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.
New invariants for 3-manifolds derived from supergroup representations.
problem Developing invariants for 3-manifolds using supergroup analogues.
method Introducing supergroup analogues of 3-manifold invariants for superunitary groups, focusing on SU(2|1). Calculating q-series for specific 3-manifolds and studying their properties.
result Explicit calculation and study of q-series for certain 3-manifolds, providing a formula relating new invariants to quantum invariants.
Study on Δ invariants of plumbed 3-manifolds, comparing with Heegaard-Floer homology.
problem Analyzing Δ invariants of plumbed 3-manifolds.
method Expressing Δ of Seifert manifolds in terms of singularity theory invariants, providing examples for non-Seifert manifolds, comparing with Heegaard-Floer homology.
result Interesting behavior of Δ invariants for non-Seifert manifolds, comparison with Heegaard-Floer homology.
Recent advances in Quantum Topology assign q-series to knots in at least three different ways. The q-series are given by generalized Nahm sums (i.e., special q-hypergeometric sums) and have unknown modular and asymptotic properties. We give an efficient method to compute those q-series that come from planar gra…
The tail of a quantum spin network in the two-sphere is a q-series associated to the network. We study the existence of the head and tail functions of quantum spin networks colored by 2n. We compute the q-series for an infinite family of quantum spin networks and give the relation between the tail of these networ…
The tail of the colored Jones polynomial of an alternating link is a q-series invariant whose first n terms coincide with the first n terms of the n-th colored Jones polynomial. Recently, it has been shown that the tail of the colored Jones polynomial of torus knots give rise to Ramanujan type identities. In th…
The colored Jones polynomial is a q-polynomial invariant of links colored by irreducible representations of a simple Lie algebra. A q-series called a tail is obtained as the limit of the sl2 colored Jones polynomials {Jn(K;q)}n for some link K, for example, an alternating link. For the $\mathf…
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 …
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…
Belief propagation (BP) can do exact inference in loop-free graphs, but its performance could be poor in graphs with loops, and the understanding of its solution is limited. This work gives an interpretable belief propagation rule that is actually minimization of a localized α-divergence. We term this algorithm as $α…
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…
Nahm sums are q-series of a special hypergeometric type that appear in character formulas in Conformal Field Theory, and give rise to elements of the Bloch group, and have interesting modularity properties. In our paper, we show how Nahm sums arise naturally in Quantum Knot Theory, namely we prove the stability of th…
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 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 R3.
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…
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…
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…
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…