On a class of semigroup graphs

Let $G=\Gamma(S)$ be a semigroup graph, i.e., a zero-divisor graph of a semigroup $S$ with zero element 0. For any adjacent vertices $x, y$ in $G$, denote $C(x,y)={z\in V(G) | N(z)={x,y}}$. Assume that in $G$ there exist two adjacent vertices $x,y$, a vertex $s\in C(x,y)$ and a vertex $z$ such that $d(s,z)=3$. In this paper, we study algebraic properties of $S$ with such graphs G=\G(S), giving some sub-semigroups and ideals of $S$. We construct some classes of such semigroup graphs and classify all semigroup graphs with the property in two cases.Comment: 16pages, 6figour

Simple Graphs and Commutative Zero-Divisor Semigroups

In this paper, we study commutative zero-divisor semigroups determined by graphs. We prove a uniqueness theorem for a class of graphs. We show two classes of graphs that have no corresponding semigroups. In particular, any complete graph $K_n$ together with more than three end vertices and any complete bipartite graph together with more than one end vertices have no corresponding semigroups. We also determine all possible zero-divisor semigroups whose zero-divisor graph is the com- plete graph $K_3$ together with two end vertices.Comment: 12 Page

RepTFD: Replay Based Transient Fault Detection

The advances in IC process make future chip multiprocessors (CMPs) more and more vulnerable to transient faults. To detect transient faults, previous core-level schemes provide redundancy for each core separately. As a result, they may leave transient faults in the uncore parts, which consume over 50% area of a modern CMP, escaped from detection. This paper proposes RepTFD, the first core-level transient fault detection scheme with 100% coverage. Instead of providing redundancy for each core separately, RepTFD provides redundancy for a group of cores as a whole. To be specific, it replays the execution of the checked group of cores on a redundant group of cores. Through comparing the execution results between the two groups of cores, all malignant transient faults can be caught. Moreover, RepTFD adopts a novel pending period based record-replay approach, which can greatly reduce the number of execution orders that need to be enforced in the replay-run. Hence, RepTFD brings only 4.76% performance overhead in comparison to the normal execution without fault-tolerance according to our experiments on the RTL design of an industrial CMP named Godson-3. In addition, RepTFD only consumes about 0.83% area of Godson-3, while needing only trivial modifications to existing components of Godson-3.Comment: 22 pages, 11 figure

On the Scale free laws of Urban Facilities

We implement a double stochastic process as the mathematical model for the spatial point patterns of urban facilities. We find that the model with power covariance function can produce the best fit not only to $K$ function (whose derivative gives the radial distribution $\rho(t) = K'(t)/2\pi t$) but also to additional facts of spatial point patterns. These facts include the mean-variance relationship of number of events in a series of expanding bins, and other statistics beyond the first two orders, such as inter-event distribution function $H(t)$ and nearest neighbor distribution functions $G(t)$ and $F(t)$.Comment: 13 pages, 6 figure

Doubly Robust Inference with Non-probability Survey Samples

We establish a general framework for statistical inferences with non-probability survey samples when relevant auxiliary information is available from a probability survey sample. We develop a rigorous procedure for estimating the propensity scores for units in the non-probability sample, and construct doubly robust estimators for the finite population mean. Variance estimation is discussed under the proposed framework. Results from simulation studies show the robustness and the efficiency of our proposed estimators as compared to existing methods. The proposed method is used to analyze a non-probability survey sample collected by the Pew Research Center with auxiliary information from the Behavioral Risk Factor Surveillance System and the Current Population Survey. Our results illustrate a general approach to inference with non-probability samples and highlight the importance and usefulness of auxiliary information from probability survey samples.Comment: 25 pages, 5 tables, this paper has been submitted for publicatio

Influences of statistics and initial size fluctuation on high-order cumulants of conserved quantities in relativistic heavy ion collisions

By the generator of the UrQMD model, event statistics for the products of kurtosis ($\kappa$) and variance ($\sigma^2$) of net-proton and net-charge multiplicity distributions are carefully studied. It is shown that the statistics at RHIC/BES below $\sqrt {s_{NN}} < 19.6$ GeV are not sufficient for using the method of Centrality Bin Width Correction (CBWC). Corresponding results are systematically underestimated. A way to improve the CBWC method is proposed. It can remove the statistics dependence of the data and reduce the initial size fluctuation as well.Comment: 6 pages, 5 figure

Parameterized algorithms for the 2-clustering problem with minimum sum and minimum sum of squares objective functions

In the {\sc Min-Sum 2-Clustering} problem, we are given a graph and a parameter $k$, and the goal is to determine if there exists a 2-partition of the vertex set such that the total conflict number is at most $k$, where the conflict number of a vertex is the number of its non-neighbors in the same cluster and neighbors in the different cluster. The problem is equivalent to {\sc 2-Cluster Editing} and {\sc 2-Correlation Clustering} with an additional multiplicative factor two in the cost function. In this paper we show an algorithm for {\sc Min-Sum 2-Clustering} with time complexity $O(n\cdot 2.619^{r/(1-4r/n)}+n^3)$, where $n$ is the number of vertices and $r=k/n$. Particularly, the time complexity is $O^*(2.619^{k/n})$ for $k\in o(n^2)$ and polynomial for $k\in O(n\log n)$, which implies that the problem can be solved in subexponential time for $k\in o(n^2)$. We also design a parameterized algorithm for a variant in which the cost is the sum of the squared conflict-numbers. For $k\in o(n^3)$, the algorithm runs in subexponential $O(n^3\cdot 5.171^{\theta})$ time, where $\theta=\sqrt{k/n}$.Comment: journal versio

On the asymptotic variance of reversible Markov chain without cycles

Markov chain Monte Carlo(MCMC) is a popular approach to sample from high dimensional distributions, and the asymptotic variance is a commonly used criterion to evaluate the performance. While most popular MCMC algorithms are reversible, there is a growing literature on the development and analyses of nonreversible MCMC. Chen and Hwang(2013) showed that a reversible MCMC can be improved by adding an antisymmetric perturbation. They also raised a conjecture that it can not be improved if there is no cycle in the corresponding graph. In this paper, we present a rigorous proof of this conjecture. The proof is based on the fact that the transition matrix with an acyclic structure will produce minimum commute time between vertices

Superconducting spin properties of Majorana nanowires and the associated superconducting anomalous Hall effect

It is difficult to unambiguously confirm the existence of Majorana zero modes (MZMs) due to the absence of smoking-gun signatures in charge transport measurements. Recent studies suggest that the spin degree of freedom of MZMs may provide an alternative detection method. We study the spin properties of the superconducting state in Majorana nanowires and the associated unconventional Josephson effect with realistic experimental parameters taken from [Zhang {\it et al.}, Nature 556, 74 (2018)]. For a superconducting thin film with in-plane polarized spin-triplet pairing, an out-of-plane electric field can generate a supercurrent perpendicular to both the superconducting spin polarization and the electric field, so we name this phenomena as superconducting anomalous Hall effect (ScAHE). In a Majorana nanowire, the regime with finite polarized spin-triplet pairing almost coincides with the chiral regime, which includes the topological regime. We further study the effects of polarized spin-triplet pairing in two types of Josephson junctions. One dramatic finding is that SOC can induce an anomalous supercurrent at zero phase difference only in the U-shape junction, a basic ingredient of scalable topological quantum computation. This can be viewed as a consequence of the ScAHE. Our work reveals that the spin degree of freedom is indeed helpful for detecting MZMs.Comment: 10 pages, 7 figure

Fractional order [PI] Controller and Smith-like Predictor Design for A Class of High Order Systems

To handle the control difficulties caused by high-order dynamics, a control structure based on fractional order [proportional integral] (PI) controller and fractional order Smith-like predictor for a class of high order systems in the type of K/(Ts+1)n is proposed in this paper. The analysis of the tracking and disturbance rejection is illustrated based on the terminal value theorem and shows that the proposed control structure can ensure that the closed-loop system converges to the set point without static error and the closed-loop system recovers to its original state when the input disturbance occurs. Then, simulations about the influence on the control performance and control signal with different are carried out based on multi-objective genetic algorithm (MO-GA). The results show that the control performance can be improved and the energy of the control signal can be reduced simultaneously when the order is chosen no more than one. This can verify that the fractional order Smith-like predictor with has an advantage over that of the integral order Smith-like predictor.Comment: 6 pages, 11 figures, conferenc