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In the Kolmogorov Theory of Consciousness, algorithmic agents utilize inferred compressive models to track coarse-grained data produced by simplified world models, capturing regularities that structure subjective experience and guide action planning. Here, we study the dynamical aspects of this framework by examining how the requirement of tracking natural data drives the structural and dynamical properties of the agent. We first formalize the notion of a generative model using the language of symmetry from group theory, specifically employing Lie pseudogroups to describe the continuous transformations that characterize invariance in natural data. Then, adopting a generic neural network as a proxy for the agent dynamical system and drawing parallels to Noether's theorem in physics, we demonstrate that data tracking forces the agent to mirror the symmetry properties of the generative world model. This dual constraint on the agent's constitutive parameters and dynamical repertoire enforces a hierarchical organization consistent with the manifold hypothesis in the neural network. Our findings bridge perspectives from algorithmic information theory (Kolmogorov complexity, compressive modeling), symmetry (group theory), and dynamics (conservation laws, reduced manifolds), offering insights into the neural correlates of agenthood and structured experience in natural systems, as well as the design of artificial intelligence and computational models of the brain. [ABSTRACT FROM AUTHOR]

Major Depressive Disorder (MDD) is a complex, heterogeneous condition affecting millions worldwide. Computational neuropsychiatry offers potential breakthroughs through the mechanistic modeling of this disorder. Using the Kolmogorov theory (KT) of consciousness, we developed a foundational model where algorithmic agents interact with the world to maximize an Objective Function evaluating affective valence. Depression, defined in this context by a state of persistently low valence, may arise from various factors—including inaccurate world models (cognitive biases), a dysfunctional Objective Function (anhedonia, anxiety), deficient planning (executive deficits), or unfavorable environments. Integrating algorithmic, dynamical systems, and neurobiological concepts, we map the agent model to brain circuits and functional networks, framing potential etiological routes and linking with depression biotypes. Finally, we explore how brain stimulation, psychotherapy, and plasticity-enhancing compounds such as psychedelics can synergistically repair neural circuits and optimize therapies using personalized computational models. [ABSTRACT FROM AUTHOR]

Introduction: Proof-of-principle human studies suggest that transcranial direct current stimulation (tDCS) over the dorsolateral prefrontal cortex (DLPFC) may improve depression severity. This open-label multicenter study tested remotely supervised multichannel tDCS delivered at home in patients (N=35) with major depressive disorder (MDD). The primary aim was to assess the feasibility and safety of our protocol. As an exploratory aim, we evaluated therapeutic efficacy: the primary efficacy measure was the median percent change from baseline to the end of the 4-week post-treatment follow-up period in the observer-rated Montgomery-Asberg Depression Mood Rating Scale (MADRS). Methods: Participants received 37 at-home stimulation sessions (30 minutes each) of specifically designed multichannel tDCS targeting the left DLPFC administered over eight weeks (4 weeks of daily treatments plus 4 weeks of taper), with a follow-up period of 4 weeks following the final stimulation session. The stimulation montage (electrode positions and currents) was optimized by employing computational models of the electric field generated by multichannel tDCS using available structural data from a similar population (group optimization). Conducted entirely remotely, the study employed the MADRS for assessment at baseline, at weeks 4 and 8 during treatment, and at 4-week follow-up visits. Results: 34 patients (85.3% women) with a mean age of 59 years, a diagnosis of MDD according to DSM-5 criteria, and a MADRS score ≥20 at the time of study enrolment completed all study visits. At baseline, the mean time since MDD diagnosis was 24.0 (SD 19.1) months. Concerning compliance, 85% of the participants (n=29) completed the complete course of 37 stimulation sessions at home, while 97% completed at least 36 sessions. No detrimental effects were observed, including suicidal ideation and/or behavior. The study observed a median MADRS score reduction of 64.5% (48.6, 72.4) 4 weeks post-treatment (Hedge's g = -3.1). We observed a response rate (≥ 50% improvement in MADRS scores) of 72.7% (n=24) from baseline to the last visit 4 weeks post-treatment. Secondary measures reflected similar improvements. Conclusions: These results suggest that remotely supervised and supported multichannel home-based tDCS is safe and feasible, and antidepressant efficacy motivates further appropriately controlled clinical studies. Clinical Trial Registration: https://clinicaltrials.gov/study/NCT05205915?tab= results, identifier NCT05205915. [ABSTRACT FROM AUTHOR]

Background: Iron deficiency correction with ferric carboxymaltose improves symptoms and reduces rehospitalization in patients with reduced left ventricular ejection fraction. The mechanisms underlying these improvements are poorly understood. This study aimed to determine changes in left ventricular contractility after iron treatment as reflected in global longitudinal strain. Methods: Prospective single‐center study including 43 adults with reduced ejection fraction, non‐anemic iron deficiency, and functional class II‐III heart failure despite optimal medical treatment. Global longitudinal strain through speckle‐tracking echocardiography was measured at baseline and 4 weeks after ferric carboxymaltose. Results: A significant improvement in global longitudinal strain was detected (from −12.3% ± 4.0% at baseline to −15.6% ± 4.1%, p <.001); ferritin and transferrin saturation index had increased, but ejection fraction presented no significant changes (baseline 35.7% ± 4.6%, follow‐up 37.2% ± 6.6%, p =.073). Conclusions: In patients with heart failure and reduced ejection fraction, the correction of iron deficiency with ferric carboxymaltose is associated with an early improvement in global longitudinal strain, possibly suggesting a direct effect of iron correction on myocardial contractility. [ABSTRACT FROM AUTHOR]

We present a theoretical model of light-beam propagation in anisotropic and inhomogeneous dielectric structures obtained as a direct extension of the scalar fast-Fourier-transform beam-propagation method. We solve Maxwell's equations in a generalized geometrical optics approximation, in which the reflected fields are neglected. This is a full-vectorial model because it accounts for the polarization effects that are due to both the anisotropy and the inhomogeneity of the medium.

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