15,210 research outputs found
Scattering states of a particle, with position-dependent mass, in a symmetric heterojunction
The study of a particle with position-dependent effective mass (pdem), within
a double heterojunction is extended into the complex domain --- when the region
within the heterojunctions is described by a non Hermitian
symmetric potential. After obtaining the exact analytical solutions, the
reflection and transmission coefficients are calculated, and plotted as a
function of the energy. It is observed that at least two of the characteristic
features of non Hermitian symmetric systems --- viz., left / right
asymmetry and anomalous behaviour at spectral singularity, are preserved even
in the presence of pdem. The possibility of charge conservation is also
discussed.Comment: 12 pages, including 6 figures; Journal of Physics A : Math. Theor.
(2012
Boundary crossing Random Walks, clinical trials and multinomial sequential estimation
A sufficient condition for the uniqueness of multinomial sequential unbiased
estimators is provided generalizing a classical result for binomial samples.
Unbiased estimators are applied to infer the parameters of multidimensional or
multinomial Random Walks which are observed until they reach a boundary. An
application to clinical trials is presented
Modular networks emerge from multiconstraint optimization
Modular structure is ubiquitous among complex networks. We note that most
such systems are subject to multiple structural and functional constraints,
e.g., minimizing the average path length and the total number of links, while
maximizing robustness against perturbations in node activity. We show that the
optimal networks satisfying these three constraints are characterized by the
existence of multiple subnetworks (modules) sparsely connected to each other.
In addition, these modules have distinct hubs, resulting in an overall
heterogeneous degree distribution.Comment: 5 pages, 4 figures; Published versio
- …