In the Figure 2, we report the evolution of the total **connectedness** between the five implied volatility indices. Figure 2 also highlights several cycles of **connectedness** where the total **connectedness** is higher or lower than the full sample average. As expected, the **connectedness** index shows a time-varying pattern over the sample period. Interestingly, during our subsample corresponding to the GFC (May 2009-April 2010), the **degree** of **connectedness** is relatively low (35% on average). This low **degree** of **connectedness** may be due to this period encompasses the worst of the GFC, such as the Lehman Bros. demise, and a period of recovery or decrease in implied volatilities. We observe several spikes in the evolution of the total **connectedness**, reaching figures of over 50% in several periods of our sample. The first spike appears after the stress observed in financial markets from May 2010, reflecting the Eurozone sovereign debt crisis, which ended in February 2011 with a second Greek bailout . A second episode 11 of increase in **connectedness** comes after the heavy losses registered in stock exchanges worldwide in August 2011. This was due to the fears of contagion of the Eurozone sovereign debt crisis and the credit rating downgraded because of the debt-ceiling crisis of the United States. These tensions were intensified in 2012 due to a growing concern about the weak US recovery and political uncertainty around the world. After some ups and downs, the **connectedness** among implied volatility indices experienced an important reduction. The stabilizing actions by central banks and the Cyprus bailout that boosted investor confidence in financial markets was possibly the cause of this

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If the heart is literally and functionally at the center of feeling, and if the **degree** of **connectedness** within the mind is what deter- mines psychosomatic plasticity, then we would expect thin- boundary persons who are on the receiving end of new hearts to evidence some remarkable changes in the aftermath of their transplant. This is exactly what Pearsall has documented. Con- sider the following accounts he and his associates have collected. In each case, information about the donor and recipient was verified by family or friends; additionally, the often striking personality changes noted preceded any contact with the donor’s family or friends. A sampling:

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markets. Given the large number of stocks included in the sample, there is a high **degree** of **connectedness** for the full sample. As we will see below there is always a high **degree** of **connectedness** even during tranquil times. There is another reason for the total connected- ness for a set of financial stocks to be higher than for a set of major national stock markets around the world or for a set of asset classes in the U.S. As the institutions included in our analysis are all operating in the finance industry, both industry-wide and macroeconomic shocks aﬀect each one of these stocks one way or the other. As some of these institutions and their stocks are more vulnerable to external and/or industry-wide shocks than others, they are likely to be transmitting these shocks to other financial stocks, generating a higher **degree** of **connectedness** to others. Obviously, to the extent that they have important im- plications for the rest of the industry, idiosyncratic volatility shocks are also transmitted to other stocks. For that reason, compared to a similar number of stocks from diﬀerent indus- tries, the **connectedness** for a group of stocks in the finance industry is likely to be higher. It is also likely to be higher compared to the **connectedness** for a group of global markets, as these markets are not subject to common shocks as frequently as the stocks from the finance industry. 24

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In addition, it has also been argued that a high degree of connectedness to the regional environment leads family business to be more concerned than other enterprises about their r[r]

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Abstract. Several speciﬁc types of ordinary and generalized **connectedness** in a generalized topological space have been deﬁned and investigated for var- ious purposes from time to time in the literature of topological spaces. Our recent research in the ﬁeld of a new type of generalized **connectedness** in a generalized topological space is reported herein as a starting point for more generalized types.

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Payments services include mobile and integrated POS solutions plus e-invoicing and gift card management. Operational and growth solutions include payroll, capital access and Caviar, a [r]

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We study macro-financial linkages and their importance within the Swiss economy from a network perspective. First, we investigate the real-financial **connectedness** in the Swiss economy, using the KOF economic barometer, obtained from real and financial variables, and, the real activity index (RAI), we distilled from a small set of real variables, as two alternative proxies for the real side. Whereas the KOF-barometer-based analysis shows that both sides transmit sizeable shocks to each other without one dominating the other, the RAI-based analysis shows that in the aggregate, the financial side turns out to be the net shock transmitter to the real sector. In the second part, we focus on the relative importance of financial markets as shock propagators using a network centrality measure. We find that 2008–2009 recession in Switzerland and the Swiss National Bank’s (SNB) exchange rate policy changes in 2011 and 2015 have significantly altered the way the shocks are transmitted across the two sides of the economy. During 2009–2011, stock, bond, and foreign exchange (FX) markets, in descending order, played important roles as shock propagators. Following the SNB’s 2015 policy decision to discontinue the lower bound for the EUR/CHF exchange rate, FX market has become equally important as the stock market but more important than the bond market as a shock propagator.

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We first show theoretically that diversification of risks within the regulated banking system leads to increased **connectedness** of banks which reduce the benefits of both diversification and risk transfer. Hence, diversification of and the transfer of risks outside the regulated banking system appears to be a superior alternative. Indeed, if the risks are transferred to outside market participants that are not (yet) connected to the banking system, the banking system may be more stable. However, this perspective with a focus on the overall stability of the banking system does not explain why individual banks transferred the risks to entities outside the regulated banking system. The demand for securitized “safe” assets (see Gorton and Metrick, 2010) suggests that the entities in the shadow banking system were willing to pay more for the securitized assets than the regulated banking system. Regulatory arbitrage further incentivized banks to diversify and transfer the risks outside the regulated banking system (Acharya et al. 2013).

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Network **connectedness** working with causal linkages can be characterized well through vari- ance decompositions from a vector autoregression approximation model (Diebold and Yilmaz, 2009, 2012). Variance decompositions provide useful information about how much of the future variance of variable j is due to shocks in variable k. Aggregating variance decompositions yields a simple way to measure how the system is interconnected. Diebold and Yılmaz (2014) argued that variance decompositions are intimately linked to modern network theory and recently proposed measures of various types of systemic risk, such as marginal expected shortfall (Acharya et al., 2017) and Delta CoVaR (Adrian and Brunnermeier, 2016). Our analysis is also adjacent to that of Song (2018), who developed technical conditions for a network to explain microfinancing de- cision. Previous literature examined how shocks to volatility measured ex post create linkages in the network. Employing implied volatility measures, we derive informatively different measures of interconnectedness. 4

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The first natural question is that of **connectedness**: does there exist a thickness r such that the graphs S(n, r) are connected for all n? A first obstruction is given by the topological notion of ends. Recall that a graph has at most k ends if the complement of any finite set has at most k connected components. By a result of Stallings [Sta], the number of ends (the least such k) of a Cayley graph of an infinite group is either 2, for virtually cyclic groups, or ∞, for free products with amalgamation and HNN-extensions over finite groups, or 1 for any other group. For instance in a free group with free generating set the number of connected components of S(n, r) is always the number of elements in the sphere of radius n. But, as groups in the two first cases of Stallings’ classification are well-understood, we may focus on the generic case of one-ended groups.

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Storefront and Shopping Cart Inventory Management/Fulfillment Loyalty/Rewards Payments/Alternative Payments Fraud Prevention/Detection Couponing.. Mobile Payments Social Media.[r]

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Aho, Nieminen, Popa, Noiri, and Jafari have studied semipreconnected- ness (= β-**connectedness**) [2, 4, 7], via semipreopen [3] (= β-open [1]) sets, and some other **connectedness** have been introduced by Modak and Noiri in [12, 13, 14, 15] and Noorena and Khan in [16].

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Then G can be decomposed into disjoint rainbow matchings of size n” to see that this is equivalent to Theorem 1.2, associate an m-edge coloured bipartite graph with any m×n Latin rectang[r]

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female), region (Southwestern Ontario versus Saskatchewan), and residence (on-reserve versus off-reserve) for each of the CCS-S subscales (see Table 11). Family affluence (i.e., low, moderate, high) was also examined through one-way analysis of variance (see Table 12). Results were interpreted at a more conservative p level of < .01 given the relatively small sample size for these analyses. Unlike Study 1, there were no differences found on the identity subscale for males and females (females M = 12.63, SD = 2.31; males M = 12.23, SD = 2.40; t(276) = -1.45, p < ns). However, respondents living on-reserve and from Saskatchewan reported significantly higher scores on the traditions subscale than respondents living off-reserve (on-reserve M = 5.57, SD = 2.78; off-reserve M = 3.78, SD = 2.56; t(275) = -4.95, p < .001) and from Southwestern Ontario (Saskatchewan M = 5.59, SD = 2.83; Southwestern Ontario M = 4.38, SD = 2.72; t(286) = 3.71, p < .001), respectively. These findings are consistent with the results from Study 1 that suggest that living on-reserve is related to a higher **degree** of participation in traditional activities among First Nations youth. The author hypothesizes that cultural activities or events may be easier to access if a youth is living in on-reserve, particularly if the First Nations community has a high **degree** of cultural continuity (Chander & Lalonde, 1998). While youth living on-reserve also reported higher scores on the spirituality subscale in Study 1, this finding was not replicated in Study 2 (on-reserve M = 8.79, SD = 2.31; off-reserve M = 8.54, SD = 2.38; t(275) = -.814, p < ns). No other significant group differences were found.

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The concept of fuzzy set was introduced by Zadeh in his classic paper [13]. The theory of fuzzy topological spaces was introduced and developed by C.L.Chang [4]. Since Atannasov [2,3] introduced the notion of intuitionistic fuzzy sets, Çoker [6] defined the intuitionistic fuzzy topological spaces.Turanlı and Çoker[11,12] introduced the investigate fuzzy **connectedness** in intuitionistic fuzzy topological spaces. In 2014, Yager [9,10] introduced the notion of Pythagorean fuzzy subsets which is a new class of non-standard fuzzy subsets and which has many effective applicants natural and social sciences. Some authors [8] studied the concept of Pythagorean fuzzy topological space by following the idea of Chang [4]. The aim of this paper is to extended the notions of fuzzy **connectedness**[1,5] and intuitionistic fuzzy **connectedness** by introducing the notion of Pythagorean fuzzy **connectedness**. This construction is based on the idea of Pythagorean fuzzy set developed by Yager [9,10].

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MSC: 54C60; 54C65; 55M10 Keywords: lower semicontinuity; almost lower semicontinuity; quasi-lower semicontinuity; approximate selection theorems; D-spaces; LC-metric spaces; topological [r]

We propose this system for senior individuals to enhance their living characteristics and encourage the social **connectedness** for them utilizing present day assistive innovation. The plan approach of this system is minimal effort and powerful so the acknowledgment is reasonable.

In 1965 Zadeh [10] in his classical paper generalized characteristic functions to fuzzy sets. Chang [2] in 1968 introduced the topological structure of fuzzy sets. Pu and Liu [7] defined the concept of fuzzy **connectedness** using fuzzy closed set. Lowen [5] also defined an extension of a **connectedness** in a restricted family of fuzzy topologies. Fuzzy Č ech closure operator and fuzzy Č ech closure space were first studied by A.S. Mashhour and M.H. Ghanim [6].

In Section we will prove our main theorems on Hu,n which give conditions for Hu,n to be connected or to be a forest, and we work out some relations between the lengths of circuits in H[r]