This paper generalizes two facts about oriented 3d TFTs to the unoriented case. On one hand, it is known that oriented 3d TFTs having a topological boundary condition admit a state-sum construction known as the Turaev-Viro construction. This is related to the string-net construction of fermionic phases of matter. We sh…
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.
A modular functor is constructed from non-semisimple 3d TFTs.
problem Constructing modular functors from non-semisimple 3d topological field theories.
method Using a 3d TFT defined in [arXiv:1912.02063], a symmetric monoidal 2-functor is constructed from a 2-category of bordisms to a 2-category of finite linear categories.
result A modular functor is explicitly described as a symmetric monoidal 2-functor.
TFT improves multi-horizon forecasting with interpretable insights.
problem Complex multi-horizon forecasting with mixed inputs.
method Attention-based Temporal Fusion Transformer combining recurrent and self-attention layers.
result Significant performance improvements over existing benchmarks.
Graph coloring is explained using a topological field theory with defects.
problem Graph coloring as a combinatorial problem is quantum in nature.
method Topological field theory with defects to interpret graph coloring.
result Graph coloring is related to sections of a certain bundle.
Adaptive TFTs improve cryptocurrency price prediction accuracy.
problem Precise short-term price prediction in volatile cryptocurrency markets.
method Dynamic subseries lengths and pattern-based categorization.
result Significantly outperforms baseline models in prediction accuracy and profitability.
Automates fitting semiconductor device models using approximate Bayesian computation.
problem Manual tuning of parameters for fitting TFT models to experimental data is inefficient and prone to errors.
method Approximate Bayesian Computation (aBc) for generating posterior distributions of estimated parameters.
result The proposed method accurately predicts model parameters from mobility curves using gradient boosted trees.
We introduce and study the Wilson loops in a general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the…
This is an introductory review of topological field theories (TFTs) called AKSZ sigma models. The AKSZ construction is a mathematical formulation for the construction and analyses of a large class of TFTs, inspired by the Batalin-Vilkovisky formalism of gauge theories. We begin by considering a simple two-dimensional t…
CityTFT models urban building energy using a data-driven approach.
problem Current UBEM methods are time-consuming and based on physics.
method CityTFT uses a TFT framework with an augmented loss function.
result CityTFT predicts energy demands with high accuracy.
Hybrid model improves geopolitical conflict forecasting.
problem Forecasting geopolitical events from sparse, bursty data.
method Sparse Temporal Fusion Transformer (TFT) + Variational Nearest Neighbor Gaussian Process (VNNGP).
result Consistently outperforms standalone TFT in long-range horizons.
STS clarifies chaos and stochastic dynamics, linking algebraic topology and physics.
problem Chaos and stochastic dynamics in arbitrary form SDEs.
method Supersymmetric theory of stochastic dynamics (STS) using generalized transfer operator (GTO) and topological field theories (TFT).
result Positive 'pressure' in GTOs corresponds to spontaneous breakdown of topological supersymmetry, explaining 1/f noise.
Open 2D TFTs extend to closed theories with circle value as Hochschild homology.
problem Extending open 2D TFTs to closed theories.
method Using symmetric monoidal ∞-categories and Hochschild homology.
result Open 2D TFTs admit initial open-closed extensions.
The paper presents new algebraic structures on the 2-sphere using topological field theories.
problem Understanding algebraic structures on the 2-sphere through topological field theories.
method Defined P-monoids and L-monoids, analyzed their properties, and related them to 3-dimensional topological field theories.
result New algebraic structures (P-monoids and L-monoids) on the 2-sphere are equivalent and have strong constraints.
We propose a method to assign non-unitary TQFTs to certain SCFTs, deriving bounds and examples.
problem Assigning non-unitary TQFTs to specific SCFTs of rank 0.
method Using degenerate limits of SCFTs, extracting modular data from supersymmetric partition functions, and proposing a dictionary.
result Deriving a lower bound on the free energy of SCFTs and showing it is saturated by a specific SCFT.
We construct a gauge fixed action for topological membranes on G2-manifold such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. Moreover on M×S1 the theory naturally reduces…
Paper proposes a method for weather-informed probabilistic forecasting and scenario generation in power systems.
problem Challenges of integrating renewable energy sources into power grids due to their stochasticity and uncertainty.
method Combines probabilistic forecasting and Gaussian copula for day-ahead prediction and scenario generation of load, wind, and solar power.
result Demonstrates superior performance of the proposed weather-informed Temporal Fusion Transformer (WI-TFT) model.
NAS for financial time series forecasts using chain-structured architectures.
problem Optimizing neural architectures for financial time series forecasting.
method Comparison of three NAS strategies (Bayesian optimization, hyperband, reinforcement learning) on chain-structured search spaces for simple and complex architectures.
result Bayesian optimization and hyperband outperform other strategies, and RNN and 1D CNN perform best among architectures.
Study on oriented disingquandles for distinguishing singular links.
problem Distinguishing singular links of different colors.
method Introduced oriented dichromatic singular links and oriented disingquandles to define invariants.
result Found invariants that can distinguish some singular links.
This paper extends the results from the author's previous paper to consider finite, fiber- and orientation- preserving group actions on closed, orientable Seifert manifolds M that fiber over a non-orientable base space. An orientable base space double cover M~ of M is constructed and then an isomorphism be…
Analog of Kauffman bracket for non-orientable knots in thickened surface.
problem Defining an invariant for non-orientable knots in a non-orientable surface.
method Proposes an analog of the Kauffman bracket polynomial with modified sign rules.
result Polynomial is an isotopy invariant and independent of classical Kauffman for orientable covers.
Paper proves achiral Lefschetz fibrations from non-orientable Lefschetz fibrations.
problem Understanding achiral Lefschetz fibrations from non-orientable ones.
method Composition of standard orientation double covering map and non-orientable Lefschetz fibration.
result Specification of a monodromy factorization for the composition.
Study trisections of non-orientable 4-manifolds with boundary.
problem Understanding trisections in non-orientable 4-manifolds.
method Introduced trisections of non-orientable 4-manifolds with boundary, proved a non-orientable analogue of a theorem, and discussed adaptation of trisection theory.
result Existence of trisection diagrams and Kirby diagrams for closed non-orientable 4-manifolds.
To any generic curve in an oriented surface there corresponds an oriented chord diagram, and any oriented chord diagram may be realized by a curve in some oriented surface. The genus of an oriented chord diagram is the minimal genus of an oriented surface in which it may be realized. Let g_n denote the expected genus o…
Study curves in non-orientable surfaces with specific intersection properties.
problem Enumerate and understand curves in non-orientable surfaces with intersection constraints.
method Generalized construction of Malestein-Rivin-Theran to non-orientable surfaces.
result Lower bound for maximum number of curves in generic non-orientable surface.
The study establishes conditions for orientability in spaces with lower Ricci curvature bounds.
problem Conditions for orientability in spaces with lower Ricci curvature bounds.
method Equivalent characterizations of orientability using Ricci limit and RCD spaces.
result Four-manifolds with Ricci curvature bounded below and volume non-collapsing are uniformly locally orientable.
Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
problem Characterize fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
method Construct a class of involutions, extend product involutions, and use double covering.
result Any fiber-preserving, orientation-reversing involution factors as a product of an orientation-preserving and a specific class of involutions.
Study shortest non-separating curves on non-orientable surfaces, proving NP-hardness and tractability.
problem Computing shortest non-separating simple closed curves on non-orientable surfaces.
method Developed tools for computing shortest curves, proving NP-hardness and tractability.
result Proved NP-hardness and fixed-parameter tractability for computing shortest orienting curves, and polynomial-time algorithm for non-orienting curves.
This paper aims to define and study a notion of orientability in the Heisenberg sense (H-orientability) for the Heisenberg group Hn. In particular, we define such notion for H-regular 1-codimensional surfaces. Analysing the behaviour of a Möbius Strip in H1, we find a 1…
We show that there exist infinitely many pairwise distinct non-closed G_2-manifolds (some of which have holonomy full G_2) such that they admit co-oriented contact structures and have co-oriented contact submanifolds which are also associative. Along the way, we prove that there exists a tubular neighborhood N of every…
Positive Thompson links are proven for oriented subgroup elements.
problem Proving properties of Thompson links with positive elements.
method Analyzing elements of the oriented subgroup of the Thompson group.
result Positive oriented Thompson links are established.
Researchers create a new compactification of character varieties using geometric and algebraic methods.
problem Compactifying character varieties of finitely generated groups in PSL2(R). method Geometric interpretation of elements of the real spectrum compactification as Γ-actions on R-trees, endowed with an orientation. result Continuous surjection from real spectrum compactification to oriented Gromov equivariant compactification.
This paper calculates the non-orientable 4-genus for knots with 10 crossings.
problem Determining the non-orientable 4-genus for knots with a specific number of crossings.
method Calculating the minimal first Betti number of non-orientable surfaces smoothly embedded in a 4-ball with boundary the knot.
result The non-orientable 4-genus for knots with 10 crossings has been calculated.
DNNs generalize object recognition in novel orientations via neurons tuned to common features.
problem Understanding how DNNs generalize to objects in novel orientations.
method Training DNNs with familiar objects from multiple viewpoints and analyzing neuron responses.
result DNNs disseminate orientation-invariance from familiar objects to recognize objects in novel orientations.
J. Boyle classified 1-handles attached to surface-knots, that are closed and connected surfaces embedded in the Euclidean 4-space, in the case that the surfaces are oriented and 1-handles are orientable with respect to the orientations of the surfaces. In that case, the equivalence classes of 1-handles correspond to th…
The study explores positive scalar curvature metrics on non-orientable manifolds and their covers.
problem Existence of positive scalar curvature metrics on non-orientable manifolds and their covers.
method Extends Schoen-Yau inductive descent approach to non-orientable manifolds.
result Examples of non-orientable manifolds with positive scalar curvature metrics on their orientation double covers but not on homotopy equivalent manifolds.
Study virtualized Delta, Sharp, and Pass moves for oriented virtual knots and links.
problem Conditions for unknotting oriented virtual knots and links.
method Local moves (Delta, Sharp, Pass) for oriented virtual links.
result Lower bounds for the unknotting numbers are proven and shown to be best possible.
We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we study the topological complexity of oriented frame bundles, derive an upper bound for this invariant and certain lower bounds from cup length co…
In the symplectization of standard contact 3-space, R×R3, it is known that an orientable Lagrangian cobordism between a Legendrian knot and itself, also known as an orientable Lagrangian endocobordism for the Legendrian knot, must have genus 0. We show that any Legendrian knot has a non-or…
Hensel-Przytycki-Webb proved that all curve graphs of orientable surfaces are 17-hyperbolic. In this paper, we show that curve graphs of non-orientable surfaces are 17-hyperbolic by applying Hensel-Przytycki-Webb's argument. We also show that arc graphs of non-orientable surfaces are 7-hyperbolic, and arc-curve graphs …
In this paper we deal with Seifert fibre spaces, which are compact 3-manifolds admitting a foliation by circles. We give a combinatorial description for these manifolds in all the possible cases: orientable, non-orientable, closed, with boundary. Moreover, we compute a potentially sharp upper bound for their complexity…
This paper adresses the following problem: Given a closed orientable three-manifold M, are there at most finitely many closed orientable three-manifolds 1-dominated by M? We solve this question for the class of closed orientable graph manifolds. More presisely the main result of this paper asserts that any closed orien…
This study simplifies verification of invariants in oriented virtual knots.
problem Verifying invariants of oriented virtual knots is complex and time-consuming.
method Identifying a minimal generating set of oriented virtual Reidemeister moves.
result A four-element subset serves as a generating set for oriented virtual Reidemeister moves.
Polynomial-time algorithm finds short non-orientable loops intersecting graph edges up to 30 times.
problem Finding short non-orientable loops intersecting graph edges efficiently.
method Combining computational biology techniques with recent graph theory results.
result Existence of short canonical non-orientable systems of loops.
New method finds non-orientable knotted surfaces in 4D.
problem Reducibility of knotted surfaces in 4D.
method Elementary obstruction to reducibility.
result Construction of stably irreducible non-orientable surfaces.
The paper extends orientability results for DT invariants on Calabi-Yau 4-folds.
problem Defining Donaldson-Thomas invariants on quasi-projective Calabi-Yau 4-folds.
method Extending orientability results to quasi-projective Calabi-Yau 4-folds and using gauge theory.
result Orientability of moduli stacks and invariants on quasi-projective Calabi-Yau 4-folds.
New combinatorial model for Milnor fibration using oriented matroids.
problem Understanding the homotopy type of Milnor fibers of complexified real arrangements.
method Introducing a poset quasi-fibration based on a subdivision of the Salvetti complex and an oriented matroid.
result Homotopy type of Milnor fiber depends only on the combinatorial structure of the oriented matroid.
Researchers refine the non-orientable 4-genus of torus knots using Batson's surfaces.
problem Finding the minimum non-orientable 4-genus for torus knots. method Developed and analyzed Batson's non-orientable spanning surfaces in B4. result Batson's surfaces minimize the non-orientable 4-genus among certain surfaces.