4,514 research outputs found
An optimal statistical testing policy for software reliability demonstration of safety-critical systems
When software reliability demonstration of safety-critical systems by statistical testing is treated as a Test, Analyse and Fix (TAAF) process, an optimal testing policy can be found, which maximises the probability of success of the whole process, over a pre-determined period of time. The optimisation problem is formulated, solved by stochastic dynamic programming, and demonstrated by two numerical examples
Reliability demonstration for safety-critical systems
This paper suggests a new model for reliability demonstration of safety-critical systems, based on the TRW Software Reliability Theory. The paper describes the model; the test equipment required and test strategies based on the various constraints occurring during software development. The paper also compares a new testing method, Single Risk Sequential Testing (SRST), with the standard Probability Ratio Sequential Testing method (PRST), and concludes that: • SRST provides higher chances of success than PRST • SRST takes less time to complete than PRST • SRST satisfies the consumer risk criterion, whereas PRST provides a much smaller consumer risk than the requirement
Chaotic Quivering of Micron-Scaled On-Chip Resonators Excited by Centrifugal Optical Pressure
Opto-mechanical chaotic oscillation of an on-chip resonator is excited by the radiation-pressure nonlinearity. Continuous optical input, with no external feedback or modulation, excites chaotic vibrations in very different geometries of the cavity (both tori and spheres) and shows that opto-mechanical chaotic oscillations are an intrinsic property of optical microcavities. Measured phenomena include period doubling, a spectral continuum, aperiodic oscillations, and complex trajectories. The rate of exponential divergence from a perturbed initial condition (Lyapunov exponent) is calculated. Continuous improvements in cavities mean that such chaotic oscillations can be expected in the future with many other platforms, geometries, and frequency spans
Opto-Mechanical Chaotic Behaviour of Micron-Scaled On-Chip Resonators
Opto-mechanical vibration of an on-chip oscillator is experimentally excited by radiation-pressure nonlinearity to a regime where oscillation is chaotic. Period-doubling and broad power spectra are measured in spherical and toroidal-resonators
Optimal nutritional intake for fetal growth
View online at publisher's website: http://www.aimsciences.org/journals/displayArticles.jsp?paperID=6249The regular nutritional intake of an expectant mother clearly affects the weight development of the fetus. Assuming the growth of the fetus follows a deterministic growth law, like a logistic equation, albeit dependent on the nutritional intake, the ideal solution is usually determined by the birth-weight being pre-assigned, for example, as a percentage of the mother's average weight. This problem can then be specified as an optimal control problem with the daily intake as the control, which appears in a Michaelis-Menten relationship, for which there are well-developed procedures to follow. The best solution is determined by requiring minimum total intake under which the preassigned birth weight is reached. The algorithm has been generalized to the case where the fetal weight depends in a detailed way on the cumulative intake, suitably discounted according to the history. The optimality system is derived and then solved numerically using an iterative method for the specific values of parameter. The procedure is generic and can be adapted to any growth law and any parameterisation obtained by the detailed physiology
Quantum Detection with Unknown States
We address the problem of distinguishing among a finite collection of quantum
states, when the states are not entirely known. For completely specified
states, necessary and sufficient conditions on a quantum measurement minimizing
the probability of a detection error have been derived. In this work, we assume
that each of the states in our collection is a mixture of a known state and an
unknown state. We investigate two criteria for optimality. The first is
minimization of the worst-case probability of a detection error. For the second
we assume a probability distribution on the unknown states, and minimize of the
expected probability of a detection error.
We find that under both criteria, the optimal detectors are equivalent to the
optimal detectors of an ``effective ensemble''. In the worst-case, the
effective ensemble is comprised of the known states with altered prior
probabilities, and in the average case it is made up of altered states with the
original prior probabilities.Comment: Refereed version. Improved numerical examples and figures. A few
typos fixe
New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation
A propagation method for the time dependent Schr\"odinger equation was
studied leading to a general scheme of solving ode type equations. Standard
space discretization of time-dependent pde's usually results in system of ode's
of the form u_t -Gu = s where G is a operator (matrix) and u is a
time-dependent solution vector. Highly accurate methods, based on polynomial
approximation of a modified exponential evolution operator, had been developed
already for this type of problems where G is a linear, time independent matrix
and s is a constant vector. In this paper we will describe a new algorithm for
the more general case where s is a time-dependent r.h.s vector. An iterative
version of the new algorithm can be applied to the general case where G depends
on t or u. Numerical results for Schr\"odinger equation with time-dependent
potential and to non-linear Schr\"odinger equation will be presented.Comment: 14 page
Transcription factor search for a DNA promoter in a three-states model
To ensure fast gene activation, Transcription Factors (TF) use a mechanism
known as facilitated diffusion to find their DNA promoter site. Here we analyze
such a process where a TF alternates between 3D and 1D diffusion. In the latter
(TF bound to the DNA), the TF further switches between a fast translocation
state dominated by interaction with the DNA backbone, and a slow examination
state where interaction with DNA base pairs is predominant. We derive a new
formula for the mean search time, and show that it is faster and less sensitive
to the binding energy fluctuations compared to the case of a single sliding
state. We find that for an optimal search, the time spent bound to the DNA is
larger compared to the 3D time in the nucleus, in agreement with recent
experimental data. Our results further suggest that modifying switching via
phosphorylation or methylation of the TF or the DNA can efficiently regulate
transcription.Comment: 4 pages, 3 figure
Resonant relaxation near a massive black hole: the stellar distribution and gravitational wave sources
Resonant relaxation (RR) of orbital angular momenta occurs near massive black
holes (MBHs) where the stellar orbits are nearly Keplerian and so do not
precess significantly. The resulting coherent torques efficiently change the
magnitude of the angular momenta and rotate the orbital inclination in all
directions. As a result, many of the tightly bound stars very near the MBH are
rapidly destroyed by falling into the MBH on low-angular momentum orbits, while
the orbits of the remaining stars are efficiently randomized. We solve
numerically the Fokker-Planck equation in energy for the steady state
distribution of a single mass population with a RR sink term. We find that the
steady state current of stars, which sustains the accelerated drainage close to
the MBH, can be up to ~10 times larger than that due to non-coherent 2-body
relaxation alone. RR mostly affects tightly bound stars, and so it increases
only moderately the total tidal disruption rate, which is dominated by stars
originating from less bound orbits farther away. We show that the event rate of
gravitational wave (GW) emission from inspiraling stars, originating much
closer to the MBH, is dominated by RR dynamics. The GW event rate depends on
the uncertain efficiency of RR. The efficiency indicated by the few available
simulations implies rates ~10 times higher than those predicted by 2-body
relaxation, which would improve the prospects of detecting such events by
future GW detectors, such as LISA. However, a higher, but still plausible RR
efficiency can lead to the drainage of all tightly bound stars and strong
suppression of GW events from inspiraling stars. We apply our results to the
Galactic MBH, and show that the observed dynamical properties of stars there
are consistent with RR.Comment: Accepted to ApJ; Minor revision
Quantum Key Distribution with Classical Bob
Secure key distribution among two remote parties is impossible when both are
classical, unless some unproven (and arguably unrealistic)
computation-complexity assumptions are made, such as the difficulty of
factorizing large numbers. On the other hand, a secure key distribution is
possible when both parties are quantum.
What is possible when only one party (Alice) is quantum, yet the other (Bob)
has only classical capabilities? We present a protocol with this constraint,
and prove its robustness against attacks: we prove that any attempt of an
adversary to obtain information (and even a tiny amount of information)
necessarily induces some errors that the legitimate users could notice.Comment: 4 and a bit pages, 1 figure, RevTe
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