We analyze relations between BPS degeneracies related to Labastida-Marino-Ooguri-Vafa (LMOV) invariants, and algebraic curves associated to knots. We introduce a new class of such curves that we call extremal A-polynomials, discuss their special properties, and determine exact and asymptotic formulas for the correspond…
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48 results for “BPS degeneracies”
Compact K3 metrics derived from string theory vacua.
problem Finding Ricci-flat metrics on K3 surfaces.
method Using little string theory and BPS degeneracies.
result Systematic procedure for determining K3 metrics.
We count the supersymmetric bound states of many distinct BPS monopoles in N=4 Yang-Mills theories and in pure N=2 Yang-Mills theories. The novelty here is that we work in generic Coulombic vacua where more than one adjoint Higgs fields are turned on. The number of purely magnetic bound states is again found to be cons…
New -BP algorithm improves belief propagation for graphs with loops.
problem Uncertainty in belief propagation for graphs with loops.
method Derive -BP algorithm motivated by minimizing -divergence.
result Proves convergence conditions for -BP.
Finding the most probable assignment (MAP) in a general graphical model is known to be NP hard but good approximations have been attained with max-product belief propagation (BP) and its variants. In particular, it is known that using BP on a single-cycle graph or tree reweighted BP on an arbitrary graph will give the …
Improved BP algorithm outperforms loopy BP in MAP inference.
problem Limited understanding and poor performance of belief propagation in graphs with loops.
method Introduced belief propagation, a minimization of localized -divergence.
result Significantly outperforms loopy BP in fully-connected graphs for MAP inference.
New cobordism invariants derived from BPS q-series.
problem Understanding BPS partition functions with different structures.
method Analyzing limits of BPS q-series and summing over Spin structures.
result Derived invariants of homology cobordisms from BPS q-series.
The paper extends BPS invariants for framed knots and links.
problem Investigating BPS invariants for framed knots and links.
method Using the dual A-polynomial and framing change formula, the paper extends the relationship between algebraic curves and BPS invariants to framed knots and links.
result Explicit formulas for extremal A-polynomials and BPS invariants of framed knots, and numerical calculations for framed Whitehead links and Borromean rings.
Existing methods for arterial blood pressure (BP) estimation directly map the input physiological signals to output BP values without explicitly modeling the underlying temporal dependencies in BP dynamics. As a result, these models suffer from accuracy decay over a long time and thus require frequent calibration. In t…
Receiver algorithms which combine belief propagation (BP) with the mean field (MF) approximation are well-suited for inference of both continuous and discrete random variables. In wireless scenarios involving detection of multiple signals, the standard construction of the combined BP-MF framework includes the equalizat…
Research on mixed polynomials, extending non-degeneracy concepts to complex variables.
problem Extending non-degeneracy concepts to mixed polynomials in complex variables.
method Generalization of Mondal's partial non-degeneracy to mixed polynomials, introducing new concepts and proving properties.
result Strong partial non-degeneracy implies isolated singularities, and mixed polynomials that are strongly inner non-degenerate satisfy the strong Milnor condition.
Researchers create BPS monopoles with any desired symmetry breaking.
problem Creating monopoles with specific symmetry breaking patterns.
method Using a new class of Nahm data to construct finite energy BPS monopoles.
result Arbitrary symmetry breaking monopoles can be constructed.
Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice, where mean-field (MF) and belief propagation (BP) are arguably the most popular an…
We provide a proof of backpropagation algorithm in matrix notation.
problem The lack of a full induction proof of backpropagation algorithm in matrix notation.
method We provide a full induction proof of the BP algorithm in matrix notation, situating it in the framework of matrix differential calculus.
result We prove the validity of the backpropagation algorithm in inductive form.
Study of continuous symmetries in Nahm data and BPS monopoles.
problem Solutions to Nahm's equations with continuous symmetries.
method Classification of Ansätze and construction of Nahm data.
result Construction of new BPS monopoles with spherical symmetry.
We develop a method for finding the zero modes of the Dirac operator in the presence of BPS monopoles. We use it to find the zero modes in the case of Abelian BPS monopoles in .
We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating fun…
Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path…
Modified BP attribution methods often ignore later layers' information, leading to misleading explanations.
problem Misleading explanations from modified BP methods ignoring later layers' information.
method Analysis of 9 modified BP methods including Deep Taylor Decomposition, LRP, Excitation BP, PatternAttribution, DeepLIFT, Deconv, RectGrad, Guided BP.
result Only DeepLIFT does not ignore later layers' information, providing a faithful explanation.
In this paper, deep neural network (DNN) is utilized to improve the belief propagation (BP) detection for massive multiple-input multiple-output (MIMO) systems. A neural network architecture suitable for detection task is firstly introduced by unfolding BP algorithms. DNN MIMO detectors are then proposed based on two m…
Variational quantum computing faces a flat optimization landscape problem.
problem Barren Plateaus (BP) in optimization landscapes.
method Theoretical and heuristic methods to understand and mitigate BPs.
result All algorithm components can lead to BPs if not well-suited.
Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typicall…
The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when this algorithm will perform well. Using recent analysis of convergence and stabilit…
Biologically plausible learning algorithms can match BP on large datasets.
problem Learning algorithms that are biologically plausible often perform poorly on large datasets.
method Evaluation of sign-symmetry and feedback alignment algorithms on ImageNet and MS COCO.
result Sign-symmetry algorithm can match BP performance on ImageNet and MS COCO.
Defines special Joyce structures for ASK manifolds encoding real HK structures.
problem Defining Joyce structures for ASK manifolds.
method Introducing special Joyce structures and showing they encode real HK structures.
result Special Joyce structures encode real hyperkähler structures on ASK manifolds.
Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.
problem Understanding the relationship between 4d and 3d BPS quivers.
method Analyzes geometric backgrounds and uses skein modules to derive quiver partition functions.
result Proves isomorphism between 4d wall-crossing and unlinking of symmetric quivers.
Classifies patterns of symmetry breaking and vacuum degeneracy in scalar and gauge fields.
problem Understanding patterns of symmetry breaking and vacuum degeneracy in complex field systems.
method Uses mathematical classification of singular foliations to encode and classify patterns of spontaneous symmetry breaking and vacuum degeneracy.
result Mathematical classification provides a qualitative understanding of possible patterns of vacuum degeneracy.
What Useful Alphas?q-fin.GN
Useful alpha returns vanished in modern stock markets.
problem The inefficiency of modern stock markets in generating useful alpha.
method Analysis of 200 published long-short anomaly equity portfolios over different time periods and stock selection criteria.
result Even modest allowances for luck or transaction costs eliminated published academic anomalies.
CP degeneracy affects tensor regression solutions, especially in high dimensions.
problem CP degeneracy in tensor regression.
method Analysis of CP degeneracy and development of a penalized strategy.
result A general penalized strategy to overcome CP degeneracy in tensor regression.
Inspired by recent advances in deep learning, we propose a novel iterative BP-CNN architecture for channel decoding under correlated noise. This architecture concatenates a trained convolutional neural network (CNN) with a standard belief-propagation (BP) decoder. The standard BP decoder is used to estimate the coded b…
Constructs BPS complexes and Chern--Simons theories from G-structures.
problem Infinitesimal moduli space computation and supersymmetric systems.
method Universal algebraic construction of BPS complexes and associated linearised BV Chern--Simons theories.
result Reproduces classic examples in gauge theory and constructs heterotic superpotential functionals.
Formula for BPS black hole entropy derived from Vinberg cones.
problem Finding entropy of BPS extremal black holes in non-symmetric scalar manifolds.
method Use of Vinberg's theory of homogeneous cones to determine the inverse of a quadratic map.
result Explicit formula for BPS black hole entropy in any N=2 supergravity with homogeneous scalar manifold.
Note removes degeneracy in Kähler geometry estimates.
problem Estimating diameter and inequalities in Kähler geometry with degeneracy.
method Technical improvement of earlier results.
result Established diameter, Green's functions, and Sobolev inequalities without small degeneracy assumption.
Paper examines convergence rate of PGD for BP objective in inverse problems.
problem Optimizing ill-posed linear inverse problems using BP vs LS.
method Analysis of PGD convergence rate for BP objective, comparison with proximal gradient method.
result PGD converges faster for BP objective due to inherent properties.
Abstract M5 branes on ADE singularities yields BPS spectrum and partition functions.
problem Determine the BPS spectrum and partition functions for M5 branes on ADE singularities.
method Analyze 6d SCFTs on geometric backgrounds, using contributions from BPS strings and particles.
result Explicit expressions for BPS string and particle contributions to partition functions.
It is known that fixed points of loopy belief propagation (BP) correspond to stationary points of the Bethe variational problem, where we minimize the Bethe free energy subject to normalization and marginalization constraints. Unfortunately, this does not entirely explain BP because BP is a dual rather than primal algo…
Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the model. To understand this dependence it is interesting to find \emph{all} fixed poi…
It is known that knot homologies admit a physical description as spaces of open BPS states. We study operators and algebras acting on these spaces. This leads to a very rich story, which involves wall crossing phenomena, algebras of closed BPS states acting on spaces of open BPS states, and deformations of Landau-Ginzb…
BP, a method for sparse recovery, shows generalization error decreases with more features.
problem Understanding the generalization error of overfitting solutions in linear regression.
method Study of Basis Pursuit (BP) for sparse recovery of linear regression models.
result BP's model error decreases with more features, showing double-descent behavior.
In this correspondence, we obtain exact recovery conditions for regularized modified basis pursuit (reg-mod-BP) and discuss when the obtained conditions are weaker than those for modified-CS or for basis pursuit (BP). The discussion is also supported by simulation comparisons. Reg-mod-BP provides a solution to the spar…
We study the existence of monopole bound states saturating the BPS bound in N=2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS solutions. Using an index theorem, we prove the existence of certain BPS stat…
We design iterative receiver schemes for a generic wireless communication system by treating channel estimation and information decoding as an inference problem in graphical models. We introduce a recently proposed inference framework that combines belief propagation (BP) and the mean field (MF) approximation and inclu…
The BPS decomposition theorem splits cohomology of symmetric stacks into invariant parts.
problem Decomposing the cohomology of smooth symmetric stacks into invariant parts.
method Using cohomological Hall induction and intersection cohomology of moduli spaces.
result Establishes the BPS decomposition theorem for various symplectic stacks.
Quantum map counts BPS states in special theories.
problem Computing protected spin characters in class S theories.
method Geometric approach from 5D supersymmetric Yang-Mills theory.
result Explicit computation of protected spin characters in various examples.
We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly produce a single satisfying assignment. Our first CSP solver, called Perturbed Blief …
This paper compares two NUTS variants and analyzes their convergence and mixing times.
problem Theoretical comparison and convergence guarantees of NUTS variants.
method Deriving necessary and sufficient conditions for geometric ergodicity, and analyzing mixing times.
result NUTS-mul and NUTS-BPS have nearly identical qualitative behavior but differ quantitatively in convergence rates.
The paper connects quivers to knot complements and studies their BPS states and 3d N=2 theories.
problem Understanding the relationship between quivers and knot complements.
method Assigning quivers to knot complements and exploring their physical interpretation.
result Proposed a physical interpretation of quivers in terms of BPS states and 3d N=2 theories.
We construct a complete convergent normal form for a real hypersurface in $\CC{N},\,N\geq 2$ at generic Levi degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. In particular, we obtain, in the spirit of the work of Chern and Moser \cite{chern}, distinguished curves in the …