arXiv subjects

Jeffrey D. Varner

Publications and source records attributed to Jeffrey D. Varner.

13 recordsLinked to original sources

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

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

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

Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and risk-analysis applications. We break this circularity with a pipeline in which implied volatility emerges as an output of a structural model of equity returns. A Jump Hidden Markov Model produces multi-asset price paths with realistic stylized facts and cross-asset tail dependence; a modified Heston variance process, whose mean-reversion target depends on regime state, days to expiration, moneyness, and a market-mood indicator, converts those paths into implied-volatility paths; and a recombining binomial lattice prices American options from the resulting surface. Initializing variance at its mean-reversion target for each strike-expiration pair lets smile, skew, and term structure emerge without external calibration. We calibrate the shape function through a hierarchy spanning a parametric baseline, a globally shared neural surrogate, and a sector-specific neural surrogate fit to a multi-ticker, multi-sector option ladder. A temporal holdout on a multi-day capture isolated scheduled corporate events as the dominant source of test-time generalization error, and calendar-derived earnings-distance and same-sector peer-coupling features recovered the anticipatory portion of that signal. We then apply the framework as a synthetic-data generator on real near-the-money put and call contracts, forward-simulating price paths, and recovering path-conditional implied volatility, finite-difference American Greeks, and terminal short-premium profit and loss from one coherent simulation, and confirm cross-ticker robustness by re-running on a second underlying from a different sector and volatility regime. The framework is released as an open-source Julia package.

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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.

cs.LG↗

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

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

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.

cs.LG↗

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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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.

cs.LG↗

arXiv2026

Hybrid Hidden Markov Model for Modeling Equity Excess Growth Rate Dynamics: A Discrete-State Approach with Jump-Diffusion

Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce heavy-tailed distributions, negligible linear autocorrelation, and persistent volatility clustering. We developed a hybrid hidden Markov framework that discretized excess growth rates into Laplace quantile-defined states and augmented regime switching with a Poisson jump-duration mechanism to enforce realistic tail-state dwell times. Parameters were estimated by direct transition counting, bypassing the Baum-Welch EM algorithm and scaling to a 424-asset pipeline. Applied to ten years of daily equity data, the framework achieved high distributional pass rates both in-sample and out-of-sample while partially reproducing the volatility clustering that standard regime-switching models miss. No single model was best at everything: GARCH(1,1) better reproduced volatility clustering but failed distributional tests, while the standard HMM without jumps passed more distributional tests but could not generate volatility clustering. The proposed framework delivered the most balanced performance overall. For multi-asset generation, copula-based dependence models that preserved each asset's marginal HMM distribution substantially outperformed a Single-Index Model factor baseline on both per-asset distributional accuracy and correlation reproduction.

q-fin.ST↗

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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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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