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.
The paper explores connections between quaternionic and Cayley calibrations in dimensions 8 and 16.
A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is expressed by spin-spin interactions as in spin glass models of disordered magnetic sys…
New transitions found in Spin(7) holonomy metrics related to a dynamical system.
New method estimates spin system mutual information using neural networks.
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian formalism for this system and possible method for its quantization are discussed. It…
New method constructs axial vector fields and defines quasi-local spin-angular momentum.
A reinforcement learning approach prepares quantum squeezed states in open spin systems.
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…
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive th…
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…
Starting from the 2001 Thomas Friedrich's work on Spin(9), we review some interactions between Spin(9) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin(9) canonical 8-form and its analogies with quaternionic geometry as well as the role of Spin(9) both…
Generative neural samplers estimate quantum spin system properties.
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…
This thesis explores emergent intelligence in disordered systems like spin glasses and neural networks.
We completely explore the system of ODE's which is equivalent to the existence of a parallel -structure on the cone over a 7-dimensional 3-Sasakian manifold. The one-dimensional family of solutions of this system is constructed. The solutions of this family correspond to metrics with holonomy SU(4) which gener…
Spin-opstrings from QMC simulations enable ML of quantum phases.
We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…
We analyze the statistics of daily price change of stock market in the framework of a statistical physics model for the collective fluctuation of stock portfolio. In this model the time series of price changes are coded into the sequences of up and down spins, and the Hamiltonian of the system is expressed by spin-spin…
Study on deformations of Spin(7)-structures on manifolds.
Unified Higgs bundle vacua from M-theory on Spin(7) spaces.
Restricted Boltzmann machines (RBMs) are energy-based neural-networks which are commonly used as the building blocks for deep architectures neural architectures. In this work, we derive a deterministic framework for the training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer (TAP) mean-field appro…
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…
Let be a simply connected spin compact inner irreducible symmetric space, endowed with the metric induced by the Killing form of sign-changed. We give a formula for the square of the first eigenvalue of the Dirac operator in terms of a root system of . As an example of application, we give the list of the …
New pseudo-Hermitian models from non-semisimple TQFTs.
Algorithm computes fundamental classes of spin components in moduli space.
In an informal way, a number of thoughts on the financial crisis 2008 are presented from a physicist's viewpoint, considering the problem as a nonergodicity transition of a spin-glass type of system. Some tentative suggestions concerning the way out of the crisis are also discussed, concerning Keynesian "deficit spendi…
We get decay rate of higher derivatives of nonlinear massless Dirac equations with a kind of "good" spin null form. The method we rely on is similar to that of Li and Zang. However, they only give the decay rate of solution itself to nonlinear massless Dirac system.
Quantum systems on coadjoint orbits yield spectra matching Dolbeault and de Rham indices.
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin group. The differential operators can be seen as a generalization to higher spin …
Researchers create topologically protected knots in a realizable system.
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 …
New kinematic model for a spin-rolling sphere using Darboux frame.
We investigate the -quotient of a torsion free -structure on an -manifold under the assumption that the quotient -manifold is Kähler. We show that there exists either a Hamiltonian or action on the quotient preserving the complex structure. Performing a Kähler reduction…
Quantum map counts BPS states in special theories.
We consider some infinitesmal and global deformations of G_2 structures on 7-manifolds. We discover a canonical way to deform a G_2 structure by a vector field in which the associated metric gets "twisted" in some way by the vector cross product. We present a system of partial differential equations for an unknown vect…
A bridge between continuous signals and discrete Ising spins for associative memory.
Symmetries of variational problems are considered as symmetries of vector bundle valued exterior differential systems. This approach is then applied to third order ordinary variational equations of motion of the semi-classical spinning particle.
New geometric approach controls motion of a spinning sphere on a plane.
Efficiently predicts long-time dynamics of quantum spin models using MLP regression.
Study isotropic embeddings of Lie group orbits and their application to magnetic geodesic flows.
In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of line bundles, rather than ordinary scalar-valued functions, are considered. In part…
Researchers solved a number-theoretic hypothesis to determine the spin parity of k-differentials.
The study develops a logic reasoner to verify MS case management specifications.
We prove boundedness and polynomial decay statements for solutions to the spin generalized Teukolsky system on a Reissner-Nordström background with small charge. The first equation of the system is the generalization of the standard Teukolsky equation in Schwarzschild for the extreme component of the curvature $…
Quantum annealing (QA) is a generic method for solving optimization problems using fictitious quantum fluctuation. The current device performing QA involves controlling the transverse field; it is classically simulatable by using the standard technique for mapping the quantum spin systems to the classical ones. In this…
We present the first estimation of the mass and spin magnitude of Kerr black holes resulting from the coalescence of binary black holes using a deep neural network. The network is trained on a dataset containing 80\% of the full publicly available catalog of numerical simulations of gravitational waves emission by bina…
Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network. This equivalence allows us to characterise the state of these systems in terms of retrieval capabilities, both at low and high load. We study the paramagnet…
A natural way to obtain a system of partial differential equations on a manifold is to vary a suitably defined sesquilinear form. The sesquilinear forms we study are Hermitian forms acting on sections of the trivial -bundle over a smooth -dimensional manifold without boundary. More specifically, we are…