The paper explores how a geometric flow can turn a black hole into a traversable wormhole.
problem The study investigates how a static, spherically symmetric black hole can be transformed into a traversable wormhole.
method The approach involves analyzing almost η-Ricci-Yamabe solitons and their geometric coupling with the Hawking temperature. result The geometric flow successfully transforms the black hole into a traversable wormhole, opening the throat and preserving the exact cosmological spacetime.
Study wormholes in surface moduli space, proving conjecture.
problem Wormholes in moduli space of surfaces of general type.
method KSBA compactification, extremal P-resolutions, general wormhole conjecture.
result Proved wormhole conjecture for many cases.
Study wormholes in Einstein-Yang-Mills theory with a phantom field.
problem Existence of wormholes in Einstein-Yang-Mills theory with a phantom scalar field.
method Rigorous mathematical proof and numerical analysis of wormhole solutions.
result Existence of an infinite sequence of symmetric wormhole solutions.
A multi-neck spacetime wormhole is constructed with a simple metric tensor.
problem Existence of multi-neck spacetime wormholes.
method Spherical inversion of a 3-torus to create a 3-neck spacetime wormhole.
result Exact solution of Einstein's field equations for a multi-neck spacetime wormhole.
Modeling wormhole creation without singularities in relativity.
problem Creating wormholes without singularities in classical relativity.
method Topological surgery and Morse theory to construct a nonsingular wormhole.
result Wormholes can be created nonsingularly in classical relativity.
We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that obser…
Because no closed timelike curve (CTC) on a Lorentzian manifold can be deformed to a point, any such manifold containing a CTC must have a topological feature, to be called a timelike wormhole, that prevents the CTC from being deformed to a point. If all wormholes have horizons, which typically seems to be the case in …
The paper studies geometric structures of wormholes using a new connection.
problem Exploring new geometric properties of wormholes.
method Extended Levi-Civita connection to semi-symmetric non-metric connections.
result Morris-Thorne wormholes exhibit specific geometric properties.
The idea is considered that a quantum wormhole in a spacetime foam can be described as a Ricci flow. In this interpretation the Ricci flow is a statistical system and every metric in the Ricci flow is a microscopical state. The probability density of the microscopical state is connected with a Perelman's functional of …
It is shown that 3D part of a spherically symmetric solution in conformal Weyl gravity interacting with Maxwell electrodynamics is a Yamabe flow as well. The Yamabe flow describes the transition from a horn of an initial wormhole to a 3D Euclidean space both filled with a radial electric field. It is supposed that such…
Extends results of math-ph/0407067
Extends results of math-ph/0407067
We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from this handle region, the initial data sets we produce can be made as close as desi…
Unified approach to verify NN properties using ReLU's unique polytope structure.
problem Lack of robustness and interpretability in ReLU NNs for risk-sensitive applications.
method Identifying and traversing the local polytopes of ReLU NNs, developing an algorithm to verify properties.
result Unified approach to examine network behavior in risk-sensitive settings.
A method for fast estimation of Wasserstein distances using sliced Wasserstein distances.
problem Efficiently computing Wasserstein distances for multiple pairs of distributions.
method Regression on sliced Wasserstein distances to predict true Wasserstein distances.
result The proposed method provides a better approximation of Wasserstein distance than state-of-the-art models, especially in low-data regimes.
We study smooth {\sf traversing} vector fields v on compact manifolds X with boundary. A traversing v admits a Lyapunov function f:X→R such that df(v)>0. We show that the trajectory spaces T(v) of {\sf traversally generic} v-flows are {\sf Whitney stratified spaces}, and thus admit tr…
We study for which polynomials F a thin shell wormhole with a continuous metric (connecting two Schwarzschild spacetimes of the same mass) satisfy the null energy condition (NEC) in F(R)-gravity. We avoid junction conditions by using the mathematical framework of the Colombeau algebra which describes a generalized …
Recent empirical results on long-term dependency tasks have shown that neural networks augmented with an external memory can learn the long-term dependency tasks more easily and achieve better generalization than vanilla recurrent neural networks (RNN). We suggest that memory augmented neural networks can reduce the ef…
We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology and natural sciences and creates a new platform for exploring geometrical physics…
A particular Riemannian metric which originally has been obtained for a well-known coordinate system in the Euclidean 3-space, is shown to specify, in fact, a manifold with boundary. There are two ways to make the manifold complete. One is to identify two halves of the boundary that turns the manifold into Euclidean 3-…
We connect topological changes that can occur in 3-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole formation. By considering the initial manifold as the 3-dimensional spatial sectio…
This study aims to improve communication between fragmented blockchain systems in finance.
problem Inefficient and insecure communication in fragmented blockchain systems.
method Analysis of cross-chain interoperability protocols and their properties.
result Comparison and evaluation of cross-chain interoperability protocols.
We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology and natural sciences and creates a new platform for exploring geometrical physics…
We give a new construction of Einstein and Kaehler-Einstein manifolds which are asymptotically complex hyperbolic, inspired by the work of Mazzeo-Pacard in the real hyperbolic case. The idea is to develop a gluing theorem for 1-handle surgery at infinity, which generalizes the Klein construction for the complex hyperbo…
Euler's theorem extended to complex structures.
problem Generalizing Euler's theorem to complex structures.
method Analyzing strongly connected, pure n-dimensional regular CW-complexes. result Evenness of cells is equivalent to generalized cycle decomposition and traversability.
A novel multi-resolution Gaussian process model for efficient time traversal.
problem Inference for long sequences with fast and slow transitions is difficult.
method A novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution.
result The combined model allows efficient inference for arbitrarily long sequences with complex dynamics.
Many tasks in computer vision can be cast as a "label changing" problem, where the goal is to make a semantic change to the appearance of an image or some subject in an image in order to alter the class membership. Although successful task-specific methods have been developed for some label changing applications, to da…
We combine Gromov's amenable localization technique with the Poincaré duality to study the traversally generic vector flows on smooth compact manifolds X with boundary. Such flows generate well-understood stratifications of X by the trajectories that are tangent to the boundary in a particular canonical fashion. Sp…
Any traversally generic vector flow on a compact manifold X with boundary leaves some residual structure on its boundary $\d X$. A part of this structure is the flow-generated causality map Cv, which takes a region of $\d X$ to the complementary region. By the Holography Theorem from \cite{K4}, the map Cv allow…
Counterfactual regret minimization (CFR) is the most popular algorithm on solving two-player zero-sum extensive games with imperfect information and achieves state-of-the-art performance in practice. However, the performance of CFR is not fully understood, since empirical results on the regret are much better than the …
Predicts node sequences in graphs using multi-order network models.
problem Predicting sequences of node traversals in graphs.
method Combines multiple higher-order network models into a multi-order model, fitting and selecting the optimal maximum order.
result Outperforms state-of-the-art algorithms for next-element and full sequence prediction.
Let X be a compact smooth manifold with boundary. In this article, we study the spaces V†(X) and V‡(X) of so called boundary generic and traversally generic vector fields on X and the place they occupy in the space V(X) of all fields (see Theorems \ref{th3.4} and Theo…
Attention-based encoder decoder network uses a left-to-right beam search algorithm in the inference step. The current beam search expands hypotheses and traverses the expanded hypotheses at the next time step. This traversal is implemented using a for-loop program in general, and it leads to speed down of the recogniti…
In this article, we introduce a mass-decreasing flow for asymptotically flat three-manifolds with nonnegative scalar curvature. This flow is defined by iterating a suitable Ricci flow with surgery and conformal rescalings and has a number of nice properties. In particular, wormholes pinch off and nontrivial spherical s…
A colored graph is a directed graph in which nodes or edges have been assigned colors that are not necessarily unique. Observability problems in such graphs consider whether an agent observing the colors of edges or nodes traversed on a path in the graph can determine which node they are at currently or which nodes wer…
A graph traversal algorithm for cold-start news recommendation using named entities.
problem Cold-start news recommendation for articles without user-specific information.
method Graph traversal algorithm and novel weighting scheme for named entities over a knowledge graph.
result Our method produces stronger Pearson correlation to human similarity scores than other cold-start methods.
Method generates counterfactual explanations for graph classifiers.
problem Generating high-quality explanations for graph predictions.
method Permutation equivariant graph variational autoencoder to traverse latent space.
result Empirically validated model is high-performing and robust.
SURF steers scalarization weights to uniformly traverse the Pareto front.
problem Non-uniform coverage of the Pareto front when using scalarization weights.
method Geometric analysis and CDF mapping to select weights for uniform coverage.
result SURF converges to uniform Pareto front coverage under provable conditions.
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to extra combinatorial constraints, the only practical algorithms to date have been v…
Let Ck1k2 denote the set of all closed curves of class Cr on the sphere S2 whose geodesic curvatures are restricted to lie in (k1,k2), furnished with the Cr topology (for some r>=2 and possibly infinite k1<k2). In 1970, J. Little proved that the space C0+∞ of closed curves ha…
This paper is the third in a series that researches the Morse Theory, gradient flows, concavity and complexity on smooth compact manifolds with boundary. Employing the local analytic models from \cite{K2}, for \emph{traversally generic flows} on (n+1)-manifolds X, we embark on a detailed and somewhat tedious study …
This paper proposes a novel type of random forests called a denoising random forests that are robust against noises contained in test samples. Such noise-corrupted samples cause serious damage to the estimation performances of random forests, since unexpected child nodes are often selected and the leaf nodes that the i…
We synthesize and extend the previous ideas about appearance of both noncommutative and Finsler geometry in string theory with nonvanishing B--field and/or anholonomic (super) frame structures \cite{vstring,vstr2,vnonc,vncf}. There are investigated the limits to the Einstein gravity and string generalizations containin…
Sparse neural networks training is difficult due to optimization failures and energy landscape issues.
problem Training sparse neural networks leads to suboptimal solutions and optimization failures.
method Investigated optimization dynamics and energy landscape in sparse neural networks.
result Sparse neural networks have a linear path with a monotonically decreasing objective from initialization to a good solution, but not from a bad solution.
Proposes a new method for completing swap cycles in decentralized exchanges.
problem Completing swap cycles in decentralized exchanges efficiently and without slippage.
method Introduces an asset matrix formulation to verify and complete CoW cycles using graph traversal and imbalance correction.
result Demonstrates efficient discovery and insertion of synthetic orders for atomic cycle closure.
As has been observed by Morse \cite{Mo}, any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary $\d X$ by compact submanifolds $\{\d_j^\pm X(v)\}_{1 \leq j \leq \dim(X)}$, where $\textup{codim}(\d_j^\pm X(v))= j$. Our main observation is that this stra…
In this paper, we present our general results about traversing flows on manifolds with boundary in the context of the flows on surfaces with boundary. We take advantage of the relative simplicity of 2D-worlds to explain and popularize our approach to the Morse theory on smooth manifolds with boundary, in which the bo…
This paper describes a mechanism by which a traversally generic flow v on a smooth connected manifold X with boundary produces a compact CW-complex T(v), which is homotopy equivalent to X and such that X embeds in T(v)×R. The CW-complex T(v) captures some resid…