Minimal learning agents can infer unobserved variables in complex environments.
problem How to infer unobserved variables in complex environments using minimal learning agents.
method Concrete operational definition of abstract concepts, minimal architecture supporting abstraction, reinforcement learning.
result Minimal learning agents can infer the existence of unobserved variables.
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…
Researchers apply concept-based explainability to EEG data.
problem Understanding the internal states of complex EEG transformer models.
method Concept Activation Vectors (CAVs) adapted for EEG data, using externally labeled datasets and anatomically defined concepts.
result Both approaches to concept formation yield valuable insights into EEG model representations.
Machine learning is usually defined in behaviourist terms, where external validation is the primary mechanism of learning. In this paper, I argue for a more holistic interpretation in which finding more probable, efficient and abstract representations is as central to learning as performance. In other words, machine le…
Study shows no closed trapped submanifolds can be tangent to certain spacelike hypersurfaces.
problem Existence of closed trapped submanifolds in spacetime regions foliated by specific hypersurfaces.
method Introduced k−future convex spacelike/null hypersurfaces and proved no k−dimensional closed trapped submanifolds can be tangent to these hypersurfaces from their future side. result Closed trapped submanifolds cannot be found in open spacetime regions foliated by k−future convex hypersurfaces. In this chapter we review some recent results on the dynamics of price formation in financial markets and its relations with the efficient market hypothesis. Specifically, we present the limit order book mechanism for markets and we introduce the concepts of market impact and order flow, presenting their recently disco…
Deep generative models are reported to be useful in broad applications including image generation. Repeated inference between data space and latent space in these models can denoise cluttered images and improve the quality of inferred results. However, previous studies only qualitatively evaluated image outputs in data…
In this paper we observe that 2-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of 2-dimensional 0-surgery with the observed dynamics. To d…
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.
Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromo…
The definition of preferences assigned to individuals is a concept that concerns many disciplines, from economics, with the search of an acceptable outcome for an ensemble of individuals, to decision making an analysis of vote systems. We are concerned in the phenomena of good selection and economic fairness. In Arrow'…
This study models AI traders' impact on financial markets using a multi-agent framework.
problem Lack of a comprehensive model to assess AI traders' effects on market price formation and volatility.
method Developed a multi-agent market model with microfoundations of the GARCH model.
result Validated the model through simulations and analyzed AI traders' impact.
State-of-the-art link prediction utilizes combinations of complex features derived from network panel data. We here show that computationally less expensive features can achieve the same performance in the common scenario in which the data is available as a sequence of interactions. Our features are based on social vec…
New theory shows perishable goods markets are more stable and efficient.
problem Lower stability and efficiency of markets for re-tradable assets compared to perishable goods.
method Reformulation of no-trade and no-arbitrage theorems in neoclassical finance.
result Perishable goods markets exhibit higher stability and efficiency.
The report attempts of apply econophysics concepts to the Eurozone crisis. It starts by examining the idea of conservation laws as applied to market economies. It formulates a measure of financial entropy and gives numerical simulations indicating that this tends to rise. We discuss an analogue for free energy released…
Study singularity formation in Ricci flow solutions.
problem Understanding singularity behavior in noncompact manifolds.
method Analyzing complete Ricci flow solutions.
result Evidence for stability of generalized cylinders as singularity models.
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.
Develops a new causal model for path-dependent link prediction.
problem Existing causal models assume fixed node factors, but real-world links can depend on existing ones.
method Introduces causal lifting and structural pairwise embeddings for path-dependent link prediction.
result Validated on three scenarios, demonstrating improved accuracy for causal link prediction.
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.
This work explains the structural origins of attention sinks in LLMs.
problem Initial tokens disproportionately monopolize attention scores in LLMs.
method Traced to self-attention's value aggregation process and FFN layer activations.
result Attention sinks form due to variance discrepancy and dimension disparity.
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.
The option is a financial derivative, which is regularly employed in reducing the risk of its underlying securities. However, investing in option is still risky. Such risk becomes much severer for speculators who utilize option as a means of leverage to increase their potential returns. In order to mitigate risk on the…
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…
The pants graph of a free group is constructed and studied.
problem Understanding the structure of free groups through graph theory.
method Developed a pants graph and studied its properties.
result The pants graph of a free group is connected and unbounded.
Complex architectures of biological neural circuits, such as parallel processing pathways, has been behaviorally implicated in many cognitive studies. However, the theoretical consequences of circuit complexity on neural computation have only been explored in limited cases. Here, we introduce a mechanism by which direc…
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.
MedCAT extracts valuable medical information from unstructured text.
problem Extracting structured information from unstructured biomedical documents.
method Unsupervised machine learning for disambiguation of entities.
result Improved entity detection and linking compared to existing tools.
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.
Chemical databases store information in text representations, and the SMILES format is a universal standard used in many cheminformatics software. Encoded in each SMILES string is structural information that can be used to predict complex chemical properties. In this work, we develop SMILES2vec, a deep RNN that automat…
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.
This paper uses spectrum analysis to understand price behavior in the Indian stock market.
problem Understanding price formation and discovery in the Indian stock market.
method Adapting mathematical physics theories and spectrum analysis to decompose price cycles.
result Decomposing price cycles helps in understanding the effect of information on price formation and discovery.
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.
This study maps systemic risks in TradFi and DeFi, highlighting their interdependence.
problem Systemic risks in traditional and decentralized finance.
method Conceptual model and comparative analysis of TradFi and DeFi.
result Systemic risks in DeFi can affect TradFi and vice versa, creating a crosstagion effect.
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.
Machine learning models predict which ideas will be innovated based on subjective perspectives.
problem Predicting high-impact innovation based on subjective perspectives and interpersonal innovation opportunities.
method Quantifying subjective perspectives and their interaction based on innovator positions within a geometric space of concepts.
result Subjective perspectives predict which ideas individuals and groups will creatively attend to and successfully combine in the future.
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.
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.
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.