2,643 research outputs found
A Monomial-Oriented GVW for Computing Gr\"obner Bases
The GVW algorithm, presented by Gao et al., is a signature-based algorithm
for computing Gr\"obner bases. In this paper, a variant of GVW is presented.
This new algorithm is called a monomial-oriented GVW algorithm or mo-GVW
algorithm for short. The mo-GVW algorithm presents a new frame of GVW and
regards {\em labeled monomials} instead of {\em labeled polynomials} as basic
elements of the algorithm. Being different from the original GVW algorithm, for
each labeled monomial, the mo-GVW makes efforts to find the smallest signature
that can generate this monomial. The mo-GVW algorithm also avoids generating
J-pairs, and uses efficient methods of searching reducers and checking
criteria. Thus, the mo-GVW algorithm has a better performance during practical
implementations
Counting Independent Sets and Colorings on Random Regular Bipartite Graphs
We give a fully polynomial-time approximation scheme (FPTAS) to count the number of independent sets on almost every Delta-regular bipartite graph if Delta >= 53. In the weighted case, for all sufficiently large integers Delta and weight parameters lambda = Omega~ (1/(Delta)), we also obtain an FPTAS on almost every Delta-regular bipartite graph. Our technique is based on the recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it to confirm an open question raised there: For all q >= 3 and sufficiently large integers Delta=Delta(q), there is an FPTAS to count the number of q-colorings on almost every Delta-regular bipartite graph
Achievable Sum Rates of Half- and Full-Duplex Bidirectional OFDM Communication Links
While full-duplex (FD) transmission has the potential to double the system
capacity, its substantial benefit can be offset by the self-interference (SI)
and non-ideality of practical transceivers. In this paper, we investigate the
achievable sum rates (ASRs) of half-duplex (HD) and FD transmissions with
orthogonal frequency division multiplexing (OFDM), where the non-ideality is
taken into consideration. Four transmission strategies are considered, namely
HD with uniform power allocation (UPA), HD with non-UPA (NUPA), FD with UPA,
and FD with NUPA. For each of the four transmission strategies, an optimization
problem is formulated to maximize its ASR, and a (suboptimal/optimal) solution
with low complexity is accordingly derived. Performance evaluations and
comparisons are conducted for three typical channels, namely symmetric
frequency-flat/selective and asymmetric frequency-selective channels. Results
show that the proposed solutions for both HD and FD transmissions can achieve
near optimal performances. For FD transmissions, the optimal solution can be
obtained under typical conditions. In addition, several observations are made
on the ASR performances of HD and FD transmissions.Comment: To appear in IEEE TVT. This paper solves the problem of sum
achievable rate optimization of bidirectional FD OFDM link, where joint time
and power allocation is involve
Relaxed Majorization-Minimization for Non-smooth and Non-convex Optimization
We propose a new majorization-minimization (MM) method for non-smooth and
non-convex programs, which is general enough to include the existing MM
methods. Besides the local majorization condition, we only require that the
difference between the directional derivatives of the objective function and
its surrogate function vanishes when the number of iterations approaches
infinity, which is a very weak condition. So our method can use a surrogate
function that directly approximates the non-smooth objective function. In
comparison, all the existing MM methods construct the surrogate function by
approximating the smooth component of the objective function. We apply our
relaxed MM methods to the robust matrix factorization (RMF) problem with
different regularizations, where our locally majorant algorithm shows
advantages over the state-of-the-art approaches for RMF. This is the first
algorithm for RMF ensuring, without extra assumptions, that any limit point of
the iterates is a stationary point.Comment: AAAI1
All pure bipartite entangled states can be semi-self-tested with only one measurement setting on each party
It has been known that all bipartite pure quantum states can be self-tested,
i.e., any such state can be certified completely by initially measuring both
subsystems of this state by proper local quantum measurements and subsequently
verifying that the correlation between the measurement choices and the outcomes
satisfies a specific condition. In such a protocol, a key feature is that the
conclusion can still be reliable even if involved quantum measurements are
untrusted, where quantum nonlocality is crucial and plays a central role, and
this means that each party has to conduct at least two different quantum
measurements to produce a desirable correlation. Here, we prove that when the
underlying Hilbert space dimension is known beforehand, an arbitrary bipartite pure state can be certified completely (up to local unitary
transformations) by a certain correlation generated by a single measurement
setting on each party, where each measurement yields only outcomes.
Notably, our protocols do not involve any quantum nonlocality. We believe that
our result may provide us a remarkable convenience when certifying bipartite
pure quantum states in quantum labs.Comment: 9 pages, comments are welcom
Interactive Behaviour Between the Dynamic Arrival Process of Complex Traffic Source and a Bottleneck Queue
This paper proposes a discrete-time heterogeneous model to represent the interaction between the dynamic arrival process of multiple TCP sources and a bottleneck queue. It utilises a novel time-variant calculation approach for transient queueing models, which modifies the conventional steady-state method by no longer requiring the equilibrium assumption. The main contributions are: (1) The limitation of the conventional queueing method is analysed and the benefits of the proposed modification is demonstrated; (2) The proposed dynamic arrival process of multiple sources is illustrated, which interacts with the queueing process and statistically responds to the positive and negative congestion feedback; (3) The fidelity of the proposed model is extensively validated by the closely matched results from MATLAB numerical solutions and NS-2 discrete-event simulation experiments
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