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 shows gain-loss asymmetry in stock indices using a q-spin Potts model.
Explains non-lorentzian theories and their dynamics.
New transitions found in Spin(7) holonomy metrics related to a dynamical system.
Efficiently predicts long-time dynamics of quantum spin models using MLP regression.
This work connects point particles to spin chains using geometric methods.
We calculate the realized volatility in the spin model of financial markets and examine the returns standardized by the realized volatility. We find that moments of the standardized returns agree with the theoretical values of standard normal variables. This is the first evidence that the return dynamics of the spin fi…
A reinforcement learning approach prepares quantum squeezed states in open spin systems.
We analyze operational risk in terms of a spin glass model. Several regimes are investigated, as a functions of the parameters that characterize the dynamics. The system is found to be robust against variations of these parameters. We unveil the presence of limit cycles and scrutinize the features of the asymptotic sta…
The paper develops a new algorithm for RBMs using dynamical mean-field theory.
A spin model is used for simulations of financial markets. To determine return volatility in the spin financial market we use the GARCH model often used for volatility estimation in empirical finance. We apply the Bayesian inference performed by the Markov Chain Monte Carlo method to the parameter estimation of the GAR…
The dynamics of a stock market with heterogeneous agents is discussed in the framework of a recently proposed spin model for the emergence of bubbles and crashes. We relate the log returns of stock prices to magnetization in the model and find that it is closely related to trading volume as observed in real markets. Th…
Mathisson's 'new mechanics' of a relativistic spinning particle is shown to follow, in the case of planar motion, from only general requirements of relativistic invariance and of the dependence on third order derivatives along with the 'variationality' feature. The Hamiltonian counterpart ultimately recovers the Dixon …
Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning. Computing the underlying structure and dynamics of such complex systems is extrem…
Finsler geometry connects to higher-spin fields and curved-space Fronsdal equations.
Motion of curves and surfaces in lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that…
This thesis explores emergent intelligence in disordered systems like spin glasses and neural networks.
When modelling stock market dynamics, the price formation is often based on an equilbrium mechanism. In real stock exchanges, however, the price formation is goverend by the order book. It is thus interesting to check if the resulting stylized facts of a model with equilibrium pricing change, remain the same or, more g…
The theory of quandle (co)homology and cocycle knot invariants is rapidly being developed. We begin with a summary of these recent advances. One such advance is the notion of a dynamical cocycle. We show how dynamical cocycles can be used to color knotted surfaces that are obtained from classical knots by twist-spinnin…
A second order variational description of the autoparallel curves of some differential-geometric connection for the third order Mathisson's 'new mechanics' of a relativistic free spinning particle is suggested starting from general requirements of invariance and 'variationality'.
A new framework for generating predictive features in noisy multivariate time series.
Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequen…
In this paper, we studied the dynamics of the log-return distribution of the Korean Composition Stock Price Index (KOSPI) from 1992 to 2004. Based on the microscopic spin model, we found that while the index during the late 1990s showed a power-law distribution, the distribution in the early 2000s was exponential. This…
Study isotropic embeddings of Lie group orbits and their application to magnetic geodesic flows.
Machine learning models accurately predict molecular magnetic anisotropy tensors.
The compact exceptional Lie groups F4, E6, E7 and E8 have spinor groups as a subgroup as follows: E8 \supset Ss(16) \supset Spin(15) \supset Spin(14) \supset Spin(13), E7 \supset Spin(12) \supset Spin(11), E6 \supset Spin(10), F4 \supset Spin(9) \supset Spin(8) \supset Spin(7) \supset \cdot \cdot \cdot \supset Spin(1) …
The paper explores spin^h structures and their obstructions.
Study -dDT connections on manifolds with -structures.
New -instantons constructed on Joyce's manifold.
This is an introduction to the construction of higher-dimensional knots by spinning methods. Simple spinning of classical knots was introduced by E. Artin in 1926, and several generalizations have followed. These include twist spinning, superspinning or p-spinning, frame spinning, roll spinning, and deform spinning. We…
The relativistic quantum mechanic approach is used to develop a stock market dynamics. The relativistic is conceptional here as the meaning of big external volatility or volatility shock on a financial market. We used a differential geometry approach with the parallel transport of the prices to obtain a direct shift of…
New -manifolds studied for their properties.
Study on harmonic flow of Spin(7)-structures in 8D manifolds.
Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
A bridge between continuous signals and discrete Ising spins for associative memory.
The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of strategic variables and reconnection rules. The inherent structure of node agent…
The paper characterizes new invariant spin spinors on projective spaces.
Spin(7) geometry linked to multisymplectic geometry.
Unified approach learns Ising models from various dynamics and data types.
We define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Because of this softer requirements, transformations allowed by spin frames are more general tha…
We explore differential and algebraic operations on the exterior product of spinor representations and their twists that give rise to cohomology, the spin cohomology. A linear differential operator is introduced which is associated to a connection and a parallel spinor , , and the algebraic o…
Proves almost flat spin^c manifolds bound compact manifolds.
Rigidity of elliptic genera proven for non-spin manifolds with -action.
First non-trivial examples of deformed Spin(7)-instantons constructed.
Study shows certain spin manifolds can't meet DEC condition.
Spin TFTs created by gauging line defects in 3D.
The paper explores connections between quaternionic and Cayley calibrations in dimensions 8 and 16.
Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi-Yau four-orbifold divided by an anti-holomorphi…
Real vector bundles are determined by their Dirac indices on specific spin manifolds.