Search Results (46)

This paper introduces a broad class of Mirror Descent (MD) and Generalized Exponentiated Gradient (GEG) algorithms derived from trace-form entropies defined via deformed logarithms. Leveraging these generalized entropies yields MD and GEG algorithms with improved convergence behavior, robustness against vanishing and exploding gradients, and inherent adaptability to non-Euclidean geometries through mirror maps. We establish deep connections between these methods and Amari’s natural gradient, revealing a unified geometric foundation for additive, multiplicative, and natural gradient updates. Focusing on the Tsallis, Kaniadakis, Sharma–Taneja–Mittal, and Kaniadakis–Lissia–Scarfone entropy families, we show that each entropy induces a distinct Riemannian metric on the parameter space, leading to GEG algorithms that preserve the natural statistical geometry. The tunable parameters of deformed logarithms enable adaptive geometric selection, providing enhanced robustness and convergence over classical Euclidean optimization. Overall, our framework unifies key first-order MD optimization methods under a single information-geometric perspective based on generalized Bregman divergences, where the choice of entropy determines the underlying metric and dual geometric structure. Full article

Kaniadakis deformed $\kappa$-mathematics is an area of mathematics that has found relevance in the analysis of complex systems. Specifically, the mathematical framework in the context of a first-order decay $\kappa$-differential equation is investigated, facilitating an in-depth examination of the $\kappa$-mathematical structure. This framework serves as a foundational platform, representing the simplest non-trivial setting for such inquiries which are demonstrated for the first time in the literature. Finally, additional avenues of study are discussed. Full article

This study explores how older Chinese migrants in London engage with climate change discourse using participatory co-design workshops. Although already practising sustainability behaviours such as recycling, this group faces significant barriers—particularly language difficulties and cultural differences—that limit their active participation in broader climate initiatives. The research addresses three key aspects: (1) identifying opportunities for sustainable practices within migrants’ daily routines; (2) understanding their influential roles within families and communities; and (3) examining their trusted sources and preferred channels for climate communication. Results highlight that family and community networks, combined with digital platforms (e.g., WeChat) and visually engaging materials, play essential roles in disseminating climate information. Participants expressed strong motivations rooted in intergenerational responsibility and economic benefits. The findings emphasise the necessity of inclusive and peer-led communication strategies that are attuned to older migrants’ linguistic preferences, media habits, and cultural values—underscoring their significant but often overlooked potential to meaningfully contribute to climate action. Full article

In this paper, we introduce a new family of Stirling polynomials of the second kind, Bell polynomials, bivariate Bell polynomials, Bernoulli polynomials of higher order, and Euler polynomials of higher order arising from the Kaniadakis calculus viewpoint. We refer to each of them as $\kappa$-polynomials. Through the defined concepts of Kaniadakis calculus, we derive explicit formulas, summation formulas, and addition formulas for the polynomials discussed in the present paper. We also present the Volkenborn integral and the fermionic p-adic integral representations in terms of the $\kappa$-Stirling polynomials of the second kind, bivariate $\kappa$-Bell polynomials, $\kappa$-Bernoulli polynomials of higher order, and $\kappa$-Euler polynomials of higher order. We establish some formulae, including old and new polynomials. Finally, we investigate determinantal representations for the $\kappa$-Euler polynomials and the $\kappa$-Bernoulli polynomials. Full article

This study employs walking interviews to examine the low-carbon practices, cultural adaptation, and policy awareness of older Chinese migrants in the UK within their everyday environments. A total of 20 participants were interviewed in public spaces such as parks, supermarkets, and their homes. Using contextual thematic analysis, the study identifies key factors influencing their environmental behaviors. The findings reveal the following: (1) Language barriers, economic pressures, and social isolation limit migrants’ understanding of environmental policies. Many participants rely on self-sufficient ethnic community networks rather than engaging with mainstream sources; (2) Generational differences are evident—younger migrants demonstrate greater theoretical awareness of environmental policies, whereas older migrants exhibit stronger low-carbon behaviors through energy conservation and waste reduction; (3) A balance between cultural identity and consumption habits—while some migrants adjust their dietary, spending, and linguistic habits, core cultural values such as frugality and family responsibility remain unchanged. This study highlights the value of walking interviews in capturing situational insights into low-carbon behaviors and cultural adaptation. It provides empirical evidence for government agencies and community organizations, advocating for cross-cultural environmental education and improved policy communication. Recommendations include targeted environmental training, community-based volunteer initiatives, intergenerational environmental education, and policy dissemination through WeChat, Chinese communities, and ethnic networks. These measures can help bridge the generational gap in policy awareness and promote social integration among older Chinese migrants. Full article

A novel approach to the quantum version of $\kappa$-entropy that incorporates it into the conceptual, mathematical and operational framework of quantum computation is put forward. Various alternative expressions stemming from its definition emphasizing computational and algorithmic aspects are worked out: First, for the case of canonical Gibbs states, it is shown that $\kappa$-entropy is cast in the form of an expectation value for an observable that is determined. Also, an operational method named “the two-temperatures protocol” is introduced that provides a way to obtain the $\kappa$-entropy in terms of the partition functions of two auxiliary Gibbs states with temperatures $\kappa$-shifted above, the hot-system, and $\kappa$-shifted below, the cold-system, with respect to the original system temperature. That protocol provides physical procedures for evaluating entropy for any $\kappa$. Second, two novel additional ways of expressing the $\kappa$-entropy are further introduced. One determined by a non-negativity definite quantum channel, with Kraus-like operator sum representation and its extension to a unitary dilation via a qubit ancilla. Another given as a simulation of the $\kappa$-entropy via the quantum circuit of a generalized version of the Hadamard test. Third, a simple inter-relation of the von Neumann entropy and the quantum $\kappa$-entropy is worked out and a bound of their difference is evaluated and interpreted. Also the effect on the $\kappa$-entropy of quantum noise, implemented as a random unitary quantum channel acting in the system’s density matrix, is addressed and a bound on the entropy, depending on the spectral properties of the noisy channel and the system’s density matrix, is evaluated. The results obtained amount to a quantum computational tool-box for the $\kappa$-entropy that enhances its applicability in practical problems. Full article

Older adults are both vulnerable to the impacts of climate change and uniquely positioned to contribute to climate action. However, their ability and willingness to engage vary significantly due to health disparities, financial constraints, and cultural factors. To ensure inclusivity, climate policies must reflect these differences and empower older adults to participate effectively. This research focused on 30 London-based older adults aged 60–85 (18 women, 12 men) selected via purposive sampling and stratified by gender and climate awareness. All participants were interested in climate issues and engaged in seven small focus groups facilitated by two researchers. Discussions addressed climate perceptions, low-carbon behaviors, and policy recommendations. The findings reveal that tailored communication, featuring simplified language and visual materials, resonates deeply with older adults, fostering better understanding and emotional connection. Participants highlighted practical low-carbon actions they already undertake, such as energy conservation, food waste reduction, and public transport use. They also proposed innovative strategies for promoting climate awareness, including integrating cultural and emotional elements, encouraging intergenerational learning, and providing economic incentives for green practices. To enhance the engagement of older adults in climate action, governments and corporations should develop inclusive communication strategies, provide financial support for adopting green technologies, and foster intergenerational collaboration to share knowledge and experiences in the communities. This study amplifies the voices of older adults in climate discourse, offering actionable insights for shaping communication strategies and policies. While this study provides valuable insights into older adults’ contributions to climate action, future research could expand the sample size and geographic diversity to enhance the generalizability of findings. Full article

In this work, we have studied the thermodynamic properties of the Van der Waals black hole in the framework of the relativistic Kaniadakis entropy. We have shown that the black hole properties, such as the mass and temperature, differ from those obtained by using the the Boltzmann–Gibbs approach. Moreover, the deformation $\kappa$-parameter changes the behavior of the Gibbs free energy via introduced thermodynamic instabilities, whereas the emission rate is influenced by $\kappa$ only at low frequencies. Nonetheless, the pressure–volume ($P\left(V\right)$) characteristics are found independent of $\kappa$ and the entropy form, unlike in other anti-de Sitter (AdS) black hole models. In summary, the presented findings partially support the previous arguments of Gohar and Salzano that, under certain circumstances, all entropic models are equivalent and indistinguishable. Full article

The photon-counting light laser detection and ranging (LiDAR), especially the Geiger mode avalanche photon diode (Gm-APD) LiDAR, can obtain three-dimensional images of the scene, with the characteristics of single-photon sensitivity, but the background noise limits the imaging quality of the laser radar. In order to solve this problem, a depth image estimation method based on a two-dimensional (2D) Kaniadakis entropy thresholding method is proposed which transforms a weak signal extraction problem into a denoising problem for point cloud data. The characteristics of signal peak aggregation in the data and the spatio-temporal correlation features between target image elements in the point cloud-intensity data are exploited. Through adequate simulations and outdoor target-imaging experiments under different signal-to-background ratios (SBRs), the effectiveness of the method under low signal-to-background ratio conditions is demonstrated. When the SBR is 0.025, the proposed method reaches a target recovery rate of 91.7%, which is better than the existing typical methods, such as the Peak-picking method, Cross-Correlation method, and the sparse Poisson intensity reconstruction algorithm (SPIRAL), which achieve a target recovery rate of 15.7%, 7.0%, and 18.4%, respectively. Additionally, comparing with the SPIRAL, the reconstruction recovery ratio is improved by 73.3%. The proposed method greatly improves the integrity of the target under high-background-noise environments and finally provides a basis for feature extraction and target recognition. Full article

This study addresses market concentration among major corporations, highlighting the utility of relative entropy for understanding diversification strategies. It introduces entropic value at risk (EVaR) as a coherent risk measure, which is an upper bound to the conditional value at risk (CVaR), and explores its generalization, relativistic value at risk (RLVaR), rooted in Kaniadakis entropy. Through extensive empirical analysis on both developed (i.e., S&P 500 and Euro Stoxx 50) and developing markets (i.e., BIST 100 and Bovespa), the study evaluates entropy-based criteria in portfolio selection, investigates model behavior across different market types, and assesses the impact of cryptocurrency introduction on portfolio performance and diversification. The key finding indicates that entropy measures effectively identify optimal portfolios, particularly in scenarios of heightened risk and increased concentration, crucial for mitigating negative net performances during low returns or high turnover. Bitcoin is primarily used for diversification and performance enhancement in the BIST 100 index, while its allocation in other markets remains minimal or non-existent, confirming the extreme concentration observed in stock markets dominated by a few leading stocks. Full article

The axiomatic structure of the $\kappa$-statistcal theory is proven. In addition to the first three standard Khinchin–Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the $\kappa$-entropy and its special limiting case, the classical Boltzmann–Gibbs–Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from $\kappa$-entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the $\kappa$-formalism, which emerges from the $\kappa$-entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on $\kappa$-entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the $\kappa$-statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized. Full article

Both classical and quantum arguments suggest that if Barrow entropy is correct, its index $\delta$ must be energy-dependent, which would affect the very early universe. Based on thermodynamic stability that sufficiently large black holes should not fragment, we argue that Barrow entropy correction must be small, except possibly at the Planckian regime. Furthermore, the fact that a solar mass black hole does not fragment implies an upper bound $\delta \lesssim O\left({10}^{-3}\right)$, which surprisingly lies in the same range as the bound obtained from some cosmological considerations assuming fixed $\delta$. This indicates that allowing $\delta$ to run does not raise its allowed value. We briefly comment on the case of Kaniadakis entropy. Full article

Because of its flexibility and multiple meanings, the concept of information entropy in its continuous or discrete form has proven to be very relevant in numerous scientific branches. For example, it is used as a measure of disorder in thermodynamics, as a measure of uncertainty in statistical mechanics as well as in classical and quantum information science, as a measure of diversity in ecological structures and as a criterion for the classification of races and species in population dynamics. Orthogonal polynomials are a useful tool in solving and interpreting differential equations. Lately, this subject has been intensively studied in many areas. For example, in statistics, by using orthogonal polynomials to fit the desired model to the data, we are able to eliminate collinearity and to seek the same information as simple polynomials. In this paper, we consider the Tsallis, Kaniadakis and Varma entropies of Chebyshev polynomials of the first kind and obtain asymptotic expansions. In the particular case of quadratic entropies, there are given concrete computations. Full article

It is known that Kaniadakis entropy, a generalization of the Shannon–Boltzmann–Gibbs entropic form, is always super-additive for any bipartite statistically independent distributions. In this paper, we show that when imposing a suitable constraint, there exist classes of maximal entropy distributions labeled by a positive real number $\aleph >0$ that makes Kaniadakis entropy multi-additive, i.e., $S_{\kappa }\left[p^{\mathrm{A}\cup \mathrm{B}}\right]=(1+\aleph )\left(S_{\kappa }\left[p^{\mathrm{A}}\right]+S_{\kappa }\left[p^{\mathrm{B}}\right]\right)$, under the composition of two statistically independent and identically distributed distributions $p^{\mathrm{A}\cup \mathrm{B}}(x,y)=p^{\mathrm{A}}\left(x\right)p^{\mathrm{B}}\left(y\right)$, with reduced distributions $p^{\mathrm{A}}\left(x\right)$ and $p^{\mathrm{B}}\left(y\right)$ belonging to the same class. Full article