Study the singular limit of a boundary reaction equation, showing energy concentration and varifold support.
problem Analyzing the singular limit of a boundary reaction equation.
method Investigates the critical points of the boundary reaction equation \((-Δ)^{\frac{1}{2}}u = \frac{1}{\varepsilon}(u-u^3)\) in \(U \subset \mathbb{R}^n\).
result Shows existence of an (n−1)-rectifiable energy concentration set and associates limit energy measures to a stationary varifold. Derives variance kernel for reaction boundary in financial models.
problem Separating components in financial volatility models.
method Operational-time variance kernel, damped Abel response kernel, closed asymptotic form.
result Operational variance has a closed asymptotic form involving various parameters.
Derives operational-time variance kernel for reaction boundaries in financial markets.
problem Separating components in volatility models to better understand market dynamics.
method Derives a variance kernel for a latent-order-book reaction boundary, separating structural boundary cumulant, clock projection, and pricing-measure choice.
result Operational variance has a closed asymptotic form for long-memory forcing, with effective signed-forcing intensity and resilience.
Deriving option prices from operational-time Markov lattices
problem Option pricing
method Operational-time Markov lattice
result Derives option-pricing equations from an operational-time Markov lattice
GF-Net learns Green's functions for linear reaction-diffusion equations.
problem Learning Green's functions for linear reaction-diffusion equations on arbitrary domains.
method GF-Net, a neural network, learns Green's functions in an unsupervised manner using physics-informed approach and symmetry.
result GF-Net efficiently solves linear reaction-diffusion equations under various boundary conditions and sources.
Machine learning models simulate molecular spectra and reactions in solvents.
problem Accurate simulation of molecular spectra and reactions in solvent environments.
method Introduced FieldSchNet, a deep neural network for modeling molecular interactions with external fields.
result Demonstrated significant lowering of Claisen rearrangement reaction activation barrier using FieldSchNet.
Unified analytic account of correlation emergence and Epps effect in coupled limit order books
problem Correlation emergence and Epps effect in coupled limit order books
method Discrete random-walk description of order flow with creation, cancellation, and diffusion, coupled reaction-diffusion equations with moving reaction boundary
result Realized correlations as a function of aggregation time
Reduces nonlinear electromechanical dynamics through quasi-steady state hypothesis.
problem Nonlinear dynamics of electromechanical systems.
method Quasi-steady state hypothesis, non-dimensionalization, scaling.
result Physical justification and characteristic time scales of dynamics.
The paper solves the Cauchy problem for Friedrichs systems on specific spacetime manifolds.
problem Investigating the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundaries.
method Admissible boundary conditions are imposed to show the existence and uniqueness of strong solutions. For hyperbolic systems, the Cauchy problem is also well-posed in the Hadamard sense.
result Existence and uniqueness of strong solutions for the Cauchy problem are proven under admissible boundary conditions.
We use the formalism of Geometrothermodynamics to describe chemical reactions in the context of equilibrium thermodynamics. Any chemical reaction in a closed system is shown to be described by a geodesic in a 2−dimensional manifold that can be interpreted as the equilibrium space of the reaction. We first show this i…
MEGAN models chemical reactions as graph edits, improving synthesis planning.
problem Generating and predicting chemical reactions under constraints.
method End-to-end encoder-decoder neural model inspired by arrow pushing formalism.
result State-of-the-art accuracy in standard benchmarks for retrosynthesis prediction.
Upper bound on CRN reaction rates derived using information geometry.
problem Challenging task of deriving an upper bound on reaction rates of nonlinear, discrete CRNs.
method Information geometric approach using natural gradient.
result Validated through numerical simulations, demonstrating faster convergence in specific CRNs.
Graphs predict reaction conditions for organic chemistry.
problem Predicting specific reaction conditions in organic chemistry.
method Graph Neural Networks (GNNs) for modeling reaction graphs.
result GNNs can identify specific graph features affecting reaction conditions.
Novel deep learning method predicts reaction coordinates and future MD trajectories.
problem Identifying optimal reaction coordinates for chemical reactions.
method Regularized Sparse Autoencoder (RSE) for discovering reaction coordinates and predicting MD trajectory evolution.
result RSE helps in choosing a small but important set of reaction coordinates.
Chemical reactions can be described as the stepwise redistribution of electrons in molecules. As such, reactions are often depicted using `arrow-pushing' diagrams which show this movement as a sequence of arrows. We propose an electron path prediction model (ELECTRO) to learn these sequences directly from raw reaction …
Chemical reactions occur in energy, environmental, biological, and many other natural systems, and the inference of the reaction networks is essential to understand and design the chemical processes in engineering and life sciences. Yet, revealing the reaction pathways for complex systems and processes is still challen…
METRO predicts reactions using minimal templates, reducing computational overhead and achieving state-of-the-art results.
problem Predicting possible reaction substrates for complex molecules from simpler precursors.
method METRO (Molecule-Edit Templates for RetrOsynthesis) uses minimal templates to predict reactions efficiently and accurately.
result METRO achieves state-of-the-art results on standard benchmarks, reducing computational overhead.
Chemical networks outperform spiking neural networks in classification tasks.
problem Learning tasks with spiking neural networks require hidden layers, which are computationally expensive.
method Used deterministic mass-action kinetics to prove chemical reaction networks without hidden layers can solve tasks previously solved by spiking neural networks.
result A chemical reaction network without hidden layers outperforms a spiking neural network with hidden layers in a handwritten digit classification task.
Schrödinger bridge solved with Weyl calculus for quadratic state cost.
problem Optimal control policy to steer joint state statistics.
method Weyl calculus in quantum mechanics for reaction-diffusion PDEs.
result Explicit Markov kernel for quadratic state cost found.
Solves probabilistic Lambert problem connecting astrodynamics with optimal mass transport.
problem Determining spacecraft velocity for given positions with probabilistic constraints.
method Generalized optimal mass transport (OMT) and Schrödinger bridge (SBP) connections.
result Existence and uniqueness of solution for probabilistic Lambert problem.
Clarifies relation for solving control-affine Schrödinger bridge problems.
problem Solving control-affine Schrödinger bridge problems via Hopf-Cole transform.
method Applies Hopf-Cole transform to conditions of optimality, resulting in nonlinear PDEs.
result Generic control-affine Schrödinger bridge requires further algorithmic development.
Bayesian inference for biochemical reaction networks using jump-diffusion approximations.
problem Estimating hidden quantities in poorly characterized biochemical processes.
method Developed a Bayesian inference algorithm based on Markov chain Monte Carlo and sequential Monte Carlo methods.
result Numerical evaluation of the algorithm for a partially observed multi-scale birth-death process.
New boundary treatment improves accuracy for complex PDEs.
problem Order reduction in high-order IMEX schemes for multidimensional PDEs.
method Novel boundary treatment algorithms for Cartesian meshes, treating implicit-explicit stages similarly to interior points.
result Recovery of designed order of convergence by numerical verification.
We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average displacement of the reaction front grows as the square-root of the imbalance. We argue t…
The prediction of organic reaction outcomes is a fundamental problem in computational chemistry. Since a reaction may involve hundreds of atoms, fully exploring the space of possible transformations is intractable. The current solution utilizes reaction templates to limit the space, but it suffers from coverage and eff…
Uniform small energy regularity for fractional geometric problems proved.
problem Proving regularity for fractional geometric problems.
method Analyzing parabolic boundary reaction Ginzburg-Landau problems and fractional harmonic maps to spheres.
result Uniform small energy regularity results for s∈(0,1), answering a posed question. New method uses machine learning to analyze catalyst reactions.
problem Understanding complex reaction mechanisms in catalytic materials.
method Combining transient kinetics and machine learning.
result Correct estimates of micro-kinetic coefficients and mechanism.
The growing ubiquity of Social Media data offers an attractive perspective for improving the quality of machine learning-based models in several fields, ranging from Computer Vision to Natural Language Processing. In this paper we focus on Facebook posts paired with reactions of multiple users, and we investigate their…
Reaction prediction remains one of the major challenges for organic chemistry, and is a pre-requisite for efficient synthetic planning. It is desirable to develop algorithms that, like humans, "learn" from being exposed to examples of the application of the rules of organic chemistry. We explore the use of neural netwo…
Considered an important macroeconomic indicator, the Purchasing Managers' Index (PMI) on Manufacturing generally assumes that PMI announcements will produce an impact on stock markets. International experience suggests that stock markets react to negative PMI news. In this research, we empirically investigate the stock…
Hopfield networks improve reaction template prediction for few/zero-shot scenarios.
problem Predicting reaction templates for new molecules in CASP.
method Adapted Hopfield networks to associate reaction templates, molecules, and structural information.
result Significantly improved performance for templates with few or zero training examples.
The study distills news sources to analyze stock reactions, finding sentiment has asymmetric and sector-specific effects.
problem Analyzing the influence of financial text sources on stock reactions.
method Mixed text sources from professional platforms, blogs, and message boards were distilled using different lexica to analyze sentiment variables.
result Sentiment has an asymmetric and sector-specific effect on stock reactions.
Paper presents a multi-label topic model for financial texts with high performance and insights into market reactions.
problem Analyzing financial text data for market reactions and understanding topic interactions.
method Trained a multi-label topic model on a financial text database, achieved high macro F1 score, and investigated topic interactions.
result Model achieves high performance (macro F1 > 85%) and reveals significant market reactions to topic co-occurrences.
Reactmine infers chemical reactions from time series data, overcoming sparse model limitations.
problem Inferring chemical reaction networks from time series data, especially when initial conditions are not varied.
method Sequential reaction inference in a search tree, ranking and re-optimizing kinetics.
result Reactmine successfully infers preponderant regulations in real datasets, matching model-based analyses.
Computer-assisted synthesis planning aims to help chemists find better reaction pathways faster. Finding viable and short pathways from sugar molecules to value-added chemicals can be modeled as a retrosynthesis planning problem with a catalyst allowed. This is a crucial step in efficient biomass conversion. The tradit…
Global solutions and smoothing effects for reaction-diffusion equations on manifolds.
problem Global existence and smoothing effects for reaction-diffusion equations on Riemannian manifolds.
method Functional analytic methods, Sobolev and Poincaré inequalities.
result Existence of global solutions under certain conditions on the manifold.
Study shows neural operators can efficiently solve complex reaction-diffusion systems.
problem Efficiently solving nonlinear reaction-diffusion systems using neural operators.
method Laplacian-based neural operators applied to a generalized Gierer-Meinhardt system.
result Explicit approximation error bounds established for neural operators in terms of network parameters.
Study shows SEC crypto classification led to significant market reactions.
problem Impact of SEC classification of crypto assets as securities.
method Event study methodology focusing on explicitly named crypto assets.
result Significant adverse market reactions, with returns plummeting 12% over one week.
Bounds on chemical reaction network relaxation rates using convex analysis.
problem Understanding relaxation dynamics in chemical reaction networks.
method Convex analysis, generalized gradient flows, singular values of stoichiometric matrix.
result Bounds on Kullback-Leibler divergence to equilibrium for CRNs.
We describe a fully data driven model that learns to perform a retrosynthetic reaction prediction task, which is treated as a sequence-to-sequence mapping problem. The end-to-end trained model has an encoder-decoder architecture that consists of two recurrent neural networks, which has previously shown great success in…
We address the problem of optimal Central Bank intervention in the exchange rate market when interventions create feedback in the rate dynamics. In particular, we extend the work done on optimal impulse control by Cadenillas and Zapatero to incorporate temporary market reactions, of random duration and level, to Bank i…
There is an intuitive analogy of an organic chemist's understanding of a compound and a language speaker's understanding of a word. Consequently, it is possible to introduce the basic concepts and analyze potential impacts of linguistic analysis to the world of organic chemistry. In this work, we cast the reaction pred…
Researchers prove inequalities for reaction-diffusion systems using a new curvature-dimension condition.
problem Proving Li-Yau and Harnack inequalities for systems of linear reaction-diffusion equations.
method Introducing a hybrid curvature-dimension condition and proving a differential Harnack estimate.
result A Harnack inequality holds under the hybrid curvature-dimension condition CDhyb(0,d) with d<∞. Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate…
DEMOTE uses neural diffusion-reaction processes to capture temporal dynamics in sparse tensor data.
problem Sparse and temporally associated tensor data with limited structural knowledge.
method Develops a neural diffusion-reaction process to estimate dynamic embeddings for tensor modes.
result Captures both commonalities and personalities in evolving tensor entries.
Adjoint SA speeds up bioprocess parameter learning.
problem Challenges in digital twin development for biomanufacturing.
method Adjoint sensitivity analysis on multi-scale enzymatic reaction networks.
result Resilient sensitivities reveal bioprocess regulatory mechanisms.
Compact models for NOX formation during methane combustion are created using a new algorithm.
problem Creating accurate models for NOX formation during complex combustion processes.
method Adapted Machine Learning Optimization of Chemical Kinetics (MLOCK) algorithm with Latin Square method for virtual reaction network generation.
result Compact models with high fidelity (>75%) in reproducing industry-defined performance targets are generated.
Microstructure of market dynamics is studied through analysis of tick price data. Linear trend is introduced as a tool for such analysis. Trend arbitrage inequality is developed and tested. The inequality sets limiting relationship between trend, bid-ask spread, market reaction and average update frequency of price inf…