Study uses DMD to analyze oceanic features in Strait of Gibraltar.
problem Understanding complex oceanic features in Strait of Gibraltar.
method Dynamic Mode Decomposition (DMD) applied to 3D MIT general circulation model simulations.
result Unveiled new elements and dynamics of the Strait of Gibraltar, including a secondary gyre and wave propagation.
Extends geometrical description of tensor manifolds in tree-based formats.
problem Geometrical description of tensor manifolds in tree-based formats.
method Provided a new geometrical description of manifolds of tensors in tree-based format.
result Geometrical description compatible with Tucker format.
The paper explores geometric invariants of null hypersurfaces using Carrollian geometry.
problem Understanding the thermodynamics of black hole solutions.
method Examining various Carrollian geometries and their connections to null hypersurface embeddings.
result A connection with torsion is the most natural object to study Carrollian manifolds.
Simulating fluid flow in geological formations requires mesh generation, lithology mapping to the cells, and computing geometric properties such as normal vectors and volume of cells. The purpose of this research work is to compute and process the geometrical information required for performing numerical simulations in…
The paper models network formation using mixed logit models.
problem Modeling network formation in various fields.
method Mixed logit models, specifically the repeated-choice (RC) model.
result The RC model outperforms the multinomial logit (MNL) model in estimating network formation.
SoccerCPD detects tactical changes in soccer matches using spatiotemporal tracking data.
problem Detecting consistent team formations in fluid sports like soccer.
method Two-step change-point detection: formation and role changes.
result Accurately detects tactical changes and estimates formation and role assignments.
Extends ONNX for quantized neural networks with new formats and operators.
problem Handling arbitrary-precision quantization in neural networks.
method Introduces new formats and operators in ONNX to represent quantized neural networks.
result Enabled representation of uniform quantization in neural networks.
Proves finite step termination of Kähler-Einstein metric singularity formation.
problem Singularity formation of Kähler-Einstein metrics.
method Finite step termination of bubble trees for singularity formation.
result Finite step termination of Kähler-Einstein metric singularity formation proved in non-collapsing situation.
Deep neural networks are commonly developed and trained in 32-bit floating point format. Significant gains in performance and energy efficiency could be realized by training and inference in numerical formats optimized for deep learning. Despite advances in limited precision inference in recent years, training of neura…
Study shows formation of Kerr black holes with complete apparent horizons and proves Penrose inequalities.
problem Formation of Kerr black holes and Penrose inequalities.
method Combining gravitational-collapse and Kerr stability results with new coordinate changes and elliptic arguments.
result Proves dynamical and spacetime Penrose inequalities in black hole formation spacetimes.
Paper proves trapped surface formation for EMCSF system without symmetry assumptions.
problem Formation of trapped surfaces for the Einstein--Maxwell--charged scalar field system.
method Scale-critical trapped surface formation result established from past null infinity.
result Focusing of gravitational waves, concentration of electromagnetic fields, or condensation of scalar fields can lead to trapped surface formation.
Study on Kähler-Ricci flow and conformal submersion singularity formation.
problem Singularity formation of Kähler-Ricci flow on manifolds with conformal submersion.
method Derive conditions for the preservation of conformal submersion and analyze singularity formation.
result Formation of type I singularity and standard splitting of Cheeger-Gromov limit.
The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor representation by means of a rooted tree. By using the tree structure and the d…
Study equilibrium consumption habits in a large population using mean field games.
problem Equilibrium consumption under external habit formation in a large population.
method Formulated and solved mean field games for linear and multiplicative habit formation preferences, constructed approximate Nash equilibria for large n-player games.
result Characterized mean field equilibrium strategies and derived financial implications.
GraphOpt learns the formation mechanism of graphs from observed structures.
problem Learning formation mechanisms from observed graphs with complex structural properties.
method GraphOpt uses maximum entropy inverse reinforcement learning to solve the link formation problem in a sequential decision-making process.
result GraphOpt discovers a latent objective function that can explain and transfer across different graphs.
Analyzes how order flow affects price formation in financial markets.
problem Understanding how prices are formed by order flow in financial markets.
method Critical discussion of modeling approaches and empirical observations, focusing on market impact and transaction costs.
result Algorithmic trading impacts the quality and cost of trading.
MiFID II impacts European stock liquidity and price formation.
problem Impact of MiFID II on European stock liquidity and price formation.
method Analyzed effects of MiFID II on European stock markets, focusing on intraday and closing auction liquidity and tick size changes.
result Closing auction volumes increased and price formation became more efficient after MiFID II.
We seek to utilize the nonextensive statistics to the microscopic modeling of the interacting many-investor dynamics that drive the price changes in a market. The statistics of price changes are known to be fit well by the Students-T and power-law distributions of the nonextensive statistics. We therefore derive models…
System predicts ice formation to improve road safety.
problem Improving road safety through accurate ice formation prediction.
method Combining physical models and machine learning for data correction.
result Machine learning effectively corrects incorrect data in forecasts.
Model asset pricing with habit formation in a large market.
problem Understanding asset pricing in large heterogeneous markets with habit formation.
method Mean field game theory and quadratic-growth mean field BSDEs.
result Derives a semi-analytic solution for asset pricing model.
The "standard" Merton formulation of optimal investment and consumption involves optimizing the integrated lifetime utility of consumption, suitably discounted, together with the discounted future bequest. In this formulation the utility of consumption at any given time depends only on the amount consumed at that time.…
Modeling price formation in intraday electricity markets with renewable generation.
problem Price formation and optimal trading strategies in intraday electricity markets with intermittent renewable generation.
method Developed a tractable equilibrium model using stochastic control theory to identify optimal strategies and exhibit Nash equilibrium.
result Identified optimal trading strategies and exhibited Nash equilibrium in closed form for a finite number of agents and in the asymptotic framework of mean field games.
Study on price formation in a market with a major player and minor firms.
problem Equilibrium price formation in a market with a major financial firm and many minor firms.
method Analyzes the equilibrium price process in both finite and mean field models, considering idiosyncratic and common noises.
result Derives the functional form of price impact for the major firm in both market sizes.
Optimal trading strategies identified in electricity markets with a major player.
problem Price formation and optimal trading in intraday electricity markets with strategic interactions.
method Stochastic control theory and mean field games with a major player.
result Nash equilibrium identified in closed form for the asymptotic case.
The paper optimizes retirement spending considering habit formation and pension income.
problem Optimizing lifetime consumption under habit formation and pension income.
method Time inhomogeneous stochastic control problem with numerical solution using finite difference scheme.
result Consumption patterns change over time based on habit and optimal strategy.
Lectures on mean curvature flow and its related equations.
problem Singularity formation, nonuniqueness, and topological change in motion by mean curvature.
method Analyzes motion by mean curvature flow and related equations.
result Exploration of singularity formation, nonuniqueness, and topological change.
We present the mathematical background of a software package that computes triangulations of mapping tori of surface homeomorphisms, suitable for Jeff Weeks's program SnapPea. It consists of two programs. jmt computes triangulations and prints them in a human-readable format. jsnap converts this format into SnapPea's t…
New study finds environment significantly suppresses star formation in galaxies, contrary to previous beliefs.
problem Understanding the role of environment in galaxy formation and evolution.
method Applied causal inference framework to IllustrisTNG simulations.
result Environment suppresses star formation by a factor of ~100, contrary to previous beliefs.
Graphs and networks are a key research tool for a variety of science fields, most notably chemistry, biology, engineering and social sciences. Modeling and generation of graphs with efficient sampling is a key challenge for graphs. In particular, the non-uniqueness, high dimensionality of the vertices and local depende…
Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation, statistical equilibrium and temporal stability of market weights.
Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.
problem Formation of trapped surfaces in Einstein-Maxwell-charged scalar field system.
method Generalized Christodoulou's approach for spherical symmetry and improved for Minkowskian data.
result Improved bound on trapped surface formation for Minkowskian data.
Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image pro…
The paper studies vector bundles over surfaces, focusing on singularity formation.
problem Understanding singularity formation in rank two holomorphic vector bundles over surfaces.
method Defining fertile families bearing bubbles and using elementary modifications to prove their existence.
result Existence of fertile families bearing bubbles for certain types of vector bundles.
Study of singularity formation in dHYM flow on a blown-up CP^3.
problem Analyzing singularity formation in the dHYM flow on a blown-up CP^3.
method Using Calabi ansatz, the paper studies the singularity formation of the dHYM cotangent flow on the one-point blow up of CP^3.
result An explicit example of singularity formation along the exceptional divisor, with a limit satisfying the corresponding singular dHYM equation.
Study optimal investment and consumption strategies for competitive agents with habit formation.
problem Optimal investment and consumption strategies for competitive agents with habit formation.
method Formulated n-agent game problems and mean field game problems, derived mean field equilibrium, constructed approximate Nash equilibrium.
result Explicit convergence order of approximate Nash equilibrium can be obtained.
We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology and natural sciences and creates a new platform for exploring geometrical physics…
We use numerical techniques to study the formation of singularities in Ricci flow. Comparing the Ricci flows corresponding to a one parameter family of initial geometries on S^3 with varying amounts of S^2 neck pinching, we find critical behavior at the threshold of singularity formation.
Deep model predicts Bitcoin price movements without retraining.
problem Stationary modelling of high-frequency Bitcoin price movements.
method Deep recurrent model based on order flow.
result Model maintains stability during volatile periods.
This paper analyzes popular time-nonseparable utility functions that describe "habit formation" consumer preferences comparing current consumption with the time averaged past consumption of the same individual and "catching up with the Joneses" (CuJ) models comparing individual consumption with a cross-sectional averag…
Financial economic models often assume that investors know (or agree on) the fundamental value of the shares of the firm, easing the passage from the individual to the collective dimension of the financial system generated by the Share Exchange over time. Our model relaxes that heroic assumption of one unique "true val…
We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology and natural sciences and creates a new platform for exploring geometrical physics…
Bayesian framework explains price formation with learning and market impact.
problem Understanding how prices form in markets with informed participants.
method Introduces a Bayesian model for updating priors on efficient prices.
result Exponential intensities for aggressive order arrivals are a natural outcome.
Transformer-M learns molecular data in 2D or 3D formats.
problem Learning models for molecules are limited to specific data formats.
method Developed a Transformer-based model that can handle 2D and 3D molecular data.
result Transformer-M achieves strong performance on both 2D and 3D molecular tasks.
We study singularity formation of complete Ricci flow solutions, motivated by two applications: (a) improving the understanding of the behavior of the essential blowup sequences of Enders-Muller-Topping on noncompact manifolds, and (b) obtaining further evidence in favor of the conjectured stability of generalized cyli…
Unified view on big bang singularities from initial data.
problem Understanding quiescent big bang singularities from initial data.
method Unified geometric perspective on various results.
result Solutions of Oude Groeniger et al. induce data on the singularity.
Optimal investment and consumption model with habit formation constraint.
problem Formulating an optimal investment and consumption model with habit formation constraint.
method Formulated an infinite-horizon optimal investment and consumption problem with habit formation model, derived explicit policies, and analyzed the system of differential equations.
result Optimal investment and consumption policies derived explicitly, showing different consumption and investment strategies based on habit formation level.
We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a di…
Greedy algorithm optimizes consumption habits with power utility.
problem Optimizing lifetime consumption with habit formation under power utility.
method Developed a greedy algorithm using Monte Carlo simulation.
result Greedy solution is a good approximation to the optimal solution.