arXiv subjects

Alexander Poltorak

Publications and source records attributed to Alexander Poltorak.

5 recordsLinked to original sources

arXiv2026

Toward a Dynamical Taxonomy of Insomnia: A Multiaxial Framework for Sleep-State Transitions and Architectural Failure

Insomnia disorder is defined at the syndrome level, yet similar complaints can arise from different abnormalities in sleep regulation, state transition, state stabilization, spatial recruitment, architectural sequencing, and state perception. We propose a multiaxial dynamical framework whose principal contribution is organizational: a candidate profile is specified by the dynamical operation that fails, the sleep stage or boundary at which it fails, and its causal status. Objective sleep duration, age, circadian phase, comorbidity, medication exposure, and night-to-night variability are modifier/covariate dimensions rather than additional mechanistic classes. A local Landau-Ginzburg formalism, adopted from prior cortical and sleep-dynamics work, supplies a phenomenological language for nested hypotheses. Its relaxational form applies only to boundary-local dynamics under an approximate gradient description; non-gradient escape requires an action or quasipotential treatment, and whole-night REM-NREM sequencing requires reactive or oscillatory dynamics. Routine polysomnography usually identifies effective combinations rather than curvature, escape action, bias, noise, and relaxation separately. The strongest boundary-level evidence concerns sleep onset, where published results are consistent with bifurcation-like or bistable dynamics but do not yet exclude a driven smooth transition produced by the homeostatic-circadian ramp. The remaining operation classes are hypothesis-generating extensions. The taxonomy is judged by pragmatic utility, including improved communication, stratification, and prediction; the scalar-field implementation and specific dynamical profiles are separately falsifiable. The framework is a phenomenological organizing model rather than a new diagnosis, validated biomarker, or treatment-selection system.

physics.bio-ph↗

arXiv2026

A Landau-Ginzburg Phenomenology of Sleep-Stage Transitions

Sleep staging provides a reproducible clinical description, but it does not by itself explain why some boundaries are abrupt while others are graded, or why transition windows contain instability, synchrony, and apparent state coexistence. We develop a local Landau-Ginzburg phenomenology in which each boundary is represented by motion in an effective potential of a spatially extended, noisy, dissipative neural field. A latent cortical-ordering coordinate phi is inferred from prespecified EEG/PSG observables through a measurement model designed to avoid circularity. The canonical boundaries are treated separately. Existing data support a fold-like loss of wake stability at sleep onset; whether that fold lies on a globally bistable cusp with hysteresis remains open. N1-to-N2 and N2-to-N3 are posed as continuous-like ordering crossovers, NREM-to-REM as a candidate first-order-like desynchronizing switch, and a possible within-N3 mixed or tricritical-like regime as a speculative hypothesis. The Ginzburg term adds spatial predictions - growth of correlation length and local-to-global recruitment - that are absent from scalar sleep-onset models. We specify the evidence needed to distinguish bifurcation, coexistence, noise-driven escape, smooth crossover, and scoring-induced discontinuity. Illustrative time-dependent Ginzburg-Landau simulations reproduce the proposed signature classes. A synthetic classification experiment partially distinguished six archetypes (cross-validated accuracy 0.49 +/- 0.005; balanced baseline 0.17), with little change under a noise-regime shift. These analyses establish the internal consistency and testability of the framework, not the proposed taxonomy in human sleep. Transition-centered EEG validation is required before clinical or neuromodulation applications are pursued.

physics.bio-ph↗

arXiv2004

Gravity as Nonmetricity: General Relativity in Metric-Affine Space (Ln,g)

A new geometric interpretation for General Relativity (GR) is proposed. We show that in the presence of an arbitrary affine connection, the gravitational field is described as nonmetricity of the affine connection. An affine connection can be interpreted as induced by a frame of reference (FR). Although the gravitational field equations are identical to Einstein's equations of GR, this formulation leads to a covariant tensor (instead of the pseudotensor) of energy-momentum of the gravitational field and covariant conservation laws. We further develop a geometric representation of FR as a metric-affine space, with transition between FR represented as affine deformation of the connection. Geodesic and autoparallel worldlines are considered. We show that the affine connection of a NIFR has curvature and may have torsion. We calculate the curvature for the uniformly accelerated FR. Finally, we show that GR is inadequate to describe the gravitational field in a NIFR. We propose a generalization of GR, which describes gravity as nonmetricity of the affine connection induced in a FR. This generalization contains GR as a special case of the inertial FR.

gr-qc↗

arXiv2004

On the Energy Problem in General Relativity

The Energy Problem (EP) in General Relativity (GR) is analyzed in the context of GR's axiomatic inconsistencies. EP is classified according to its local and global aspects. The local aspects of the EP include noncovariance of the energy-momentum pseudotensor (EMPT) of the gravitational field, non-uniqueness of the EMPT, asymmetry of EMPT, and vanishing metric energy-momentum tensor. The global aspect of the EP relates to the lack of integral conservation laws due to the general difficulties in defining invariant integrals of tensors in non-Euclidean space. These difficulties are related to the lack of precise definition of a reference frame in the GR. A reference frame is defined here as a differential manifold with an affine connection. The resulting unique decomposition of the Levi-Civita connection into its affine and nonmetric parts allows for a covariant definition of the gravitational energy-momentum tensor. It is pointed out that the invariance of the Lagrangian (or action functional) is a necessary but not sufficient condition to secure the covariance of the Lagrange-Euler field theory. A rigorous definition of the Lagrange Field Structure (LFS) on differential manifolds is proposed. A covariant generalization of the first Noether theorem for LFS is obtained. Different approaches to the EP are discussed.

gr-qc↗

arXiv2004

Towards a Covariant Theory of Gravitation

A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame as a differential manifold with an affine connection results in separation of the respective contributions of inertial and gravitational fields represented by the affine connection and the tensor of nonmetricity within the Levi-Civita connection of GR. Resulting decomposition of the Einstein curvature tensor into affine and nonmetric parts allows to recast Einstein's field equations in a form invariant with respect to the choice of a reference frame wherein the gravity is described by nonmetricity of space-time . A covariant Lagrangian is proposed leading to the same field equation. All three approaches ultimately lead to the same fully covariant theory of gravitation with a covariant tensor of energy-momentum of the gravitational field and differential and integral conservation laws. The role of the frames of reference, as distinguished from coordinate systems, is discussed.

gr-qc↗