Defines a universal state sum construction for various TQFTs.
problem No specific problem stated; universal construction for TQFTs.
method Defines a universal state sum construction using n-categories with specific conditions.
result Produces state sums from n-categories and handle decompositions of n+1-manifolds.
SRVs improve MSMs for Trp-cage miniprotein, revealing new folding states.
problem Constructing high-resolution MSMs for complex protein dynamics.
method Employing SRVs as feature set for MSM construction, leveraging slowest modes identified by SRVs.
result SRV-MSMs reveal new folding states and faster convergence.
Echo state networks with random weights can approximate any continuous system.
problem Approximating continuous dynamical systems using echo state networks.
method Randomly generated internal weights and a sampling procedure for activation functions.
result Echo state networks with random weights can approximate any continuous casual time-invariant operators with high probability.
A new RNN architecture GVFN improves RNN trainability by constraining states to future predictions.
problem Improving RNN trainability in complex environments.
method Developed a novel RNN architecture called General Value Function Network (GVFN) that constrains states to future predictions.
result GVFNs are more robust to truncation levels, requiring only one-step gradient updates.
In this paper, we provide a construction of a state-sum model for finite gauge-group Dijkgraaf-Witten theory on surfaces with codimension 1 defects. The construction requires not only that the triangulation be subordinate to the filtration, but flag-like: each simplex of the triangulation is either disjoint from the de…
Clusters of financial market states identified over 2006-2019.
problem Understanding the statistical properties of financial markets.
method Clustering analysis of correlation matrices constructed from sliding epochs.
result Financial markets can be classified into distinct states with transitions indicating precursors to catastrophic events.
Characterizes optimal-speed quantum state evolution Hamiltonians.
problem Optimal-speed unitary time evolution of pure and quasi-pure quantum states.
method Construction of the manifold of pure states and isometry with flag manifold, characterization of equigeodesic vectors.
result Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of the flag manifold.
We derive the general state sum construction for 2D topological quantum field theories (TQFTs) with source defects on oriented curves, extending the state-sum construction from special symmetric Frobenius algebra for 2-D TQFTs without defects (cf. Lauda \& Pfeiffer \cite{LP}). From the extended Pachner moves (Crane \& …
Quantum link invariants derived from skein algebras.
problem Defining invariants for framed links with SL2 local systems.
method Theory of representations of stated skein algebras, quantum coadjoint action, Drinfeld double, Bonahon-Wong quantum trace.
result Explicit formulas for link invariants and alternative proof of Murakami-Murakami relation.
Constructs Ricci-flat K3 metrics using D-geometry.
problem Computing the BPS index of a heterotic string theory.
method Hyper-Kähler quotient and D-geometry technology.
result Contains solution to BPS state counting problem.
Study of Chebyshev-Frobenius homomorphism in 3-manifold skein modules.
problem Exploring the Chebyshev-Frobenius homomorphism in 3-manifold skein modules.
method Generalization of splitting homomorphism for stated skein modules of 3-manifolds.
result Existence and properties of Chebyshev-Frobenius homomorphism for 3-manifold skein modules.
F. Jaeger presented the two-variable Kauffman polynomial of an unoriented link L as a weighted sum of HOMFLY-PT polynomials of oriented links associated with L. Murakami, Ohtsuki and Yamada (MOY) used planar graphs and a recursive evaluation of these graphs to construct a state model for the sl(n)-link invariant (a one…
Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.
problem Anomalies in (2+1)D fermionic topological phases and their computation.
method Combining (2+1)D fermionic topological order with symmetry fractionalization data to construct a (3+1)D path integral.
result Reproduces the Z16 anomaly indicator for time-reversal symmetric topological superconductors. TSSC images enhance chaotic signal classification using ConvNets.
problem Classifying chaotic signals accurately and robustly.
method Triad State Space Construction (TSSC) for image encoding, Convolutional Neural Network (ConvNet) for classification.
result TSSC-ConvNet achieves high accuracy and robustness in chaotic signal classification.
The article constructs Feynman propagators for normally hyperbolic operators on curved spacetimes.
problem Constructing Feynman propagators for non-scalar geometric operators on curved spacetimes.
method Global microlocalisation constructions for normally hyperbolic operators on globally hyperbolic spacetimes.
result Feynman propagators can be constructed to satisfy a positivity property for selfadjoint normally hyperbolic operators.
Geometric approach to Dirac operator evolution on spacetimes.
problem Constructing the Cauchy evolution operator for Lorentzian Dirac operators.
method Realizing the operator as a sum of oscillatory integrals, relating to Feynman propagator.
result Relating Cauchy evolution operators to Feynman propagators and constructing Hadamard states.
3D HQFTs constructed using graded monoidal categories.
problem Constructing 3D HQFTs with specific targets.
method Using spherical χ-fusion categories and the state sum method.
result 3D HQFTs constructed with target Bχ.
We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta-Bleuler representations satisfy the t…
Innovative 2-categories create 4-manifold invariants.
problem Constructing invariants for 4-manifolds.
method Semisimple 2-categories, fusion 2-categories, and state-sum construction.
result Construct a state-sum invariant for 4-manifolds.
A. S. Lipson constructed two state models yielding the same classical link invariant obtained from the Kauffman polynomial F(a,z). In this paper, we apply Lipson's state models to marked graph diagrams of surface-links, and observe when they induce surface-link invariants.
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past…
A polynomial counts knot states for a specific type of knot.
problem Counting states of two-bridge knots with Conway notation.
method Constructing an integer polynomial to enumerate Kauffman states.
result The polynomial accurately counts states of knots with C(n,r) notation.
HiPPO-Prophecy models can learn dynamical systems without fine-tuning.
problem Learning dynamical systems in context without fine-tuning parameters.
method Introduced a novel weight construction for SSMs that approximates derivatives of input signals.
result Discrete SSMs can predict the next state of any dynamical system after observing previous states.
We study Khovanov homology classes which have state cycle representatives, and examine how they interact with Jacobsson homomorphisms and Lee's map Φ. As an application, we describe a general procedure, quasipositive modification, for constructing H-thick knots in rational Khovanov homology. Moreover, we show that sp…
We introduce a novel mechanism to tighten the local polytope relaxation for MAP inference in Markov random fields with low state space variables. We consider a surjection of the variables to a set of hyper-variables and apply the local polytope relaxation over these hyper-variables. The state space of each individual h…
The paper classifies market states to predict trading strategies, outperforming traditional methods.
problem Directly predicting prices or returns is unreliable; classifying market states is a better approach.
method Classify market states using various labels and features, then combine probabilities from neural networks.
result Trading strategy ensembles outperform traditional methods in returns and risk-adjusted returns.
Deep learning improves material recognition in construction monitoring.
problem Varying illuminations and low accuracy rates in material classification.
method Deep learning methods, including convolutional neural networks, were used to classify and recognize materials in construction sites.
result Achieved 97.35% accuracy rate for material classification.
The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following subjects are discussed via the coherent states: the geodesics, the conjugate locus a…
SPEDER extracts state-action abstraction from dynamics for reinforcement learning.
problem Curse of dimensionality and limited applicability of spectral methods.
method Spectral Decomposition Representation (SPEDER) that extracts state-action abstraction from dynamics without policy dependence.
result Theoretical analysis establishes sample efficiency in online and offline settings.
Study optimal offline RL with uncertainty sets and distribution shifts.
problem Optimal offline reinforcement learning with limited data.
method Construct uncertainty sets and distribution shifts, solve robust Markov decision process.
result Least conservative estimator for unknown true distribution.
We construct default-free interest rate models in the spirit of the well-known Markov funcional models: our focus is analytic tractability of the models and generality of the approach. We work in the setting of state price densities and construct models by means of the so called propagation property. The propagation pr…
State surfaces are spanning surfaces of links that are obtained from link diagrams guided by the combinatorics underlying Kauffman's construction of the Jones polynomial via state models. Geometric properties of such surfaces are often dictated by simple link diagrammatic criteria, and the surfaces themselves carry imp…
Bayesian control prepares GHZ states in Rydberg atoms.
problem Preparing non-classical states robustly for quantum sensors.
method Bayesian optimal control of trapped Rydberg atoms.
result Control pulses drive atoms into GHZ states with scalable preparation times.
New construction of Turaev-Viro invariants invariant under Morita equivalence.
problem Constructing Turaev-Viro invariants invariant under Morita equivalence.
method Pivotal bicategory construction of spherical module categories.
result The invariant recovers the standard Turaev-Viro invariant and is independent of the skeleton.
New invariant for spin 3-manifolds using super 3-cocycles.
problem Constructing an invariant for spin 3-manifolds.
method State sum construction based on super 3-cocycles and combinatorial representation.
result The invariant is sensitive to the spin structure.
Optimal estimator derived for partially observable LTI systems.
problem Optimal estimator for partially observable LTI systems.
method State-space representation for derivation of optimal estimator.
result Derivation of minimum error variance estimator for partially observable LTI systems.
We study an open problem of risk-sensitive portfolio allocation in a regime-switching credit market with default contagion. The state space of the Markovian regime-switching process is assumed to be a countably infinite set. To characterize the value function, we investigate the corresponding recursive infinite-dimensi…
Quantum states associated with subsets of product manifolds are separable.
problem Characterizing quantum states associated with subsets of product manifolds.
method Using holomorphic sections of quantum line bundles and restriction maps.
result Quantum states associated with finite unions of products are separable.
Study uses artificial counterfactuals to show lockdowns reduced US case and death counts.
problem Impact of lockdowns on US case and death counts during the pandemic.
method Artificial counterfactual approach comparing states with and without lockdowns.
result Average two times more cases would have occurred without lockdowns.
In this short note, a question of patching together globally hyperbolic manifolds is adressed which appeared in the context of the construction of Hadamard states.
3D quantum trace map connects 3-manifold quantizations.
problem Quantization of 3-manifold character varieties.
method Study of stated skein modules and face suspensions.
result Existence of 3D quantum trace map proved.
Develops RL algorithm for non-Markovian, non-stationary reward streams.
problem Maximizing rewards from non-Markovian, non-stationary reward streams.
method Uses causal DAG to construct Markov states, solves periodic MDP.
result Optimal state construction maximizes discounted rewards.
Method learns latent states from rich observations to improve RL exploration.
problem Improving RL performance with rich observations and latent states.
method Estimates latent states from observations through regression and clustering, providing finite-sample guarantees.
result Exponential improvement over Q-learning with naïve exploration. Paper proves a rigidity result for static perfect fluids.
problem Proving a rigidity result for static perfect fluids.
method Robinson's divergence formula and boundary conditions.
result Rigidity result for static perfect fluids.
This paper constructs cohomological Hall algebras for 3-Calabi-Yau categories.
problem Mathematical definition of the algebra of BPS states.
method Construction of cohomological Hall algebras for 3-Calabi-Yau categories.
result Construction of cohomological Hall algebras and proof of Joyce's conjecture.
A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional sparse random graph to model state transitions. Depending on the sparsity pattern of…
Symbolic regression constructs simple equations for complex systems.
problem Creating accurate yet simple models for dynamic systems.
method Employing symbolic regression with two genetic programming algorithms.
result Analytic models outperform neural networks and local regression.
Introduces sheaf quantization, a topological approach to geometric quantization.
problem Topological realization of WKB-states in geometric quantization.
method Enhancement of constructible sheaves, Betti counterpart of Fukaya--Floer theory.
result Introduction to sheaf quantization as a topological realization of WKB-states.