2,153 research outputs found
Note on vanishing power sums of roots of unity
For a given positive integers and , we give a complete list of
positive integers for which their exist th roots of unity such that . This extends
the earlier result of Lam and Leung on vanishing sums of roots of unity.
Furthermore, we prove that for which integers with , there
are distinct th roots of unity such that
.Comment: 5 pages, 1 table, to appear in Math. Studen
Techniques and Applications of Computation Slicing
Writing correct distributed programs is hard. In spite of extensive testing
and debugging, software faults persist even in commercial grade software. Many
distributed systems, especially those employed in safety-critical environments,
should be able to operate properly even in the presence of software faults.
Monitoring the execution of a distributed system, and, on detecting a fault,
initiating the appropriate corrective action is an important way to tolerate
such faults. This gives rise to the predicate detection problem which requires
finding a consistent cut of a given computation that satisfies a given global
predicate, if it exists.
Detecting a predicate in a computation is, however, an NP-complete problem.
To ameliorate the associated combinatorial explosion problem, we introduce the
notion of computation slice. Formally, the slice of a computation with respect
to a predicate is a (sub)computation with the least number of consistent cuts
that contains all consistent cuts of the computation satisfying the predicate.
To detect a predicate, rather than searching the state-space of the
computation, it is much more efficient to search the state-space of the slice.
We prove that the slice exists and is uniquely defined for all predicates. We
present efficient slicing algorithms for several useful classes of predicates.
We develop efficient heuristic algorithms for computing an approximate slice
for predicates for which computing the slice is otherwise provably intractable.
Our experimental results show that slicing can lead to an exponential
improvement over existing techniques for predicate detection in terms of time
and space.Comment: 50 pages, 14 figure
Diffusive Molecular Communication with Nanomachine Mobility
This work presents a performance analysis for diffusive molecular
communication with mobile transmit and receive nanomachines. To begin with, the
optimal test is obtained for symbol detection at the receiver nanomachine.
Subsequently, closed-form expressions are derived for the probabilities of
detection and false alarm, probability of error, and capacity considering also
aberrations such as multi-source interference, inter-symbol interference, and
counting errors. Simulation results are presented to corroborate the
theoretical results derived and also, to yield various insights into the
performance of the system. Interestingly, it is shown that the performance of
the mobile diffusive molecular communication can be significantly enhanced by
allocating large fraction of total available molecules for transmission as the
slot interval increases.Comment: To be submitted in 52th Annual Conference on Information Sciences and
Systems (CISS
Cognitive MIMO-RF/FSO Cooperative Relay Communication with Mobile Nodes and Imperfect Channel State Information
This work analyzes the performance of an underlay cognitive radio based
decode-and-forward mixed multiple-input multiple-output (MIMO) radio
frequency/free space optical (RF/FSO) cooperative relay system with multiple
mobile secondary and primary user nodes. The effect of imperfect channel state
information (CSI) arising due to channel estimation error is also considered at
the secondary user transmitters (SU-TXs) and relay on the power control and
symbol detection processes respectively. A unique aspect of this work is that
both fixed and proportional interference power constraints are employed to
limit the interference at the primary user receivers (PU-RXs). Analytical
results are derived to characterize the exact and asymptotic outage and bit
error probabilities of the above system under practical conditions of node
mobility and imperfect CSI, together with impairments of the optical channel,
such as path loss, atmospheric turbulence, and pointing errors, for orthogonal
space-time block coded transmission between each SU-TX and relay. Finally,
simulation results are presented to yield various interesting insights into the
system performance such as the benefits of a midamble versus preamble for
channel estimation.Comment: revision submitted to IEEE Transactions on Cognitive Communications
and Networkin
Diffusion Based Cooperative Molecular Communication in Nano-Networks
This work presents a novel diffusion based dual-phase molecular communication
system where the source leverages multiple cooperating nanomachines to improve
the end-to-end reliability of communication. The Neyman-Pearson Likelihood
Ratio Tests are derived for each of the cooperative as well as the destination
nanomachines in the presence of multi-user interference. Further, to
characterize the performance of the aforementioned system, closed form
expressions are derived for the probabilities of detection, false alarm at the
individual cooperative, destination nanomachines, as well as the overall
end-to-end probability of error. Simulation results demonstrate a significant
improvement in the end-to-end performance of the proposed cooperative framework
in comparison to multiple-input single-output and single-input single-output
molecular communication scenarios in the existing literature.Comment: Revised IEEE WCL Draft (in review process
On the discriminant of pure number fields
Let be an extension of degree of the field
\Q of rational numbers, where the integer is such that for each prime
dividing either or the highest power of dividing is
coprime to ; this condition is clearly satisfied when are coprime or
is squarefree. The paper contains an explicit formula for the discriminant
of involving only the prime powers dividing
Design and Performance Analysis of Dual and Multi-hop Diffusive Molecular Communication Systems
This work presents a comprehensive performance analysis of diffusion based
direct, dual-hop, and multi-hop molecular communication systems with Brownian
motion and drift in the presence of various distortions such as inter-symbol
interference (ISI), multi-source interference (MSI), and counting errors.
Optimal decision rules are derived employing the likelihood ratio tests (LRTs)
for symbol detection at each of the cooperative as well as the destination
nanomachines. Further, closed-form expressions are also derived for the
probabilities of detection, false alarm at the individual cooperative,
destination nanomachines, as well as the overall end-to-end probability of
error for source-destination communication. The results also characterize the
impact of detection performance of the intermediate cooperative nanomachine(s)
on the end-to-end performance of dual/multi hop diffusive molecular
communication systems. In addition, capacity expressions are also derived for
direct, dual-hop, and multi-hop molecular communication scenarios. Simulation
results are presented to corroborate the theoretical results derived and also,
to yield insights into system performance.Comment: in preparatio
On Hybrid MoSK-CSK Modulation based Molecular Communication: Error Rate Performance Analysis using Stochastic Geometry
Data transmission rate in molecular communication systems can be improved by
using multiple transmitters and receivers. In molecular multiple-input
multiple-output (MIMO) systems which use only single type of molecules, the
performance at the destination is limited by inter-symbol interference (ISI),
inter-link interference (ILI) and multi-user interference (MUI). This work
proposes a new hybrid modulation for a system with multiple transmitters and
receivers which uses different types of molecules to eliminate ILI. Further, to
enhance the data rate of the proposed system under ISI and MUI, Mary CSK
modulation scheme is used between each transmitter-receiver pair. In this
paper, the random locations of transmitters present in the three dimensional
(3-D) space are modeled as homogeneous Poisson point process (HPPP). Using
stochastic geometry tools, analytical expression is derived for the probability
of symbol error for the aforementioned scenario. Finally, the performance of
the proposed system is compared using the different existing modulation schemes
such as on-off keying (OOK), binary concentration shift keying (BCSK) and
quadruple concentration shift keying (QCSK) to develop several important
insights
Weakening of the spin density wave gap at low temperatures in SrFeAs single crystals
We report on temperature dependent scanning tunneling microscopy and
spectroscopy studies of undoped SrFeAs single crystals from 6 K to
292 K. Resistivity data show spin density wave (SDW) transition at T
205 K and the superconducting transition at 21 K while
magnetic susceptibility does not show any superconductivity. Conductance maps
and local tunneling spectra show an electronically homogeneous surface at all
studied temperatures. Tunnel spectra correlate well with the SDW transition
with a depression in the density of states near the Fermi energy below
T. On further lowering the temperature, the width of this partial
energy gap associated with the SDW decreases. Using the anti-correlation of
superconducting phase with SDW, we interpret this gap weakening as a precursor
to superconductivity. This may give rise to a facile nucleation of
superconductivity near defects
Distributed Abstraction Algorithm for Online Predicate Detection
Analyzing a distributed computation is a hard problem in general due to the
combinatorial explosion in the size of the state-space with the number of
processes in the system. By abstracting the computation, unnecessary
explorations can be avoided. Computation slicing is an approach for abstracting
dis- tributed computations with respect to a given predicate. We focus on
regular predicates, a family of predicates that covers a large number of
commonly used predicates for runtime verification. The existing algorithms for
computation slicing are centralized in nature in which a single process is
responsible for computing the slice in either offline or online manner. In this
paper, we present a distributed online algorithm for computing the slice of a
distributed computation with respect to a regular predicate. Our algorithm
distributes the work and storage requirements across the system, thus reducing
the space and computation complexities per process. In addition, for
conjunctive predicates, our algorithm also reduces the message load per
process
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