Evidential deep learning, built upon belief theory and subjective logic, offers a principled and computationally efficient way to turn a deterministic neural network uncertainty-aware. The resultant evidential models can quantify fine-grained uncerta...
Model-based analysis tools, built on assumptions and simplifications, are difficult to handle smart grids with data characterized by 4Vs data. This paper, using random matrix theory (RMT), motivates data-driven tools to perceive the complex grids in...
Frozen Density Embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on the electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has...
Very recently we present a theory [Wei-long She, Chin. Phys. 14, 2514(2005); Online: http://www.jop.org/journals/cp; http://arxiv.org/abs/quant-ph/0512097] to show that the quantization of light energy in vacuum can be derived directly from classic...
This paper presents a brief account of some of the my early research interests. This historical account starts from my laurea thesis on Signal Theory and my master thesis on Computation Theory. It recalls some results in Combinatory Logic and Term Re...
Modern dynamical systems theory has previously had little to say about finite difference and finite element approximations of partial differential equations (Archilla, 1998). However, recently I have shown one way that centre manifold theory may be...
The Keldysh theory of photoionization for solids is generalized to atomically thin two-dimensional semiconductors. We derive a closed-form formula and its asymptotic forms for a two-band model with a Kane dispersion. These formulas exhibit characteri...
This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives the algori...
Topological constraint theory has become an increasingly popular tool to predict the compositional dependence of glass properties or pinpoint promising compositions with tailored functionalities. This approach reduces complex disordered networks into...
The primary sourcebook for developments based on the data of the world components "Theory of Intellectualities and Mathematical Statistics" (TIMS) collections of the Department of Mathematics, Physics and Astronomy of Odessky National Maritime Univer...
**The New Order: Last Days of Europe** **v1.2.0 “Toolbox Theory”** **Major Additions** - Entirely reworked the economy mechanic, including but not limited to production, construction, and trade...
A new method for multinomial inference is proposed by representing the cell probabilities as unordered segments on the unit interval and following Dempster-Shafer (DS) theory. The resulting DS posterior is then strengthened to improve symmetry and le...
In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that empirical sci...
We find an interesting relationship between the golden ratio, the Moebius function, the Euler totient function and the natural logarithm - central players in the theory of numbers. A number of identities involving the golden ratio and its reciprocal...
We prove that the Real Johnson-Wilson theories ER(n) are homotopy associative and commutative ring spectra up to phantom maps. We further show that ER(n) represents an associatively and commutatively multiplicative cohomology theory on the category o...
We summarize the general results of El Karoui [1981] on optimal stopping problems for processes which are measurable with respect to Meyer-$σ$-fields. Meyer-$σ$-fields are due to Lenglart [1980] and include the optional and predictable $σ$-field a...
Static reduction of information structures (ISs) is a method that is commonly adopted in stochastic control, team theory, and game theory. One approach entails change of measure arguments, which has been crucial for stochastic analysis and has been a...
We show that the YARK theory of gravity, proposed in Eur. Phys. J. Plus 133, 261 (2018) by Kholmetskii et al. and in previous papers of the same research group is wrong....
A recent paper by Davies et al (2021) describes how deep learning (DL) technology was used to find plausible hypotheses that have led to two original mathematical results: one in knot theory, one in representation theory. I argue here that the signif...
We systematically develop a theory of stratification in the context of tensor triangular geometry and apply it to classify the localizing tensor-ideals of certain categories of spectral $G$-Mackey functors for all finite groups $G$. Our theory of str...