Abolhassan Ali Eslami

We propose a unified framework to model human working memory (WM) dynamics using **Markovian Parallax Denigrate (MPD)** writing tasks, convexity of WM trajectories, and the formation of **mental logic circuits** (flip-flops, MUX, classical and quantum gates). This framework captures three phases: 1. **MPD-induced convex WM growth** 2. **Transition to logic-based WM under cognitive fatigue** 3. **Dynamic feedback loops enabling online object manipulation** We show both **neuroscientific and mathematical evidence** for convexity, Markovian O(1) computations, and the generalization to complex classical and quantum mental circuits.

We introduce the **Compressed Probabilistic Yoneda Tree (CPYT)**, a framework for representing, comparing, and compressing probability distributions. By integrating Yoneda lemma principles, minimum spanning trees (MST), and ternary tree structures, CPYT enables a hierarchical and minimal structural representation of distributions based on a selected set of probes (e.g., Markov blankets). This approach allows provably correct reconstruction, comparison, and analysis of complex probabilistic systems without relying on traditional Shannon entropy or Kolmogorov complexity measures.

We propose a mathematical framework using category theory and partially ordered sets (posets) to analyze psychiatric disorders from the DSM-5 based on their neural substructures and functional impacts, termed _affordances_ (e.g., memory, emotional regulation). We define a monotone mapping between neural substructures and their functional affordances, proving that disorders with the greatest functional impact correspond to maximal elements in the affordance poset. This approach provides a systematic ranking of disorders by their neurofunctional severity, offering a tool to prioritize treatment strategies.

This paper presents a minimal tree-based framework for verifying object isomorphism in arbitrary categories using Minimum Spanning Trees (MSTs) over a fixed set of probes. The system is strictly weaker than $RCA_0$, avoiding numeric or comprehension axioms. By leveraging MST traversal, it ensures the minimal set of Hom-set comparisons for isomorphism verification. The framework extends to structured formula verification via Abstract Syntax Trees (ASTs). Explicit weight functions, rigorous proofs, and concrete examples ensure mathematical correctness and reproducibility.

In pharmacology, most drugs are designed to produce specific, predictable effects. However, certain medications exhibit both causal and stochastic (random) effects, leading to outcomes that are not entirely deterministic. These "noisy drugs" can alter the probability distributions of physiological states, making their effects complex and sometimes unpredictable. Understanding how these drugs introduce stochasticity and reshape physiological Markov blankets is crucial for advancing personalized medicine and improving therapeutic strategies.

This paper develops a comprehensive, multi-layered framework integrating thermodynamics, game theory, fuzzy logic, and self-referential information theory to analyze social welfare in systems with self-referential agents (Quine agents) and bounded rationality. We formalize the concept of 'Demonic Agents' as actors capable of manipulating, erasing, and reproducing their information states, analogous to Maxwell's demon. Using probabilistic phase entropy and fuzzy action distributions, we rigorously prove that social welfare (SW) is globally superior to Nash equilibria (NE), bounded, and foundational, even in worlds without overt demons. Quine self-replication ensures irreducible, non-trivial information for all agents, making every agent inherently demonic and capable of shaping collective outcomes. The model integrates economic allocation mechanisms inspired by Nakamoto (2008), including Bitcoin-based anchors, the genesis hash, and dynamic fairness mechanisms.

Accurately evaluating high-dimensional embeddings is crucial in machine learning and data analysis. This study introduces a geometric framework for assessing embeddings by integrating Banach and hyperbolic space mappings with convex hull construction and Ramsey-3,3 triple analysis. Extreme points of the data are identified, convex hulls are constructed, and all points are analyzed with respect to their proximity to nearest triples of anchor points. The resulting geometric band serves as an intrinsic metric for embedding fidelity, outlier detection, and model evaluation. The methodology is demonstrated on synthetic datasets, highlighting its ability to capture core structures and identify anomalies in both Euclidean and non-Euclidean embeddings.

This paper presents a computational framework that models the brain as a maze-like network for tumor localization and surgical planning. Starting from an abstract structure without prior information about healthy or malignant regions, we generate a voxel-based maze. Once MRI data is available, voxel weights are assigned according to tumor probability. Multiple maze variants are generated and analyzed using A* and Minimum Spanning Tree (Prim) algorithms. This allows the identification of critical voxels—points where malignant tissue is likely concentrated—providing precise targets for neurosurgery.

This paper introduces a comprehensive framework for modeling neural activity using a Karnaugh-map-inspired (Carno) representation, encoded in binary format for computational efficiency. The approach integrates an 8-state neuron model with polar coordinate mapping, vectorial synaptic aggregation interpreted as electromagnetic vector fields, and multimodal brain imaging data from magnetic resonance imaging (MRI), functional MRI (fMRI), and diffusion tensor imaging (DTI). The model incorporates probabilistic synaptic states, hyperbolic forced states arising from field instabilities, and multidimensional cortical visualizations. Designed for clinical applicability in neurosurgery, the framework facilitates integration with established software platforms such as 3D Slicer and Brainlab, supporting real-time tumor localization, three-dimensional cortical mapping, and AI-assisted simulations for functional-preserving surgical interventions.

The fundamental paradigm of molecular biology posits that 64 codons encode 20 canonical amino acids and stop signals, necessitating codon degeneracy. However, the assumption of functional equivalence among synonymous codons is flawed. We posit that this very non-equivalence—manifested in translation kinetics and fidelity—provides a novel therapeutic avenue. This paper explores two sophisticated strategies to exploit the genetic code's redundancy: first, **Codon Optimization and Rescripting**, which replaces non-optimal codons to enhance the production of functional proteins; and second, **Pharmacologically-Induced Translational Readthrough**, which deliberately manipulates the ribosome to ignore premature termination codons. By moving beyond the mere amino acid sequence to the informational context of the codon itself, these approaches offer a promising framework for treating a wide array of genetic diseases caused by missense and nonsense mutations.

We propose a novel transformer-based architecture that directly maps continuous waveform signals into discrete token sequences, and subsequently into intelligible speech. Our framework integrates a neural waveform-to-token encoder with a transformer-based language model for sequence generation, followed by a token-to-speech decoder for acoustic realization. Unlike traditional speech recognition or text-to-speech pipelines, our model unifies acoustic, symbolic, and generative components into a single transformer-based paradigm, enabling controlled charge-like modulation of information flow and interpretable latent structures. We validate our design using MATLAB/Simulink co-simulation, demonstrating both the theoretical feasibility and practical applicability of this approach.

We introduce a **hybrid digital-analog Transformer** capable of learning and simulating discrete-time chaotic sequences. Unlike conventional floating-point neural networks, all computations—including attention, feed-forward layers, and residual connections—are mapped to **bitwise logical gates** (XOR, AND, OR) augmented by **RC circuit-based feedback and inductive memory (L)**, inspired by digital Lorenz systems. Differentiable approximations of gates enable **bitwise gradient-based training**, while RC circuits and inductors emulate previous-step memory, enabling low-power, hardware-efficient implementation. Experiments demonstrate emergent pseudo-chaotic sequences, and analysis shows superior computational efficiency in hardware relative to software.

This paper presents a novel method for enhancing generative models by leveraging **probabilistic top-k feature extraction** combined with a **Transformer** applied to the most informative features. Inspired by the concept of **Markov blankets**, our approach identifies and boosts the features that most influence output generation, allowing improved sample quality in Autoencoder-based frameworks. We provide an information-theoretic proof demonstrating that our method maximizes mutual information between selected latent features and the target output, reducing redundancy compared to standard Autoencoders (AEs) and Variational Autoencoders (VAEs). Experiments on the MNIST dataset show improved reconstruction quality while maintaining computational efficiency.

This study investigates the factors contributing to perceived difficulty in video games, integrating user scores, cognitive requirements, novelty, and structural complexity. Using a dataset of 100 video games across multiple genres, we performed logistic regression analyses to identify the relative contributions of various gameplay and cognitive factors to player-perceived difficulty. Our findings indicate that task complexity and cognitive load are primary predictors of perceived difficulty, whereas narrative novelty and kinetic demands exert secondary but meaningful influences. This framework provides a quantitative approach for evaluating and predicting game difficulty in both design and research contexts.

We propose a framework that models computation and information flow in terms of **white holes, black holes, and damping mechanisms**. This system enables a **recursive transfer of information from future states to present computations**, suggesting conditions under which P = NP could be realized in a physically grounded network. The model formalizes **white hole activation, black hole storage, and dynamic loops** with cross-entropy and autocorrelation characteristics, providing a bridge between temporal computation and structured information flow.

We present a practical, hybrid algorithm for exact multiplication of large integers combining multiple advanced techniques to achieve practically faster performance than standard implementations while maintaining deterministic correctness. This method integrates: - Fibonacci multiples with recursive doubling - Zeckendorf decomposition and block aggregation to reduce the effective number of blocks r_effective - FFT convolution on smaller, cache-friendly arrays - Hierarchical B-Tree merging with Strassen-style divide-and-conquer for multi-digit addition - SHA verification for deterministic exactness The algorithm achieves asymptotic complexity O(n \log n), matching Van der Hoeven (2019), but reduces practical runtime constants significantly.

The digital implementation of the Lorenz equations using logical gates, as described in this paper, provides a framework for modeling chaotic behavior in discrete systems. This approach can be extended to biological systems, where chaotic dynamics may underlie critical cellular processes such as energy production and epigenetic regulation. Here, we propose that the genetic codes of mitochondrial DNA (mtDNA) and nuclear DNA exhibit self-similar and chaotic properties, analogous to the strange attractors generated by our digital system. Furthermore, we explore the role of ATP and histones as state variables within this chaotic framework, regulated by feedback mechanisms and a bijective mapping between mtDNA and nuclear DNA.

The Lorenz system is a classic chaotic system exhibiting the butterfly effect and strange attractor behavior. In this paper, we propose a digital implementation of the Lorenz equations using logical gates. We map derivative, difference, multiplication, and addition operations to digital equivalents—previous step feedback, XOR, AND, and OR gates respectively. This allows the construction of a fully digital, discrete-time chaotic system capable of exploring complex state spaces and demonstrating algorithmic strange attractor behavior.

We propose a probabilistic algorithm for multiple-choice exams with negative marking that combines deterministic knowledge and data-driven guessing. The algorithm leverages the portion of questions a student knows for certain, alongside historical exam data, to optimize guesses on unknown questions. Recursive iterations and goodness-of-fit analysis enhance the expected score, providing a principled method to maximize the probability of passing, even when only a fraction of questions are fully understood.

We analyze deterministic search algorithms where selection paths are entirely determined by a seed. By studying the cumulative distribution function (CDF) and tail behavior of the search steps, we show that for most seeds, the search completes in constant-time O(1). We discuss applications in hash cracking, black-box optimization, and cognitive modeling, emphasizing the predictive power of tail analysis for worst-case seeds. We also examine the effect of conscious choice, showing that when agents systematically select problem-causing seeds, failure becomes the dominant outcome.

Effective knowledge management in organizations, universities, libraries, and research institutions requires optimizing the flow of information while accounting for uncertainty. We propose a probabilistic framework that models knowledge as a graph of facts, where each node represents a knowledge unit characterized by its entropy H(v), and edges indicate dependency or influence relationships. Transitions of information between nodes are represented as a Markov Jump Process (MJP), and transition probabilities are optimized using the Metropolis–Hastings algorithm to maximize knowledge flow. This framework identifies low-cost, high-impact pathways of knowledge transfer, enabling strategic decision-making in organizational learning and research. Simulation results demonstrate that maximizing mutual information between nodes reduces operational cost while promoting efficient knowledge dissemination.

This paper proposes a formal criterion for philosophical habitability, defined as the capacity of an environment to sustain self-aware conscious agents without catastrophic collapse of subjective experience. We introduce a smooth experiential function E(t), representing the quality and coherence of consciousness over time, and demonstrate that the existence of at least one positive odd-order derivative and one convex even-order derivative is sufficient to ensure a dynamically stable and self-sustaining experiential trajectory, rendering an environment philosophically habitable.

This paper presents a conceptual framework integrating philosophical and neurophysiological perspectives on consciousness. Drawing on Schopenhauer's notion of _Will and Representation_, Bernardo Kastrup's idealist philosophy, and the physics of neuronal signaling, we propose a model where consciousness emerges as a process of energy transformation. ATP-driven ionic activity generates neural signals, which are processed as waveforms and decoded by a “receiver,” producing the first representation of “not-wanting itself,” the foundational form of will. This model provides a bridge between metaphysical idealism and measurable neural dynamics, offering a holistic view of consciousness as a distributed, energy-dependent phenomenon.