Gholamreza Anbarjafari

We study the information-theoretic structure of multi-scale binary detection, a problem in which a noisy observation is to be classified at each of $L$ disjoint scale strata, with a known prior $p_S$ over the strata and a total channel budget $\Cl_{\rm tot}$ to be apportioned across the strata. The problem is the classification analogue of the parallel-Gaussian-channel water-filling problem of classical rate-distortion theory, and we develop a parallel set of analytical results. Three theorems are proved. First, under a localised-generator model in which each stratum's contribution is band-limited in Fourier space, the scale-matched sufficient statistics for two distant strata are asymptotically conditionally independent given the labels, with conditional mutual information $O((s/s')^2)$. The decoupling is a property of the sufficient statistics; the full feature representations need not, and in general do not, decouple. Second, the rate-distortion problem of maximising prior-weighted Bayes accuracy subject to a budget on total channels admits a unique Karush--Kuhn--Tucker solution, which in the high-resolution asymptotic regime reduces to a closed-form water-filling expression $\Cl_\Lev^\star \propto (p_\Lev \, \Ent(Y_{s_\Lev})\,\log(1+\SNR_\Lev))^{2/3}\,\tau_\Lev^{-2/3}$. We show that this allocation strictly dominates prior-proportional allocation whenever the per-stratum signal-to-noise profiles differ in shape, and coincides with it whenever they do not. Third, the binary detection error rate at each stratum admits a Fano-type lower bound $h_2(P_e^{(s)}) \ge \Ent(Y_s) - \I(\Feat_s;Y_s)$, providing a direct information-theoretic objective for representation learning at each stratum. Synthetic experiments on a 1-D scale-stratified detection problem with computable ground-truth information quantities validate each theorem: the sufficient-statistic mutual-information matrix is strongly diagonal (peak ratio $>90{:}1$ between matched and mismatched strata), and the closed-form rate-distortion allocation matches brute-force grid search exactly across nine channel budgets, outperforming prior-proportional allocation by up to $1.02$ percentage points of weighted accuracy in the differentiated-SNR regime. An information-driven detector architecture, AaroNet, is derived as a direct application of the three theorems and discussed as a case study.

Low-cost commercial-off-the-shelf (COTS) microcontroller-based loitering munitions have emerged as a significant asymmetric threat in modern conflicts. Their low unit cost—typically $20,000–$50,000—and ability to operate in coordinated swarms strain conventional kinetic and broadband electronic countermeasures, both in effectiveness and in cost-per-engagement economics. This paper presents a theoretically grounded, experimentally actionable framework for frequency-selective high-power microwave (HPM) electromagnetic coupling targeting the resonant modes of internal printed-circuit-board (PCB) trace geometries found in COTS autopilot systems. We derive closed-form expressions for: (i) the resonant frequencies of PCB trace dipole structures as a function of substrate propagation velocity; (ii) the induced open-circuit voltage and coupled power at a semi-conductor load; (iii) the inverse-Friis requirement on transmit power as a function of range and antenna gain; and (iv) the gain-in-coupling achieved by resonant targeting relative to broadband illumination. Analytical results demonstrate that resonant coupling reduces the required transmit power by 14.8 dB (factor ≈ 30×) compared with broadband excitation for the same damage effect at the target. A portable vehicle-mounted system architecture is proposed with an estimated component cost of $8,500 and a predicted functional engagement range of 500 m–1 km for CMOS semiconductor upset and hard-kill, respectively. The principal contributions of this work are: (v) a closed-loop Resonance-Tracking Loop (RTL) that adaptively locks onto the target PCB resonance via hill-climbing gradient ascent on backscattered power, achieving frequency lock in under 170 ms; and (vi) a lumped-element Pulse-Forming Network (PFN) generating 100 ns, 20 kW peak pulses—exceeding the CMOS junction damage energy threshold by a factor of 2 × 104. The framework is validated against published electromagnetic compatibility (EMC) data for STM32-family microcontrollers and publicly documented reverse-engineering analyses of representative loitering munitions.

Large language model (LLM) agents are increasingly deployed in sequential decision-making pipelines where each action irrevocably modifies the environment. Existing agentic architectures commit to action sequences generated by the LLM without systematically evaluating the downstream consequences of those sequences prior to execution - a fundamental gap that amplifies risk and limits accountability. We introduce Consequence-Aware Agentic AI (CA2I), a formal framework that augments the standard generate-then-execute paradigm with a dedicated Consequence Assessment Module (CAM). CAM evaluates every candidate action sequence against a historical consequence model and selects the sequence whose predicted outcome optimally balances return and risk before any irreversible action is taken. We formalise the framework as a constrained sequential decision problem and prove that, under mild stationarity assumptions, Sharpe-ratio-based selection dominates random selection in expectation. To validate the framework empirically, we instantiate CA2I in the domain of LLM-driven financial trading strategy selection, using GPT-5.4 to generate five candidate strategies per asset and a backtesting engine as the consequence model. Experiments on ten diversified US equities over a strictly held-out three-month out-of-sample window (August--October~2025) demonstrate that CA2I achieves a mean test-period Sharpe ratio of 0.51 - a 4.25 times improvement over random strategy selection (Sharpe = 0.12, p = 0.041) - while reducing mean maximum drawdown relative to buy-and-hold by 18%. Sensitivity analysis confirms selection stability: Sharpe-ratio and Calmar-ratio selection agree on 100% of strategy choices across all ten assets. We further demonstrate that CA2I provides a concrete, computationally tractable pathway toward Responsible AI in agentic systems: by making consequence evaluation an explicit, auditable, and mathematically grounded architectural step, the framework operationalises transparency, accountability, and harm avoidance as mandated by the EU AI Act, NIST AI Risk Management Framework, and IEEE Ethically Aligned Design standards.

Current responsible artificial intelligence (RAI) frameworks overwhelmingly rely on the assumption that ethical principles—fairness, transparency, accountability—can be positively and completely specified. This assumption is demonstrably false: mathematical impossibility theorems prove that standard fairness definitions are mutually incompatible, and empirical evidence shows that value alignment remains intractable under positive specification alone. We argue that this impasse stems from an unexamined epistemological commitment shared across the RAI literature and propose an alternative grounded in the millennia-old tradition of apophatic (negative) theology. Drawing on three theological traditions—the apophatic via negativa of Pseudo-Dionysius, Maimonides, and Al-Ghaz ¯al¯ı; the Christological concept of kenosis (voluntary self-limitation of power); and the Buddhist principle of prat¯ıtyasamutp ¯ada (dependent origination)—we develop a formal framework called Via Negativa Fairness (VNF). Rather than selecting a single fairness metric to optimise, VNF defines a set of unfairness constraints—outcomes that are demonstrably unjust across reasonable moral disagreement—and proves that the feasible region under these constraints is non-empty under practically relevant conditions. We complement VNF with two architectural design principles: the Kenotic Restraint Principle, which mandates designed self-limitation of AI capabilities independent of risk calculus, and the Relational Audit Protocol, derived from dependent origination, which evaluates bias as an emergent property of system-context interaction rather than a static model attribute. A formal case study on the COMPAS recidivism dataset demonstrates that VNF produces Pareto-dominant outcomes compared to single-metric optimisation, reducing worst-case group disparity by up to 31% while maintaining predictive performance within 2% of unconstrained baselines. This work provides the first rigorous bridge between theological epistemology and machine learning fairness, offering actionable, testable principles that current RAI frameworks lack.

Democracy has long been celebrated as the most legitimate form of governance, yet it rests on a foundational tension that remains unresolved: should democratic authority derive from the will of the majority, or from the quality of the decisions it produces? This paper examines the classical debate between popular sovereignty and epistemic governance through the lens of con-temporary digital media, arguing that platforms such as TikTok and Instagram have introduced unprecedented challenges to the epistemic foundations of democratic decision-making. Drawing on democratic theory from Plato to Habermas, and engaging with contemporary scholars inclu-ding Jason Brennan, David Estlund, and Hélène Landemore, the paper traces how algorithmic content curation, viral misinformation, and engagement-driven platform design systematically distort the conditions necessary for informed democratic participation. However, the paper also demonstrates that epistemic alternatives to democracy—including epistocracy and technocratic guardianship—inevitably confront the problem of self-legitimating authority, as illustrated by the Iranian theocratic model. The paper proposes that deliberative democratic innovations, such as citizens’ assemblies and structured public deliberation, offer a viable middle path that im-proves the epistemic quality of collective decisions without sacrificing democratic legitimacy. The paper concludes by outlining a framework for democratic resilience in the digital age that centres on institutional design, platform accountability, and civic epistemic infrastructure.

Crying is arguably the first emotional expression exhibited by human neonates, yet its theoretical status within affective science remains underspecified. We propose the Emotional Saturation Threshold (EST) model, a mathematical framework that formalizes crying as the universal overflow response---an "unknown state" ($\Omega$) that is activated whenever the intensity of any core emotion exceeds the capacity of its associated behavioral expressions. For each emotion $e_k$ in the set of basic emotions $\mathcal{E} = \{e_1, \dots, e_n\}$, we define an intensity function $I_k(t) \in [0, \infty)$ and a finite set of behavioral expressions $\mathcal{B}_k = \{b_{k,1}, \dots, b_{k,m_k}\}$, each bounded by a maximum expression capacity $C(b_{k,j})$. The saturation threshold is defined as $\tau_k = \max_j C(b_{k,j})$. When $I_k(t) > \tau_k$, the system enters the $\Omega$-state, manifesting as lacrimation (crying). We model the transition probability as $P(\Omega \mid I_k) = 1 - \exp\!\bigl(-\alpha_k \cdot [I_k - \tau_k]^+\bigr)$, where $\alpha_k > 0$ is an emotion-specific sensitivity parameter. This framework unifies the observation that crying occurs across the entire valence spectrum---from extreme joy to profound grief---and explains why neonates, who possess no learned behavioral expressions (i.e., $\tau_k \approx 0$ for all $k$), default to crying as their first and only emotional response. We validate the model via a cross-sectional survey ($N = 7{,}812$) across 14 countries. Non-linear regression yields excellent model fits ($R^2 > 0.92$ for all eight emotions tested). Agreement rates with core EST postulates exceed 74\% across all survey items. The model extends the Russell circumplex by introducing a third, radial "overflow" dimension and provides a principled, falsifiable account of one of humanity's most fundamental yet least understood behaviors.

The problem of theodicy is about understanding how evil can exist if there is a God who knows everything, can do anything, and is all-good. This question has troubled people for a long time. In this paper, I present a new way to look at this issue using mathematics concepts like game theory, dynamic programming, and Markov decision processes. We will see God as a player who is very patient and knows everything. God tries to find the right balance between stepping in and letting people make their own choices. On the other side, humans are limited in their understanding. They make moral decisions in a game that has consequences that last forever. Through rigorous analytical proofs and extensive computational simulations (10,000+ Monte Carlo iterations), we demonstrate that an optimal divine intervention rate $\lambda^* \approx 0.15$ exists that maximizes aggregate eternal utility while preserving substantive free will. Our main theorem shows that evil is not just allowed. It comes from any divine strategy that follows libertarian freedom and is Pareto-optimal. This gives a new way to solve the logical problem of evil. It shows that divine qualities and moral evil can exist together in a stable Nash equilibrium. This idea brings new insights into theology. For example, we can interpret Romans 8:28, which says "all things work together for good," as a way to reach the best long-term results. It also suggests that divine hiddenness is important for allowing real choices. We find that traditional answers to the problem of evil are not just reasonable but also mathematically the best.

The six-day creation of Genesis and the 13.8-billion-year cosmic history appear irreconcilable. This paper demonstrates their mathematical consistency as measurements from different relativistic reference frames. We derive a Lorentz factor γ = 8.40 × 10^11 and construct an exponential mapping wherein each creation day corresponds to twice the cosmic duration of the previous. The resulting chronology aligns the six days with major cosmic epochs from primordial light to human emergence. The observer-dependence of time, experimentally verified in special relativity, provides a framework for reconciling scriptural accounts with scientific findings without rejecting either.

Affective aspects of a stimulus can be processed rapidly and before cognitive attribution, acting much earlier for verbal stimuli than previously considered. Aimed for specific mechanisms, event-related brain potentials (ERPs), expressed in facial expressions or word meaning and evoked by six basic emotions – anger, disgust, fear, happy, sad, and surprise – relative to emotionally neutral stimuli were analysed in a sample of 116 participants. Brain responses in the occipital and left temporal regions elicited by the sadness in facial expressions or words were indistinguishable from responses evoked by neutral faces or words. Confirming previous findings, facial fear elicited an early and strong posterior negativity. Instead of expected parietal positivity, both the happy faces and words produced significantly more negative responses compared to neutral. Surprise in facial expressions and words elicited a strong early response in the left temporal cortex, which could be a signature of appraisal. The results of this study are consistent with the view that both types of affective stimuli, facial emotions and word meaning, set off rapid processing and responses occur very early in the processing stage.