11,472 research outputs found
Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution
A birth-death process is a continuous-time Markov chain that counts the
number of particles in a system over time. In the general process with
current particles, a new particle is born with instantaneous rate
and a particle dies with instantaneous rate . Currently no robust and
efficient method exists to evaluate the finite-time transition probabilities in
a general birth-death process with arbitrary birth and death rates. In this
paper, we first revisit the theory of continued fractions to obtain expressions
for the Laplace transforms of these transition probabilities and make explicit
an important derivation connecting transition probabilities and continued
fractions. We then develop an efficient algorithm for computing these
probabilities that analyzes the error associated with approximations in the
method. We demonstrate that this error-controlled method agrees with known
solutions and outperforms previous approaches to computing these probabilities.
Finally, we apply our novel method to several important problems in ecology,
evolution, and genetics
Power Beacon-Assisted Millimeter Wave Ad Hoc Networks
Deployment of low cost power beacons (PBs) is a promising solution for
dedicated wireless power transfer (WPT) in future wireless networks. In this
paper, we present a tractable model for PB-assisted millimeter wave (mmWave)
wireless ad hoc networks, where each transmitter (TX) harvests energy from all
PBs and then uses the harvested energy to transmit information to its desired
receiver. Our model accounts for realistic aspects of WPT and mmWave
transmissions, such as power circuit activation threshold, allowed maximum
harvested power, maximum transmit power, beamforming and blockage. Using
stochastic geometry, we obtain the Laplace transform of the aggregate received
power at the TX to calculate the power coverage probability. We approximate and
discretize the transmit power of each TX into a finite number of discrete power
levels in log scale to compute the channel and total coverage probability. We
compare our analytical predictions to simulations and observe good accuracy.
The proposed model allows insights into effect of system parameters, such as
transmit power of PBs, PB density, main lobe beam-width and power circuit
activation threshold on the overall coverage probability. The results confirm
that it is feasible and safe to power TXs in a mmWave ad hoc network using PBs.Comment: This work has been submitted to the IEEE for possible publication.
Copyright may be transferred without notice, after which this version may no
longer be accessibl
Achieving Max-Min Throughput in LoRa Networks
With growing popularity, LoRa networks are pivotally enabling Long Range
connectivity to low-cost and power-constrained user equipments (UEs). Due to
its wide coverage area, a critical issue is to effectively allocate wireless
resources to support potentially massive UEs in the cell while resolving the
prominent near-far fairness problem for cell-edge UEs, which is challenging to
address due to the lack of tractable analytical model for the LoRa network and
its practical requirement for low-complexity and low-overhead design. To
achieve massive connectivity with fairness, we investigate the problem of
maximizing the minimum throughput of all UEs in the LoRa network, by jointly
designing high-level policies of spreading factor (SF) allocation, power
control, and duty cycle adjustment based only on average channel statistics and
spatial UE distribution. By leveraging on the Poisson rain model along with
tailored modifications to our considered LoRa network, we are able to account
for channel fading, aggregate interference and accurate packet overlapping, and
still obtain a tractable and yet accurate closed-form formula for the packet
success probability and hence throughput. We further propose an iterative
balancing (IB) method to allocate the SFs in the cell such that the overall
max-min throughput can be achieved within the considered time period and cell
area. Numerical results show that the proposed scheme with optimized design
greatly alleviates the near-far fairness issue, and significantly improves the
cell-edge throughput.Comment: 6 pages, 4 figures, published in Proc. International Conference on
Computing, Networking and Communications (ICNC), 2020. This paper proposes
stochastic-geometry based analytical framework for a single-cell LoRa
network, with joint optimization to achieve max-min throughput for the users.
Extended journal version for large-scale multi-cell LoRa network:
arXiv:2008.0743
Markovian versus non-Markovian stochastic quantization of a complex-action model
We analyze the Markovian and non-Markovian stochastic quantization methods
for a complex action quantum mechanical model analog to a Maxwell-Chern-Simons
eletrodynamics in Weyl gauge. We show through analytical methods convergence to
the correct equilibrium state for both methods. Introduction of a memory kernel
generates a non-Markovian process which has the effect of slowing down
oscillations that arise in the Langevin-time evolution toward equilibrium of
complex action problems. This feature of non-Markovian stochastic quantization
might be beneficial in large scale numerical simulations of complex action
field theories on a lattice.Comment: Accepted for publication in the International Journal of Modern
Physics
Statistics of non-linear stochastic dynamical systems under L\'evy noises by a convolution quadrature approach
This paper describes a novel numerical approach to find the statistics of the
non-stationary response of scalar non-linear systems excited by L\'evy white
noises. The proposed numerical procedure relies on the introduction of an
integral transform of Wiener-Hopf type into the equation governing the
characteristic function. Once this equation is rewritten as partial
integro-differential equation, it is then solved by applying the method of
convolution quadrature originally proposed by Lubich, here extended to deal
with this particular integral transform. The proposed approach is relevant for
two reasons: 1) Statistics of systems with several different drift terms can be
handled in an efficient way, independently from the kind of white noise; 2) The
particular form of Wiener-Hopf integral transform and its numerical evaluation,
both introduced in this study, are generalizations of fractional
integro-differential operators of potential type and Gr\"unwald-Letnikov
fractional derivatives, respectively.Comment: 20 pages, 5 figure
Spectral Efficiency Scaling Laws in Dense Random Wireless Networks with Multiple Receive Antennas
This paper considers large random wireless networks where
transmit-and-receive node pairs communicate within a certain range while
sharing a common spectrum. By modeling the spatial locations of nodes based on
stochastic geometry, analytical expressions for the ergodic spectral efficiency
of a typical node pair are derived as a function of the channel state
information available at a receiver (CSIR) in terms of relevant system
parameters: the density of communication links, the number of receive antennas,
the path loss exponent, and the operating signal-to-noise ratio. One key
finding is that when the receiver only exploits CSIR for the direct link, the
sum of spectral efficiencies linearly improves as the density increases, when
the number of receive antennas increases as a certain super-linear function of
the density. When each receiver exploits CSIR for a set of dominant interfering
links in addition to the direct link, the sum of spectral efficiencies linearly
increases with both the density and the path loss exponent if the number of
antennas is a linear function of the density. This observation demonstrates
that having CSIR for dominant interfering links provides a multiplicative gain
in the scaling law. It is also shown that this linear scaling holds for direct
CSIR when incorporating the effect of the receive antenna correlation, provided
that the rank of the spatial correlation matrix scales super-linearly with the
density. Simulation results back scaling laws derived from stochastic geometry.Comment: Submitte
From non-Brownian Functionals to a Fractional Schr\"odinger Equation
We derive backward and forward fractional Schr\"odinger type of equations for
the distribution of functionals of the path of a particle undergoing anomalous
diffusion. Fractional substantial derivatives introduced by Friedrich and
co-workers [PRL {\bf 96}, 230601 (2006)] provide the correct fractional
framework for the problem at hand. In the limit of normal diffusion we recover
the Feynman-Kac treatment of Brownian functionals. For applications, we
calculate the distribution of occupation times in half space and show how
statistics of anomalous functionals is related to weak ergodicity breaking.Comment: 5 page
- …