146 research outputs found
On an effective solution of the optimal stopping problem for random walks
We find a solution of the optimal stopping problem for the case when a reward function is an integer power function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first crossing time through a level defined as the largest root of Appell's polynomial associated with the maximum of the random walk. It is also shown that a value function of the optimal stopping problem on the finite interval {0, 1, . . . , T} converges with an exponential rate as T â â to the limit under the assumption that jumps of the random walk are exponentially bounded
An Exact Formula for the Average Run Length to False Alarm of the Generalized Shiryaev-Roberts Procedure for Change-Point Detection under Exponential Observations
We derive analytically an exact closed-form formula for the standard minimax
Average Run Length (ARL) to false alarm delivered by the Generalized
Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a
shift in the baseline mean of a sequence of independent exponentially
distributed observations. Specifically, the formula is found through direct
solution of the respective integral (renewal) equation, and is a general result
in that the GSR procedure's headstart is not restricted to a bounded range, nor
is there a "ceiling" value for the detection threshold. Apart from the
theoretical significance (in change-point detection, exact closed-form
performance formulae are typically either difficult or impossible to get,
especially for the GSR procedure), the obtained formula is also useful to a
practitioner: in cases of practical interest, the formula is a function linear
in both the detection threshold and the headstart, and, therefore, the ARL to
false alarm of the GSR procedure can be easily computed.Comment: 9 pages; Accepted for publication in Proceedings of the 12-th
German-Polish Workshop on Stochastic Models, Statistics and Their
Application
Random walk with barriers: Diffusion restricted by permeable membranes
Restrictions to molecular motion by barriers (membranes) are ubiquitous in
biological tissues, porous media and composite materials. A major challenge is
to characterize the microstructure of a material or an organism
nondestructively using a bulk transport measurement. Here we demonstrate how
the long-range structural correlations introduced by permeable membranes give
rise to distinct features of transport. We consider Brownian motion restricted
by randomly placed and oriented permeable membranes and focus on the
disorder-averaged diffusion propagator using a scattering approach. The
renormalization group solution reveals a scaling behavior of the diffusion
coefficient for large times, with a characteristically slow inverse square root
time dependence. The predicted time dependence of the diffusion coefficient
agrees well with Monte Carlo simulations in two dimensions. Our results can be
used to identify permeable membranes as restrictions to transport in disordered
materials and in biological tissues, and to quantify their permeability and
surface area.Comment: 8 pages, 3 figures; origin of dispersion clarified, refs adde
Long Lived Fourth Generation and the Higgs
A chiral fourth generation is a simple and well motivated extension of the
standard model, and has important consequences for Higgs phenomenology. Here we
consider a scenario where the fourth generation neutrinos are long lived and
have both a Dirac and Majorana mass term. Such neutrinos can be as light as 40
GeV and can be the dominant decay mode of the Higgs boson for Higgs masses
below the W-boson threshold. We study the effect of the Majorana mass term on
the Higgs branching fractions and reevaluate the Tevatron constraints on the
Higgs mass. We discuss the prospects for the LHC to detect the semi-invisible
Higgs decays into fourth generation neutrino pairs. Under the assumption that
the lightest fourth generation neutrino is stable, it's thermal relic density
can be up to 20% of the observed dark matter density in the universe. This is
in agreement with current constraints on the spin dependent neutrino-neutron
cross section, but can be probed by the next generation of dark matter direct
detection experiments.Comment: v1: 19 pages, 5 figures; v2: References added; v3: version to appear
in JHE
Electric field gradients in s-, p- and d-metal diborides and the effect of pressure on the band structure and T in MgB
Results of FLMTO-GGA (full-potential linear muffin-tin orbital -- generalized
gradient approximation) calculations of the band structure and boron electric
field gradients (EFG) for the new medium-T superconductor (MTSC), MgB,
and related diborides MB, M=Be, Al, Sc, Ti, V, Cr, Mo and Ta are reported.
The boron EFG variations are found to be related to specific features of their
band structure and particularly to the M-B hybridization. The strong charge
anisotropy at the B site in MgB is completely defined by the valence
electrons - a property which sets MgB apart from other diborides. The boron
EFG in MgB is weakly dependent of applied pressure: the B p electron
anisotropy increases with pressure, but it is partly compensated by the
increase of core charge assymetry. The concentration of holes in bonding
bands is found to decrease slightly from 0.067 to 0.062 holes/B under
a pressure of 10 GPa. Despite a small decrease of N(E), the Hopfield
parameter increases with pressure and we believe that the main reason for the
reduction under pressure of the superconducting transition temperature, T,
is the strong pressure dependence of phonon frequencies, which is sufficient to
compensate the electronic effects.Comment: 12 pages, 3 figure
Witten index in supersymmetric 3d theories revisited
We have performed a direct calculation of Witten index in N = 1,2,3
supersymmetric Yang-Mills Chern-Simons 3d theories. We do it in the framework
of Born-Oppenheimer (BO) approach by putting the system into a small spatial
box and studying the effective Hamiltonian depending on the zero field
harmonics. At the tree level, our results coincide with the results of Witten,
but there is a difference in the way the loop effects are implemented. In
Witten's approach, one has only take into account the fermion loops, which
bring about a negative shift of the (chosen positive at the tree level)
Chern-Simons coupling k. As a result, Witten index vanishes and supersymmetry
is broken at small k. In the effective BO Hamiltonian framework, fermion, gluon
and ghost loops contribute on an equal footing. Fermion loop contribution to
the effective Hamiltonian can be evaluated exactly, and their effect amounts to
the negative shift k -> k - h/2 for N =1 and k -> k - h for N = 2,3 in the
tree-level formulae for the index. In our approach, with rather natural
assumptions on the structure of bosonic corrections, the shift k -> k + h
brought about by the gluon loops also affects the index. Since the total shift
of k is positive or zero, Witten index appears to be nonzero at nonzero k, and
supersymmetry is not broken. We discuss possible reasons for such disagreement.Comment: A bug in Eq.(2.20) is fixe
Search for Heavy Neutral and Charged Leptons in e+ e- Annihilation at LEP
A search for exotic unstable neutral and charged heavy leptons as well as for
stable charged heavy leptons is performed with the L3 detector at LEP.
Sequential, vector and mirror natures of heavy leptons are considered. No
evidence for their existence is found and lower limits on their masses are set
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