The average cut-rank of graphs

The cut-rank of a set $X$ of vertices in a graph $G$ is defined as the rank of the $X \times (V(G)\setminus X)$ matrix over the binary field whose $(i,j)$-entry is $1$ if the vertex $i$ in $X$ is adjacent to the vertex $j$ in $V(G)\setminus X$ and $0$ otherwise. We introduce the graph parameter called the average cut-rank of a graph, defined as the expected value of the cut-rank of a random set of vertices. We show that this parameter does not increase when taking vertex-minors of graphs and a class of graphs has bounded average cut-rank if and only if it has bounded neighborhood diversity. This allows us to deduce that for each real $\alpha$, the list of induced-subgraph-minimal graphs having average cut-rank larger than (or at least) $\alpha$ is finite. We further refine this by providing an upper bound on the size of obstruction and a lower bound on the number of obstructions for average cut-rank at most (or smaller than) $\alpha$ for each real $\alpha\ge0$. Finally, we describe explicitly all graphs of average cut-rank at most $3/2$ and determine up to $3/2$ all possible values that can be realized as the average cut-rank of some graph.Comment: 22 pages, 1 figure. The bound $x_n$ is corrected. Accepted to European J. Combinatoric

Performance analysis with wireless power transfer constraint policies in full-duplex relaying networks

In practice, full-duplex (FD) transmission mode not only helps extend the coverage but also lengthen network lifetime. In this paper, we develop wireless power supply policies, namely separated power (SP) and harvested power (HP) to propose a flexible architecture at the relay node in FD decode-and-forward (DF) relaying networks considering time switching-based relaying protocol (TSR) to achieve optimal time used for a communication process. This transmission mode requires more processing procedure at the relay, i.e. antenna installations and radio frequency (RF) self-interference cancellation. We evaluate the optimal power constraints in case of SP and HP to achieve better power consumption efficiency at the relay node. More importantly, closed-form expressions for outage probability and throughput are provided, and we also use numerical and simulation results to compare SP with HP.Web of Science234767

Cyclically presented modules, projective covers and factorizations

We investigate projective covers of cyclically presented modules, characterizing the rings over which every cyclically presented module has a projective cover as the rings $R$ that are Von Neumann regular modulo their Jacobson radical $J(R)$ and in which idempotents can be lifted modulo $J(R)$. Cyclically presented modules naturally appear in the study of factorizations of elements in non-necessarily commutative integral domains. One of the possible applications is to the modules $M_R$ whose endomorphism ring $E:=(M_R)$ is Von Neumann regular modulo $J(E)$ and in which idempotents lift modulo $J(E)$.Comment: 17 page

Intra-regional Currency Linkages and the Evolution of Exchange Rate Regime of the ASEAN Region

This paper investigates the intra-regional currency linkages and evolution of exchange rate regimes of the Association of South East Asian Nations (A SEAN) region. Do nations follow regimes they are classified into? Have exchange rate regimes of ASEAN nations become more flexible and less dependent on the US dollar? Are the intra-regional currency linkages strong enough for ASEAN nations to form a monetary union? Answers to these are important as the official regimes announced by ASEAN countries may not reflect their actual behaviors. Using monthly exchange rates per unit SDR and foreign exchange reserves data spanning the entire post-Bretton Woods era (1973-2014), and employing the Frankel-Wei estimation model, I find that before the Asian financial crisis period (1973-1996), ASEAN currencies were mostly defacto dollar peggers and the intra-regional currency linkages were very weak. However, post-crisis (1999-201 4) ASEAN currencies have become more flexible and the intra-regional currency linkages have increased considerably

Construction of Spline Type Orthogonal Scaling Functions and Wavelets

In this paper, we present a method to construct orthogonal spline-type scaling functions by using B-spline functions. B-splines have many useful properties such as compactly supported and refinable properties. However, except for the case of order one, B-splines of order greater than one are not orthogonal. To induce the orthogonality while keeping the above properties of B-splines, we multiply a class of polynomial function factors to the masks of the B-splines so that they become the masks of a spline-type orthogonal compactly-supported and refinable scaling functions in L2. In this paper we establish the existence of this class of polynomial factors and their construction. Hence, the corresponding spline-type wavelets and the decomposition and reconstruction formulas for their Multiresolution Analysis (MRA) are obtained accordingly

Potential effects of chatbot technology on customer support: A case study

This study analyzed an experiment with using a chatbot for the customer support department at the case company. A modified version of the updated DeLone and McLean information system success model was utilized to evaluate potential effects of the chatbot on the operation of the customer support. Five dimensions of the model were measured before and after the chatbot implementation and then compared to determine if the chatbot can help improve the customer experience with the customer support of the case company. Responses from 60 customers who had used the chatbot were obtained through a web-based survey. Results indicated that the addition of a chatbot to a traditional customer support model can improve customer experience, mainly on responsiveness measure, while maintain a similar level on information quality, system quality and user satisfaction dimensions. Results also suggested that unsuccessful chatbot attempts which require further human involvement may not necessarily worsen customer experience as many expect. Based on the experiment, the study also provided three suggestions for firms when planning to adopt chatbot technology. First, the potential of chatbot should not be overestimated, it cannot replace human agents completely in customer support. Second, chatbot should handle only simple enough tasks and leave the more complex and trickier ones to human. And third, building a chatbot is a continuous process that requires careful resource planning not only for the initial development but also for the later stage of analyzing and turning conversations of the chatbot