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Orest Hrycyna

Publications and source records attributed to Orest Hrycyna.

At least 19 recordsLinked to original sources
arXiv2026

GraphSeek: Next-Generation Graph Analytics with LLMs

Graphs are foundational across domains but remain hard to use without deep expertise. LLMs promise accessible natural language (NL) graph analytics, yet they fail to process industry-scale property graphs effectively and efficiently: such datasets are large, highly heterogeneous, structurally complex, and evolve dynamically. To address this, we devise a novel abstraction for complex multi-query analytics over such graphs. Its key idea is to replace brittle generation of graph queries directly from NL with planning over a Semantic Catalog that describes both the graph schema and the graph operations. Concretely, this induces a clean separation between a Semantic Plane for LLM planning and broader reasoning, and an Execution Plane for deterministic, database-grade query execution over the full dataset and tool implementations. This design yields substantial gains in both token efficiency and task effectiveness even with small-context LLMs. We use this abstraction as the basis of the first LLM-enhanced graph analytics framework called GraphSeek. GraphSeek achieves substantially higher success rates (e.g., 86% over enhanced LangChain) and points toward the next generation of affordable and accessible graph analytics that unify LLM reasoning with database-grade execution over large and complex property graphs.

cs.DB↗
arXiv2024

On the structural stability of a simple cosmological model in $R+αR^{2}$ theory of gravity

The theory of gravity with a quadratic contribution of scalar curvature is investigated using a dynamical systems approach. The simplest Friedmann--Robertson--Walker metric is employed to formulate the dynamics in both the Jordan frame and the conformally transformed Einstein frame. We show that, in both frames, there are stable de Sitter states where the expansion of the Hubble function naturally includes terms corresponding to an effective dark matter component. Using the invariant center manifold, we demonstrate that, in the Einstein frame, there exists a zero-measure set of initial conditions that lead from an unstable to a stable de Sitter state. Additionally, the initial de Sitter state is associated with a parallelly propagated singularity. We show that the formulations of the theory in the Jordan frame and the Einstein frame are physically nonequivalent.

gr-qc↗
arXiv2021

A new generic and structurally stable cosmological model without singularity

Dynamical systems methods are used to investigate a cosmological model with non-minimally coupled scalar field and asymptotically quadratic potential function. We found that for values of the non-minimal coupling constant parameter $\frac{3}{16}<ξ<\frac{1}{4}$ there exists an unstable asymptotic de Sitter state, free from a parallelly propagated singularity for $\frac{5}{24}\leξ<\frac{1}{4}$, giving rise to non-singular beginning of the universe. The energy density associated with this state depends on value of the non-minimal coupling constant and can be much smaller than the Planck energy density. For $ξ=\frac{1}{4}$ we found that the initial state is in form of the static Einstein universe. Proposed evolutional model, contrary to the seminal Starobinsky's model, do not depend on the specific choice of initial conditions in phase space, moreover, a small change in the model parameters do not change the evolution thus the model is generic and structurally stable. The values of the non-minimal coupling constant can indicate for a new fundamental symmetry in the gravitational theory. We show that Jordan frame and Einstein frame formulation of the theory are physically nonequivalent.

gr-qc↗
arXiv2020

The non-minimal coupling constant and the primordial de Sitter state

Dynamical systems methods are used to investigate dynamics of a flat Friedmann-Robertson-Walker cosmological model with the non-minimally coupled scalar field and a potential function. Performed analysis distinguishes the value of non-minimal coupling constant parameter $ξ=\frac{3}{16}$, which is the conformal coupling in five dimensional theory of gravity. It is shown that for a monomial potential functions at infinite values of the scalar field there exist generic de Sitter and Einstein-de Sitter states. The de Sitter state is unstable with respect to expansion of the Universe for potential functions which do not change faster than linearly. This leads to a generic cosmological evolution without the initial singularity.

gr-qc↗
arXiv2017

What $ξ$? Cosmological constraints on the non-minimal coupling constant

In dynamical system describing evolution of universe with the flat Friedmann-Robertson-Walker symmetry filled with barotropic dust matter and non-minimally coupled scalar field with a constant potential function an invariant manifold of the de Sitter state is used to obtain exact solutions of the reduced dynamics. Using observational data coming from distant supernovae type Ia, the Hubble function $H(z)$ measurements and information coming from the Alcock-Paczy$ń$ski test we find cosmological constraints on the non-minimal coupling constant $ξ$ between the scalar curvature and the scalar field. For all investigated models we can exclude negative values of this parameter at the $68\%$ confidence level. We obtain constraints on the non-minimal coupling constant consistent with condition for conformal coupling of the scalar field in higher dimensional theories of gravity.

astro-ph.CO↗
arXiv2015

Cosmological dynamics with non-minimally coupled scalar field and a constant potential function

Dynamical systems methods are used to investigate global behavior of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We show that the system can be reduced to an autonomous three-dimensional dynamical system and additionally is equipped with an invariant manifold corresponding to an accelerated expansion of the universe. Using this invariant manifold we find an exact solution of the reduced dynamics. We investigate all solutions for all admissible initial conditions using theory of dynamical systems to obtain a classification of all evolutional paths. The right-hand sides of the dynamical system depend crucially on the value of the non-minimal coupling constant therefore we study bifurcation values of this parameter under which the structure of the phase space changes qualitatively. We found a special bifurcation value of the non-minimal coupling constant which is distinguished by dynamics of the model and may suggest some additional symmetry in matter sector of the theory.

gr-qc↗
arXiv2014

Dynamics and cosmological constraints on Brans-Dicke cosmology

We investigate observational constraints on the Brans-Dicke cosmological model using observational data coming from distant supernovae type Ia, the Hubble function $H(z)$ measurements, information coming from the Alcock-Paczy{ń}ski test, and baryon acoustic oscillations. Our analysis is based on the modified Friedmann function resulting form dynamical investigations of Brans-Dicke cosmology in the vicinity of a de Sitter state. The qualitative theory of dynamical systems enables us to obtain three different behaviors in the vicinity of this state. We find for a linear approach to the de Sitter state $ω_{\textrm{BD}}=-0.8606^{+0.8281}_{-0.1341}$, for an oscillatory approach to the de Sitter state $ω_{\textrm{BD}}=-1.1103^{+0.1872}_{-0.1729}$, and for the transient de Sitter state represented by a saddle-type critical point $ω_{\textrm{BD}}=-2.3837^{+0.4588}_{-4.5459}$. We obtain the mass of the Brans-Dicke scalar field at the present epoch as $m_ϕ\sim H_{0}$. The Bayesian methods of model comparison are used to discriminate between obtained models. We show that observational data point toward vales of the $ω_{\textrm{BD}}$ parameter close to the value suggested by the low-energy limit of the bosonic string theory.

astro-ph.CO↗
arXiv2014

Quantum theory of the Bianchi II model

We describe the quantum evolution of the vacuum Bianchi II universe in terms of the transition amplitude between two asymptotic quantum Kasner-like states. For large values of the momentum variable the classical and quantum calculations give similar results. The difference occurs for small values of this variable due to the Heisenberg uncertainty principle. Our results can be used, to some extent, as a building block of the quantum evolution of the vacuum Bianchi IX universe.

gr-qc↗
arXiv2013

Dynamical complexity of the Brans-Dicke cosmology

The dynamics of the Brans-Dicke theory with a quadratic scalar field potential function and barotropic matter is investigated. The dynamical system methods are used to reveal complexity of dynamical evolution in homogeneous and isotropic cosmological models. The structure of phase space crucially depends on the parameter of the theory $ω_{\textrm{BD}}$ as well as barotropic matter index $w_{m}$. In our analysis these parameters are treated as bifurcation parameters. We found sets of values of these parameters which lead to generic evolutional scenarios. We show that in isotropic and homogeneous models in the Brans-Dicke theory with a quadratic potential function the de Sitter state appears naturally. Stability conditions of this state are fully investigated. It is shown that these models can explain accelerated expansion of the Universe without the assumption of the substantial form of dark matter and dark energy. The Poincare construction of compactified phase space with a circle at infinity is used to show that phase space trajectories in a physical region can be equipped with a structure of a vector field on nontrivial topological closed space. For $ω_{\textrm{BD}}<-3/2$ we show new types of early and late time evolution leading from the anti-de Sitter to the de Sitter state through an asymmetric bounce. In the theory without a ghost we find bouncing solutions and the coexistence of the bounces and the singularity. Following the Peixoto theorem some conclusions about structural stability are drawn.

gr-qc↗
arXiv2013

Brans-Dicke theory and the emergence of ΛCDM model

The dynamics of the Brans-Dicke theory with a scalar field potential function is investigated. We show that the system with a barotropic matter content can be reduced to an autonomous three-dimensional dynamical system. For an arbitrary potential function we found the values of the Brans-Dicke parameter for which a global attractor in the phase space representing de Sitter state exists. Using linearized solutions in the vicinity of this critical point we show that the evolution of the Universe mimics the $Λ$CDM model. From the recent Planck satellite data, we obtain constraints on the variability of the effective gravitational coupling constant as well as the lower limit of the mass of the Brans-Dicke scalar field at the de Sitter state.

gr-qc↗
arXiv2013

Scalar Field Cosmology -- Geometry of Dynamics

We study the Scalar Field Cosmology (SFC) using the geometric language of the phase space. We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric. The metric in the ensemble is used to measure a distance between different models. We point out the advantages of visualisation of dynamics in the phase space. It is investigated the genericity of some class of models in the context of fine tuning of the form of the potential function in the ensemble of SFC. We also study the symmetries of dynamical systems of SFC by searching for their exact solutions. In this context we stressed the importance of scaling solutions. It is demonstrated that scaling solutions in the phase space are represented by unstable separatrices of the saddle points. Only critical point itself located on two dimensional stable submanifold can be identified as scaling solution. We have also found a class of potentials of the scalar fields forced by the symmetry of differential equation describing the evolution of the universe. A class of potentials forced by scaling (homology) symmetries was given. We point out the role of the notion of a structural stability in the context of the problem of indetermination of the potential form of the Scalar Field Cosmology. We characterise also the class of potentials which reproduces the ΛCDM model, which is known to be structurally stable. We show that the structural stability issue can be effectively used is selection of the scalar field potential function. This enables us to characterise a structurally stable and therefore a generic class of SFC models. We have found a nonempty and dense subset of structurally stable models. We show that these models possess symmetry of homology.

gr-qc↗
arXiv2012

Dynamics of the Bianchi I model with non-minimally coupled scalar field near the singularity

Dynamical systems methods are used to study the evolution of the Bianchi I model with a scalar field. We show that inclusion of the non-minimal coupling term between the scalar field and the curvature changes evolution of the model compared with the minimally coupled case. In the model with the non-minimally coupled scalar field there is a new type of singularity dominated by the non-minimal coupling term. We examine the impact of the non-minimal coupling on the anisotropy evolution and demonstrate the existence of its minimal value in the generic case.

gr-qc↗
arXiv2012

Scalar Field Cosmology -- Improving the Cosmological Evolutional Scenario

We study evolution of cosmological models filled with the scalar field and barotropic matter. We consider the scalar field minimally and non-minimally coupled to gravity. We demonstrated the growth of degree of complexity of evolutional scenario through the description of matter content in terms of the scalar field. In study of all evolutional paths for all initial conditions methods of dynamical systems are used. Using linearized solutions we present simple method of derivation corresponding form of the Hubble function of the scale factor $H(a)$.

astro-ph.CO↗
arXiv2010

Uniting cosmological epochs through the twister solution in cosmology with non-minimal coupling

We investigate dynamics of a flat FRW cosmological model with a barotropic matter and a non-minimally coupled scalar field (both canonical and phantom). In our approach we do not assume any specific form of a potential function for the scalar field and we are looking for generic scenarios of evolution. We show that dynamics of universe can be reduced to a 3-dimensional dynamical system. We have found the set of fixed points and established their character. These critical points represent all important epochs in evolution of the universe : (a) a finite scale factor singularity, (b) an inflation (rapid-roll and slow-roll), (c) a radiation domination, (d) a matter domination and (e) a quintessence era. We have shown that the inflation, the radiation and matter domination epochs are transient ones and last for a finite amount of time. The existence of the radiation domination epoch is purely the effect of a non-minimal coupling constant. We show the existence of a twister type solution wandering between all these critical points.

astro-ph.CO↗
arXiv2010

Scalar field cosmology -- toward description of dynamic complexity of cosmological evolution

We study the dynamical evolution of cosmological models with the Robertson-Walker symmetry with a scalar field non-minimally coupled to gravity and barotropic matter. For this aim we use dynamical system methods. We have found a type of evolutional path which links between all important events during the evolution, the cosmological singularity of finite time, inflation, radiation and matter dominating epoch and the accelerated phase expansion of the universe. We point out importance of finding the new generic solution called a twister solution for a deeper description of the evolution of the Universe. We demonstrate that including the non-minimal coupling leads to a new, richer evolutional cosmological scenario in comparison to the case of minimal coupling.

astro-ph.CO↗
arXiv2010

Twister quintessence scenario

We study generic solutions in a non-minimally coupled to gravity scalar field cosmology. It is shown that dynamics for both canonical and phantoms scalar fields with the potential can be reduced to the dynamical system from which the exact forms for an equation of the state parameter can be derived. We have found the stationary solutions of the system and discussed their stability. Within the large class of admissible solutions we have found a non-degenerate critical points and we pointed out multiple attractor type of trajectory travelling in neighborhood of three critical points at which we have the radiation dominating universe, the barotropic matter dominating state and finally the de Sitter attractor. We have demonstrated the stability of this trajectory which we call the twister solution. Discovered evolutional path is only realized if there exist the non-minimal coupling constant. We have found simple duality relations between twister solutions in phantom and canonical scalar fields in the radiation domination phase. For the twister trajectory we have found an oscillating regime of approaching the de Sitter attractor.

astro-ph.CO↗
arXiv2010

From model dynamics to oscillating dark energy parameterisation

We develop here a relatively simple description of dark energy based on the dynamics of non-minimally coupled to gravity phantom scalar field which, in limit, corresponds to cosmological constant. The dark energy equation of state, obtained directly from the dynamics of the model, turns out to be an oscillatory function of the scale factor. This parameterisation is compared to other possible dark energy parameterisations, among them, the most popular one, linear in the scale factor. We use the Bayesian framework for model selection and make a comparison in the light of SN Ia, CMB shift parameter, BAO A parameter, observational H(z) and growth rate function data. We find that there is evidence to favour a parameterisation with oscillations over {\it a priori} assumed linear one.

astro-ph↗