5,038 research outputs found
Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
We investigate properties of the most general PT-symmetric non-Hermitian
Hamiltonian of cubic order in the annihilation and creation operators as a ten
parameter family. For various choices of the parameters we systematically
construct an exact expression for a metric operator and an isospectral
Hermitian counterpart in the same similarity class by exploiting the
isomorphism between operator and Moyal products. We elaborate on the subtleties
of this approach. For special choices of the ten parameters the Hamiltonian
reduces to various models previously studied, such as to the complex cubic
potential, the so-called Swanson Hamiltonian or the transformed version of the
from below unbounded quartic -x^4-potential. In addition, it also reduces to
various models not considered in the present context, namely the single site
lattice Reggeon model and a transformed version of the massive sextic
x^6-potential, which plays an important role as a toy modelto identify theories
with vanishing cosmological constant.Comment: 21 page
Directional selection effects on patterns of phenotypic (co)variation in wild populations.
Phenotypic (co)variation is a prerequisite for evolutionary change, and understanding how (co)variation evolves is of crucial importance to the biological sciences. Theoretical models predict that under directional selection, phenotypic (co)variation should evolve in step with the underlying adaptive landscape, increasing the degree of correlation among co-selected traits as well as the amount of genetic variance in the direction of selection. Whether either of these outcomes occurs in natural populations is an open question and thus an important gap in evolutionary theory. Here, we documented changes in the phenotypic (co)variation structure in two separate natural populations in each of two chipmunk species (Tamias alpinus and T. speciosus) undergoing directional selection. In populations where selection was strongest (those of T. alpinus), we observed changes, at least for one population, in phenotypic (co)variation that matched theoretical expectations, namely an increase of both phenotypic integration and (co)variance in the direction of selection and a re-alignment of the major axis of variation with the selection gradient
Higgs Sector of the Left-Right Model with Explicit CP Violation
We explore the Higgs sector of the Minimal Left-Right (LR) Model based on the
gauge group SU(2)_L x SU(2)_R x U(1)_{B-L} with explicit CP violation in the
Higgs potential. Since flavour-changing neutral current experiments and the
small scale of neutrino masses both place stringent constraints on the Higgs
potential, we seek to determine whether minima of the Higgs potential exist
that are consistent with current experimental bounds. We focus on the case in
which the right-handed symmetry-breaking scale is only ``moderately'' large, of
order 15-50 TeV. Unlike the case in which the Higgs potential is CP-invariant,
the CP noninvariant case does yield viable scenarios, although these require a
small amount of fine-tuning. We consider a LR model supplemented by an
additional U(1) horizontal symmetry, which results in a Higgs sector consistent
with current experimental constraints and a realistic spectrum of neutrino
masses.Comment: 20 pages, 2 figure
Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters
Recent analyses of the field enhancement factor (FEF) from multiple emitters
have revealed that the depolarization effect is more persistent with respect to
the separation between the emitters than originally assumed. It has been shown
that, at sufficiently large separations, the fractional reduction of the FEF
decays with the inverse cube power of separation, rather than exponentially.
The behavior of the fractional reduction of the FEF encompassing both the range
of technological interest ( being the separation and is
the height of the emitters) and , has not been predicted by
the existing formulas in field emission literature, for post-like emitters of
any shape. In this letter, we use first principles to derive a simple
two-parameter formula for fractional reduction that can be of interest for
experimentalists to modeling and interpret the FEF from small clusters of
emitters or arrays in small and large separations. For the structures tested,
the agreement between numerical and analytical data is
Two novel evolutionary formulations of the graph coloring problem
We introduce two novel evolutionary formulations of the problem of coloring
the nodes of a graph. The first formulation is based on the relationship that
exists between a graph's chromatic number and its acyclic orientations. It
views such orientations as individuals and evolves them with the aid of
evolutionary operators that are very heavily based on the structure of the
graph and its acyclic orientations. The second formulation, unlike the first
one, does not tackle one graph at a time, but rather aims at evolving a
`program' to color all graphs belonging to a class whose members all have the
same number of nodes and other common attributes. The heuristics that result
from these formulations have been tested on some of the Second DIMACS
Implementation Challenge benchmark graphs, and have been found to be
competitive when compared to the several other heuristics that have also been
tested on those graphs.Comment: To appear in Journal of Combinatorial Optimizatio
Modeling the input history of programs for improved instruction-memory performance
When a program is loaded into memory for execution, the relative position of
its basic blocks is crucial, since loading basic blocks that are unlikely to be
executed first places them high in the instruction-memory hierarchy only to be
dislodged as the execution goes on. In this paper we study the use of Bayesian
networks as models of the input history of a program. The main point is the
creation of a probabilistic model that persists as the program is run on
different inputs and at each new input refines its own parameters in order to
reflect the program's input history more accurately. As the model is thus
tuned, it causes basic blocks to be reordered so that, upon arrival of the next
input for execution, loading the basic blocks into memory automatically takes
into account the input history of the program. We report on extensive
experiments, whose results demonstrate the efficacy of the overall approach in
progressively lowering the execution times of a program on identical inputs
placed randomly in a sequence of varied inputs. We provide results on selected
SPEC CINT2000 programs and also evaluate our approach as compared to the gcc
level-3 optimization and to Pettis-Hansen reordering
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