Narrow Results

This study explores the connectedness between cryptocurrencies (Bitcoin, Ethereum, Ripple, Bitcoin cash and Ethereum Operating System) and major stock markets (NYSE composite index, NASDAQ composite index, Shanghai Stock Exchange, Nikkei 225 and Euronext NV). Using the asymmetric dynamic conditional correlation (ADCC) and wavelet coherence approaches, we document a significant time-varying conditional correlation between the majority of the cryptocurrencies and stock market indices and that the negative shocks play a more prominent role than the positive shocks of the same magnitude. Overall, our findings explore potential avenues for diversification for investors across cryptocurrencies and major stock markets.

The world is a global village, and all economies are connected (negatively or positively) with each other. A financial crisis in one economy is likely to have an impact on the other economies. Since the stock exchange plays an important role for a country due to its ability to mobilize local resources for fruitful investment, thus it is mandatory to detect, and date-stamp any bubble(s) in the stock market of a particular country and its major trading partners to save these economies from any crises leading them toward sustainable growth. Current literature on Pakistan though discusses the bubble detection issues but no study is available that analyzes bubbles in Pakistan as well as its major trading partners. In addition, if there is any bubble in one of the chosen countries then what will be the impact of this bubble on a specific or any other country and with what magnitude? This study fills in this void by contributing to the existing literature in two ways, first, it analyzes the presence of bubbles in the stock markets of Pakistan and its major trading partners and in addition, it also provides the level of connectedness among these stock markets and the impact of any shock in one of the chosen countries on a specific country or on the rest of the countries. The empirical analysis is based on monthly data from Jan 2000 till Oct 2022 and the bubbles are detected via state of art generalized supremum ADF (GSADF) test while the connectedness is tested via the Diebold and Yilmaz [(2012). Better to give than to receive: Predictive directional measurement of volatility spillovers. International Journal of Forecasting, 28(1), 57–66] approach. Some interesting results are obtained based on the empirical findings and relevant policy recommendations are made.

This paper employs the local Bayesian likelihood methodology to estimate a medium-scale dynamic stochastic general equilibrium (DSGE) model on different frequencies and uses frequency-domain tools to evaluate the time-varying parameter model and the fixed-parameter model. These techniques yield fresh insights into theoretical and empirical implications conveyed by alternative models beyond what conventional time-domain approaches can offer. We show that parameter estimates are sensitive to frequencies, and goodness-of-fit varies substantially with the frequency bands. Overall, the estimated time-varying parameter model captures the properties of the U.S. data better in the business cycle frequency band, and beyond this band, the fixed-parameter model performs better. Additionally, our study also reveals the importance of structural shocks in improving the fit between models and data. Finally, we utilize the spectral representation of generalized forecast error variance decomposition to investigate the frequency dynamics of volatility connectedness. We find shocks to economic activity have an impact on variables at different frequencies with different strengths, and markets become more connected during crisis periods. Furthermore, this study provides insights into a question policymakers are much concerned with: which shocks are major sources of economic volatilities and which sectors serve as major recipients of shocks?

Let $A$ be an expanding lower triangular matrix and ${𝒟}=\{0,1,\dots ,m-1\}\times \{0,1,\dots ,n-1\}$. Let $T(A,{𝒟})$ be the associated self-affine set. In the paper, we generalize some connectedness results on self-affine tiles to self-affine sets and provide a necessary and sufficient condition for $T(A,{𝒟})$ to be connected.

Let $A=\left(\right.\begin{array}{cc}\hfill n\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill m\hfill \end{array}\left)\right.$, where $n,m\ge 3$ are integers and ${𝒟}=\{0,1,\dots ,n-1\}\times \{0,1,\dots ,m-1\}$ be a digit set. Then the pair $(A,{𝒟})$ generates a fractal set $T:=T(A,{𝒟})$ satisfying $AT=T+{𝒟}$ which is a unit square. However, if we remove one digit from ${𝒟}$, then the structure of $T$ will become very interesting. A well-known example is the Sierpinski carpet. In this paper, we study the resulting self-affine sets of moving a digit in ${𝒟}$ to a different place. That is, we consider a digit set ${{𝒟}}^{\ast }={𝒟}\setminus \{d_0\}\cup \{d^{\ast }\}$, where $d_0\in {𝒟},d^{\ast }\in {\mathbb{Z}}^2$. We give a complete characterization for the connectedness of self-affine carpet $T(A,{{𝒟}}^{\ast })$ in terms of the domains of $d_0$ and $d^{\ast }$.

Random sets arise as distinguished models to study probability under imprecision. This work aims to determine the connectedness of a random set in terms of its capacity functional (the probability of hitting a set). This problem is linked to the celebrated Choquet–Kendall–Matheron theorem, which states that a random closed set is characterized by its capacity functional. Hence, such functional must also characterize any topological property of a random set, such as its connectedness. While the capacity functional of a random closed set operates over the large class of compact sets, we show that the determination of connectedness can be checked only over a simple family of sets.

In the framework of the Hudson–Parthasarathy quantum stochastic calculus, we employ a recent generalization of the Michael selection results in the present noncommutative settings to prove that the function space of the matrix elements of solutions to discontinuous quantum stochastic differential inclusion (DQSDI) is arcwise connected.

Due to the increasing connectedness of international financial markets, the measurement of dynamic connectedness among large-scale assets has become a key component of modern financial risk regulation and asset allocation principles. We quantify the dynamic connectedness among large-scale assets and visualize the return spillover paths using cutting-edge complex network spillover measurement theory and physical complex network methods. For the sample period of January 2, 2018 to June 30, 2022, we calculate the daily returns for thirteen representative global large-scale assets. Then, we construct a time-varying parameter-vector autoregressive-stochastic volatility (TVP-VAR-SV) model and measure the time-varying spillover matrix of returns across large-scale assets. From our analyses, the 10-year U.S. treasury rate (shorted for the US10YR) and Brent oil are found to be the core subject matter of global assets. The US10YR has a significant impact on the commodity market. Moreover, there is a significant impact of foreign exchange on other global large-scale assets, and the spillover effects vary from one country to another. On the basis of the empirical findings, this paper proposes recommendations for financial regulators regarding risk monitoring and forward-looking investment recommendations for financial institutions and investors.

In this paper, we introduce and study a new class of Cayley graphs.

As an extension of ${𝔸𝔾}_z(L)$ (the annihilation graph of the commutator poset (lattice) $L$ with respect to an element $z\in L$), we discuss when ${𝔸𝔾}_I(L)$ (the annihilation graph of the commutator poset (lattice) $L$ with respect to an ideal $I\subseteq L$) is a complete bipartite ($r$-partite) graph together with some of its other graph-theoretic properties. We investigate the interplay between some (order-) lattice-theoretic properties of $L$ and graph-theoretic properties of its associated graph ${𝔸𝔾}_I(L)$. We provide some examples to show that some conditions are not superfluous assumptions. We prove and show by a counterexample that the class of lower sets of a commutator poset $L$ is properly contained in the class of $m$-ideals of $L$ (i.e. multiplicatively absorptive ideals (sets) of $L$ that are defined by commutator operation).

Let $R$ be a ring with nonzero identity. The Idempotent graph of $R$, denoted by $G_{\mathrm{\text{Id}}}(R)$, has its set of vertices equal to the set of all elements of $R$; Distinct vertices $x$ and $y$ are adjacent if and only if $x+y$ is an idempotent of $R$. In this paper, we study some basic properties of $G_{\mathrm{\text{Id}}}(R)$ such as connectedness, diameter and girth.

Let $𝔞$ be an ideal of a Noetherian local ring $R$ with $dimR=d$ and $t$ be a positive integer. In this paper, it is shown that the top local cohomology module $H_{𝔞}^d(R)$ (equivalently, its Matlis dual $H_{𝔞}^d{(R)}^{\vee }$) can be written as a direct sum of $t$ indecomposable summands if and only if the endomorphism ring ${Hom}_R(H_{𝔞}^d{(R)}^{\vee },H_{𝔞}^d{(R)}^{\vee })$ can be written as a direct product of $t$ local endomorphism rings if and only if the set of minimal primes $𝔭$ of $R$ with $H_{𝔞}^d(R/𝔭)\ne 0$ can be written as disjoint union of $t$ non-empty subsets $U_1,U_2,\dots ,U_t$ such that for all distinct $i,j\in \{1,\dots ,t\}$ and all $𝔭\in U_i$ and all $𝔮\in U_j$, we have $ht(𝔭+𝔮)\ge 2$. This generalizes Theorem 3.6 of Hochster and Huneke [Contemp. Math. 159 (1994) 197–208].

In this paper, we study almost Cohen–Macaulay bipartite graphs. In particular, we prove that if $G$ is an almost Cohen–Macaulay bipartite graph with at least one vertex of positive degree, then there is a vertex of $deg(v)\le 2$. In particular, if $G$ is an almost Cohen–Macaulay bipartite graph and $u$ is a vertex of degree one of $G$ and $v$ its adjacent vertex, then $G\setminus \{v\}$ is almost Cohen–Macaulay. Also, we show that an unmixed Ferrers graph is almost Cohen–Macaulay if and only if it is connected in codimension two. Moreover, we give some examples.

While strategic foresight is relevant for radical innovation, many companies fail to produce radical innovation despite blown-up foresight units. We take into consideration the extent of formalisation and social connectedness in a firm to consider how they moderate the effect of strategic foresight on a firm’s ability to produce radical innovations. In a multi-industry study among 212 European companies, we find that formalisation and connectedness interact to enhance the effect of strategic foresight on radical innovation. When formalisation and connectedness are both high, they jointly improve a firm’s ability to use strategic foresight to produce radical innovation. When social connectedness is low, high formalisation, however, reduces a firm’s ability to turn foresight action into radical innovation. We discuss these findings relative to the controversial role of formalisation in radical innovation and provide managerial advice based on our findings.

In this paper, we examine properties of the division topology on the set of positive integers introduced by Rizza in 1993. The division topology on $\mathbb{N}$ with the division order is an example of $T_0$-Alexandroff topology. We mainly concentrate on closures of arithmetic progressions and connected and compact sets. Moreover, we show that in the division topology on $\mathbb{N}$, the continuity is equivalent to the Darboux property.

In this paper, we extend our research on Cayley graphs of gyrogroups by exploring connections between the algebraic characteristics of gyrogroups and the combinatorial characteristics of their Cayley graphs. We look into some automorphisms of right Cayley graphs, give sufficient and necessary criteria for a right Cayley graph to be vertex-transitive by left gyrotranslations, and prove a similar result for quotient gyrogroups. Some sufficient and necessary criteria for a left gyroaddition to preserve edge color and for a gyration to be an automorphism on the graph are also given. Lastly, we show that certain Cayley graphs of a gyrogroup encode the gyroaddition table and provide an algorithm to compute the gyroaddition with the aid of the gyration table.

For a lattice $L$, we associate a graph called the strongly annihilator ideal graph of $L$, which is denoted by $\mathrm{\text{SAnnIG}}(L)$. It is a graph with vertex set consists of all ideals of $L$ having nontrivial annihilators, and any two distinct vertices $I$ and $J$ are adjacent in $\mathrm{\text{SAnnIG}}(L)$ if and only if the annihilator of $I$ contains a nonzero element of $J$ and the annihilator of $J$ contains a nonzero element of $I$. We show that $\mathrm{\text{SAnnIG}}(L)$ is connected with the diameter at most two and its girth is 3, 4, or infinity. We characterize all lattices whose $\mathrm{\text{SAnnIG}}(L)$ is planar. Among other results, it is proved that $\mathrm{\text{SAnnIG}}(L)$ is perfect.

Let $R$ be a ring with nonzero identity. By the Von Neumann regular graph of $R$, we mean the graph that its vertices are all elements of $R$ such that there is an edge between vertices $x,y$ if and only if $x+y$ is a Von Neumann regular element of $R$, denoted by $G_{{\mathrm{\text{Vnr}}}^{+}}(R)$. In this paper, the basic properties of $G_{{\mathrm{\text{Vnr}}}^{+}}(R)$ are investigated and some characterization results regarding connectedness, diameter, girth and planarity of $G_{{\mathrm{\text{Vnr}}}^{+}}(R)$ are given.

If $R$ is a ring then the square element graph $𝕊q(R)$ is the simple undirected graph whose vertex set consists of all non-zero elements of $R$ and two distinct vertices $u,v$ are adjacent if and only if $u+v=x^2$ for some $x\in R\setminus \{0\}$. In this paper, we provide some necessary and sufficient conditions for the connectedness of $𝕊q(R)$, where $R$ is a ring with identity. We mainly characterize some special class of ring $R$ which we call square-subtract ring for which the graph $𝕊q(M_n(R))$ is connected.

The rings considered in this paper are commutative with identity which are not integral domains. Let $R$ be a ring. An ideal $I$ of $R$ is said to be an annihilating ideal if there exists $r\in R\backslash \{0\}$ such that $Ir=(0)$. Let $𝔸(R)$ denote the set of all annihilating ideals of $R$ and we denote $𝔸(R)\backslash \{(0)\}$ by $𝔸{(R)}^{\ast }$. With $R$, in this paper, we associate an undirected graph denoted by $S\mathrm{\Omega }(R)$ whose vertex set is $𝔸{(R)}^{\ast }$ and two distinct vertices $I,J$ are adjacent in this graph if and only if either $IJ=(0)$ or $I+J\in 𝔸(R)$. The aim of this paper is to study the interplay between some graph properties of $S\mathrm{\Omega }(R)$ and the algebraic properties of $R$ and to compare some graph properties of $S\mathrm{\Omega }(R)$ with the corresponding graph properties of the annihilating ideal graph of $R$ and the sum annihilating ideal graph of $R$.