury, including sight-threatening ocular injuries ranging from corneal burns to full-thickness corneoscleral laceration

Photon wave mechanics and position eigenvectors

One and two photon wave functions are derived by projecting the quantum state vector onto simultaneous eigenvectors of the number operator and a recently constructed photon position operator [Phys. Rev A 59, 954 (1999)] that couples spin and orbital angular momentum. While only the Landau-Peierls wave function defines a positive definite photon density, a similarity transformation to a biorthogonal field-potential pair of positive frequency solutions of Maxwell's equations preserves eigenvalues and expectation values. We show that this real space description of photons is compatible with all of the usual rules of quantum mechanics and provides a framework for understanding the relationships amongst different forms of the photon wave function in the literature. It also gives a quantum picture of the optical angular momentum of beams that applies to both one photon and coherent states. According to the rules of qunatum mechanics, this wave function gives the probability to count a photon at any position in space.Comment: 14 pages, to be published in Phys. Rev.

On the inconsistency of the Bohm-Gadella theory with quantum mechanics

The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom asserts that the solutions of the Lippmann-Schwinger equation are functionals over spaces of Hardy functions. The preparation-registration arrow of time provides the physical justification for the Hardy axiom. In this paper, it is shown that the Hardy axiom is incorrect, because the solutions of the Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also shown that the derivation of the preparation-registration arrow of time is flawed. Thus, Hardy functions neither appear when we solve the Lippmann-Schwinger equation nor they should appear. It is also shown that the Bohm-Gadella theory does not rest on the same physical principles as quantum mechanics, and that it does not solve any problem that quantum mechanics cannot solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page

On the nonlinearity interpretation of q- and f-deformation and some applications

q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a special type of spectral nonlinearity, which may be generalized to a wider class of f-oscillator algebras. In the framework of this nonlinear interpretation, we discuss the structure of the stochastic process associated to q-deformation, the role of the q-oscillator as a spectrum-generating algebra for fast growing point spectrum, the deformation of fermion operators in solid-state models and the charge-dependent mass of excitations in f-deformed relativistic quantum fields.Comment: 11 pages Late

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru