The bipolar filtration introduced by T. Cochran, S. Harvey, and P. Horn is a framework for the study of smooth concordance of topologically slice knots and links. It is known that there are topologically slice 1-bipolar knots which are not 2-bipolar. For knots, this is the highest known level at which the filtration do…
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48 results for “bipolar”
Flatness of manifolds with open flat subsets proven using bipolar comparisons.
problem Conditions for flatness in Riemannian manifolds.
method Using (3,3)-bipolar comparisons and open flat subsets.
result Flatness of manifolds proven under specific conditions.
Let T denote the group of smooth concordance classes of topologically sice knots. We show that the first quotient in the bipolar filtration of T (i.e. 0-bipolar knots modulo 1-bipolar knots) has infinite rank, even modulo Alexander polynomial one knots. Any 0-bipolar knot has vanishing tau-, epsilon-, and s-invariants.…
Paper generalizes bipolar theorems for non-negative random variables.
problem Problems with existing bipolar theorems under stronger assumptions.
method Generalizes existing theorems in a robust probabilistic framework.
result Provides necessary and sufficient conditions for bipolar representation.
Study shows infinite rank in bipolar filtration of topologically slice knots.
problem Understanding deeper structures in the smooth concordance group of topologically slice knots.
method Used higher order amenable Cheeger-Gromov -invariants and infinitely many Heegaard Floer correction term -invariants.
result Graded quotient of bipolar filtration has infinite rank at each stage greater than one.
Topology classifies bipolar surfaces; they are not embedded.
problem Classifying bipolar surfaces in the 5-sphere.
method Topological classification and area bounds calculation.
result Bipolar surfaces are not embedded.
Proposes bipolar activation functions to shift layer mean activations towards zero.
problem Training deep neural networks with high layer mean activations.
method Extends ReLU-family activation functions to shift mean activations towards zero.
result Improves language modeling and classification tasks with competitive results.
The paper bounds the Morse index and nullity of bipolar surfaces related to Otsuki tori.
problem Bounding the Morse index and nullity of bipolar surfaces.
method Lawson's bipolar surface construction applied to Otsuki tori.
result Upper and lower bounds on the Morse index and nullity for close to .
A signature-based machine learning model for bipolar disorder and borderline personality disorderstat.ML
Machine learning identifies distinctive mood patterns in bipolar and borderline personality disorders.
problem Challenges in diagnosing bipolar and borderline personality disorders using retrospective mood recall.
method Signature-based machine learning model using daily mood ratings from smartphone apps.
result The model effectively separates participants into three groups with high accuracy.
Extends RCNNs to handle hypercomplex-valued data.
problem Processing high-dimensional data.
method Develops mathematical background and conditions for hypercomplex-valued RCNNs.
result Hypercomplex-valued RCNNs can always settle at an equilibrium.
Detecting early signs of mood episodes in bipolar disorder patients.
problem Early identification of mood episodes in bipolar disorder patients for timely treatment.
method Signature-based model derived from stochastic analysis applied to real-time mood data.
result The signature method can identify the onset of mood episodes in bipolar disorder patients.
The i-th eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of fixed area. Extremal points of these functionals correspond to surfaces admitting minimal isometric immersions into spheres. Recently, critical metrics for the first eigenvalue were classified on tori a…
New knots with specific properties have larger 4-genus than previously known bounds.
problem Finding knots with large 4-genus values.
method Constructing 2-solvable and 2-bipolar knots using specific representations and signatures.
result Knots have 4-genus greater than any given integer g.
Novel ramp loss method improves weakly supervised machine translation and parsing.
problem Training neural models without gold labels in weak supervision scenarios.
method Adapted ramp loss objectives to promote positive outputs and discourage negative ones.
result Bipolar ramp loss objectives outperform other methods on weakly supervised tasks.
Recently Penskoi [J. Geom. Anal. 25 (2015), 2645-2666, arXiv:1308.1628] generalized the well known two-parametric family of Lawson tau-surfaces minimally immersed in spheres to a three-parametric family of tori and Klein bottles minimally immersed in spheres. It was remarked that this family inclu…
Established a Hardy inequality on Finsler manifolds.
problem Hardy inequality on Finsler manifolds.
method Used geometric properties of Finsler structures to prove the inequality.
result Depends on reversibility constant and uniformity constant of Finsler structure.
Study uses interviews to automatically detect BD and BPD with good accuracy.
problem Challenges in distinguishing BD and BPD from clinical interviews.
method Developed a multi-modal dataset and used a linear classifier with selected features from interviews.
result Different sets of features characterize BD and BPD, providing insights into their differences.
The study shows a new way to prove a fundamental group property.
problem Proving a specific property of a group of knots.
method Employing a collection of knots to demonstrate a fundamental group property.
result Proves a new fundamental group property.
This study uses smartphone data to predict when mood interventions are needed for bipolar disorder.
problem Chronic mental illness with extreme mood changes that lead to personal or social consequences.
method Anomaly detection framework using Temporal Normalization to predict mood anomalies from natural speech data.
result A framework for real-world speech-focused mood monitoring using deep learning.
Autoencoders identify brain networks linked to stress and genotype.
problem Designing effective brain stimulation protocols for mental illnesses.
method Supervised autoencoders to model multi-region brain activity.
result Autoencoders reveal a stress-related brain network associated with a bipolar disorder genotype.
We show that Lawson's bipolar surface is after stereographic projection the unique minimizer among immersed Klein bottles in its conformal class. We conjecture that it actually is the unique minimizer among immersed Klein bottles into , , whose existence the authors and P. Breunin…
The -th eigenvalue of the Laplace-Beltrami operator on a surface can be considered as a functional on the space of all Riemannian metrics of unit volume on this surface. Surprisingly only few examples of extremal metrics for these functionals are known. In the present paper a new countable family of extremal m…
Bipolar comparisonmath.DG
Defines a new metric comparison related to optimal transport.
problem Metric comparison on Riemannian manifolds.
method Connections to continuity of optimal transport and MTW condition.
result Strong connections to optimal transport and MTW condition.
We define two transforms between minimal surfaces with non-circular ellipse of curvature in the 5-sphere, and show how this enables us to construct, from one such surface, a sequence of such surfaces. We also use the transforms to show how to associate to such a surface a corresponding ruled minimal Lagrangian submanif…
STNMF method uncovers neural circuit components in retinal ganglion cells.
problem Deciphering complex neuronal circuit components in the brain.
method Spike-triggered non-negative matrix factorization (STNMF) method.
result STNMF can detect various properties of upstream bipolar cells and recover synaptic connection strengths.
M2E embeds multi-view multi-graph brain networks for better clustering.
problem Clustering brain networks from multiple views to understand disease mechanisms.
method Stack multi-graphs into tensors, use tensor techniques to leverage multi-view and multi-graph interactions.
result M2E outperforms existing methods on clustering brain networks.
Deep model diagnoses psychiatric disorders from fMRI data.
problem Diagnosing psychiatric disorders from brain imaging data.
method Deep neural generative model using Bayes' rule.
result Improved diagnostic accuracy over competitive models.
Towards automated symptoms assessment in mental healthphysics.med-ph
Research uses activity analysis to identify mental health symptoms.
problem Identifying mental health symptoms using objective activity metrics.
method Proposes a framework for mHealth monitoring of psychiatric patients based on physical activity time series.
result Identifies distinct behavioural phenotypes and measures for mood assessment.
The paper shows infinite rank in T_1/T_2 and new insights into Alexander polynomials and concordance.
problem Understanding the structure of topologically slice knots and their concordance.
method Analyzing surgery manifolds of satellite links and using Ozsváth-Szabó d-invariants.
result There exist infinitely many knots with specific Alexander polynomials that are not concordant to any knot with coprime Alexander polynomial.
The classification procedure of streaming data usually requires various ad hoc methods or particular heuristic models. We explore a novel non-parametric and systematic approach to analysis of heterogeneous sequential data. We demonstrate an application of this method to classification of the delays in responding to the…
The goal of this paper is to classify parametrically parabolic submanifolds in any codimension. First, we describe the ones that are ruled and show that they are the only parabolic submanifolds that admit an isometric immersion as a hypersurface. Then, we classify the nonruled ones by two different means. In fact, we p…
New method estimates composite outcomes for precision medicine.
problem Balancing multiple outcomes in precision medicine.
method Optimal treatment rule for composite outcomes.
result Estimates composite outcomes and optimal treatment rule.
An optimal control problem associated with the dynamics of the orientation of a bipolar molecule in the plane can be understood by means of tools in differential geometry. For first time in the literature -symplectic formalism is used to provide the optimal control problems associated to some families of partial dif…
Paper develops duality theory for robust utility maximization in continuous time.
problem Maximizing utility in the presence of uncertainty.
method Introduces a duality theory for continuous-time robust utility maximization problems.
result Shows duality between robust utility maximization and a conjugate problem under certain conditions.
Investigates the effects of nondominated sets of probability measures in robust models of finance.
problem Uncertainty in financial models due to multiple possible probability measures.
method Analyzes various results from mathematical finance literature under the assumption of nondominated sets of probability measures.
result Many classical results in robust models do not hold when the set of measures is nondominated.
Study confirms conjectures for topologically slice knots' concordance group.
problem Primary decomposition conjectures for knot concordance groups.
method Use of amenable -signatures, Ozsváth-Szabó -invariants, and Némethi's Heegaard Floer homology results.
result Smooth concordance group of topologically slice knots has large subgroup with true primary decomposition.
Explains conformal maps and holomorphic structures for surfaces in higher-dimensional Euclidean spaces.
problem Explains conformal maps and holomorphic structures for surfaces in higher-dimensional Euclidean spaces.
method Uses Clifford algebra and spin transforms to explain conformal maps and holomorphic structures.
result Calculates the degree of the spinor bundle associated with a conformal immersion and defines analogues of polar and bipolar surfaces.
The first eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of a given area. Critical points of this functional are called extremal metrics. The only known extremal metrics are a round sphere, a standard projective plane, a Clifford torus and an equilateral torus.…
Holographic Invariant Storage: Design-Time Safety Contracts via Vector Symbolic Architecturesstat.ML
Holographic Invariant Storage uses vector architectures to ensure LLM safety at design time.
problem Mitigating context drift in large language models (LLMs) during deployment.
method Introduces Holographic Invariant Storage (HIS) protocol that combines known properties of bipolar Vector Symbolic Architectures into a design-time safety contract.
result Closed-form guarantees for single-signal recovery fidelity, continuous-noise robustness, and multi-signal capacity degradation are provided and validated.
The paper examines how the first Steklov-Dirichlet eigenvalue changes with the distance between two concentric circles.
problem Investigating the monotonicity of the first Steklov-Dirichlet eigenvalue on eccentric annuli.
method The approach involves showing differentiability, deriving integral expressions for the derivative, and using variational formulations to find upper and lower bounds.
result The paper proves the monotonicity of the first Steklov-Dirichlet eigenvalue on eccentric annuli with respect to the distance between the centers of the inner and outer boundaries.
Deep learning predicts mental disorders from audio and text samples.
problem Predicting mental disorders from speech samples.
method Multimodal deep learning structure using various pre-trained models for audio and text embeddings, transfer learning, and auxiliary corpora.
result Acceptable accuracy in predicting mental disorders through multimodal analysis.
A global agreement on how to reduce and cap human footprint, especially their GHG emissions, is very unlikely in near future. At the same time, bilateral agreements would be inefficient because of their neural and balanced nature. Therefore, unilateral actions would have attracted attention as a practical option. Howev…
Deep learning detects sleep state fluctuations in neonates from single EEG channel.
problem Monitoring sleep state fluctuations in neonatal intensive care units.
method Deep learning-based algorithm trained on 53 EEG recordings, validated on 30 polysomnography recordings.
result High accuracy (90%) in detecting quiet sleep states from single EEG channel, generalizing well to external dataset.
We present a quantitative characterisation of the fluctuations of the annualized growth rate of the real US GDP per capita growth at many scales, using a wavelet transform analysis of two data sets, quarterly data from 1947 to 2015 and annual data from 1800 to 2010. Our main finding is that the distribution of GDP grow…
Improved 3D MRI classification using contrastive learning with continuous proxy metadata.
problem Insufficient labelled data for 3D medical image classification.
method Proposed a new loss function (y-Aware InfoNCE) to leverage continuous proxy metadata in contrastive learning.
result 3D CNN model pre-trained on 10^4 multi-site healthy brain MRI scans outperforms fully-supervised methods.
New knots show cable sets are linearly independent in knot concordance.
problem Understanding linear independence in knot concordance group.
method Produced infinite families of knots and their cables.
result Cable sets of knots are linearly independent in knot concordance group.
New algorithm balances personalization and statistical validity in MRTs.
problem Optimizing decisions in nonstationary settings with habituation and recovery.
method ROGUE-TS Thompson Sampling with probability clipping.
result Achieves lower regret and maintains high statistical power.
The paper finds the optimal wealth growth rate in betting games.
problem Optimizing wealth growth in Kelly betting games against arbitrary hypotheses.
method Analyzes the growth rate using KL divergence and proves it equals a specific limit.
result The optimal wealth growth rate is characterized and proven to be achievable.