Study phase transitions with prescribed mean curvature in Riemannian manifolds.
problem Understanding phase transitions with prescribed mean curvature in geometric settings.
method Analyzing solutions to inhomogeneous semilinear elliptic PDEs, establishing bounds and asymptotics.
result Established upper and lower bounds for eigenvalues of phase transition problems.
The Allen-Cahn system on manifolds yields multiple phase distributions.
problem Finding the number of solutions to the Allen-Cahn system on manifolds.
method Volume-fixing variations approach to classify isoperimetric clusters.
result The number of solutions is bounded by topological invariants for parallelizable manifolds.
Study on stable partitions in convex domains with three phases, finding disconnected phase stability.
problem Stability of partitions in convex domains with multiple phases.
method Careful derivation of the second variation of area, proving existence of stable partitions involving disconnected phases.
result Existence of stable partitions involving a disconnected phase in three phase problem.
We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie, Nardone, Scardovelli, …
Paper tackles joint community detection and phase synchronization in stochastic block models.
problem Jointly recover cluster structure and phase angles in stochastic block models.
method Proposes two algorithms: a spectral method based on multi-frequency QR factorization and an iterative multi-frequency generalized power method.
result Proposed algorithms significantly improve recovery of cluster structure and phase angles compared to existing methods.
Convolutional neural networks learn phase-dependent frequency representations.
problem Capturing phase dependence in frequency representations for better signal analysis.
method Convolutional neural networks learn filters with different phases, which rectify to phase-dependent descriptors.
result Phase harmonics correlations can compressively represent signals with sparse wavelet coefficients.
For simple Lie groups, the only homogeneous manifolds G/K, where K is maximal compact subgroup,for which the phase of the scalar product of two coherent state vectors is twice the symplectic area of a geodesic triangle are the hermitian symmetric spaces. An explicit calculation of the multiplicative factor on the c…
A novel method detects multiple mitosis events and mitigates annotation gaps in phase-contrast microscopy.
problem Detecting multiple mitosis events and handling annotation gaps in closely placed cells.
method Estimating a spatiotemporal likelihood map via 3DCNN to detect multiple mitosis events and mitigate annotation gaps.
result Our method outperformed compared methods in terms of F1-score using a challenging dataset.
We propose a generic model for multiple choice situations in the presence of herding and compare it with recent empirical results from a Web-based music market experiment. The model predicts a phase transition between a weak imitation phase and a strong imitation, `fashion' phase, where choices are driven by peer press…
PHASE dataset simulates complex social interactions in physical environments.
problem Lack of datasets for evaluating physically grounded perception of complex social interactions.
method Created PHASE dataset of 2D animations with procedural generation and physics engine.
result SIMPLE model outperforms neural networks in recognizing complex social interactions.
Solves a challenging problem in imaging and communication.
problem Simultaneous source separation and phase retrieval.
method Uses deep generative models to constrain the search space.
result Demonstrates solving a highly under-determined, non-convex problem.
New method for incremental meta-learning reduces forgetting and improves performance.
problem Incremental meta-learning for few-shot classification tasks.
method Indirect Discriminant Alignment (IDA) with incremental updates.
result Incremental learning reduces forgetting and improves performance.
New framework uses deep generative priors for robust phase retrieval.
problem Highly ill-posed and non-linear phase retrieval problem.
method Regularization through deep generative priors with gradient descent.
result Effective for random Gaussian and Fourier friendly measurements.
Study on detecting hierarchical community structures in networks.
problem Detecting hierarchical community structures in networks.
method Analysis of planted hierarchies of partitions in networks, identifying additional detectability phases.
result There are additional phases in which the presence of multiple consistent partitions can either help or hinder detection of hierarchical structures.
Improved neural networks by averaging late-stage weights.
problem Improving the performance of neural networks.
method Ensemble late-stage weights and average them.
result Augmenting standard models with late-phase weights improves generalization.
This work improves interpretability and calibration of complex-valued neural networks using Newton-Puiseux analysis.
problem Insufficient interpretability and probability calibration of complex-valued neural networks.
method Newton-Puiseux framework to examine local decision geometry, fitting a polynomial surrogate and factorizing it using Newton-Puiseux expansions.
result Enhanced Expected Calibration Error in ECG and wireless modulation datasets compared to uncalibrated softmax and standard post-hoc baselines.
Torus graphs analyze multivariate phase coupling among brain signals.
problem Identifying coordinated phase changes across multiple brain regions.
method Torus graphs based on full exponential family with pairwise interactions.
result Torus graphs accurately identify conditional associations in multivariate phase data.
The paper studies phase transitions in Information Bottleneck for representation learning.
problem Understanding the behavior of compression and prediction terms in IB objective.
method Studied phase transitions in IB objective using second-order calculus of variations and Fisher information matrix.
result IB phase transitions correspond to learning new classes and are related to maximum correlation between input and target orthogonal to the learned representation.
Moon phases added to stock market analysis for better pattern recognition.
problem Finding meaningful patterns in stock market data using irregular time sampling.
method Incorporating Moon phases into the Gregorian calendar time sampling methods for stock market analysis.
result Moon phases provide unique, irregular sampling features for stock market pattern recognition.
PhaseDNN speeds up learning of high-dimensional functions across wide frequencies.
problem Training high-dimensional functions at wide frequencies is slow and inefficient.
method Parallel DNNs with frequency-specific training and phase shifts.
result PhaseDNN achieves uniform learning across wide frequencies.
Paper introduces REED for noncoherent OTA-FL, reducing latency without phase alignment.
problem Noncoherent OTA-FL requires signed model updates without phase alignment.
method Introduces REED for continuous signed aggregation using resource-element energy difference.
result Exact variance laws for REED and chip-diverse extension in Rayleigh fading.
In his seminal paper, A. N. Varchenko precisely investigates the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase. He expresses the order of this term by means of the geometry of the Newton polyhedron of the phase. The purpose of this paper is to generalize and improve his re…
PH-VAE models heavy-tailed data with flexible Phase-Type distributions.
problem Standard VAEs fail to capture heavy-tailed behavior in real-world data.
method PH-VAE uses Phase-Type distributions defined by continuous-time Markov chains to adaptively model tail behavior.
result PH-VAE significantly outperforms existing heavy-tail-aware VAEs in approximating diverse heavy-tailed distributions.
The paper proposes a thermodynamic potential to guide training of generative models, breaking ergodicity to improve functionality.
problem Improving generative model functionality while limiting access to underrepresented patterns.
method Constructing a thermodynamic potential that guides training, leading to multiple minima in the free energy.
result Training a generative model breaks ergodicity, preventing escape into the high-temperature phase.
Improved statistical inference for expensive data using machine learning predictions.
problem Statistical inference under adaptive two-phase multiwave sampling with expensive measurements.
method Multiwave Predict-Then-Debias estimator combining proxy information and expensive measurements.
result Valid estimators and confidence intervals for M-estimation under adaptive sampling.
Proposes a new framework for evaluating diagnostic models with multiple co-primary endpoints.
problem Overoptimistic assessments of predictive performance in automated medical testing devices.
method Multiple testing framework for diagnostic accuracy studies with co-primary endpoints, using a parametric simultaneous test procedure and Bayesian approach to determine optimal number of models.
result Our approach leads to a better final diagnostic model and increased statistical power.
Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
A new approach uses circuit topology to study complex polymer interactions.
problem Understanding structural phase transitions in entangled polymer systems.
method Braided circuit topology framework for multiple-chain systems.
result Circuit topological motif fractions are effective order parameters for structural transitions.
SpecGD mitigates misalignment in phase retrieval models with anisotropic inputs.
problem Misalignment during gradient descent in phase retrieval models with anisotropic inputs.
method Spectral gradient descent modifies gradient updates to preserve directional information and remove spike amplification.
result SpecGD removes spike amplification, leading to stable alignment and accelerated noise contraction.
Study on phase transitions on surfaces using Allen-Cahn equation.
problem Existence of critical points with specific nodal sets on surfaces.
method Analysis of Allen-Cahn functional on compact surfaces, focusing on nodal sets and energy.
result Existence of countable families of critical points with nodal sets converging to geodesics.
Gradient descent with random initialization solves phase retrieval problems efficiently.
problem Solving systems of quadratic equations for phase retrieval.
method Gradient descent with random initialization for nonconvex least squares problem.
result Gradient descent achieves near-optimal computational and sample complexities for phase retrieval.
We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence t…
Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its propert…
New dropout technique reduces training time by 20-77%.
problem Efficient training of deep neural networks consumes excessive time and energy.
method Approximate Random Dropout replaces random neuron/synapse dropout with regular patterns to reduce computation and data access.
result Reduces training time by 20-77% with minimal accuracy loss.
We recover phase from intensity measurements using optics-based random projections.
problem Recovering phase from intensity measurements with unknown transmission matrix.
method Our method leverages conjugation of rows in the unknown matrix and interference with reference signals to cast the problem as a Euclidean distance geometry.
result We accurately recover the missing phase and mitigate quantization and sensitivity effects.
This paper studies MMV problem and its performance, proving a decoupling property for MMV algorithms.
problem Joint estimation of multiple signal realizations with common sparse support.
method Proved a decoupling property for ℓ2,1-LS algorithm, decomposing it into coupled and decoupled phases. result Performance of ℓ2,1-LS and MMV algorithms are affected by signal correlations and dictionary mismatch. Two-stage risk control for ranked retrieval systems.
problem Assessing prediction uncertainty and risk control in sequential machine learning systems.
method Developed two-stage risk control methods based on LTT and CRC frameworks, leveraging sequential nature of retrieval and ranking phases.
result The proposed methods provide theoretical guarantees and reduce computational burden compared to prior work.
Indoor localization based on SIngle Of Fingerprint (SIOF) is rather susceptible to the changing environment, multipath, and non-line-of-sight (NLOS) propagation. Building SIOF is also a very time-consuming process. Recently, we first proposed a GrOup Of Fingerprints (GOOF) to improve the localization accuracy and reduc…
WSD schedule improves model training efficiency by adapting learning rates dynamically.
problem Fixed compute budgets limit training efficiency of language models.
method Introduces a WSD schedule that uses a constant learning rate followed by a rapid decay phase.
result WSD schedule generates a non-traditional loss curve with stable and decay phases.
Framework predicts remaining useful life of DSH subsystems under unknown failure modes.
problem Predicting remaining useful life of DSH subsystems with unknown failure modes.
method Unsupervised framework using mixture of Gaussian regressions and Expectation-Maximization algorithm.
result Improved prediction accuracy and interpretability of RUL.
Solves complex clustering and rotation synchronization problem.
problem Challenges in classifying and synchronizing rotated objects into multiple categories.
method Semidefinite programming relaxations to solve the joint problem of community detection and synchronization.
result Exact recovery of community detection and synchronization when extending stochastic block model.
Symmetry in inverse problems leads to multiple solutions, but breaking symmetry helps deep learning.
problem Symmetry in physical systems causes multiple solutions in inverse problems, hindering deep learning.
method Careful symmetry breaking on training data helps solve inverse problems and improve deep learning performance.
result Symmetry breaking on training data significantly improves deep learning performance in inverse problems.
Study energy functional's second variation on manifolds, proving Morse index bounds.
problem Understanding the stability and index of phase transition interfaces.
method Extending gradient theory to minimal hypersurfaces, proving upper semicontinuity of stability operator eigenvalues.
result Upper bounds for the Morse index of limit interfaces without multiplicity or orientability conditions.
New AMP algorithms reveal phase transitions in tensor recovery.
problem Understanding algorithmic behavior of low-rank tensor decompositions.
method Derive Bayesian AMP algorithms and use dynamic mean field theory.
result Reveals phase transitions between easy, hard, and impossible inference regimes.
Method identifies unknown intervention targets in structural causal models from diverse data.
problem Identifying unknown intervention targets in structural causal models from heterogeneous data.
method Two-phase approach: first recovers exogenous noises, second matches with endogenous variables.
result Proposed method uniquely identifies intervention targets under causal sufficiency assumption.
Improved heteroscedastic regression with machine learning techniques.
problem Estimating weights in heteroscedastic linear regression with varying noise.
method Alternating minimization with weighted least squares and pseudogradient descent.
result Achieved a tighter error bound for estimating weights.
Early SGD hyperparameters affect deep neural network training, showing a break-even point.
problem Understanding how early SGD hyperparameters influence deep neural network training.
method Analysis of stochastic gradient descent (SGD) hyperparameters and their effects on the optimization trajectory.
result A break-even point exists where SGD implicitly regularizes the loss surface and improves gradient conditioning.
We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques à la De Dominicis. The control parameters in this model are the ratio α=p/N of the number p o…