This study analyzes satellite communication latency using a stochastic geometry model.
problem Latency analysis of LEO satellite relay communication systems.
method Stochastic geometry framework with spherical BPP models, suboptimal satellite relay selection strategy.
result Derives distance distributions and analytical expressions for transmission delays.
Starfield optimizes satellite links for LEO mega-constellations by aligning ISLs with regional traffic patterns.
problem Forming a stable satellite topology in LEO mega-constellations with limited ISLs and unstable acquisition.
method Starfield uses a demand-aware heuristic algorithm based on traffic flows and Riemannian geometry to assign satellite links.
result Starfield reduces hop count and improves stretch factor by up to 30% compared to existing methods.
FedSpace optimizes ML training on satellites and ground stations.
problem Training machine learning models on satellites with limited bandwidth.
method Federated Learning framework that dynamically schedules model aggregation based on satellite orbits.
result Reduces training time by 1.7 days over state-of-the-art algorithms.
Enhances cooperative multi-task SemCom for distributed users.
problem Performance degradation in cooperative multi-tasking due to negative information transfer.
method Federated learning (FL) with semantic-aware task clustering.
result Constructive cooperation across distributed users with semantic-aware task clustering.
New local equivalence groups refine Rasmussen's s-invariant.
problem Refining Rasmussen's s-invariant for knot concordance.
method Introducing local equivalence groups combining Khovanov homologies.
result A refined s-invariant that determines triviality of knot images.
Gradient-based meta-learning techniques are both widely applicable and proficient at solving challenging few-shot learning and fast adaptation problems. However, they have practical difficulties when operating on high-dimensional parameter spaces in extreme low-data regimes. We show that it is possible to bypass these …
Leo Breiman's Rashomon Effect and Occam Dilemma are re-evaluated in the context of modern machine learning.
problem The tradeoff between model complexity and accuracy in machine learning.
method Modern perspective on Breiman's arguments using current computational capabilities.
result Algorithmic models can be accurate without being complex, nullifying the Occam Dilemma.
Examines algorithmic modeling across three cultures.
problem Tackles algorithmic modeling in different cultural contexts.
method Uses parametric regressions, interpretable algorithms, and complex algorithms.
result Extension of Leo Breiman's thesis to include cultural differences.
Formula for τ-invariant of satellite knots derived from L-space satellite operators.
problem Calculating the τ-invariant of satellite knots using L-space satellite operators.
method Algorithm to compute knot Floer complexes and formula for τ-invariant.
result Formula recovers existing formulas and proves new properties of τ-invariant.
In this paper, we construct two families of satellite constructions for Brunnian links, called the satellite sum and the satellite tie. An interesting fact is that by applying the satellite sum and the satellite tie constructions, we can build infinitely many new Brunnian links from any given Brunnian links. With the h…
Satellite knots can be trivialized by a single band move.
problem Satellite knots and their trivialization.
method Infinite family of satellite knots and a single band move.
result No disjoint band unknotting exists for satellite knots.
Satellite links of fully positive braids are characterized.
problem Characterizing satellite links of fully positive braids.
method Analyzing fully positive braids and their satellites.
result Satellite links of fully positive braids are characterized by specific conditions.
Any knot in a solid torus, called a pattern or satellite operator, acts on knots in the 3-sphere via the satellite construction. We introduce a generalization of satellite operators which form a group (unlike traditional satellite operators), modulo a generalization of concordance. This group has an action on the set o…
Satellite links with many twists have simpler companions.
problem Relationship between satellite and companion links' complexity.
method Constructing satellite links with multiple full twists and analyzing their companion links.
result Satellite links with many twists have simpler companion links.
Develops a new framework for integrating satellite allocations in small portfolios.
problem Feasibility constraints in small portfolios, not return predictability, are the primary concerns.
method A four-layer feasibility framework: physical, economic, structural, and epistemic.
result Closed-form feasibility bounds on satellite size, turnover, and breadth without return forecasts.
New proof for minimizing tunnel systems in satellite chain links.
problem Minimizing the tunnel number of satellite chain links.
method Proving the tunnel number is minimized for links with a specific number of components and bridge number.
result The result is sharp for satellite chain links over a 2-bridge knot.
The Gluck twist preserves the diffeomorphism type of certain satellite 2-knots.
problem Preserving the diffeomorphism type of satellite 2-knots under the Gluck twist.
method Using new descriptions of satellite 2-knots, the paper shows that the Gluck twist does not change the diffeomorphism type of certain satellite 2-knots in three ways.
result The Gluck twist preserves the diffeomorphism type of certain satellite 2-knots.
Researchers compute Khovanov polynomials for satellite knots.
problem Computing Khovanov polynomials for satellite knots.
method Explicit computation using a computer program for two families of satellite knots.
result Khovanov polynomials can be expressed as a linear combination of pattern and companion invariants, with a jump at a critical point.
New satellite knots counter a conjecture about Lorenz knots.
problem A conjecture about satellite knots and Lorenz knots was disproven.
method Constructed infinitely many counterexamples of satellite knots that are not cables.
result The conjecture was amended and shown to hold for many Lorenz knots.
Formula for satellite operators using knot Floer homology.
problem Computing knot Floer homology for satellite knots.
method Using Heegaard Floer Dehn surgery formulas and formal knot Floer complexes.
result Formulas to compute knot Floer homology for satellite knots.
We give sufficient conditions for a satellite knot to admit an L-space surgery, and use this result to give new infinite families of patterns which produce satellite L-space knots.
Satellite formula connects knot concordance invariants to surgery.
problem Understanding knot concordance invariants.
method Excision theorem for real Floer homotopy types.
result Concordance invariants depend only on zero-framed surgery.
Necessary and sufficient conditions are given for a satellite knot to be fibered. Any knot k~ embeds in an unknotted solid torus V~ with arbitrary winding number in such a way that no satellite knot with pattern (V~,k~) is fibered. In particular, there exist nonfibered satellite knots wit…
The study computes invariants of satellite knots using bordered Floer homology.
problem Computing invariants of satellite knots with specific patterns.
method Using bordered Floer homology and the immersed curve interpretation of the bordered pairing theorem.
result Satellites with thin fibered companions or specific patterns have thin knot Floer homology.
A simplified proof for satellite knot signatures.
problem Proving Litherland's formula for satellite knots.
method Uses linear algebra and basic knot theory.
result A new, elementary proof of the signature formula.
Unsupervised method removes satellite noise without paired data.
problem Image artifacts from satellite sensor noises affect quality and applications.
method Wavelet subband cycleGAN using adversarial and cycle-consistency losses.
result Effectively removes satellite noise while preserving high frequency features.
We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use SO(3) gauge theory to provide a general criterion sufficient for the image of a satellite operation to generate an infinite rank s…
Satellite operations with winding number ≠ 1 are not homomorphisms.
problem Characterizing homomorphisms in satellite operations.
method Using d-invariants of branched covers and Torelli group properties. result Satellite operations with winding number ≠ 1 are not homomorphisms.
Satellite knots have a higher trunk number than their base knots.
problem Understanding the relationship between satellite knots and their base knots.
method Using the Thurston norm and properties of satellite patterns.
result The trunk number of satellite knots is strictly greater than the product of the Thurston norm and the trunk number of their base knots.
Study satellite operations on knot invariant θ, proving additivity and distinguishing knots.
problem Behavior of knot invariant θ under satellite operations.
method Proved additivity, introduced computational tool, verified conjecture for 2977 knots.
result Distinguished knots using invariant θ and verified conjecture for 2977 primes.
The paper analyzes optimal overbetting strategies for a satellite investment account.
problem Optimal control of leverage in a satellite investment account with limited leverage.
method Recursive overbetting strategy to maximize growth rate, solved via HJB equation.
result Optimal overbetting strategy balances growth rate of satellite and composite bankroll.
New findings on cosmetic surgeries for satellite knots.
problem Cosmetic surgeries on knots and their properties.
method Analyzing satellite knots and their hyperbolic structures.
result Existence of hyperbolic satellite knots with cosmetic surgeries.
Mutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general their m-string satellites can have different Homfly polynomials for m>2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the…
Study satellite knots using bordered Floer theory, proving non-thinness and calculating genus.
problem Properties of twisted Mazur pattern satellite knots.
method Use bordered Floer theory to analyze knots and calculate genus.
result Prove non-thinness of Qn(K) and calculate 3-genus in terms of n and K. New links identified with Alexander polynomial signs to detect satellite links.
problem Detecting satellite links using Alexander polynomial coefficients.
method Introduced a set of links including positive braids and arborescent Hopf plumbings. Showed links in this set have opposite signs for leading and second coefficients of Alexander polynomials.
result Certain satellite links, like (n,1)-cables, are not in the set of links with opposite sign coefficients.
New invariants help study satellite knots and their concordance.
problem Understanding the concordance of satellite knots.
method Filtered instanton homology and classical knot theory techniques.
result Criteria for satellite knots to be linearly independent.
Satellite imagery improves house price prediction models.
problem Improving accuracy of housing price estimation models.
method Transfer learning from ImageNet-pretrained Inception-v3 model to satellite images.
result Achieved a 10% improvement in R-squared score.
We investigate the ramifications of the Legendrian satellite construction on the relation of Lagrangian cobordism between Legendrian knots. Under a simple hypothesis, we construct a Lagrangian concordance between two Legendrian satellites by stacking up a sequence of elementary cobordisms. This construction narrows the…
Satellite images improve real-estate price predictions.
problem Improving accuracy of real-estate price predictions.
method Used convolutional neural networks (CNN) to incorporate satellite image data.
result CNN model trained on satellite images and structured data performs 7% better in MAE.
The virtual genus of a virtual satellite link is equal to that of its companion.
In the paper we prove the conjecture by Alexander Zupan that w(K)⩾n2w(J) where w denote the width and K and J are satellite knot and its companion with winding number n. Also we proved that for satellite knot with braid pattern, the equality holds.
Thin position for knots in the 3-sphere was introduced by Gabai and has been used in a variety of contexts. We conjecture an analogue to a theorem of Schubert and Schultens concerning the bridge number of satellite knots. For a satellite knot K, we use the companion torus T to provide a lower bound for w(K), proving th…
A new clustering algorithm tracks satellite hotspot data for bushfire tracking.
problem Tracking bushfires using satellite data.
method Spatiotemporal clustering algorithm with adjustable parameters.
result The algorithm effectively clusters satellite hotspot data for tracking bushfires.
New satellite knots found that can't be represented by positive braids with full twists.
problem Satellite knots that cannot be represented by positive braids with full twists.
method Analyzing positive minimal braids and their closures to find satellite knots.
result Infinitely many satellite knots with Lorenz patterns and companions are not Lorenz knots.
Formulae for Rasmussen invariant of satellite knots with wrapping number 2 proved.
problem Proving formulae for Rasmussen invariant of satellite knots.
method Using multicurve technology for Khovanov and Bar-Natan homology, a new concordance homomorphism.
result Formulae for F2-Rasmussen invariant of satellite knots with wrapping number 2 proved. Knot Floer homology is an invariant for knots in the three-sphere for which the Euler characteristic is the Alexander-Conway polynomial of the knot. The aim of this paper is to study this homology for a class of satellite knots, so as to see how a certain relation between the Alexander-Conway polynomials of the satelli…
Most of the 50-year history of the study of the set of knot concordance classes, C, has focused on its structure as an abelian group. Here we take a different approach, namely we study C as a metric space admitting many natural geometric operators, especially satellite operators. We consider several knot concordance sp…
We show that the crossing number of a satellite knot is at least 10^{-13} times the crossing number of its companion knot.