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.

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.

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

Small longitudinal clinical cohorts, common in maternal health, rare diseases, and early-phase trials, limit computational modeling: too few patients to train reliable models, yet too costly and slow to expand through additional enrollment. We present multiplicity-weighted Stochastic Attention (SA), a generative framework based on modern Hopfield network theory that addresses this gap. SA embeds real patient profiles as memory patterns in a continuous energy landscape and generates novel synthetic patients via Langevin dynamics that interpolate between stored patterns while preserving the geometry of the original cohort. Per-pattern multiplicity weights enable targeted amplification of rare clinical subgroups at inference time without retraining. We applied SA to a longitudinal coagulation dataset from 23 pregnant patients spanning 72 biochemical features across 3 visits (pre-pregnancy baseline, first trimester, and third trimester), including rare subgroups such as polycystic ovary syndrome and preeclampsia. Synthetic patients generated by SA were statistically, structurally, and mechanistically indistinguishable from their real counterparts across multiple independent validation tests, including an ordinary differential equation model of the coagulation cascade. A downstream utility test further showed that a mechanistic model calibrated entirely on synthetic patients predicted held-out real patient outcomes as well as one calibrated on real data. These results demonstrate that SA can produce clinically useful synthetic cohorts from very small longitudinal datasets, enabling data-augmented modeling in small-cohort settings.

Conditioning Protein Generation via Hopfield Pattern Multiplicity

Protein sequence generation via stochastic attention produces plausible family members from small alignments without training, but treats all stored sequences equally and cannot direct generation toward a functional subset of interest. We show that a single scalar parameter, added as a bias to the sampler's attention logits, continuously shifts generation from the full family toward a user-specified subset, with no retraining and no change to the model architecture. A practitioner supplies a small set of sequences (for example, hits from a binding screen) and a multiplicity ratio that controls how strongly generation favors them. The method is agnostic to what the subset represents: binding, stability, specificity, or any other property. We find that the conditioning is exact at the level of the sampler's internal representation, but that the decoded sequence phenotype can fall short because the dimensionality reduction used to encode sequences does not always preserve the residue-level variation that defines the functional split. We term this discrepancy the calibration gap and show that it is predicted by a simple geometric measure of how well the encoding separates the functional subset from the rest of the family. Experiments on five Pfam families (Kunitz, SH3, WW, Homeobox, and Forkhead domains) confirm the monotonic relationship between separation and gap across a fourfold range of geometries. Applied to omega-conotoxin peptides targeting a calcium channel involved in pain signaling, curated seeding from 23 characterized binders produces over a thousand candidates that preserve the primary pharmacophore and all experimentally identified binding determinants. These results show that stochastic attention enables practitioners to expand a handful of experimentally characterized sequences into diverse candidate libraries without retraining a generative model.

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

Most protein families have fewer than 100 known members, a regime where deep generative models overfit or collapse. We propose stochastic attention (SA), a training-free sampler that treats the modern Hopfield energy over a protein alignment as a Boltzmann distribution and draws samples via Langevin dynamics. The score function is a closed-form softmax attention operation requiring no training, no pretraining data, and no GPU, with cost linear in alignment size. Across eight Pfam families, SA generates sequences with low amino acid compositional divergence, substantial novelty, and structural plausibility confirmed by ESMFold and AlphaFold2. Generated sequences fold more faithfully to canonical family structures than natural members in six of eight families. Against profile HMMs, EvoDiff, and the MSA Transformer, which produce sequences that drift far outside the family, SA maintains 51 to 66 percent identity while remaining novel, in seconds on a laptop. The critical temperature governing generation is predicted from PCA dimensionality alone, enabling fully automatic operation. Controls confirm SA encodes correlated substitution patterns, not just per-position amino acid frequencies.

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 statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches, from parametric models to deep generative networks, struggle to simultaneously reproduce heavy-tailed distributions, negligible linear autocorrelation, and persistent volatility clustering. We propose a hybrid hidden Markov framework that discretizes continuous excess growth rates into Laplace quantile-defined market states and augments regime switching with a Poisson-driven jump-duration mechanism to enforce realistic tail-state dwell times. Parameters are estimated by direct transition counting, bypassing the Baum-Welch EM algorithm. Synthetic data quality is evaluated using Kolmogorov-Smirnov and Anderson-Darling pass rates for distributional fidelity, and ACF mean absolute error for temporal structure. Applied to ten years of SPY data across 1,000 simulated paths, the framework achieves KS and AD pass rates exceeding 97% and 91% in-sample and 94% out-of-sample (calendar year 2025), partially reproducing the ARCH effect that standard regime-switching models miss. No single model dominates all quality dimensions: GARCH(1,1) reproduces volatility clustering more accurately but fails distributional tests (5.5% KS pass rate), while the standard HMM without jumps achieves higher distributional fidelity but cannot generate persistent high-volatility regimes. The proposed framework offers the best joint quality profile across distributional, temporal, and tail-coverage metrics. A Single-Index Model extension propagates the SPY factor path to a 424-asset universe, enabling scalable correlated synthetic path generation while preserving cross-sectional correlation structure.