Suppose that f (x) E 1[8[x1, ... , xn] and g(x) E 1[8[x1, ... , xn] are two real polynomials of degree d in n variables. If the polynomials f and g are the same up to orthogonal symmetry, a natural question is then what element of the orthogonal group induces the orthogonal symmetry; i.e. to find the element R E O(n) such that f (R inverted perpendicular x) = g(x). One may directly solve this problem by constructing a nonlinear system of equations induced by the relation f (R inverted perpendicular x) = g(x) along with the identities of the orthogonal group. However, this approach becomes quite computationally expensive for larger values of nand d. To give an alternative and significantly more scalable solution to this problem, we introduce the concept of Polynomial-Weighted Principal Component Analys is (PW-PCA). We in particular show how PW-PCA can be effectively computed and how these techniques can be used to obtain a certificate of orthogonal equivalence, that is we find the R E O(n) such that f (R inverted perpendicular x) = g(x). (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The rapid advancement of low-power microelectronic technologies has stimulated growing interest in vibration-based energy harvesting as a promising alternative to conventional batteries. While batteries are widely used at these scales, their replacement becomes highly challenging for systems deployed within inaccessible or remote locations. The major drawback of linear harvesters is their limited frequency bandwidth. This limitation, together with the wide frequency spectrum of ambient excitations, significantly diminishes the energy conversion efficiency of linear harvesters. To address this challenge and improve the performance of such systems in practical environments, it is essential to broaden their frequency bandwidth. Among the various approaches for broadening the frequency bandwidth, employing nonlinear techniques has proven to be highly effective in enhancing the efficiency of vibration energy harvesters. This study proves the theoretical modeling of frequency bandwidth analysis in a piezoelectric energy harvester for a series of experimental cases considering magnetic nonlinearity and impact-induced nonlinearity. Applying both approaches together increases the system efficiency by about 80 % compared to using either method separately. Furthermore, the influence of key system parameters—including magnetic strength, input acceleration amplitude, electrical resistance, and initial gap—on the system's dynamic behavior is investigated. Finally, an efficiency index is introduced to assess the harvester's efficiency relative to the conventional design.
This study investigates the notion of the varying unpredictable volatility in the prices of green and traditional cryptocurrencies, and its symbiotic relationship with investor sentiment. Accordingly, the structural time varying parameter vector autoregression (TVP-VAR) method is employed for the 1 January 2018-23 September 2022 period. The findings revealed variable relationships of the sentiment index (SI) with cryptocurrencies amid various economic situations. The stochastic volatility of Bitcoin and Ethereum peaked around January 2018, trending lower since then, and rising back from 2021 to 2022, particularly in early 2021 and early 2022. During the Russia-Ukraine conflict, the stochastic volatility of Cardano was lower than those of Bitcoin and Ethereum. The simultaneous relationship of SI to the Bitcoin, IOTA, Cardano, and Ethereum shock vary between positive and negative in 2021 before turning negative in 2022. Bitcoin's initial reactions to a positive investor mood shock are insignificantly different from zero. These results of SI to positive Bitcoin and IOTA shock decrease during our sample except in 2021. The impulse responses of Bitcoin to positive Ethereum and Cardano shocks decrease in 2018 and fluctuate during 2021-2022 and these results of SI to these negative shocks are significant due to the COVID-19 duration. In summary, the findings provide a novel and comprehensive analysis of the interdependencies between investor sentiment, and green and nongreen cryptocurrencies. In particular, the stochastic volatility of the cryptocurrency classes highlights spikes of investor sentiment during the Black Swan events (the COVID-19, the Russia-Ukraine conflict). The research offers valuable insights and cautionary implications regarding the transmission of uncertainty, and policy implications for regulators and investors.
This study examines the role of business incubators in supporting start-ups in emerging markets, where resource limitations require entrepreneurs to either rely on entrepreneurial bricolage or invest in developing dynamic capabilities in their early stages. Although prior research has explored incubators, less attention has been given to how they help start-ups move beyond static short-term bricolage toward building long-term dynamic capabilities under resource-constrained conditions. Using data from 403 start-ups, the study tests the moderating effect of incubator support on the relationship between bricolage, dynamic capabilities, and venture performance. The findings suggest that incubators significantly strengthen the positive impact of dynamic capabilities on start-up performance compared to that of bricolage. In emerging markets, incubators thus enable start-ups to cultivate adaptive, growth-oriented capabilities rather than relying solely on static bricolage practices. The study offers implications for policymakers, founders, and incubator managers seeking to promote sustainable start-up development and scaling.
The aim of this study is to examine the impacts of overconfidence and disposition biases on investor behaviour at the Shanghai Stock Exchange in China. We employ vector autoregression and impulse response functions on the SSE 50 index and its constituent stocks between 1 January 2016 and 30 April 2023, further splitting the data into pre- and post-uncertain time periods, i.e., the COVID-19 pandemic and the Russia-Ukraine war to identify overconfidence bias and the disposition effect. The results show investors in the China stock market are disposed to overconfidence bias at the market level as they are following past market returns. The disposition effect also exists during the study period. It is however determined that the overconfidence bias is the more prevalent of the two. Furthermore, these two biases have been clearly segregated for all 50 stocks before and after the aforementioned crises. Our analysis in this connection reveals that behavioural finance may be able to explain the odd patterns and swings on the Chinese financial markets that the efficient market model cannot. The study suggests that investors, policymakers, and market regulators should perform a post analysis of each investment so that they become aware of past behavioural mistakes and refrain from repeating the same. This also might help investors to minimize the negative impact of overconfidence and disposition biases on their expected utility over wartime and the regulators could build favourable policies for investors through which market volatility could be controlled during stressful periods such as the Russia-Ukraine war.
