Dualities in deformed N=2 SCFTs from link monodromy on D3-brane states.
problem Understanding dualities in deformed N=2 superconformal theories.
method Analyzing D3-brane theories via link monodromy on a small three-sphere.
result Reduction of differing flavor algebras to the same, projecting out charged states.
This research builds foundations for D3-branes in string theory.
problem Constructing dynamical fermionic D3-branes in string theory.
method Develops algebraic and geometric foundations, hybrid connections, and chiral maps.
result Provides a framework for constructing supersymmetric actions.
We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a system of D3-branes ending on an NS5-brane with a nonzero theta-angle. On the one hand, this system can be related to a Chern…
D3-brane solutions derived from Ricci-flat metrics on Kähler-Einstein surfaces.
problem Constructing D3-brane solutions in supergravity.
method Classical ansatz involving harmonic warp factor and Ricci-flat metrics.
result Existence of Kähler-Einstein metrics and Ricci-flat metrics on canonical bundles.
Study D3-brane solutions on resolved C^3/Γ singularities, proving metric conjecture.
problem Existence of Ricci-flat metrics on resolved C^3/Γ singularities.
method Generalized Kronheimer construction, Monge-Ampère equation, series solutions.
result Kronheimer metric and Ricci-flat metric coincide on exceptional divisor.
Study electric-magnetic duality in M-theory compactifications.
problem Restoring supersymmetry and understanding dualities in compactified M-theory.
method Dualizing M-theory on G2 manifolds with F-theory and studying D3-branes. result Demonstrates correspondence between D3-branes and shrinking surfaces/curves, revealing light particles with electric and magnetic charges.
This is the written version of my talk at SUSY '98. It presents a geometric characterisation of the allowed near-horizon geometries of supersymmetric branes. We focus primarily on the M2-brane, but results for other branes (e.g., the D3-brane) are also presented. Some new examples are discussed.
We derive and study supergravity BPS flow equations for M5 or D3 branes wrapping a Riemann surface. They take the form of novel geometric flows intrinsically defined on the surface. Their dual field-theoretic interpretation suggests the existence of solutions interpolating between an arbitrary metric in the UV and the …
Departing from the observation that the Penrose limit of AdS_3 x S^3 is a group contraction in the sense of Inonu and Wigner, we explore the relation between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a six-dimensional symmetric plane wave analogous to the four-dimensional Nappi--Witten space…
We define a notion of stability for chiral ring of four dimensional N=1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only if it is stable. We then study N=1 field theory derived from D3 branes probing …
In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted as moduli in various compactifications of a higher-dimensional `master theory'. T…
Extending previous work that involved D3-branes ending on a fivebrane with θYM=0, we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional Chern-Simons theory of a supergroup U(m∣n) or OSp(m∣2n) rather than an ordinary …
Reinterprets M-theory geometry and identifies Wess-Zumino terms.
problem Understanding and interpreting M-theory geometry and Wess-Zumino terms.
method Using AKSZ construction and L∞-algebroid, the paper reinterprets M-theory geometry and identifies Wess-Zumino terms. result Identifies the M-theory Wess-Zumino term with a 7-dimensional Chern-Simons theory.
We use the formalism of generalized geometry to study the generic supersymmetric AdS_5 solutions of type IIB supergravity that are dual to N=1 superconformal field theories (SCFTs) in d=4. Such solutions have an associated six-dimensional generalized complex cone geometry that is an extension of Calabi-Yau cone geometr…
WZW models are abstract conformal field theories with an infinite dimensional symmetry which accounts for their integrability, and at the same time they have a sigma model description of closed string propagation on group manifolds which, in turn, endows the models with an intuitive geometric meaning. We exploit this d…
Neural-Network Quantum States connect to Tensor-Network states, enhancing quantum state representation.
problem Describing complex quantum wave functions efficiently.
method Introducing Neural-Network Quantum States and showing their connections to Tensor-Network states.
result Neural-Network Quantum States and String-Bond States can approximate chiral topological states with better accuracy.
Classifies fibering of state surfaces for various knot families.
problem Determining which state surfaces are fibered.
method Algebraic characterization of fibers from state graphs, decomposing graphs into planar components.
result Characterizes fibering for many families of state surfaces.
Paper finds coefficients of Catalan states using Θ_A-state expansion.
problem Finding coefficients of Catalan states of lattice crossings.
method Uses Θ_A-state expansion to express coefficients as a linear combination of other states.
result Shows that coefficients can be found using Θ_A-state expansion.
We propose the application of a high-speed maximum likelihood clustering algorithm to detect temporal financial market states, using correlation matrices estimated from intraday market microstructure features. We first determine the ex-ante intraday temporal cluster configurations to identify market states, and then st…
Variational autoencoders improve state representation for hard quantum systems.
problem Simulating and storing quantum states is computationally infeasible.
method Introduced variational autoencoders for quantum state representation.
result Deep networks better represent hard quantum states, suggesting compositional structure.
This paper tackles belief-state selection in simulators with latent states.
problem Selecting among approximate belief-state samplers for simulators with latent variables.
method Reduces belief-state selection to conditional distribution selection, develops algorithms and analyses.
result Different formulations of belief-state selection have varying guarantees under different roll-out methods.
Classifies state functions for framed tangles in a disk.
problem Understanding quantum invariants of framed tangles.
method Introduces state function for framed tangles, local and topologically invariant.
result Classified all state functions for the Kauffman bracket and quantum SU(3)-invariant. New method for state inference in state-space models with unknown dynamics.
problem State inference in state-space models with computationally expensive and undefined dynamics.
method Estimate state transition dynamics using a multi-output Gaussian process and Bayesian Neural Network as a surrogate model.
result Significant improvement in accuracy for state inference and prediction in non-stationary user models.
New proof for knot state-sum formula using bijection between states.
problem Proving a knot state-sum formula for colored Jones polynomial.
method Established bijection between states on arc-graph and bichromatic digraph, used flow property of R-matrix.
result Two state models are essentially the same, extending formula to links.
Backtracking model predicts state-action pairs leading to high-reward states for efficient RL.
problem Efficiently learning from environments where only a few states yield high reward.
method Backtracking model that predicts state-action pairs leading to high-reward states.
result Improves sample efficiency of RL algorithms across various environments and tasks.
EvoNet predicts events in time-series data by evolving state graphs.
problem Predicting events in time-series data with interpretable patterns.
method Evolutionary State Graph (ESG) and EvoNet model.
result EvoNet outperforms baselines and provides insights into event predictions.
New method uses entropy to improve policy gradient exploration.
problem Limited exploration in policy gradient methods.
method Entropy regularization with discounted future state distribution.
result Proves convergence to locally optimal policy.
Spectral methods reduce the complexity of Markov processes.
problem Modeling and simplifying state-transition systems.
method Spectral decomposition and state aggregation.
result Developed methods to estimate low-rank Markov models.
A new method learns state and proposal dynamics in state-space models using neural networks.
problem Inference in non-linear state-space models.
method StateMixNN method using neural networks for proposal and transition distributions.
result Significantly improved recovery of hidden state, especially in highly non-linear scenarios.
InfoBot learns decision states from prior experience to guide exploration.
problem Discovering effective policies in sparse reward environments.
method InfoBot uses an information bottleneck to learn decision states from prior experience.
result InfoBot effectively identifies decision states, even in partially observed settings.
In this letter we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for Explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting…
The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.
problem Efficient regression and state estimation for deep Gaussian processes.
method Hierarchical transformed Gaussian process priors, state-space representation, linear stochastic differential equations, sequential methods.
result The state-space approach enables efficient state estimation and regression for deep Gaussian processes.
Method learns CTMC models from steady-state data, predicting unseen states.
problem Learning CTMC models from aggregate steady-state statistics without sequence examples.
method ∞-SGD, a stochastic gradient descent method that avoids infinite sums.
result Successfully learns CTMC models and predicts unseen states.
This work improves policy optimization by maximizing entropy of state distribution, leading to better exploration.
problem Lack of exploration in state space when maximizing policy entropy.
method Proposes maximizing the entropy of a lower bound approximation to the state weighting distribution, based on latent space representation.
result Entropy regularization based on marginal state distribution achieves superior state space coverage and better performance in various domains.
State-regularized RNNs improve interpretability and performance on long-term memory tasks.
problem RNNs struggle with long-term memory and lack of interpretability.
method Introduce a stochastic state transition mechanism to limit state transitions to a finite set.
result State-regularized RNNs perform better on tasks requiring long-term memory.
Study state-dependent Hawkes processes for limit order book modeling.
problem Modeling feedback loop between order flow and limit order book shape.
method Existence and uniqueness of state-dependent Hawkes processes, simulation, maximum likelihood estimation.
result Excitation effects in order flow are strongly state-dependent.
A new asset allocation model uses Markov states from clustered efficient frontier coefficients.
problem Characterizing market regimes using efficient frontiers for better asset allocation.
method Hierarchical clustering of monthly efficient frontier coefficients to define states, then a Markov process on these states for portfolio optimization.
result The model significantly outperforms benchmark portfolios empirically.
Quantum states can be learned efficiently using gentle measurements.
problem Efficiently learning quantum states with minimal measurements.
method Introducing α-LGM measurements and proving strong quantum DPI.
result The number of states needed for accurate learning is of order 1/(ε^2 α^2).
PSDs improve RNN performance by predicting future observations.
problem Modeling dynamic processes with unknown latent states.
method Augmenting RNNs with Predictive-State Decoders (PSDs) that target predicting future observations.
result PSDs improve statistical performance of state-of-the-art RNNs with fewer iterations and less data.
Bayesian model detects altered neural circuits in MCI patients.
problem Detecting altered neural circuits in Mild Cognitive Impairment patients.
method Hierarchical Bayesian recurrent state space model.
result Model discovers latent states predominantly observed in MCI patients.
Proposes a new model for time series that considers smooth transitions between states.
problem Models assume instantaneous transitions between discrete states, ignoring gradual changes.
method Dynamical Wasserstein Barycentric (DWB) model that estimates system state and pure state distributions over time.
result Accurately learns pure state distributions and improves state estimation for transition periods.
Method forecasts market states using sparse precision matrix and penalized Mahalanobis distance.
problem Forecasting market states and distinguishing bull and bear markets.
method Identifies market states via sparse precision matrix and expectation values. Uses penalized Mahalanobis distance for clustering and forecasting.
result Successfully clusters market states and forecasts future market conditions with significant accuracy.
The paper proposes a method to learn low-dimensional state embeddings from time series data.
problem Finding compact state embeddings from high-dimensional Markov state trajectories.
method The paper introduces a method based on diffusion maps to learn a low-dimensional state embedding and captures the dynamics of the process.
result The method reveals metastable structures in state clustering, providing sharp statistical error bounds and misclassification rates.
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.
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.
Paper proposes an algorithm to estimate state aggregation from Markov transition data.
problem Estimating probabilistic aggregation map from system's trajectory.
method Two-step algorithm: spectral decomposition and linear transformation of singular vectors.
result Sharp error bounds for estimating aggregation and disaggregation distributions.
This paper simplifies OPE in large state spaces using state abstractions.
problem Accurately evaluating policies offline in large state spaces.
method Developed a backward-model-irrelevance condition and an iterative state abstraction procedure.
result Deeply-abstracted states substantially simplify OPE sample complexity.
The paper proposes an algorithm to learn causal state representations for partially observable environments.
problem Learning task-agnostic state abstractions in partially observable environments.
method The approach involves learning approximate causal state representations from RNNs trained to predict observations given the history.
result The learned state representations are useful for efficient policy learning in reinforcement learning problems with rich observation spaces.