arXiv subjects

Jeffrey D. Varner

Publications and source records attributed to Jeffrey D. Varner.

14 recordsLinked to original sources

arXiv2026

Interpretable Allocation and Model-Predictive Rebalancing of Equity Portfolios, Tested on Real and Synthetic Markets

A live equity portfolio poses three problems: which stocks to hold, when to trade, and whether the strategy holds up beyond the observed market. We built one system for all three and tested it on 373 US equities, calibrated on 2014-2024 and traded from January 2025 to September 2026. A selection rule chose stocks by score, by a bandit, or at random, and one of seven weighting rules, four consumer-theory utilities, and three standard portfolios, set share counts under limits on budget, single-stock weight, portfolio volatility, and turnover, with each stock's preference weight a bounded score of its trend, market beta, and the market's recent direction. A model-predictive controller forecasts portfolio value with a multi-asset geometric Brownian motion and re-planned at its horizon, when the value left its forecast band, or at a drawdown stop. To probe deeper declines than the real window held, we also ran the system on simulated markets from per-asset hidden Markov generators with jumps, linked by market and sector factors. On real prices, the stocks chosen mattered more to terminal wealth than the weighting rule, and the early re-plans shrank the worst drawdown in most rule combinations against a fixed calendar without consistently raising wealth. In the deepest simulated declines, every combination, random picks included, ended above simulated SPY and the equal-weight universe in the median, even without early re-plans, so the margin came from shared parts of the system, not from stock selection or re-plan timing. A market hedge that tightened a beta cap as the market weakened cost wealth on real prices but paid off in the most sustained simulated declines, and the generator's persistent trends favored score-based selection more than the real market did, which suggests a synthetic test judges stock selection fairly only if its generator does not build in that persistence.

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arXiv2026

Variance-Corrected Multi-Asset Equity Simulation with Hybrid Hidden Markov Marginals

Synthetic multi-asset equity data must reproduce each asset's return distribution and its relationship with the market. Reusing a generator fitted to full asset returns creates a problem: adding its draws to a market factor counts market variance twice. We derived a correction that centers and rescales each draw over a fixed horizon before adding the market factor, allowing reuse without fitting a second generator to regression residuals. We tested the correction on 423 non-market assets in a 424-asset United States equity and exchange-traded-fund universe, using hidden Markov generators with heavy-tailed emissions. The corrected paths retained heavy tails and recovered the calibrated market loadings with low error. On 416 complete asset histories held out from 2025, the correction improved the mean Kolmogorov-Smirnov pass rate over naive composition and brought the median ratio of synthetic to observed variance close to one. Its one-day left-tail 99% Value-at-Risk exceedance rate, using thresholds pooled across separate simulated paths, was 1.12%, compared with 1.16% for the residual-fit hidden Markov comparator and a nominal rate of 1%. We also tested a jump-duration mechanism that extended visits to extreme-return states and improved volatility clustering for the broad-market exchange-traded fund with ticker SPY. The multi-asset correction remained effective with jumps enabled, but transferring the SPY jump settings improved temporal fit in training and worsened it in the 2025 holdout. The method provides a way to reuse fitted asset generators for daily-fit comparisons. Its zero-sum residual constraint removes terminal residual uncertainty, and unmodeled dependence among asset-specific residuals can lead to overstated rebalancing returns. Code, cached inputs, result summaries, and instructions for fitting the per-asset models accompany the paper.

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arXiv2026

Synthetic American Option Pricing via Jump-HMM-Driven Heston Implied Volatility

Valuing American options along simulated stock paths requires an implied volatility (IV) for every option on every date. A stock-return model alone does not provide it. We built a simulator that assigned IV to American options on simulated dates for any chosen stock model. We fitted parametric and neural IV surfaces to vendor option quotes for 31 tickers. Each surface predicted IV from moneyness and time to expiration. Stock paths came from a jump hidden Markov model with capped daily returns. Each day, every option's implied variance moved partway toward its surface prediction, following the form of the Heston variance equation. Random shocks tended to raise IV when the stock fell. A binomial tree converted IV into option values and price sensitivities. Neural surfaces fitted by sector or ticker matched the quotes more closely than one parametric surface. Their errors still varied by date and carried into dollar prices. Repricing identical stock paths under five ways of updating IV changed option values before expiration, and the worst simulated short-position losses at a fixed horizon. Payoffs at expiration did not change. In forecasts of later Goldman Sachs and Eli Lilly option prices, stochastic IV did little better than fixed IV. Rerunning the forecasts with the realized stock paths pointed to stock prediction as a major source of option-price error. The hidden Markov model and an adaptive-volatility model predicted stock prices about as accurately as assuming no change, and tuning found no gain from predicting direction. The adaptive-volatility model improved predicted price ranges for Eli Lilly but not Goldman Sachs. The simulator supported reproducible comparisons of IV and stock assumptions but did not forecast better than simpler alternatives. Complete option histories and prices consistent across strikes are needed before simulated prices can replace market data.

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arXiv2026

Validated Synthetic Patient Generation for Small Longitudinal Cohorts: Coagulation Dynamics Across Pregnancy

Small longitudinal cohorts, common in maternal health, rare diseases, and early-phase trials, limit computational modeling because enrollment is slow and the data are too sparse to train reliable models. We present multiplicity-weighted Stochastic Attention (SA), a generative framework based on modern Hopfield networks. Stochastic attention stores real patient profiles as memory patterns in a continuous energy landscape. The resulting distribution is a finite mixture with one component centered on each stored profile. We generated the reported cohort with Langevin dynamics; direct sampling from the same distribution reproduced its fidelity and membership-inference results. Multiplicity weights amplify selected subgroups at inference time without retraining. We applied the method to longitudinal coagulation data from 23 patients, with 72 features measured before pregnancy and during the first and third trimesters. The cohort included three patients with polycystic ovary syndrome and five who developed preeclampsia. Across statistical, structural, and mechanistic tests, including a separately specified coagulation model that was blind to the generator but calibrated on the same cohort, the synthetic profiles closely matched the real profiles under the measures applied at this sample size. A model calibrated on synthetic profiles predicted held-out real-patient TGA measurements as well as one calibrated on real profiles. These results provide proof of concept for using SA in the tested modeling tasks, including mechanistic calibration and hypothesis generation, with very small longitudinal cohorts.

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arXiv2026

Conditioning Protein Generation via Hopfield Pattern Multiplicity

Small protein-family alignments often contain a subset of interest but not enough labeled data to train a conditional generator. We condition a training-free stochastic-attention sampler by adding one multiplicity ratio to its logits. Increasing this ratio shifts generation from the full family toward the designated subset. For unit-norm memories, the resulting Boltzmann distribution is exactly a Gaussian mixture whose component weights are set by the multiplicities. This result separates exact conditioning in latent space from losses caused by sampling, PCA reconstruction, and sequence decoding. Across five Pfam families, attention followed the analytic target, but recovery of single-residue markers depended on how well PCA separated the designated and background sequences. A matched weighted profile HMM reproduced these markers more directly, while stochastic attention gave lower ESM2 pseudo-perplexity in the Kunitz comparison. Using a curated set of 23 omega-conotoxin sequences as the target subset produced diverse sequences that preserved the cysteine scaffold and Tyr13 and shifted other residues toward the designated set. These sequences are candidates for experimental testing; they do not establish binding.

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arXiv2026

Rethinking the Choice Behavior of Sugar Metabolism in Bacteria

Ramkrishna, Kompala, and Tsao proposed the cybernetic model of microbial growth, in which cells allocate enzyme synthesis resources according to a matching rule that mimics rational decision-making. The matching rule was later shown to be optimal under general assumptions about the underlying return-on-investment structure, yet the specific objective the cell maximizes, and the constraints bounding that choice, were never written down as an explicit economic decision. Here we supply that missing decision, recasting cybernetic enzyme-synthesis control as a consumer choice problem from microeconomic theory: the cell allocates a limited proteome budget among competing catabolic enzymes as a linear program (LP), maximizing a linear growth utility subject to a linear proteome budget constraint. Because the utility is linear, the LP's solution is geometric: whenever the iso-utility line's slope differs from the budget constraint's, the optimum is a corner, and the entire proteome budget is allocated to the enzyme for the single most profitable substrate. Corner solutions correspond to diauxic growth, and sequential substrate consumption follows from the choice of corner rather than a distinct regulatory mechanism. Only when the two slopes coincide does the optimum spread across the entire budget line instead of concentrating at a single corner; this degenerate case underlies simultaneous substrate use. Using only parameters estimated independently from single-substrate experiments, the LP-derived cybernetic variables reproduced the diauxic and triauxic batch growth of Klebsiella oxytoca on glucose-xylose and glucose-xylose-lactose mixtures, achieving a fit comparable to the classical matching law. Thus, sequential substrate use is the generic outcome of growth-maximizing specialization under perfect substitutability, and co-utilization is the degenerate case of equal profitability.

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arXiv2026

Training-Free Generation of Protein Sequences from Small Family Alignments via Stochastic Attention

Generating novel protein sequences that respect a family's statistical constraints typically requires training deep generative models on thousands to millions of examples. Yet most protein families are small: the median Pfam seed alignment contains only 22 sequences, a regime where learned models overfit or collapse. We propose \emph{stochastic attention} (SA), a training-free sampler that treats the modern Hopfield energy over stored sequences as a Boltzmann distribution and draws samples via Langevin dynamics. The score function is the residual of a single softmax attention operation, eliminating the need for a trained score network, pretraining data, or graphics processing units (GPUs). Across eight Pfam families spanning 37 to 420 sequences and 23 to 262 residues, SA generates sequences with low composition divergence, novelty, and structural plausibility supported by ESMFold and AlphaFold2. Compared with profile hidden Markov models (HMMs), EvoDiff, and the multiple sequence alignment (MSA) Transformer, SA is the only tested method to simultaneously achieve low composition divergence, genuine novelty, and sequence identity within each family's nearest-neighbor identity range; the others drift outside this range or produce near-copies. The critical inverse temperature is predicted from principal component analysis (PCA) dimensionality alone, enabling fully automatic operation from a seed alignment. In two domains with deep mutational scanning data, SA-generated substitutions are enriched for experimentally tolerated mutations beyond a position-matched null, and an independent language model (ESM2-650M) scores them within the natural range. Stochastic attention thus opens training-free sequence generation to the long tail of protein families too small for deep learning.

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arXiv2026

Continuous Hidden Markov Models for Equity Returns: Heavy-Tail Emission Families and Regime-Conditional Value-at-Risk

Synthetic generators of daily equity returns let practitioners stress test, backtest, and design scenarios that a single realized market history cannot supply, but only if the generator reproduces the stylized facts of real returns: heavy tails, negligible linear autocorrelation, and slow decay of the absolute-return autocorrelation. Hidden Markov models with few Gaussian states were long thought unable to reproduce that slow decay, and the standard fix was to abandon them for more complex hidden semi-Markov models. We revisit this issue with a continuous hidden Markov model whose regime chain governs the autocorrelation while per-regime densities govern the marginal, separating the temporal and distributional sides of the original failure. A unified expectation-maximization framework fits Gaussian, Student-t, Laplace, and generalized-error emissions under shared forward-backward recursions and quantile-based initialization, and a spectral identity bounds the number of decay modes by the rank of the centred transition matrix. Across SPY walk-forward folds, a sector-balanced 30-ticker panel, a CRSP cross-decade transfer, and a six-asset basket, that bound was not binding once a few states were used: heavy-tailed marginals, not additional decay modes, closed most of the fit gap, recovering volatility clustering above the i.i.d. baseline and narrowing the kurtosis gap without a tuning hyperparameter. The original failure is therefore distributional, not temporal. On daily US equities, a simple, interpretable Markov model suffices, and unlike a bootstrap or semi-Markov fit that wins only on a single-window fit, the fitted model also yields a regime-conditional Value-at-Risk that passes a joint conditional-coverage test and a copula that reproduces cross-asset correlations: one interpretable generator serving both path simulation and downstream risk and portfolio tasks.

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arXiv2026

Stochastic Attention via Langevin Dynamics on the Modern Hopfield Energy

Attention heads retrieve: given a query, they return a weighted average of stored values. We showed that this computation is one step of gradient descent on the modern Hopfield energy, and that Langevin sampling from the corresponding Boltzmann distribution yielded stochastic attention, a training-free sampler controlled by a single temperature parameter. Lowering the temperature gave exact retrieval; raising it gave open-ended generation. Because the energy gradient equals the attention map, no score network, training loop, or learned model was required, making the approach particularly suited to the low-data regime where learned generative models are starved of training signal. We derived an entropy inflection condition that identified the retrieval-to-generation transition temperature for any memory geometry and validated the sampler on five domains spanning two orders of magnitude in dimension. A single Boolean mask on the attention softmax, identical to the causal mask used in transformers but applied along the memory axis rather than the sequence axis, turned the sampler into a zero-shot class-conditional generator on Olivetti faces with no retraining and no learned classifier. On MNIST digit images, stochastic attention produced samples that were markedly more novel and more diverse than the best learned baseline while matching a Metropolis-corrected gold standard. On protein sequences from a small Pfam family, the generation regime preserved amino acid composition far more faithfully than a variational autoencoder at matched novelty, indicating that the training-free score function retained family-level fidelity that learned models lost. A denoising diffusion baseline failed across all memory sizes tested, producing samples indistinguishable from isotropic noise. The approach required no architectural changes to the underlying attention mechanism.

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arXiv2026

Computational framework for multistep metabolic pathway design

In silico tools are important for generating novel hypotheses and exploring alternatives in de novo metabolic pathway design. However, while many computational frameworks have been proposed for retrobiosynthesis, few successful examples of algorithm-guided xenobiotic biochemical retrosynthesis have been reported in the literature. Deep learning has improved the quality of synthesis and retrosynthesis in organic chemistry applications. Inspired by this progress, we explored combining deep learning of biochemical transformations with the traditional retrobiosynthetic workflow to improve in silico synthetic metabolic pathway designs. To develop our computational biosynthetic pathway design framework, we assembled metabolic reaction and enzymatic template data from public databases. A data augmentation procedure, adapted from literature, was carried out to enrich the assembled reaction dataset with artificial metabolic reactions generated by enzymatic reaction templates. Two neural network-based pathway ranking models were trained as binary classifiers to distinguish assembled reactions from artificial counterparts; each model output a scalar quantifying the plausibility of a 1-step or 2-step pathway. Combining these two models with enzymatic templates, we built a multistep retrobiosynthesis pipeline and validated it by reproducing some natural and non-natural pathways computationally.

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arXiv2026

ParetoEnsembles.jl: A Julia Package for Multiobjective Parameter Estimation Using Pareto Optimal Ensemble Techniques

Mathematical models of natural and man-made systems often have many adjustable parameters that must be estimated from multiple, potentially conflicting datasets. Rather than reporting a single best-fit parameter vector, it is often more informative to generate an ensemble of parameter sets that collectively map out the trade-offs among competing objectives. This paper presents ParetoEnsembles.jl, an open-source Julia package that generates such ensembles using Pareto Optimal Ensemble Techniques (POETs), a simulated-annealing-based algorithm that requires no gradient information. The implementation corrects the original dominance relation from weak to strict Pareto dominance, reduces the per-iteration ranking cost from $O(n^2 m)$ to $O(nm)$ through an incremental update scheme, and adds multi-chain parallel execution for improved front coverage. We demonstrate the package on a cell-free gene expression model fitted to experimental data and a blood coagulation cascade model with ten estimated rate constants and three objectives. A controlled synthetic-data study reveals parameter identifiability structure, with individual rate constants off by several-fold yet model predictions accurate to 7%. A five-replicate coverage analysis confirms that timing features are reliably covered while peak amplitude is systematically overconfident. Validation against published experimental thrombin generation data demonstrates that the ensemble predicts held-out conditions to within 10% despite inherent model approximation error. By making ensemble generation lightweight and accessible, ParetoEnsembles.jl aims to lower the barrier to routine uncertainty characterization in mechanistic modeling.

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arXiv2026

BSTModelKit.jl: A Julia Package for Constructing, Solving, and Analyzing Biochemical Systems Theory Models

We present BSTModelKit.jl, an open-source Julia package for constructing, solving, and analyzing Biochemical Systems Theory (BST) models of biochemical networks. The package implements S-system representations, a canonical power-law formalism for modeling metabolic and regulatory networks. BSTModelKit.jl provides a declarative model specification format, dynamic simulation via ordinary differential equation (ODE) integration, steady-state computation, and global sensitivity analysis using the Morris and Sobol methods. The package leverages the Julia scientific computing ecosystem, in particular the SciML suite of differential equation solvers, to provide efficient and flexible model analysis tools. We describe the mathematical formulation, software design, and demonstrate the package capabilities with illustrative examples.

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arXiv2024

MarketGPT: Developing a Pre-trained transformer (GPT) for Modeling Financial Time Series

This work presents a generative pre-trained transformer (GPT) designed for modeling financial time series. The GPT functions as an order generation engine within a discrete event simulator, enabling realistic replication of limit order book dynamics. Our model leverages recent advancements in large language models to produce long sequences of order messages in a steaming manner. Our results demonstrate that the model successfully reproduces key features of order flow data, even when the initial order flow prompt is no longer present within the model's context window. Moreover, evaluations reveal that the model captures several statistical properties, or 'stylized facts', characteristic of real financial markets and broader macro-scale data distributions. Collectively, this work marks a significant step toward creating high-fidelity, interactive market simulations.

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arXiv2024

Scalable Agent-Based Modeling for Complex Financial Market Simulations

In this study, we developed a computational framework for simulating large-scale agent-based financial markets. Our platform supports trading multiple simultaneous assets and leverages distributed computing to scale the number and complexity of simulated agents. Heterogeneous agents make decisions in parallel, and their orders are processed through a realistic, continuous double auction matching engine. We present a baseline model implementation and show that it captures several known statistical properties of real financial markets (i.e., stylized facts). Further, we demonstrate these results without fitting models to historical financial data. Thus, this framework could be used for direct applications such as human-in-the-loop machine learning or to explore theoretically exciting questions about market microstructure's role in forming the statistical regularities of real markets. To the best of our knowledge, this study is the first to implement multiple assets, parallel agent decision-making, a continuous double auction mechanism, and intelligent agent types in a scalable real-time environment.

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