New Spin(7)-instantons constructed on Joyce's manifold.
problem Constructing Spin(7)-instantons on Joyce's compact manifold. method Gluing non-flat connections on local model spaces to a flat connection on the Spin(7)-orbifold. result More than 20,000 new four-parameter families of Spin(7)-instantons. Topological field theory computes Arf invariant of r-spin surfaces.
problem Computing the Arf invariant of r-spin surfaces.
method Combinatorial model of r-spin surfaces, state sum construction of topological field theories.
result The r-spin Arf invariant is constant on orbits of the mapping class group.
Study finds spin model returns align with normal distribution.
problem Understanding return dynamics in financial markets.
method Calculated realized volatility and examined standardized returns.
result Moments of standardized returns match theoretical values.
Generative model learns spin-glass dynamics and properties.
problem Complex behavior of many-body systems in statistical physics and computer science.
method Self-supervised learning with normalizing flows.
result Key physical and computational properties of spin-glasses are learned.
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…
Study shows gain-loss asymmetry in stock indices using a q-spin Potts model.
problem Understanding the dynamics of stock indices in complex markets.
method Developed a q-spin Potts model to represent stock market dynamics.
result Observed a self-organized gain-loss asymmetry in stock indices.
Study on spin random fields using chaos decomposition for cosmic microwave background modeling.
problem Modeling polarization of Cosmic Microwave Background using spin random fields.
method Explicit Wiener-Itô chaos decomposition of area measures of level sets.
result Reveals a clear difference between high frequency regime and zero spin case.
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) …
We reformulate the Cont-Bouchaud model of financial markets in terms of classical "super-spins" where the spin value is a measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend this simplified model by switching on interactions among the super-spins to mod…
A financial market model uses spin variables to represent and predict agent behavior.
problem Predicting and understanding financial market behavior.
method Agent-based model with Potts model interpretation, focusing on spin variables representing opinions and actions.
result Model accurately predicts market behavior and statistical properties of financial returns.
Machine learning classifies phases of spin models using improved correlation configurations.
problem Classifying phases of spin models using machine learning.
method Improved correlation configuration estimator applied to machine learning.
result Classifies Berezinskii-Kosterlitz-Thouless transition in quantum XY model.
The paper explores spin^h structures and their obstructions.
problem Understanding which manifolds are spin^h.
method Analyzing the fifth Stiefel-Whitney class and constructing generalised spin structures.
result Every compact orientable manifold of dimension 7 or lower is spin^h, and there are higher-dimensional manifolds that are not.
Study mSpin(7)-dDT connections on manifolds with mSpin(7)-structures.
problem Understanding moduli spaces of mSpin(7)-dDT connections. method Introduced and studied mSpin(7)-dDT connections using fully nonlinear PDEs. result Moduli space MmSpin(7)′ has finite expected dimension and smoothness under certain conditions. Constructs differential models for twisted Spin^c-bordism and its dual, defining a new anomaly map.
problem Modeling and understanding twisted Spin^c-bordism and its dual.
method Geometric construction using bundle gerbes, gerbe modules, and eta-invariants.
result Definition of a twisted anomaly map from differential twisted K-theory to differential Anderson dual of twisted Spin^c-bordism.
Spin-opstrings from QMC simulations enable ML of quantum phases.
problem Capturing and predicting quantum phase transitions using ML.
method Spin-opstrings derived from QMC simulations used as ML input.
result Spin-opstrings accurately predict quantum phase transitions.
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…
Paper improves volatility forecasting for new issues and spin-offs.
problem Forecasting volatility with limited historical data.
method Multi-source transfer learning approach.
result Transfer learning approach outperforms alternative models.
New spin frame transformations affect Dirac equations without preserving metric structures.
problem Extending spin structures to spin manifolds with fixed signature.
method Defining spin frames and studying their effects on connections and Dirac equations.
result New transformations affect Dirac equations more generally than usual spin transformations.
New mSpinh-manifolds studied for their properties.
problem Understanding new manifold classifications.
method Exploring mSpinh-manifolds as a new category. result Highlights of mSpinh-manifolds discussed. The paper characterizes the geometry and topology of spin random fields.
problem Understanding the expected geometry and topology of spin random fields.
method Investigating the asymptotic behavior of geometric and topological functionals for spin random fields under scaling assumptions.
result Explicit results for monochromatic fields, showing non-universal asymptotic behavior and new generalized models.
Study on harmonic flow of Spin(7)-structures in 8D manifolds.
problem Comparing isometric Spin(7)-structures.
method Developed a notion of harmonicity for Spin(7)-structures and studied the harmonic flow.
result Analytical properties of the harmonic flow of Spin(7)-structures presented.
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and …
Study spin structures on Kac-Moody symmetric spaces.
problem Existence of spin structures on affine Kac-Moody symmetric spaces.
method Sufficient conditions for spin structures existence.
result Obtained spin-c representation of certain Kac-Moody subgroups.
Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
problem Understanding higher spin Killing spinors on 3D manifolds.
method Definition and detailed study of higher spin Killing spinors in arbitrary dimension, focusing on 3D manifolds. Rigidity result and explicit expressions for 3-sphere and 3-hyperbolic space.
result Proved a rigidity result for 3D manifolds admitting higher spin Killing spinors and provided explicit expressions for these spinors.
Review of sigma models on flag manifolds, linking to spin chains and integrable theories.
problem Understanding phase transitions and anomalies in spin chains and sigma models.
method Analyzing topological angles, discrete 't Hooft anomalies, and integrable models.
result Gapless phases in certain spin chains can be explained by discrete anomalies in continuum theories.
The paper characterizes new invariant spinr spinors on projective spaces.
problem Characterizing new invariant spinr spinors on projective spaces. method Adapting spin representation via exterior forms to the generalised spinr context. result Complete description of the space of invariant spinr spinors for CPn, HPn, and OP2. Spin-harmonic structures on low-dimensional manifolds.
problem Defining geometric structures on low-dimensional manifolds.
method Introducing spin-harmonic structures defined by harmonic unitary spinors.
result Spin-harmonic structures are equivalent to balanced Spin(7) structures in dimension 8.
Spin(7) geometry linked to multisymplectic geometry.
problem Understanding Spin(7) structures through multisymplectic geometry.
method Utilized Spin(7) identities to prove non-degeneracy of Cayley four-form in multisymplectic context.
result Spin(7) geometry is a special case of multisymplectic geometry.
Study spin chains and sigma models on flag manifolds, calculating spectra and geodesics.
problem Understanding the spectrum and geodesics of sigma models on flag manifolds.
method Connecting SU(n) spin chains to sigma models and calculating spectra and geodesics.
result Calculated the spectrum of the Laplace-Beltrami operator and geodesics for CP1 and F3. 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 d is introduced which is associated to a connection ∇ and a parallel spinor ζ, ∇ζ=0, and the algebraic o…
New method estimates spin system mutual information using neural networks.
problem Estimating mutual information in spin systems.
method Monte Carlo sampling enhanced by autoregressive neural networks.
result Area law satisfied for temperatures away from critical temperature.
Rigidity of elliptic genera proven for non-spin manifolds with S1-action.
problem Rigidity of elliptic genera for non-spin manifolds with S1-action. method Analysis of universal covering spin condition and π2(M) for rigidity. result Rigidity of elliptic genera is proven for spin universal coverings but not for non-spin universal coverings.
Proves almost flat spin^c manifolds bound compact manifolds.
problem Proving almost flat spin^c manifolds bound compact manifolds.
method Long-standing conjecture of Farrell--Zdravkovska and S. T. Yau settled.
result Every almost flat spin^c manifold bounds a compact orientable manifold.
New method classifies spin 4-manifolds using Kervaire-Milnor invariant.
problem Classifying spin 4-manifolds up to stabilisation.
method Using Kervaire-Milnor invariant to compute Arf invariants and classify.
result New stable classification of spin 4-manifolds with 2-dimensional fundamental groups.
First non-trivial examples of deformed Spin(7)-instantons constructed.
problem Constructing deformed Spin(7)-instantons and connections.
method Constructing on cotangent bundles of CP2 and cones over 3-Sasakian 7-manifolds. result First non-trivial examples of deformed Spin(7)-instantons.
Spin TFTs created by gauging line defects in 3D.
problem Creating spin TFTs from oriented TFTs with framed line defects.
method Constructing a spin TFT from an oriented TFT with framed line defects and a commutative Frobenius algebra.
result Spin TFTs extend earlier classifications and reproduce abelian spin Chern-Simons theories.
Study shows certain spin manifolds can't meet DEC condition.
problem Non-existence of spin fill-ins meeting DEC condition.
method Analyzes spin Riemannian manifolds and generalized mean curvature functions.
result Closed spin manifolds cannot satisfy DEC if curvature is large.
Study homogeneous 8-manifolds with invariant Spin(7)-structures.
problem Classify and describe invariant Spin(7)-structures on homogeneous 8-manifolds.
method Examine canonical presentations G/H, construct invariant Spin(7)-structures, analyze associated connections.
result Explicit examples and classifications of invariant Spin(7)-structures on homogeneous 8-manifolds.
The paper explores connections between quaternionic and Cayley calibrations in dimensions 8 and 16.
problem Exploring connections between quaternionic and Cayley calibrations in dimensions 8 and 16.
method Starting from collections of 'Kähler 2-forms', the paper constructs canonical 4-forms and calibrated 4-planes in dimensions 8 and 16.
result Explicit formulas for canonical 4-forms ΦSpin(8) and ΦSpin(7)U(1) are derived, and their calibrated 4-planes are characterized. 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…
Study harmonic flow of Spin(7)-structures on compact 8-manifolds.
problem Isometric flow of Spin(7)-structures on compact 8-manifolds.
method Establishing Shi-type estimates, self-similar solutions, monotonicity formula, compactness theorems, and Bryant-type description.
result Conditions for long-time existence and characterisation of singularities.
Reviews interactions between Spin(9) and octonionic geometries.
problem Understanding the role of Spin(9) in octonionic geometry.
method Analyzes canonical 8-forms, vector fields, Hopf fibrations, and manifolds.
result Discovers new insights into the geometry of octonionic Hopf fibrations.
The paper studies curvature identities and solitons on Spin(7)-manifolds.
problem Curvature identities and solitons on Spin(7)-manifolds.
method Analyzes the curvature and torsion of Spin(7)-manifolds, proving identities and conditions.
result Conditions for closed torsion and implications for Ricci flatness and solitons.
Real vector bundles are determined by their Dirac indices on specific spin manifolds.
problem Determining real vector bundles using Dirac indices.
method Mapping spin or spinh manifolds into a compact smooth manifold and using Dirac indices. result Real vector bundles are uniquely determined by their Dirac indices on prescribed manifolds.
CNN detects phase transitions in Potts models without prior knowledge.
problem Detecting phase transitions in q-state Potts models using deep learning. method Trained a deep CNN on Ising model spin configurations and temperatures, then tested on Potts model images.
result Deep CNN accurately detects phase transitions in Potts models, including high- and low-temperature regions.
Machine learning identifies hidden spin nematics in magnetic configurations.
problem Challenging identification of unconventional magnetic states.
method Interpretable machine learning protocol for detecting nematic order.
result Extracted analytical forms of nematic order parameters up to rank 6.
Characterizes Spinor groups using cohomology operations.
problem Understanding the cohomology and invariants of Spinor groups.
method Constructing integral cohomology rings and characteristic classes.
result Determined the ring of integral Weyl invariants of Spin(n).
Study pinching of small Dirac eigenvalues on spin^c manifolds.
problem Pinching small Dirac eigenvalues on spin^c manifolds.
method Classification of spin^c and spin manifolds with nontrivial Killing spinors, introducing convergence for spin^c manifolds involving principal S^1-bundles.
result Derive pinching results for small Dirac eigenvalues.