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 $d\times d$ 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 $3d$ 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