Machine learning predicts phase behavior in active matter suspensions.
problem Predicting phase behavior in active matter systems using machine learning.
method Used deep learning techniques, including fully connected networks and graph neural networks, to predict motility-induced phase separation (MIPS) in ABP suspensions.
result Strong agreement between machine learning predictions and MIPS binodal from simulations, suggesting machine learning as an effective method for phase behavior determination.
To investigate the detection of students' behavioral engagement (On-Task vs. Off-Task), we propose a two-phase approach in this study. In Phase 1, contextual logs (URLs) are utilized to assess active usage of the content platform. If there is active use, the appearance information is utilized in Phase 2 to infer behavi…
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.
We study the phase transition of dynamical herd behaviors for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution of returns satisfies the power-law behavior with three different values of the scaling exponent 3.11 (one time lag τ = 1 minute), 2.81 (30 minut…
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, a…
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase transition as splitting an underlying manifold into two sub-manifolds with distinct…
Recent years, many researches attempt to open the black box of deep neural networks and propose a various of theories to understand it. Among them, Information Bottleneck (IB) theory claims that there are two distinct phases consisting of fitting phase and compression phase in the course of training. This statement att…
Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent h(q) -- the fundament…
We present an agent behavior based microscopic model that induces jumps, spikes and high volatility phases in the price process of a traded asset. We transfer dynamics of thermally activated jumps of an unexcited/ excited two state system discussed in the context of quantum mechanics to agent socio-economic behavior an…
To date, most studies on spam have focused only on the spamming phase of the spam cycle and have ignored the harvesting phase, which consists of the mass acquisition of email addresses. It has been observed that spammers conceal their identity to a lesser degree in the harvesting phase, so it may be possible to gain ne…
Modeling financial markets with memory using fractional calculus and Brownian motion.
problem Capturing memory effects in financial markets using stochastic models.
method Fractional Langevin equation with colored noise generated by fractional Brownian motion.
result Anomalous marginal glass phase observed in some regions of the system.
Gradient descent dynamics in neural networks show quenching and activation phases.
problem Understanding training dynamics in neural networks.
method Numerical and phenomenological study of gradient descent algorithm for two-layer neural networks.
result Gradient descent dynamics exhibit quenching and activation phases in under-parametrized networks.
Characterizes RFF regression in large n,p,N setting, providing precise learning phases and double descent curve.
problem Characterizes RFF regression in large n,p,N setting. method Characterizes the exact asymptotics of random Fourier feature (RFF) regression in the realistic setting of large n,p,N. result Characterizes two qualitatively different phases of learning and the corresponding double descent test error curve.
A phase plot of the oil economy is built using the literature data of world oil production, price, and EROEI (Energy Returned on Energy Invested). An analogy between the oil economy and the Benard convection is proposed; some methods of interpretation and forecast of the system behavior are also shown based on "phase p…
A set of relations between the modulus and phase is derived for amplitudes of the form $\mels{\hatu(x)}$ where U^(x)∈SU(n) in the fundamental representation and x denotes the coordinates on the group manifold. An illustration is given for the case n=2 as well as a brief discussion of phase singularities …
Study of two-layer ReLU neural network phase diagram at infinite-width limit.
problem Characterize the dynamical regimes of two-layer ReLU neural networks.
method Combining experimental and theoretical approaches, including phase diagram analogy.
result Identification of three regimes: linear, critical, and condensed.
New algorithm solves phase retrieval with adaptive stopping criteria.
problem Robust phase retrieval problem as nonsmooth, nonconvex optimization.
method Inexact proximal linear algorithm with adaptive stopping criteria.
result Proposed methods are more efficient than existing methods.
A novel framework interprets driving patterns using Action phases clustering.
problem Challenges in comprehending driving heterogeneity from underlying behavior mechanisms.
method Resampling and Downsampling Method (RDM) followed by iterative clustering calibration.
result Six driving patterns identified in real-world datasets, revealing dynamic nature of driving.
The paper examines stability of shares in Proof of Stake protocol, identifying different investor behaviors and phase transitions.
problem Stability of shares in Proof of Stake protocol.
method Identification of large, medium, and small investors under various rewarding schemes; dynamical population model analysis.
result Phase transitions and thresholds for stability are characterized; chaotic centralization leads to concentration of shares.
Study rotational surfaces with prescribed Gauss curvature in 3D space.
problem Classify and analyze rotational surfaces with prescribed Gauss curvature.
method Phase plane analysis and mild assumptions on the prescribed function.
result Existence of singular radial solutions intersecting orthogonally the axis of rotation.
Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering. In the first stage a quaternion extended Kalman filter, which provides a unified…
Tyler's M-estimator's phase transition at DS-SNR = 1 is resolved.
problem Robust Subspace Recovery
method Tyler's M-estimator
result TME converges exactly to the true subspace for DS-SNR >= 1 under a new stability condition.
We examine the out-of-equilibrium phase reported by Plerou {\it et. al.} in Nature, {\bf 421}, 130 (2003) using the data of the New York stock market (NYSE) between the years 2001 --2002. We find that the observed two phase phenomenon is an artifact of the definition of the control parameter coupled with the nature of …
In order to model volatile real-world network behavior, we analyze phase-flipping dynamical scale-free network in which nodes and links fail and recover. We investigate how stochasticity in a parameter governing the recovery process affects phase-flipping dynamics, and find the probability that no more than q% of nodes…
This paper demonstrates the use of genetic algorithms for evolving a grandmaster-level evaluation function for a chess program. This is achieved by combining supervised and unsupervised learning. In the supervised learning phase the organisms are evolved to mimic the behavior of human grandmasters, and in the unsupervi…
Study of 17 surface behaviors and singularities for elliptic Weingarten equations.
problem Characterizing and understanding elliptic Weingarten surfaces and their singularities.
method Phase space analysis and classification of surface behaviors.
result Classification of 17 possible qualitative behaviors for rotational surfaces.
Enhances neural network dynamics to boost computational capacity.
problem Improving computational capacity of neural networks.
method Introducing Phase Transition Adaptation to drive system dynamics towards edge of stability.
result Consistently achieves enhancement in computational capacity over multiple datasets.
A new image completion method inspired by brain cells.
problem Image restoration from corrupted data.
method Biologically-inspired sub-Riemannian model with frequency and phase.
result Completion of two-dimensional images using cortical cell responses.
Continuum mechanics theory describes skin's complex anisotropic behavior.
problem Modeling the anisotropic tearing of skin.
method Finsler geometry fiber bundle approach, variational method, phase-field mechanics.
result Analytical solutions capture experimental data on skin tearing.
Descending phase retrieval algorithms show a phase transition with increasing sample complexity.
problem Theoretical limits of descending phase retrieval algorithms.
method Utilizing Random duality theory (RDT), the study develops a generic program to characterize algorithm performance.
result As sample complexity increases, the parametric manifold transitions from multi to single funneling points, leading to a phase transition in algorithm success.
Paper analyzes LPSA algorithm for constrained optimization, revealing phase transitions and bias-variance trade-offs.
problem Optimization problems with linear constraints.
method Loopless projection stochastic approximation (LPSA) with jump diffusion approximation.
result LPSA trajectories converge to SDEs, revealing asymptotic behaviors and phase transitions.
In this paper we study the global behavior of the Ricci flow equation for two classes of homogeneous manifolds with two isotropy summands. Using methods of the qualitative theory of differential equations, we present the global phase portrait of such systems and derive some geometrical consequences on the structure of …
In this paper we present a novel model of the primary visual cortex (V1) based on orientation, frequency and phase selective behavior of the V1 simple cells. We start from the first level mechanisms of visual perception: receptive profiles. The model interprets V1 as a fiber bundle over the 2-dimensional retinal plane …
This paper presents a phase diagram for two-layer neural networks under different initialization scales.
problem Understanding the behavior of neural networks under varying scales of initialization.
method Analysis of a phase diagram for two-layer neural networks.
result Condensation of weight vectors on isolated orientations during training.
We find optimal learning rate schedules for a random feature model.
problem Choosing optimal learning rates for deep learning models.
method We analyze a powerlaw random feature model trained with SGD, considering optimal schedules as numerical and analytical problems.
result We discover two regimes: easy and hard phases, with different optimal learning rate schedules.
Quadratic models explain neural network behavior during training.
problem Understanding neural network dynamics during training with large learning rates.
method Developed and tested Neural Quadratic Models.
result Neural Quadratic Models exhibit the 'catapult phase' similar to neural networks.
The study examines the dynamic behavior of RMSprop and Adam algorithms.
problem Understanding the training loss curve patterns of adaptive gradient algorithms.
method Careful numerical experiments and theoretical explanations using the signGD flow.
result Adam converges smoother and faster when momentum factors are close to each other.
We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of n objects from data through interactions of comparison or collaboration. Under a general framework of approximate ranking models, we characterize the exact optimal statistical error …
Inspired by the recent literature on aggregation theory, we aim at relating the long range correlation of the stocks return volatility to the heterogeneity of the investors' expectations about the level of the future volatility. Based on a semi-parametric model of investors' anticipations, we make the connection betwee…
The two phase behavior in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon in Hang-Seng index is carefully investigated. It is observed that the bifurcation phenom…
We analyze the linear response of a market network to shocks based on the bipartite market model we introduced in an earlier paper, which we claimed to be able to identify the time-line of the 2009-2011 Eurozone crisis correctly. We show that this model has three distinct phases that can broadly be categorized as "stab…
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.
Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena, as do the influential stocks (leaders) and sectors (communities), during market e…
Twitter promotes cryptocurrency pump-and-dumps, affecting trading behavior and returns.
problem The influence of Twitter on cryptocurrency pump-and-dump events.
method Analysis of abnormal returns, trading volume, and tweet activity.
result Investors relying on Twitter information sell later, leading to significant losses.
Firm foundation theory estimates a security's firm fundamental value based on four determinants: expected growth rate, expected dividend payout, the market interest rate and the degree of risk. In contrast, other views of decision-making in the stock market, using alternatives such as human psychology and behavior, bou…
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…
In this paper, we introduce the concept of collective learning (CL) which exploits the notion of collective intelligence in the field of distributed semi-supervised learning. The proposed framework draws inspiration from the learning behavior of human beings, who alternate phases involving collaboration, confrontation …
New model uses symmetries and scaling laws to predict consumer advertising response.
problem Understanding consumer response to advertising efforts.
method Introduces a physics-based mathematical model to describe consumer response dynamics.
result The model better captures nonlinearities in advertising effects and provides new parameters for audience engagement.