New method splits Einstein field equations for general spacetime threading.
problem Solving Einstein field equations in complex spacetime geometries.
method General (1+3) threading approach to split EFE and conservation laws.
result Perturbation Friedman equations derived in almost FLRW universe.
Study on bit threads and their locking properties in holographic spacetimes.
problem Understanding the conditions under which regions can be locked in holographic spacetimes.
method Investigation of different density bounds and their implications on the locking of regions.
result Non-crossing regions can be locked under the most stringent bound, but crossing regions cannot.
We develop a new approach on the (1+3) threading of spacetime (M,g) with respect to a congruence of curves defined by an arbitrary timelike vector field. The study is based on spatial tensor fields and on the Riemannian spatial connection ∇⋆, which behave as 3D geometric objects. We obtain new formul…
Bit threads prove holographic monogamy of mutual information.
problem Proving the monogamy of mutual information in holographic entanglement.
method Using bit threads and multicommodity flow adapted from network theory, combined with convex optimization tools.
result Proved the monogamy of mutual information property of holographic entanglement entropies.
We discuss Darboux-Staude type of thread configurations for the ellipsoid similar to Chasles-Graves type of thread configurations for the ellipse. These threads are formed by rectilinear segments, geodesic and line of curvature segments on the considered ellipsoid and with tangents tangent to the given ellipsoid and a …
Innocent musing on geodesics on the surface of helical pasta shapes leads to a single continuous 4-parameter family of surfaces invariant under at least a 1-parameter symmetry group and which contains as various limits spheres, tori, helical tubes, and cylinders, all useful for illustrating various aspects of geometry …
Algorithm uncovers roles and sub-communities in online forums.
problem Identifying roles and sub-communities in online forums.
method Scalable algorithm based on stochastic variational inference and topic models.
result Model outperforms existing methods in predicting user behavior.
Closed formulas for η-corrections in the once-punctured torus identified.
problem Identifying η-corrections in the Kauffman bracket skein algebra of the once-punctured torus.
method Explicit closed formulas for Chebyshev-threaded families and η-corrections.
result Explicit Chebyshev expansions and coefficients for η-corrections.
(NOTE: per referee comments, this article has been split; it is now superseded by "Existence of thread-wire minimizers" and "Near-wire thread-wire minimizers"; please see http://www.bkstephens.net.) Alt's thread problem asks for least-area surfaces bounding a fixed "wire" curve and a movable "thread" curve of length L.…
Study of motion equations in a 5D universe with special threading.
problem Formulating equations of motion in a 5D spacetime.
method Covariant formulation of motion equations with respect to (1+1+3) threading. result Introduction and study of a 5D Robertson-Walker universe.
New approach to holographic entanglement using bit threads and max flow-min cut principle.
problem Clarifying the Ryu-Takayanagi formula and its applications in holographic theories.
method Introducing bit threads and max flow-min cut principle to rewrite Ryu-Takayanagi formula.
result Flow-based proofs of strong subadditivity and related properties clarify the RT formula.
Study identifies stable configurations of intertwined threads with repulsive interactions.
problem Stable configurations of entangled systems with repulsive interactions.
method Analysis of steepest descent flow of an energy functional.
result Existence and uniqueness of stable configuration of two layers drifting apart at t1/3 rate. Given a knot diagram D, we construct a semi-threading circle for it which can be an axis of D as a closed braid depending on knot diagrams. In particular, we consider semi-threading circles for minimal diagrams of a knot with respect to overpasses which give us some information related to the braid index. By this n…
System classifies Twitter and Reddit posts' stance towards hidden rumour threads.
problem Classifying posts' stance towards hidden rumour threads.
method Used pre-trained deep bidirectional transformers (BERT) for stance classification.
result Reached F1 score of 61.67% on test data, 2nd place in competition.
A new deep metric learning method for defect classification in threaded pipe connections.
problem Defect classification in threaded pipe connections with limited and imbalanced multichannel functional data.
method COMPILED approach based on deep metric learning for imbalanced, multichannel, and partially observed functional data.
result Superior accuracy compared to existing benchmarks in a real-world case study.
Accelerator synthesizes deep learning inference from C code using FPGA hardware.
problem Efficiently implementing deep learning models on FPGAs.
method Parallelized C code using Pthreads, high-level synthesis, reduced precision, zero-weight-skipping.
result Peak performance of 138 effective GOPS on VGG-16 on Intel Arria 10 SoC FPGA.
HiGrad provides statistical inference for SGD without extra cost.
problem Statistical inference for online learning with SGD.
method Hierarchical SGD with covariance structure decorrelation.
result HiGrad confidence intervals achieve asymptotically exact coverage.
Study G2 skein algebra elements using Kuperberg webs and threading operations.
problem Identify and analyze central elements in G2 skein algebra. method Use Kuperberg webs, threading operations, and skein-theoretic arguments.
result Verify central elements and obtain uniqueness of transparent polynomials.
DeepTraderX learns from other strategies to place market orders.
problem Creating efficient trading strategies in multi-threaded market simulations.
method Deep Learning model trained on historical market data to predict optimal market orders.
result DeepTraderX outperforms existing strategies in multi-threaded market simulations.
GoSGD speeds up deep learning training with gossip exchange.
problem Speeding up the training of deep learning models.
method Distributed optimization using stochastic gradient descent with gossip algorithms.
result GoSGD achieves fully asynchronous and decentralized training.
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of …
Quantum Frobenius map for SL3 skein modules constructed and described.
problem Constructing a quantum Frobenius map for SL3 skein modules. method Using threading polynomials and the Frobenius map of Parshall-Wang for quantum group Oq(SL3). result Described the quantum Frobenius map for SL3 skein modules. A new gossip-based method speeds up deep learning training.
problem Speeding up the training of convolutional networks.
method A distributed method inspired by gossip algorithms, using asynchronous and decentralized parallel optimization.
result GoSGD shows good consensus convergence properties and competitive performance compared to EASGD.
New simulation shows trading algorithms' performance varies with parallelism.
problem Validation of trading algorithms' performance in parallel markets.
method Used TBSE, a threaded market simulator, to compare algorithms' performance.
result Trading algorithms' performance differs in parallel vs. sequential markets.
We expect manifolds obtained by Dehn filling to inherit properties from the knot manifold. To what extent does that hold true for the Heegaard structure? We study four changes to the Heegaard structure that may occur after filling: (1) Heegaard genus decreases, (2) a new Heegaard surface is created, (3) a non-stabilize…
Self-Organizing Maps (SOM) are popular unsupervised artificial neural network used to reduce dimensions and visualize data. Visual interpretation from Self-Organizing Maps (SOM) has been limited due to grid approach of data representation, which makes inter-scenario analysis impossible. The paper proposes a new way to …
AI agents on social networks rarely engage in extended conversations.
problem Understanding the persistence of interactions in AI-agent social networks.
method Analysis of Moltbook, a social network of AI agents, using interaction half-life and spectral tests.
result Most comments on Moltbook receive a direct reply within seconds, indicating a ``fast response or silence'' regime.
This paper optimizes object tracking on edge devices with small matrices.
problem Efficiently tracking objects in video sequences on edge devices with small matrices.
method Parallelized a Simple Online and Real-time Tracking (SORT) application on shared-memory multicores.
result Throughput-based parallelization technique outperforms multi-threading for small matrices.
The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.
problem Characterizing pseudosymmetric spacetimes as perfect fluids.
method Analyzes generalized Robertson-Walker spacetimes, conformally flat spacetimes, and dust fluids.
result Conditions for pseudosymmetric spacetimes to be perfect fluids are established.
SYMSGD improves parallel SGD by combining local models to match sequential SGD's results.
problem Inherently sequential nature of SGD limits parallel scalability and convergence.
method SYMSGD combines local models with a combiner to mimic sequential SGD's semantics.
result SYMSGD achieves up to 11x speedup on 16 cores compared to a sequential baseline.
We consider (flat) Cauchy-complete GH spacetimes, i.e., globally hyperbolic flat lorentzian manifolds admitting some Cauchy hypersurface on which the ambient lorentzian metric restricts as a complete riemannian metric. We define a family of such spacetimes - model spacetimes - including four subfamilies: translation sp…
Jebsen-Birkhoff theorem extended to Berwald spacetimes.
problem Generalizing Birkhoff theorem to Berwald spacetimes.
method Proving Ricci-flat, spatially spherically symmetric Berwald spacetimes are pseudo-Riemannian or flat.
result Jebsen-Birkhoff theorem extended to Berwald spacetimes.
The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.
problem Characterizing and analyzing pseudo generalized Ricci-recurrent spacetimes in modified gravity.
method Introducing and characterizing pseudo generalized Ricci-recurrent spacetimes, proving their properties, and studying their impact under modified gravity scenarios.
result Pseudo generalized Ricci-recurrent spacetimes represent specific spacetime types under modified gravity scenarios.
This paper classifies a specific weave type by their crossing number.
problem Classifying doubly periodic untwisted (p,q)-weaves.
method Classification by crossing number, introducing crossing matrix for equivalence.
result Classification of untwisted (p,q)-weaves by their crossing number.
The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in F(R)-gravity.
problem Characterizing spacetimes with quasi-constant sectional curvature.
method Investigation through examples, proofs, and analysis of energy conditions.
result A spacetime of quasi-constant sectional curvature can represent a Robertson Walker spacetime or a static spacetime.
The article introduces pseudo generalized Ricci-recurrent spacetimes and their applications in modified gravity.
problem Characterizing and understanding pseudo generalized Ricci-recurrent spacetimes.
method Introduced and characterized pseudo generalized Ricci-recurrent spacetimes, provided examples, and studied their implications in modified gravity.
result Pseudo generalized Ricci-recurrent spacetimes represent perfect fluid spacetimes and can model dark energy epochs or static spacetimes.
We present a generic framework for parallel coordinate descent (CD) algorithms that includes, as special cases, the original sequential algorithms Cyclic CD and Stochastic CD, as well as the recent parallel Shotgun algorithm. We introduce two novel parallel algorithms that are also special cases---Thread-Greedy CD and …
Algorithm of construction of all knots, links with given number of crosses on diagram of knot, link is offered. This algorithm is based on simple proposition, that there is a representation of knot (link) as closure of braid with n threads and length of this braid does not exceed n(4n-5)+2.
Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.
problem Exploring geometric properties of Vaidya-Bonner-de Sitter spacetime.
method Analyzing conformal curvature, conharmonic curvature, and other curvatures.
result VBdS spacetime exhibits various pseudosymmetric structures and geometric features.
The paper studies the past inextendibility of FLRW spacetimes using the VDR asymptote.
problem Investigating the past inextendibility of FLRW spacetimes.
method Using the volume-distance-ratio (VDR) asymptote to assess spacetime inextendibility criteria.
result Conditions for past inextendibility of FLRW spacetimes are identified.
The study characterizes GRW spacetimes with gradient solitons and phantom era.
problem Characterizing generalized Robertson-Walker spacetimes with gradient solitons.
method Examined gradient type Ricci solitons and (m,τ)-quasi Einstein solitons in GRW spacetimes. result Demonstrated that GRW spacetimes can be Robertson-Walker or phantom era spacetimes under certain conditions.
Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.
problem Identifying Lorentzian manifolds embeddable in Minkowski spacetime.
method Characterization and proof of embeddability conditions.
result Lorentzian manifolds embeddable in Minkowski spacetime coincide with globally hyperbolic spacetimes.
SplitSGD dynamically adjusts learning rate based on stationarity detection.
problem Optimizing learning rates for stochastic optimization.
method SplitSGD uses a simple stationarity detection method to adjust learning rates.
result SplitSGD improves generalization and outperforms other adaptive methods.
New proof shows FLRW spacetimes can't be extended smoothly in certain axisymmetric cases.
problem Proving smooth extension of FLRW spacetimes in specific spacetime classes.
method Extending previous work on spherically symmetric spacetimes to axisymmetric spacetimes.
result Demonstrates C0-inextendibility for FLRW spacetimes in a subclass of axisymmetric spacetimes. Study shows how certain expanding spacetimes can collapse into flat or Kasner spacetimes.
problem Understanding the collapse of expanding vacuum spacetimes.
method Analysis of spacetimes with CMC foliations and scale invariant a priori bounds.
result Arbitrarily large future time intervals can be modelled by flat or Kasner spacetimes.
Study of quasilocal mass using isometric embedding in various spacetimes.
problem Understanding quasilocal mass in different spacetimes.
method Application of isometric embedding theory to quasilocal mass.
result Recent progress in quasilocal mass calculations with specific spacetimes.
Study directed completion of spacetimes, focusing on Schwarzschild spacetime.
problem Characterizing directed completions of spacetimes.
method Directed completion of Lorentzian pre-length spaces, focusing on Schwarzschild spacetime.
result Directed completion of Schwarzschild spacetime coincides with future causal completion.
Identifies all type D^k spacetimes in arbitrary dimensions.
problem Characterizing and distinguishing type D^k spacetimes.
method Analyzing curvature tensors and their invariants for degenerate Kundt metrics.
result Locally boost isotropic spacetimes are type D^k spacetimes.