26,620 research outputs found
Doubly nonlocal reaction-diffusion equation and the emergence of species
The paper is devoted to a reaction-diffusion equation with doubly nonlocal
nonlinearity arising in various applications in population dynamics. One of the
integral terms corresponds to the nonlocal consumption of resources while
another one describes reproduction with different phenotypes. Linear stability
analysis of the homogeneous in space stationary solution is carried out.
Existence of travelling waves is proved in the case of narrow kernels of the
integrals. Periodic travelling waves are observed in numerical simulations.
Existence of stationary solutions in the form of pulses is shown, and
transition from periodic waves to pulses is studied. In the applications to the
speciation theory, the results of this work signify that new species can emerge
only if they do not have common offsprings. Thus, it is shown how Darwin's
definition of species as groups of morphologically similar individuals is
related to Mayr's definition as groups of individuals that can breed only among
themselves.Comment: 15 pages, 4 figure
Qubit rotation and Berry Phase
A quantized fermion can be represented by a scalar particle encircling a
magnetic flux line. It has the spinor structure which can be constructed from
quantum gates and qubits. We have studied here the role of Berry phase in
removing dynamical phase during one qubit rotation of a quantized fermion. The
entanglement of two qubit inserting spin-echo to one of them results the change
of Berry phase that can be considered as a measure of entanglement. Some effort
is given to study the effect of noise on the Berry phase of spinor and their
entangled states.Comment: 12 page
Data-Efficient Quickest Change Detection with On-Off Observation Control
In this paper we extend the Shiryaev's quickest change detection formulation
by also accounting for the cost of observations used before the change point.
The observation cost is captured through the average number of observations
used in the detection process before the change occurs. The objective is to
select an on-off observation control policy, that decides whether or not to
take a given observation, along with the stopping time at which the change is
declared, so as to minimize the average detection delay, subject to constraints
on both the probability of false alarm and the observation cost. By considering
a Lagrangian relaxation of the constraint problem, and using dynamic
programming arguments, we obtain an \textit{a posteriori} probability based
two-threshold algorithm that is a generalized version of the classical Shiryaev
algorithm. We provide an asymptotic analysis of the two-threshold algorithm and
show that the algorithm is asymptotically optimal, i.e., the performance of the
two-threshold algorithm approaches that of the Shiryaev algorithm, for a fixed
observation cost, as the probability of false alarm goes to zero. We also show,
using simulations, that the two-threshold algorithm has good observation
cost-delay trade-off curves, and provides significant reduction in observation
cost as compared to the naive approach of fractional sampling, where samples
are skipped randomly. Our analysis reveals that, for practical choices of
constraints, the two thresholds can be set independent of each other: one based
on the constraint of false alarm and another based on the observation cost
constraint alone.Comment: Preliminary version of this paper has been presented at ITA Workshop
UCSD 201
Data-Efficient Quickest Outlying Sequence Detection in Sensor Networks
A sensor network is considered where at each sensor a sequence of random
variables is observed. At each time step, a processed version of the
observations is transmitted from the sensors to a common node called the fusion
center. At some unknown point in time the distribution of observations at an
unknown subset of the sensor nodes changes. The objective is to detect the
outlying sequences as quickly as possible, subject to constraints on the false
alarm rate, the cost of observations taken at each sensor, and the cost of
communication between the sensors and the fusion center. Minimax formulations
are proposed for the above problem and algorithms are proposed that are shown
to be asymptotically optimal for the proposed formulations, as the false alarm
rate goes to zero. It is also shown, via numerical studies, that the proposed
algorithms perform significantly better than those based on fractional
sampling, in which the classical algorithms from the literature are used and
the constraint on the cost of observations is met by using the outcome of a
sequence of biased coin tosses, independent of the observation process.Comment: Submitted to IEEE Transactions on Signal Processing, Nov 2014. arXiv
admin note: text overlap with arXiv:1408.474
Magnetic glass in Shape Memory Alloy : Ni45Co5Mn38Sn12
The first order martensitic transition in the ferromagnetic shape memory
alloy Ni45Co5Mn38Sn12 is also a magnetic transition and has a large field
induced effect. While cooling in the presence of field this first order
magnetic martensite transition is kinetically arrested. Depending on the
cooling field, a fraction of the arrested ferromagnetic austenite phase
persists down to the lowest temperature as a magnetic glassy state, similar to
the one observed in various intermetallic alloys and in half doped manganites.
A detailed investigation of this first order ferromagnetic austenite (FM-A) to
low magnetization martensite (LM-M) state transition as a function of
temperature and field has been carried out by magnetization measurements.
Extensive cooling and heating in unequal field (CHUF) measurements and a novel
field cooled protocol for isothermal MH measurements (FC-MH) are utilized to
investigate the glass like arrested states and show a reverse martensite
transition. Finally, we determine a field -temperature (HT) phase diagram of
Ni45Co5Mn38Sn12 from various magnetization measurements which brings out the
regions where thermodynamic and metastable states co-exist in the HT space
clearly depicting this system as a 'Magnetic Glass'.Comment: Magnetic field tunes kinetic arrest and CHUF shows devitrification
and melting of Magnetic glas
Aging and Death under a Dollar a Day
This paper uses household survey data form several developing countries to investigate whether the poor (defined as those living under 2 dollars a day at PPP) and the non poor have different mortality rates in old age. We construct a proxy measure of longevity, which is the probability that an adult's mother and father are alive. The non-poor's mothers are more likely to be alive than the poor's mothers. Using panel data set for Indonesia and Vietnam, we also find that older adults are significantly more likely to have died five years later if they are poor. The direction of causality is unclear: the poor may be poor because they are sick (and thus more likely to die), or they could die because they are poor.
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