Linear control theory provides a rich source of inspiration and motivation for development in the matrix theory. Accordingly, in this paper, a generalization of Matrix Determinant Lemma to the finite sum of outer products of column vectors is derived...
In supersymmetric models the mass of the stops can be considered as the naturalness measure of the theory. Roughly, the lighter the stops are, the more natural the theory is. Both, the absence of supersymmetric signals at experiment and the measureme...
We apply the causal Israel-Stewart theory of irreversible thermodynamics to model the matter content of the universe as a dissipative fluid with bulk and shear viscosity. Along with the full transport equations we consider their widely used truncated...
In this paper, we present an innovative non-linear discrete system trying to model the historic battle of Salamis between Greeks and Persians. September 2020 marks the anniversary of the 2500 years that have passed since this famous naval battle, whi...
We replace ordinary chiral SU(3)_L * SU(3)_R perturbation theory CHPT_3 by a new theory CHPT_sigma based on a low-energy expansion about an infrared fixed point alpha_IR for 3-flavor QCD. At alpha_IR, the quark condensate <bar{q}q>_vac =\= 0 induces...
This article gives details of our proposal to replace ordinary chiral $SU(3)_L\times SU(3)_R$ perturbation theory $χ$PT$_3$ by 3-flavor chiral-scale perturbation theory $χ$PT$_σ$. In $χ$PT$_σ$, amplitudes are expanded at low energies and small $...
We review the failure of lowest order chiral $SU(3)_L \times SU(3)_R$ perturbation theory $χ$PT$_3$ to account for amplitudes involving the $f_0(500)$ resonance and $O(m_K)$ extrapolations in momenta. We summarize our proposal to replace $χ$PT$_3$...
The Bohr-Sommerfeld quantization rule lies at the heart of the modern semiclassical theory of a Bloch electron in a magnetic field. This rule is predictive of Landau levels and quantum oscillations for conventional metals, as well as for a host of to...
We propose a non-lattice simulation for studying supersymmetric matrix quantum mechanics in a non-perturbative manner. In particular, our method enables us to put M theory on a computer based on its matrix formulation proposed by Banks, Fischler, S...
We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compar...
This survey article is dedicated to the life of the famous American economist H. Markowitz (1927--2023). We do revisit the main statements of the portfolio selection theory in terms of mathematical completeness including all the necessary auxiliary d...
In this paper, we aims to state some proprieties of willingness to pay (WTP) for partial risk reduction and links with insurance within the dual theory of decision. In the case of partial reduction, we get as Langlais (2005) that a risk-averse decisi...
In the past decade the mathematical theory of machine learning has lagged far behind the triumphs of deep neural networks on practical challenges. However, the gap between theory and practice is gradually starting to close. In this paper I will attem...
\# The Physics of Mind: A Unified Theory of Cognitive Dynamics at the Edge of Chaos --- ## Abstract We present a unified physical framework for cognition, proposing that all complex information-pro...
The publication of a revised edition of a monograph devoted to the two-band theory of superconductivity provides us the opportunity of a short comment on two classical papers, published independently some 50 years ago, where the generalization of t...
We present a pilot-wave model for quantum field theory in which the Dirac sea is taken seriously. The model ascribes particle trajectories to all the fermions, including the fermions filling the Dirac sea. The model is deterministic and applies to...
For any field $F$ (of characteristic not equal to 2), we determine the Zariski spectrum of homogeneous prime ideals in $K^{MW}_*(F)$, the Milnor-Witt $K$-theory ring of $F$. As a corollary, we recover Lorenz and Leicht's classical result on prime ide...
The renormalization-group theory of the d=3 tJ model is extended to further-neighbor antiferromagnetic or electron-hopping interactions, including the ranges of frustration. The global phase diagram of each model is calculated for the entire ranges...
I'm u/bornluckiest you're local tinfoil-hat wearing story-teller with a round-up of the latest conspiracy theory revolving around the Wu-Tang Clan NFT. &#x200B; [The MOASS being delivered?](http...
This is a repository of my own learning notes, also could be a tutorial. I will I will continue to update this new repository, which may include machine learning, deep learning, probability theory, information theory, pytorch, tensorflow, and some learning mat…