Introduces 'social bow tie' to quantify tie strength in social networks.
problem Understanding tie strength and its influencing factors in social networks.
method Introduced 'social bow tie' framework, defined metrics, used random forests and regression models.
result Bow tie metrics are highly predictive of tie strength, and tie strength is influenced by overlapping and non-overlapping social circles.
Classifies 85 tie knots into mathematical categories.
problem Classifying and understanding the mathematical properties of tie knots.
method Formal language and sequence of moves to describe tie knots, classification based on knot theory.
result Proves that any tie knot is prime and alternating.
The study identifies relationship lending in interbank markets using statistical tests.
problem Lack of consensus on measuring relationship strength in lending between banks.
method Statistical tests to identify relationship lending as significant ties between banks.
result The fraction of relationship lending is stable and lenders impose high interest rates during financial distress.
TIE framework detects out-of-distribution samples and estimates uncertainty without external datasets.
problem Detecting and estimating uncertainty for out-of-distribution samples in neural networks.
method TIE framework extends a classifier to an (n+1)-class model, iteratively refining through training, inversion, and exclusion.
result Unified and interpretable framework for robust anomaly detection and calibrated uncertainty estimation.
Researchers create coordinates for hyperbolic surfaces, proving a magic formula.
problem Constructing coordinates for hyperbolic structures on genus-2 surfaces.
method Developed Fenchel-Nielsen coordinates and Wolpert's magic formula analogues.
result Found Darboux charts for the Goldman symplectic form on branched hyperbolic structures.
Hashing, or learning binary embeddings of data, is frequently used in nearest neighbor retrieval. In this paper, we develop learning to rank formulations for hashing, aimed at directly optimizing ranking-based evaluation metrics such as Average Precision (AP) and Normalized Discounted Cumulative Gain (NDCG). We first o…
New satellite constructions create infinite Brunnian links.
problem Creating new Brunnian links from existing ones.
method Satellite sum and satellite tie constructions.
result Every Brunnian link has a unique tree-arrow structure.
This paper gives mathematical models for flat knotted ribbons, and makes specific conjectures for the least length of ribbon (for a given width) needed to tie the trefoil knot and the figure eight knot. The first conjecture states that (for width one) the least length of ribbon needed to tie an open-ended trefoil knot …
Systemic risks of default contagion in the Russian interbank market are investigated. The analysis is based on considering the bow-tie structure of the weighted oriented graph describing the structure of the interbank loans. A probabilistic model of interbank contagion explicitly taking into account the empirical bow-t…
Characterizes Lebesgue points using nearest neighbor methods.
problem Consistency of classification algorithms based on nearest neighbors.
method Characterization of Lebesgue points via 1-Nearest Neighbor regression.
result Proves convergence of 1-Nearest Neighbor classification algorithms in metric spaces.
In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. The presence of ties in the agents' best-response correspondences yields discontinuous payoff functi…
Modelling of contagion in interbank networks is discussed. A model taking into account bow-tie structure and dissasortativity of interbank networks is developed. The model is shown to provide a good quantitative description of the Russian interbank market. Detailed arguments favoring the non-percolative nature of conta…
Recovering edge activities from node activity data in temporal networks.
problem Recovering lost edge activity data from aggregated node activity data in temporal networks.
method Analyzing the relationship between edge activity and node activity data, using both theoretical and empirical methods to show recovery is possible and under what conditions.
result Recovery of edge activities from node activities is possible with surprising accuracy, even when network density increases.
Differential Evolution outperforms SMAC in hyperparameter tuning.
problem Automated hyperparameter tuning for machine learning.
method Empirical study comparing Differential Evolution to SMAC.
result Differential Evolution outperforms SMAC on most datasets.
Study higher-order interactions in networks, proposing link prediction as a new benchmark.
problem Understanding higher-order interactions in complex systems.
method Temporal analysis of 19 datasets, focusing on interactions involving more than two nodes.
result Higher-order interactions are consistent across different systems, with tie strength and edge density influencing their presence.
The study examines complex tangles in Curve Shortening Flow singularities.
problem Classifying all knots in R3 is a challenging problem. method Examine solutions to plane Curve Shortening Flow to identify tangles.
result A vanishing n-loop converges to a 'squeezed bow-tie' under rescaling. Study reveals structure of Bitcoin's crypto flow network.
problem Understanding crypto flows among Bitcoin users.
method Blockchain data, user identification, network construction, bow-tie structure, Hodge decomposition, non-negative matrix factorization.
result Users are located in upstream, downstream, and core of the crypto flow network.
Statistical framework improves LLM chatbot ranking.
problem Improving evaluation of LLM-based chatbots through pairwise comparisons.
method Factored tie model, covariance modeling, and parameter constraints.
result Substantial improvements in modeling pairwise comparison data.
Paper explains dynamics of homeomorphisms to mapping tori geometry.
problem Understanding dynamics of end-periodic homeomorphisms.
method Illustration-driven overview of recent results.
result Analogue of Brock's theorem for infinite-type surfaces.
What length of rope (of given diameter) is required to tie a particular knot? To answer this question, we define some new notions of thickness for a space curve, one based on Gromov's distortion, and another generalizing the thickness of Litherland, Simon et al. We prove a basic inequality between these thickness measu…
C-index varies among software, complicating model comparison.
problem Variation in C-index calculations across software.
method Comparison of C-index estimators in R and Python.
result Different implementations yield varying results.
Consistent estimator derived for confounding strength in observational data.
problem Estimating confounding strength in observational data is challenging due to unobserved confounders.
method Derived and adapted a consistent estimator using tools from random matrix theory.
result The original estimator is not consistent, but an adapted one is.
Alternating-sign Hopf plumbing along a tree yields fibered alternating links whose homological monodromy is, up to a sign, conjugate to some alternating-sign Coxeter transformation. Exploiting this tie, we obtain results about the location of zeros of the Alexander polynomial of the fibered link complement implying a s…
The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international …
Bayesian model infers strengths from noisy tennis match outcomes.
problem Ranking tennis players from match outcomes.
method Bayesian approach to infer unobserved strengths and mapping function.
result Bayesian approach robust to different model specifications.
Neural network memorizes external stimuli through synaptic strength changes.
problem Memory and classification in neural networks.
method One-to-one mapping between stimulus and synaptic strength under synaptic plasticity constraints.
result Neural network can memorize external stimuli through synaptic changes.
Novel method uses information theory to measure causal influences during transient neural events.
problem Characterizing network interactions during transient neural events.
method Structural Causal Models, Information Theory, Transfer Entropy, Dynamic Causal Strength, Relative Dynamic Causal Strength.
result Introduced a novel measure, relative Dynamic Causal Strength, with theoretical and empirical support.
Paper shows softmax output misleads in evaluating adversarial example strength.
problem Softmax output misleads in evaluating adversarial example strength.
method Demonstrates how adversarial examples can exploit softmax properties.
result Softmax output is a poor indicator of adversarial example strength.
This paper calculates interaction strength for translation surfaces with multiple singularities.
problem Computing the interaction strength of translation surfaces with multiple singularities is challenging.
method The authors study interaction strength of specific families of translation surfaces, including regular polygons and Bouw-Möller surfaces.
result The paper provides exact computations of KVol on translation surfaces with multiple singularities.
Study shows CNNs can perform well with less data using biological synaptic distributions.
problem Training deep neural networks with limited data.
method Synthesizing CNNs using log-normal or correlated center-surround synaptic strength distributions.
result CNNs with biological synaptic strength distributions can perform well with fewer data samples.
Synaptic pruning reduces CNNs by 96% on CIFAR-10.
problem Memory and computation constraints in CNNs for mobile devices.
method Synaptic Pruning: data-driven method to prune connections based on Synaptic Strength.
result Significant size reduction and computation saving with up to 96% pruning on CIFAR-10.
Study XRP network, propose Flow Index to analyze transaction frequencies.
problem Analyze transaction frequencies in XRP network.
method Analyze XRP transaction history, propose Flow Index.
result Flow Index reveals bow-tie/walnut structure in XRP network.
Adversarial examples are due to non-robust features in data.
problem Understanding the reasons behind adversarial examples in machine learning.
method Developed a theoretical framework to identify non-robust features and demonstrated their widespread existence.
result Adversarial examples are a result of non-robust features in data.
A new method uses randomized trials to estimate the strength of unobserved confounding.
problem Unobserved confounding compromises causal conclusions from non-randomized studies.
method Designs a statistical test to detect unobserved confounding strength and estimates a lower bound.
result Estimates an asymptotically valid lower bound on unobserved confounding strength.
Approximates discounted moments for financial products using polynomial expansions.
problem Approximating discounted moments of stochastic processes for financial applications.
method High-order power series expansion of the infinitesimal generator.
result Error decreases to around 10 to 100 times machine precision for higher orders.
We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are available at regular primes, but we seek more conceptual answers in terms of lo…
The abstract discusses parallels between Galois theory and Stone-Weierstrass theorem in various fields.
problem Connecting distinguishing power and expressive power in different fields.
method Elementary theorem connecting distinguishing power and expressive power.
result Foundational principle in linguistics linking distinguishing power and expressive power.
The paper examines how spike strengths and alignments affect overfitting in linear regression models.
problem The impact of spike strengths and alignments on overfitting in linear regression models.
method Characterization of generalization error through exact expressions and analysis of spike strengths, aspect ratio, and target alignment.
result Increasing spike strength can lead to catastrophic overfitting before benign overfitting, especially in well-specified aligned problems.
In this paper we extend the concept of Competitivity Graph to compare series of rankings with ties ({\em partial rankings}). We extend the usual method used to compute Kendall's coefficient for two partial rankings to the concept of evolutive Kendall's coefficient for a series of partial rankings. The theoretical frame…
We propose an original model for inferring team strengths using a Markov Random Field, which can be used to generate historical estimates of the offensive and defensive strengths of a team over time. This model was designed to be applied to sports such as soccer or hockey, in which contest outcomes take value in a limi…
Study of Milnor invariants and ropelength of spherical links.
problem Understanding the relationship between the thickness of spherical links and their Milnor invariants.
method Generalized Massey products and Milnor invariants to spherical links, finding optimal asymptotic bounds.
result Optimal asymptotic bounds on Milnor invariants in terms of thickness, revealing a polynomial vs exponential regime.
We present a simple model of firm rating evolution. We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. The existence of the collective phase depends…
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge et al. (2012), it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of d…
Develops new tests for high-dimensional models with mixed signal strengths.
problem Challenges in testing models with many signals and high-dimensional data.
method Moment matching formulation for developing new tests.
result Demonstrates optimality of GRIP test for various model types.
Multi-modal data collections, such as corpora of paired images and text snippets, require analysis methods beyond single-view component and topic models. For continuous observations the current dominant approach is based on extensions of canonical correlation analysis, factorizing the variation into components shared b…
In economic and financial networks, the strength of each node has always an important economic meaning, such as the size of supply and demand, import and export, or financial exposure. Constructing null models of networks matching the observed strengths of all nodes is crucial in order to either detect interesting devi…
Introduces P-tensors for generalized higher-order message passing in graph neural networks.
problem Expanding the expressive power of graph neural networks through higher-order structures.
method Introduces P-tensors to define the most general form of permutation equivariant message passing.
result Achieves state-of-the-art performance on molecular datasets.
Fixed angles of convex polygons lead to combinatorially rich polytopes.
problem Understanding the structure of convex polygons with fixed vertex angles.
method Combining combinatorial and geometric approaches, including dual polytopes and Schwarz-Christoffel maps.
result Fixed-angles polytopes are dual to cyclic polytopes under certain conditions.