Twenty years of one method, two published domains. Mathematical modeling of nonlinear systems: applied to molten polymers in extrusion equipment (2010–2022), now applied to advertising auctions and media budgets (2025–). Both bodies of work are published and DOI-indexed: preprints, proceedings, patents, monographs.
- ORCID 0000-0002-9749-6414
- Google Scholar
- Wikidata Q134698095
- Both corpora — one author
The flow of a non-Newtonian polymer melt through an extruder channel is a nonlinear system with feedback: change one parameter and the whole system responds, often against intuition. You cannot brute-force such a system into an optimum. You model it, find its governing equations, and only then touch the controls. That discipline is where my PhD (Igor Sikorsky Kyiv Polytechnic Institute, 2016) and 200+ scientific publications were built.
An advertising account at scale behaves the same way. An auction is a nonlinear system with feedback. A media budget spread across campaigns is a portfolio under uncertainty, the same mathematical object finance has optimized since Markowitz. Average ROAS hides the truth the way average temperature hides a patient’s fever. My recent papers make the transfer explicit, and the titles say it literally: impedance matching applied to conversion funnels, reflection coefficients of multi-stage systems, matched-filter theory for message optimization. The same class of operators and equations, adapted and stated in the papers below (start with Funnel Resonance Theory).
The transfer ran through applied industry research in real-time click-fraud detection before the first advertising papers appeared. This page is the registry of both corpora: the 2025–2026 advertising-science papers with resolvable identifiers and a one-line summary of what each paper claims, and the 2010–2022 engineering corpus where the method was forged.
Career scale: $770M+ ad spend overseen since 2006 (practice metric, not a research result) · Research data: $133M+ of ad spend examined by Ivitskiy Ads Lab.
Advertising Science, 2025–2026
25 papers · 11 resolvable DOIs (4 Zenodo preprints, 7 conference-proceedings DOIs) · the rest link to preprint or proceedings pages directly.
Featured
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Funnel resonance theory: An impedance-matching framework for advertising conversion optimizationConversion capacity bounded by multi-stage audience intersection and impedance mismatch; simultaneous stage alignment yields Lorentzian resonance amplification.
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Data integrity as the terminal constraint in AI-driven advertising: An information-theoretic analysis of conversion fraud and agentic threat evolutionProves data-processing inequality hard-caps AI ad optimization under poisoned conversions; four-generation fraud taxonomy plus signal-hygiene verification.
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The MATH Framework: A First-Principles Approach to Quant Marketing in High-Uncertainty EnvironmentsDefines Linear-Exponential Gap and M.A.T.H. recursive Measure–Analyze–Tweak–Harvest protocol with cycle velocity, causal deconfounding, and privacy-compatible aggregate optimization.
Budget Optimization & Portfolio Theory6
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Marginal Analysis Vs. Average ROAS: the Profit-maximization Fallacy in Digital Advertising Budget AllocationUnder concave R(x)=ax^b, average-ROAS rules systematically under-invest profitable channels; profit max requires equating marginal revenue to marginal cost.
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Fix Unit Economics First: a Causal LTV Model That Aligns Pricing, Payback, and RetentionUnit economics fail more from wrong causal targets in LTV definitions than missing definitions; proposes causal LTV aligning pricing, payback, retention.
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Feedback Loop Amplification in Algorithmic Budget Allocation: a Discrete Logistic Model of the Advertiser Death Spiral
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The Marketing Efficient Frontier: Balancing Short, Mid, and Long-horizon Assets for Compounding RoicCasts short/mid/long-horizon media as mean–variance ROIC portfolio with adstock/Hill response; efficient frontier plus floors/caps compounds log-growth under causal checks.
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From playbooks to code: translating bidding strategy into rigorous objective functions and constraintsTranslates budget, ROAS, and CPA playbook rules into convex bidding programs; dual variables act as shadow prices for online primal–dual pacing.
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A Portfolio Optimization Model for Media Investment under Incrementality UncertaintyMean–variance (or robust) media allocation over channels using geo-experiment iROAS posteriors and concave MMM response under budget and incrementality uncertainty.
Causality & Incrementality3
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Causal Identification under Confounding in Digital Advertising: from Pearl’s Adjustment Formula to Operational Lift StudiesMaps Pearl adjustment and potential outcomes to ad lift studies; holdout randomization deconfounds spend–outcome links for incremental revenue estimation.
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Calibrate or Crash: a Guide to Using Incrementality Tests to Stop Model Drift in MMM and MTATreats geo incrementality tests as causal calibrators that re-anchor drifting Bayesian MMM/MTA via ROAS priors and residual drift sensing.
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Incrementality At Scale: a Blueprint for Corporate Holdouts, Geo-experiments, and Platform Leakage ControlBlueprint for corporate holdouts and geo-experiments with leakage/interference controls; DiD and BSTS estimators convert lift into iROAS for portfolio finance decisions.
Funnel Physics4
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Reflection Coefficients in Multi-stage Conversion Systems: an Impedance-mismatch Model of Funnel Boundary LossesAdapts transmission-line reflection coefficients to funnel boundaries; cascaded |Γ| multiplies irreversible mismatch losses budget cannot fix.
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Matched Filter Theory Applied to Marketing Message Optimization: SNR Maximization via Cauchy–schwarz EqualityMaps message optimization to matched filters: Cauchy–Schwarz equality maximizes conversion SNR when message conjugate-matches audience need profile.
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Lorentzian Response in Conversion Systems: Nonlinear Amplification under Simultaneous Stage AlignmentModels funnel conversion as multi-stage Lorentzian resonance; peak CR multiplies stage Q-factors only when all alignment deviations approach zero.
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Funnel resonance theory: An impedance-matching framework for advertising conversion optimizationConversion capacity bounded by multi-stage audience intersection and impedance mismatch; simultaneous stage alignment yields Lorentzian resonance amplification.
Data Integrity & Privacy4
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The Regulatory Paradox: Asymmetric Signal Attenuation under Privacy Regulation in Adversarial Advertising EnvironmentsPrivacy rules attenuate only genuine conversion signal (λ), not bot fraud, collapsing SNR so compliance degrades learnability without changing adversary activity.
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The Programmatic Waste Paradox: Why Suppression of Individual Fraud Vectors Fails to Reduce Aggregate LossesFraud capacity is conserved: suppressing one vector (e.g. MFA) redistributes adversarial mass to other vectors, so aggregate waste can rise despite vector wins.
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Signal Hygiene as a Privacy-compatible Verification Paradigm for Conversion Event IntegrityReframes fraud defense as event-level signal hygiene with three-tier verify-then-trust hierarchy, privacy-compatible under DPI and tracking collapse.
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Data integrity as the terminal constraint in AI-driven advertising: An information-theoretic analysis of conversion fraud and agentic threat evolutionProves data-processing inequality hard-caps AI ad optimization under poisoned conversions; four-generation fraud taxonomy plus signal-hygiene verification.
System Limits3
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The Audience Intersection Bound: a Set-theoretic Ceiling on Conversion Capacity Independent of Traffic VolumeDefines conversion-eligible set as intersection of stage audiences; cardinality is a traffic-independent ceiling under independent targeting.
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Entropy of Inaction: Degradation Dynamics and Steady-state Performance in Recursive Optimization SystemsModels ad performance decay via ODE with fatigue, competition, and drift; continuous M.A.T.H. loops set steady-state Pss; halt yields ~14-month half-life.
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Antifragility in Advertising Systems: Conditions for Converting Environmental Volatility Into Informational AdvantageAntifragility needs three conditions together: measurement sovereignty, high cycle velocity, and experimental budget reserves for disruption-triggered exploration.
AI Architectures for Decisions5
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The Diversity Prediction Theorem as a Mathematical Guarantee of Ensemble Superiority: Implications for Structured AI DeliberationUses Page’s Diversity Prediction Theorem as algebraic identity: collective squared error equals average error minus prediction diversity.
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Synthetic Consilium: Multi-Agent AI Architecture Against Cognitive Bias Amplication in Executive Decision-MakingProposes multi-agent Synthetic Consilium enforcing adversarial deliberation and diversity (Diversity Prediction Theorem) to debias executive LLM-aided decisions.
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Degeneration-of-thought in Single-agent Self-correction: Quantitative Evidence and the Structural Case for External Adversarial CritiqueSynthesizes evidence that single-agent LLM self-correction fails structurally (DoT/epistemic lock-in); external heterogeneous adversarial critique is the minimum viable fix.
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The MATH Framework: A First-Principles Approach to Quant Marketing in High-Uncertainty EnvironmentsDefines Linear-Exponential Gap and M.A.T.H. recursive Measure–Analyze–Tweak–Harvest protocol with cycle velocity, causal deconfounding, and privacy-compatible aggregate optimization.
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API-native Marketing Operations: a Reference Architecture for Automated Decision LoopsReference architecture of Observe–Decide–Execute–Learn API loops using uplift utilities, Lagrange budget shadow prices, and continuous bandit/retraining for counterfactual-aware automation.
Engineering Corpus, 2010–2022
200+ scientific publications, 3 scientific monographs, 50+ patents
- 200+publications
- 50+patents
- 3monographs
- PhDKPI, 2016
Mathematical modeling of polymer processing at Igor Sikorsky Kyiv Polytechnic Institute: 61 journal articles, 92 conference papers, 40 patents catalogued in the registry below (full patent list: Google Patents inventor query), monographs and applied R&D reports.
Named anchors:
- Wall Effects in Polymer Flow Processes (Пристінні ефекти в процесах течії полімерів) · monograph, Kyiv Polytechnic, 2016
- Analysis of the Preform Blowing Stage when Obtaining a Polymeric Product · DOI: 10.15587/1729-4061.2018.126015, 2018
- Experimental studies of wall-slip effects in polymer materials · article series, 2015
- Intelligent sensors in polymer composites · article and patent series, 2016–2017
Awards: President of Ukraine Prize for Young Scientists (2018) · Young Scientist of the Year, Ukraine (2020) · Cabinet of Ministers scholarship (2016, 2018) · Best Research Paper ISAPAM (2019).
Identifiers & Data
- ORCID 0000-0002-9749-6414 · Scopus 57193360633 · ResearcherID N-6430-2014 · Wikidata Q134698095
- Google Scholar profile (citation metrics as of August 2026 visible on profile)
- Machine-readable registry: CSV · JSON (240 entries, each with evidence source)