Minimal stretch factors for certain pseudo-Anosov maps are bounded.
problem Bounding the stretch factor of orientation-reversing pseudo-Anosov maps.
method Using the silver ratio and properties of puncture orbits to derive bounds.
result The bound λ(f)−χ(S)≥σ2 is asymptotically sharp. New method trains generative models by reversing generator maps.
problem Training deep neural network generators.
method Non-parametrically estimate flexible code distributions by reversing generator maps.
result More powerful generative models, better latent structure modeling, explicit generalization control.
In this paper, we give a classification of orientation reversing periodic maps on closed surfaces which generalizes the theory of Nielsen for the orientation preserving periodic maps. On one hand, we give a group of data for each orientation reversing periodic map such that two periodic maps with the same data must be …
Improves neural network mapping functionality using latent feature generation.
problem Improving neural network performance in visual recognition tasks.
method Reversible learning for generating and learning latent features.
result The proposed method outperforms existing state-of-the-art methods in visual recognition.
A surface diffeo reversing orientation is isotopic to identity.
problem Understanding diffeomorphisms reversing orientation on surfaces.
method Analyzing Morse functions and diffeomorphisms preserving them.
result Reversing orientation homeomorphisms squared are isotopic to identity.
We prove that the extended mapping class group is generated by three orientation reversing involutions.
Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.
problem Approximating target distributions in conditional diffusion models.
method Using finite Gaussian mixtures with ReLU-network logits as reverse kernels, reducing the problem to static conditional density approximation.
result The resulting neural reverse-kernel class is dense in conditional KL divergence under exact terminal matching.
We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smoo…
In this paper we classify maps from a torus phase space X to Hn∗, the space of n×n, non-singular hermitian operators up to equivariant homotopy. The equivariance is with respect to a time-reversal involution on X and an involution on Hn∗ defining a certain symmetry class. Furthe…
New method trains Markov kernels for efficient sampling.
problem Efficient sampling from complex probability distributions.
method Adversarial learning of involutive Metropolis-Hastings kernels.
result Minimizes total variation distance to empirical data.
Unified framework for efficient trans-dimensional Bayesian inference using VI and NFs.
problem Efficient trans-dimensional Bayesian inference with reduced computational cost.
method Variational inference with normalizing flows to train transport proposals.
result Our approach minimizes reverse KL divergence and reduces computational cost.
The paper proves reverse inequalities in various geometric settings using curvature radius data.
problem Proving reverse Alexandrov-Fenchel inequalities in different geometric settings.
method Using curvature radius data and associated evolute or focal maps.
result Sharp reverse Alexandrov-Fenchel estimates and inequalities in smooth convex curves and hypersurfaces.
Proposes a new model for flood extent mapping.
problem Noise, obstacles, heterogeneity, and spatial dependency issues in traditional classification methods.
method Geographical hidden Markov tree, incorporating anisotropic spatial dependency.
result Outperforms multiple baselines in flood mapping.
We prove that both the hyperelliptic mapping class group and the extended hyperelliptic mapping class group are generated by two torsion elements. We also compute the index of the subgroup of the hyperelliptic mapping class group which is generated by involutions and we prove that the extended hyperelliptic mapping cla…
Map projections can reverse district compactness scores, affecting fairness evaluations.
problem District compactness scores can be reordered by map projections, impacting fairness evaluations.
method Mathematical proof and empirical demonstration of map projection effects on compactness scores.
result Map projections can reverse the order of compactness scores, altering fairness evaluations.
Adds layers to NNs to protect them from reverse engineering.
problem Extracting the underlying model of a Neural Network.
method Introducing parasitic layers that approximate a noisy identity mapping with a Convolutional NN.
result The protected NN's predictions remain mostly unchanged while making reverse-engineering more complex.
Defines signed quasiregular curves and proves growth theorem.
problem Understanding growth of signed quasiregular curves.
method Proves weak reverse Hölder inequality and uses it to prove growth theorem.
result Proves growth theorem for signed quasiregular curves.
New method learns distribution shifts caused by predictive models in social computing.
problem Learning distribution shifts due to predictive models in social computing.
method Reverse causal model with microfoundation for agents' actions.
result Effective in minimizing performative prediction risk.
Study stretch factors on nonorientable surfaces, proving nonorientable techniques ineffective.
problem Determine stretch factors on nonorientable surfaces.
method Analyzing pseudo-Anosov maps with orientable foliations on specific surfaces.
result Stretch factors do not have Galois conjugates on the unit circle.
Classifies orientation-reversing homeomorphisms of even periods on surfaces.
problem Classifying orientation-reversing homeomorphisms of even periods on surfaces.
method Following the approach of [1] and correcting errors in [1] for the case of periods multiple of 4.
result Classification for orientation-reversing homeomorphisms of periods multiple of 4.
TSC uses HMC and adaptive transport maps to optimize forward KL for variational inference.
problem Variational inference underestimates uncertainty when minimizing reverse KL.
method TSC uses Hamiltonian Monte Carlo and adaptive transport maps to optimize KL(p||q).
result TSC achieves competitive performance in training variational autoencoders on large-scale data.
In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic Riemannian manifolds to be harmonic map. Then we investigate the constancy of certain map…
A new method predicts dynamical systems better by using two different latent spaces.
problem Predicting the future of dynamical systems with optimal accuracy.
method Uses two different latent mappings for present and future states.
result Optimal 2-mapping method significantly outperforms single latent representation methods.
Study homology products on loop spaces with orientation reversal.
problem Computing homology products on loop spaces with orientation reversal.
method Defined transfer product on loop space quotients using transfer maps and Chas-Sullivan loop product.
result Computed homology of loop spaces with orientation reversal and defined product.
Following the recent work by T.-H. Chan in [HOMFLY polynomial of some generalized Hopf links, J. Knot Theory Ramif. 9 (2000) 865--883] on reverse string parallels of the Hopf link we give an alternative approach to finding the Homfly polynomials of these links, based on the Homfly skein of the annulus. We establish tha…
RML improves generative modeling of complex distributions.
problem Learning complex distributions in applications.
method RML defines a forward process to a known distribution, then learns a reverse Markov process.
result RML efficiently captures complex distributions in simulations and climate data.
Open and discrete maps with specific branch set images are equivalent to PL branched covers.
problem Understanding the equivalence of open and discrete maps and PL branched covers.
method Demonstrated that an open and discrete map f:SnoSn with a specific branch set image is equivalent to a PL branched cover up to homeomorphism. result Open and discrete maps with a specific branch set image are equivalent to PL branched covers.
We develop the basics of a theory of almost isometries for spaces endowed with a quasi-metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particular interest, and it is studied in more detail. The main motivation arises from General Relativity, and more specifically in spacetimes endo…
We present a complete classification of elements in the mapping class group of the torus which have a representative that can be written as a product of two orientation reversing involutions. Our interest in such decompositions is motivated by features of the monodromy maps of real fibrations. We employ the property th…
We show that conformally compact, globally hyperbolic, Lorentzian Einstein-Weyl 3-manifolds are in natural one-to-one correspondence with orientation-reversing diffeomorphisms of the 2-sphere. The proof hinges on a holomorphic-disk analog of Hitchin's mini-twistor correspondence.
Faster diffusion-based models generate data with fewer steps.
problem Slow and costly diffusion-based generative models.
method Truncate diffusion process to generate data more efficiently.
result Truncated models provide consistent improvements in performance.
Certain classes of 3-manifolds, following Thurston, give rise to a 'skinning map', a self-map of the Teichmüller space of the boundary. This paper examines the skinning map of a 3-manifold M, a genus-2 handlebody with two rank-1 cusps. We exploit an orientation-reversing isometry of M to conclude that the skinning map …
The paper studies sections of time-like twistor spaces with specific covariant derivatives.
problem Sections of time-like twistor spaces with light-like or zero covariant derivatives.
method Analyzes conformal Gauss maps of time-like minimal surfaces and properties of almost paracomplex structures.
result Sections of time-like twistor spaces have light-like or zero covariant derivatives.
This work improves understanding of symmetrizing Bregman divergences on positive definite matrices.
problem Understanding which mean to use for symmetrizing Bregman divergences on positive definite matrices.
method Axiomatic definition of mean functionals and variational principles over the cone of positive definite matrices.
result The arithmetic mean is canonical for forward symmetrization, and the arithmetic, log-Euclidean, and harmonic means for reverse symmetrization.
Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding bounding pair maps generate a free group. This supports the conjecture stated b…
In this paper we provide a systematic treatment of Willmore surfaces with orientation reversing symmetries and illustrate the theory by (old and new) examples. We apply our theory to isotropic Willmore two-spheres in S4 and derive a necessary condition for such ( possibly branched) isotropic surfaces to descend to (…
Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair (S3,Σg) for possible embeddings e:Σg→S3. We determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the p…
The paper sets new bounds for Ricci-curvature in submersions and maps.
problem Establishing bounds for Ricci-curvature in submersions and maps.
method Developed upper and lower bounds for Ricci-curvature in submersions and maps, providing geometric characterizations.
result New bounds for Ricci-curvature in submersions and maps have been derived.
We introduce a toy probabilistic model to analyze job-matching processes in recent Japanese labor markets for university graduates by means of statistical physics. We show that the aggregation probability of each company is rewritten by means of non-linear map under several conditions. Mathematical treatment of the map…
Classifies reversible and strongly reversible elements in quaternionic groups.
problem Classifying reversible and strongly reversible elements in quaternionic groups.
method Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
result Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
The paper classifies reversible and strongly reversible elements in Hermitian isometry groups.
problem Classifying reversible and strongly reversible elements in Hermitian isometry groups.
method Classification through group theory and algebraic manipulation.
result New classification of strongly reversible elements in Sp(n).
The paper classifies reversible and strongly reversible elements in quaternionic hyperbolic spaces.
problem Classifying reversible and strongly reversible elements in quaternionic hyperbolic spaces.
method Analyzing conjugacy classes and using properties of quaternionic hyperbolic spaces and their isometry groups.
result All elements of the isometry group of quaternionic hyperbolic spaces are strongly reversible.
We propose a novel method to forecast the future from the present using time-reversed data.
problem Forecasting the future from past data, exploiting temporal asymmetry.
method Retrodictive forecasting via inverse MAP optimization over a Conditional Variational Autoencoder (CVAE).
result The method successfully predicts future events in time-reversible and irreversible processes.
The braid group Bn, endowed with Artin's presentation, admits an antiautomorphism Bn→Bn, such that v↦vˉ is defined by reading braids in reverse order (from right to left instead of left to right). We prove that the map Bn→Bn, v↦vvˉ is injective. We also give s…
This paper classifies reversible and strongly reversible elements in affine groups.
problem Classifying reversible and strongly reversible elements in affine groups.
method Identifying affine transformations and using conjugacy by involutions.
result Classification of reversible and strongly reversible elements in affine groups.
Paper extends cobordism maps in Khovanov and instanton homologies.
problem Define and prove compatibility of cobordism maps in Khovanov and instanton homologies.
method Extend embedded cobordism map to immersed cobordisms and prove compatibility.
result Induced map on Khovanov homology is injective for certain concordances.
Defines a super analog of Plücker embedding for Grassmannian.
problem Generalizing Plücker embedding to super vector spaces with mixed parity.
method Combines super vector space and its parity-reversion to construct embedding.
result Proves the embedding is an isomorphism to a weighted projective space.
Study finds mean reversion strategies perform well on historical data but fail in recent market conditions.
problem Performance of mean reversion strategies in recent market data.
method Empirical investigation of three mean reversion strategies (PAMR, OLMAR, TCO) on historical S&P 500 data and benchmark datasets.
result Mean reversion strategies may fail in recent market conditions, especially with transaction costs.