arXiv research

Investigates the rotating Kepler problem for energy values ≤ -3/2.

We survey some recent developments in the quest for global surfaces of section for Reeb flows in dimension three using methods from Symplectic Topology. We focus on applications to geometry, including existence of closed geodesics and sharp systolic inequalities. Applications to topology and celestial mechanics are als…

Machine learning models classify celestial objects like pulsars and black holes.

We apply Arnold's theory of generic smooth plane curves to Stark-Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric and magnetic field, and includes many systems from celestial mechanics. Based on Arnold's $J^+$-invariant, we introduce inv…

The study of Reeb dynamics on contact manifolds without periodic orbits.

Sturm theory applied to symplectic geometry and mechanics.

Classical Morse theory proceeds by considering sublevel sets $f^{-1}(-\infty, a]$ of a Morse function $f: M \to R$, where $M$ is a smooth finite-dimensional manifold. In this paper, we study the topology of the level sets $f^{-1}(a)$ and give conditions under which the topology of $f^{-1}(a)$ changes when passing a cri…

A reconstruction theorem in terms of the topology and geometrical structures on the spaces of light rays and skies of a given space-time is discussed. This result can be seen as part of Penrose and Low's programme intending to describe the causal structure of a space-time $M$ in terms of the topological and geometrical…

New spaces at infinity identified for Minkowski spacetime.

Robot science discovers new materials faster.

We present a new, fully generative model of optical telescope image sets, along with a variational procedure for inference. Each pixel intensity is treated as a Poisson random variable, with a rate parameter dependent on latent properties of stars and galaxies. Key latent properties are themselves random, with scientif…

Macroeconomic theories of growth and wealth distribution have an outsized influence on national and international social and economic policies. Yet, due to a relative lack of reliable, system wide data, many such theories remain, at best, unvalidated and, at worst, misleading. In this paper, we introduce a novel econom…

We define a conformal reference frame, i.e., a special projection of the six-dimensional sky bundle of a Lorentzian manifold (or the five-dimensional twistor space) to a three-dimensional manifold. We construct an example, a conformal compactification, for Minkowski space. Based on the complex structure on the skies, w…

Gaussian processes model sparse data in astrophysics and chemistry.

A large amount of data accommodated in knowledge graphs (KG) is actually metric. For example, the Wikidata KG contains a plenitude of metric facts about geographic entities like cities, chemical compounds or celestial objects. In this paper, we propose a novel approach that transfers orometric (topographic) measures to…

The paper models star dynamics using Ricci flow and Perelman entropy, revealing chaotic behavior.

Once first answers in any dimension to the Green-Griffiths and Kobayashi conjectures for generic algebraic hypersurfaces $\mathbb{X}^{n-1} \subset \mathbb{P}^n(\mathbb{C})$ have been reached, the principal goal is to decrease (to improve) the degree bounds, knowing that the `celestial' horizon lies near $d \geqslant 2n…

It is shown that if $M$ is a strongly causal free of naked singularities space-time, then its causal structure is completely characterized by a partial order in the space of skies defined by means of a class non-negative Legendrian isotopies. It is also proved that such partial order is determined by the class of futur…

In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its generating function. Black-Scholes pricing model is a special linear case of this pricin…

A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or Finsler mechanical (?; ?)-systems and we develop their geometries. We obtain the ca…

New mechanics on non-associative octonions discovered.

A new description, different by the classical theory of Hamiltonian Mechanics, in the general framework of generalized Lie algebroids is presented. In the particular case of Lie algebroids, new and important results are obtained. We present the \emph{dual mechanical systems} called by use, \emph{dual mechanical}$(ρ,η) …

This paper assesses Gaussian and Exponential mechanisms for certifying adversarial robustness.

We propose a new input perturbation mechanism for publishing a covariance matrix to achieve $(ε,0)$-differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definitene…

New mechanisms improve differential privacy for scalar queries.

We design two mechanisms for the recommender system to collect user ratings. One is modified Laplace mechanism, and the other is randomized response mechanism. We prove that they are both differentially private and preserve the data utility.

Quantum mechanics models for financial Black-Scholes model.

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it for…

Expands differential privacy mechanisms to include the Generalized Gaussian mechanism for improved private machine learning.

Optimal DP mechanisms for vector queries are found to be staircase distributions.

New approach identifies latent properties from mechanisms, not just data.

New RL approach learns dynamic VCG mechanisms in unknown MDP environments.

Paper connects dynamics of mechanical systems to Reeb dynamics.

Exact discrete mechanics for nonholonomic systems defined.

A new Gaussian mechanism for differential privacy in the shuffle model is introduced.

The key to a Transformer model is the self-attention mechanism, which allows the model to analyze an entire sequence in a computationally efficient manner. Recent work has suggested the possibility that general attention mechanisms used by RNNs could be replaced by active-memory mechanisms. In this work, we evaluate wh…

We study the problem of what causes prices to change. We define the mechanical impact of a trading order as the change in future prices in the absence of any future changes in decision making, and its it informational impact as the remainder of the total impact once mechanical impact is removed. We introduce a method o…

New mechanism for pure differential privacy on functional summaries using Laplace-like process.

Unified framework for subsampling mechanisms with tighter privacy guarantees.

New geometric mechanism solves four envelope problems.

This text explains how fiber bundle structure is fundamental for classical physics.

The paper improves privacy accounting for discrete-valued mechanisms and the subsampled Gaussian mechanism.

This paper examines allocation mechanisms in markets with transfer costs, showing how these costs affect economic efficiency.

The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important limitations. Our analysis reveals that the variance formula for the original mechanism is …

Paper introduces a new deep-learning method for quantum mechanics.

Associating stock mechanics to real economy, in terms of volume, number of transactions, and cost, i.e. money flow for shares, we obtained the fundamental laws of stock mechanics.

CICME estimates common and domain-specific causal mechanisms from multi-sensor data.

New method compares DP mechanisms beyond $(\varepsilon, δ)$ pairs.