arXiv research

Macroscopic price evolution models are commonly used for investment strategies. There are first promising achievements in defining microscopic agent based models for the same purpose. Microscopic models allow a deeper understanding of mechanisms in the market than the purely phenomenological macroscopic models, and thu…

This study compares microscopic and macroscopic models for commodity index derivatives pricing.

Study macroscopic equity market properties affecting active strategies.

Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first principles. Some of these processes can also be successfully modeled at the macroscopic level using e.g. partial differential equations (PDEs) desc…

The study shows a 3D manifold's macroscopic dimension is 1 under specific curvature constraints.

Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between processes on these two scales is essential to both the derivation of macroscopic models of, e.g., transport phenomena in natural porous media,…

We present examples of agent-based and stochastic models of competition and business processes in economics and finance. We start from as simple as possible models, which have microscopic, agent-based, versions and macroscopic treatment in behavior. Microscopic and macroscopic versions of herding model proposed by Kirm…

In this note we construct a closed 4-manifold having torsion-free fundamental group and whose universal covering is of macroscopic dimension 3. This yields a counterexample to Gromov's conjecture about the falling of macroscopic dimension.

We introduce a $\mathbb{Z}$--coefficient version of Guth's macroscopic stability inequality for almost-minimizing hypersurfaces. In manifolds with a lower bound on macroscopic scalar curvature, we use the inequality to prove a lower bound on areas of hypersurfaces in terms of the Gromov simplicial norm of their homolog…

The paper proves conditions for the existence of small Urysohn width hypersurfaces in manifolds with positive scalar curvature.

Study curvature and symplectic properties of symmetric products of surfaces.

The macroscopic version of Urysohn width for scalar curvature is disproven in high dimensions.

Motivated by a zero-intelligence approach, the aim of this paper is to connect the microscopic (discrete price and volume), mesoscopic (discrete price and continuous volume) and macroscopic (continuous price and volume) frameworks for the modelling of limit order books, with a view to providing a natural probabilistic …

We construct a counterexamples in dimensions $n>3$ to Gromov's conjecture \cite{Gr1} that the macroscopic dimension of rationally essential $n$-dimensional manifolds equals $n$.

The paper proves macroscopic versions of conjectures about scalar curvature and volume bounds.

We give a homological characterization of $n$-manifolds whose universal covering $\Wi M$ has Gromov's macroscopic dimension $\dim_{mc}\Wi M<n$. As the result we distinguish $\dim_{mc}$ from the macroscopic dimension $\dim_{MC}$ defined by the author \cite{Dr}. We prove the inequality $\dim_{mc}\Wi M<\dim_{MC}\Wi M=n$ f…

A new macroscopic market making model connects market making and optimal execution.

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show tha…

We prove a conjecture of Gromov's to the effect that manifolds with isotropic curvature bounded below by 1 (after possibly rescaling) are macroscopically 1-dimensional on the scales greater than 1. As a consequence we prove that compact manifolds with positive isotropic curvature have virtually free fundamental groups.…

We proposed a market simulation model (micro model) which displays multifractality and reproduces many important stylized facts of speculative markets. From this model we analytically extracted the MMAR model (Multifractal Model of Asset Returns) for the macroscopic limit.

The paper extends macroscopic market making to stochastic games, revealing properties and solving equations.

Meta-materials simulation sped up with energy surrogates.

A new model for defective media using two scales.

Proves Gromov's conjecture for a specific type of groups.

We give the first examples of rationally inessential but macroscopically large manifolds. Our manifolds are counterexamples to the Dranishnikov rationality conjecture. For some of them we prove that they do not admit a metric of positive scalar curvature, thus satisfy the Gromov positive scalar curvature conjecture. Fu…

Take a torus with a Riemannian metric. Lift the metric on its universal cover. You get a distance which in turn yields balls. On these balls you can look at the Laplacian. Focus on the spectrum for the Dirichlet or Neumann problem. We describe the asymptotic behaviour of the eigenvalues as the radius of the balls goes …

Study on functions computed by deep-layered machines finds same distribution in neural networks and Boolean circuits.

We show that for a rationally inessential orientable closed $n$-manifold $M$ whose fundamental group $π$ is a duality group the macroscopic dimension of its universal cover is strictly less than $n$:$$ \dim_{MC}\Wi M<n.$$ As a corollary we obtain the following 0.1 Theorem. The inequality $ \dim_{MC}\Wi M<n$ holds for t…

New methods connect low-loss points on neural network surfaces.

We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial…

Constructs infinitely many examples of large manifolds with circle bundles of positive scalar curvature.

We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and on the Good-Turing missing mass estimator. We prove two different regret bounds on t…

We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, long term memory of volatility and non-Poissonian intervals. We also clarify the causality between microscopic dealers' dynamics and macroscopic market's empirical laws.

In this paper we present a kinetic model with stochastic game-type interactions, analyzing the relationship between the level of political competition in a society and the degree of economic liberalization. The above issue regards the complex interactions between economy and institutional policies intended to introduce…

We introduce a microscopic model which describes the dynamics of each dealer in multiple foreign exchange markets, taking account of the triangular arbitrage transaction. The model reproduces the interaction among the markets well. We explore the relation between the parameters of the present microscopic model and the …

This paper proposes a percolation-based model of new-product diffusion in the spirit of Solomon et al. (2000) and Goldenberg et al. (2000). A consumer buys the new product if she has formed her individual valuation of the product (reservation price) and if this valuation is greater or equal than the price of the produc…

The current economic crisis has provoked an active response from the interdisciplinary scientific community. As a result many papers suggesting what can be improved in understanding of the complex socio-economics systems were published. Some of the most prominent papers on the topic include (Bouchaud, 2009; Farmer and …

We prove that given a hyperbolic manifold endowed with an auxiliary Riemannian metric whose sectional curvature is negative and whose volume is sufficiently small in comparison to the hyperbolic one, we can always find for any radius at least $1$ a ball in its universal cover whose volume is bigger than the hyperbolic …

Take a riemanniann nilmanifold, lift its metric on its universal cover. In that way one obtains a metric invariant under the action of some co-compact subgroup. We use it to define metric balls and then study the spectrum of the laplacian for the dirichlet problem on them. We describe the asymptotic behaviour of the sp…

Entropy helps explain disorder in both macro and micro systems.

Machine learning uncovers hidden correlations in granular material behavior.

Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is typically simulated with differential equations parameterized by a Hamiltonian,…

We prove that for 4-manifolds $M$ with residually finite fundamental group and non-spin universal covering $\Wi M$, the inequality $\dim_{mc}\Wi M\le 3$ implies the inequality $\dim_{mc}\Wi M\le 2$.

Economic systems are similar with physic systems for their large number of individuals and the exist of equilibrium. In this paper, we present a model applying the equilibrium statistical model in economic systems. Consistent with statistical physics, we define a series of concepts, such as economic temperature, econom…

The definition of the covariant space-time averaging scheme for the objects (tensors, geometric objects, etc.) on differentiable metric manifolds with a volume n-form, which has been proposed for the formulation of macroscopic gravity, is analyzed. An overview of the space-time averaging procedure in Minkowski spacetim…

We present a class of macroscopic models of the Limit Order Book to simulate the aggregate behaviour of market makers in response to trading flows. The resulting models are solved numerically and asymptotically, and a class of similarity solutions linked to order book formation and recovery is explored. The main result…

New PRGP model improves traffic flow estimation.

Study essentiality and simplicial volume of manifolds fibered over spheres.