A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study quantizes eigenstates of Bochner-Laplacian on symplectic manifolds.
We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask" eigenstates. Matrix elements of price operator fluctuate in time which results in ph…
Detailed study of the financial empirical correlation matrix of the 30 companies comprised by DAX within the period of the last 11 years, using the time-window of 30 trading days, is presented. This allows to clearly identify a nontrivial time-dependence of the resulting correlations. In addition, as a rule, the draw d…
Financial empirical correlation matrices of all the companies which both, the Deutsche Aktienindex (DAX) and the Dow Jones comprised during the time period 1990-1999 are studied using a time window of a limited, either 30 or 60, number of trading days. This allows a clear identification of the resulting correlations. O…
Market strategies minimize Fisher information to minimize risk.
Improved bounds for eigenfunctions on hyperbolic surfaces found.
We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non-degenerate. The Laplacian acting on high tensor powers (the semiclassical regime) of the bundle exhibits a cluster of low-energy states. We demonstrate that the orthogonal projectors onto these states are the Fourier component…
Study gaps and clusters in eigenvalues of magnetic Laplacian on manifolds.
Quantum computing uses Bianchi groups to build gates.
Two new methods estimate quantum density matrices using machine learning.
Using the new data from the OECD-WTO world network of economic activities we construct the Google matrix of this directed network and perform its detailed analysis. The network contains 58 countries and 37 activity sectors for years 1995 and 2008. The construction of , based on Markov chain transitions, treats a…
Quantum theory explains price dynamics in financial markets, capturing bid-ask spread and ergodicity.
We design non-singular cloaks enabling objects to scatter waves like objects with smaller size and very different shapes. We consider the Schrodinger equation which is valid e.g. in the contexts of geometrical and quantum optics. More precisely, we introduce a generalized non-singular transformation for star domains, a…
Unified geometric framework for adiabatic quantum mechanics.
The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact connected Lie groups and G is simple. An elementary discussion of the differential geome…
Using the United Nations COMTRADE database \cite{comtrade} we construct the Google matrix of multiproduct world trade between the UN countries and analyze the properties of trade flows on this network for years 1962 - 2010. This construction, based on Markov chains, treats all countries on equal democratic grounds …
Eigen component analysis combines quantum mechanics with machine learning for efficient data analysis.
This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space-time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the 6-dimensional case in which twisto…
This is the first of two articles aiming to introduce symplectic spinors into the field of symplectic topology and the subject of Frobenius structures. After exhibiting a (tentative) axiomating setting for Frobenius structures resp. 'Higgs pairs' in the context of symplectic spinors, we present immediate observations c…