Search NASA⌕ Search

SEARCH · Search NASA

Results for “chain distribution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Synthesis of End-Functionalized Poly(norbornenes) and Poly(ethylidene norbornenes) Using a Pd(II) Catalyst in Combination with Chain Transfer Agents

Synthesis of end-functionalized poly(norbornene)s (PNBs) and poly(ethylidenenorbornene)s (PENBs) were prepared using the palladium catalyst t Bu 3 PPdMeCl/NaBAr f in combination with chain transfer agents (CTAs) 4-penten-1-ol and 10-undecenal. These CTAs produce polymers end-capped with -OH and -CHO groups, respectively, in high yields with M n values in the range of 6K to 17K, depending on the molar ratio of the CTA: monomer. End-functionalized PNBs and PENBs with precisely controlled Mn values and very narrow molecular weight distributions were accessed by using 4-penten-1-ol and 10-undecenal as chain-terminating agents following living polymerizations in which monomer is completely consumed. The utility of the aldehyde-functionalized polymers is illustrated via coupling to a dye molecule and by synthesis of ambiphilic diblock copolymers, PNB-b-PEG and PENB-b-PEG.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A fast particle-based approach for calibrating a 3-D model of the Antarctic ice sheet

We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases. Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea level rise in 2300 increases from 6.5 m to 13.1 m when we increase the number of calibrated parameters from three to 11. With previous calibration methods, it would be challenging to go beyond five parameters. Here, this work provides an important next step toward improving the uncertainty quantification of complex, computationally intensive and decision-relevant models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

How to Obtain the Redshift Distribution from Probabilistic Redshift Estimates

Abstract A reliable estimate of the redshift distribution n ( z ) is crucial for using weak gravitational lensing and large-scale structures of galaxy catalogs to study cosmology. Spectroscopic redshifts for the dim and numerous galaxies of next-generation weak-lensing surveys are expected to be unavailable, making photometric redshift (photo- z ) probability density functions (PDFs) the next best alternative for comprehensively encapsulating the nontrivial systematics affecting photo- z point estimation. The established stacked estimator of n ( z ) avoids reducing photo- z PDFs to point estimates but yields a systematically biased estimate of n ( z ) that worsens with a decreasing signal-to-noise ratio, the very regime where photo- z PDFs are most necessary. We introduce Cosmological Hierarchical Inference with Probabilistic Photometric Redshifts ( CHIPPR ), a statistically rigorous probabilistic graphical model of redshift-dependent photometry that correctly propagates the redshift uncertainty information beyond the best-fit estimator of n ( z ) produced by traditional procedures and is provably the only self-consistent way to recover n ( z ) from photo- z PDFs. We present the chippr prototype code, noting that the mathematically justifiable approach incurs computational cost. The CHIPPR approach is applicable to any one-point statistic of any random variable, provided the prior probability density used to produce the posteriors is explicitly known; if the prior is implicit, as may be the case for popular photo- z techniques, then the resulting posterior PDFs cannot be used for scientific inference. We therefore recommend that the photo- z community focus on developing methodologies that enable the recovery of photo- z likelihoods with support over all redshifts, either directly or via a known prior probability density.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Shoulder fillet effects in strength distributions of microelectromechanical system components

The failure forces and fracture strengths of polysilicon microelectromechanical system (MEMS) components in the form of stepped tensile bars with shoulder fillets were measured using a sequential failure chain methodology. Approximately 150 specimens for each of four fillet geometries with different stress concentration factors were tested. The resulting failure force and strength distributions of the four geometries were related by a common sidewall flaw population existing within different effective stressed lengths. The failure forces, strengths, and flaw population were well described by a weakest-link based analytical framework. Finite element analysis was used to verify body-force based expressions for the stress concentration factors and to provide insight into the variation of specimen effective length with fillet geometry. Monte Carlo simulations of flaw size and location, based on the strength measurements, were also used to provide insight into fillet shape and size effects. The successful description of the shoulder fillet specimen strengths provides further empirical support for application of the strength and flaw framework in MEMS fabrication and design optimization.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Securing Digital Energy Infrastructure: BESS Procurement Guidance & Sample Contract Terms

Presentation for Procurement webinar providing technical guidance for entities, procuring Battery Energy Storage Systems (BESS), Inverter Based Resources (IBR), Distributed Energy Resource Management Systems (DERMS) and other energy digital systems and services on how to incorporate cybersecurity requirements into the procurement process to enhance both supply chain security as well as entity-specific supply chain risk management (SCRM) programs.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Joint estimation of biogeochemical model parameters from multiple experiments: A bayesian approach applied to mercury methylation

Here, to characterize complex biogeochemical systems, results from multiple experiments, where each targets a specific subprocess, are commonly combined. The resulting datasets are interpreted through the calibration of biogeochemical models for process inference and predictions. Commonly used calibration approaches of fitting datasets from individual experiments to subprocess models one at a time is prone to missing information shared between datasets and incomplete uncertainty propagation. We propose a Bayesian joint-fitting scheme addressing the above-mentioned concerns by jointly fitting all the available datasets, thus calibrating the entire biogeochemical model in one go using Markov Chain Monte Carlo (MCMC). The identification of null spaces in the parameter distributions from MCMC guided the simplification of certain subprocess models. For example, fast kinetic sorption was replaced by equilibrium sorption, and Monod demethylation was replaced by first-order demethylation. Joint fitting of datasets resulted in complete uncertainty propagation with parameter estimates informed by all available data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Size and Structure Effects of Carbon-Supported Ruthenium Nanoparticles on Waste Polypropylene Hydrogenolysis Activity, Selectivity, and Product Microstructure

Hydrogenolysis of plastic waste using Ru-based catalysts is promising for deconstructing polyolefins into lower molecular weight products. Yet, the effect of catalyst atomic structure and size on activity and product selectivity is poorly understood. Herein, we expose the effect of metal particle size and atomic structure on isotactic-polypropylene (i-PP) hydrogenolysis over Ru supported on carbon. Despite similar molecular weight distributions of solid and liquid products, their physical properties are distinct due to different chain regio-irregular CH3 sequences of steric pentads containing racemo configurations. We propose that i-PP hydrogenolysis entails an interplay of C–C bond scission and stereoisomerization. The active site’s local electronic environment and structure dictate the former, whereas polymer–catalyst surface interactions creating suitable polymer conformations control the latter. C–C scission and stereoisomerization are structure-sensitive. Small, disordered nanoclusters are effective in C–C bond scission, whereas larger metal nanoparticles promote stereoisomerization. Finally, we hypothesize that a heterogeneous distribution of metal active sites is essential for deconstruction and product (lubricant base oil) quality control.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Fine structure of the isovector giant dipole resonance in Nd 142 – 150 and Sm 152

Inelastic proton scattering at energies of a few hundred MeV and very-forward scattering angles including 0° has been established as a tool for the study of electric-dipole strength distributions in nuclei. The present work reports a systematic investigation of the chain of stable even-mass Nd isotopes representing a transition from spherical to quadrupole-deformed nuclei. Extraction of the equivalent photo-absorption cross sections and analysis of their fine structure in the energy region of the isovector giant dipole resonance (IVGDR). Method: Proton inelastic scattering reactions of 200 MeV protons were measured at the iThemba Laboratory for Accelerator Based Sciences in Cape Town, South Africa. The scattering products were momentum-analyzed by the K600 magnetic spectrometer positioned at θ Lab = 0°. Using dispersion-matching techniques, energy resolutions of ΔE ≈ 40–50 keV (full width at half maximum) were obtained. After subtraction of background and contributions from other multipoles, the spectra were converted to photoabsorption cross sections using the equivalent virtual-photon method. Wavelet-analysis techniques are used to extract characteristic energy scales of the fine structure of the IVGDR from the experimental data. Fine structure of the IVGDR is observed even for the most deformed nuclei studied. Comparisons between the extracted experimental energy scales and those energy scales obtained from the quasiparticle-phonon model (QPM) and Skyrme separable random phase approximation (SSRPA) predictions provide insight into the role of different giant-resonance damping mechanisms. It can be seen that the scales in the spherical and most likely also in the deformed nuclei mainly result from the fragmentation of the one-particle-one-hole (1p1h) strength into several dominant transitions serving as doorway states. In cases where calculations beyond the 1p1h level are available, some impact of the spreading due to coupling of the two-particle-two-hole (2p2h) states to the 1p1h doorway states is observed. New virtual-photon absorption data for the chain of stable Nd isotopes and 152 Sm are presented, with a focus on the phenomenon of nonstatistical cross-section fluctuations, referred to as fine structure, in the energy region of the IVGDR. The wavelet-analysis techniques used allowed for the features of the fine structure to be quantified in the form of characteristic scales. Finally, comparisons between experimental results and model predictions indicate that Landau damping seems to be the main source of the fine structure in both the spherical and deformed nuclei, but calculations including 2p2h degrees of freedom would be beneficial to confirm this for the deformed cases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Uncertainty quantification of mass models using ensemble Bayesian model averaging

Developments in the description of the masses of atomic nuclei have led to various nuclear mass models that provide predictions for masses across the whole chart of nuclides. These mass models play an important role in understanding the synthesis of heavy elements in the rapid neutron capture ( r ) process. However, it is still a challenging task to estimate the size of uncertainty associated with the predictions of each mass model. In this work, a method called ensemble Bayesian model averaging (EBMA) is introduced to quantify the uncertainty of one-neutron separation energies (S 1 n ) which are directly relevant in the calculations of r -process observables. Here, this Bayesian method provides a natural way to perform model averaging, selection, and uncertainty quantification, by combining the mass models as a mixture of normal distributions whose parameters are optimized against the experimental data, employing the Markov chain Monte Carlo method using the no-u-turn sampler. The EBMA model optimized with all the experimental S 1 n from the AME2003 nuclides are shown to provide reliable uncertainty estimates when tested with the new data in the AME2020.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping

Here, we study the one-dimensional nearest-neighbor tight-binding model of electrons with independently distributed random hopping and no on-site potential (i.e., off-diagonal disorder with particle-hole symmetry, leading to sublattice symmetry, for each realization). For nonsingular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states $ρ(E) ~ 1/|E\: \text{ln}^3 |E||$ and of the localization length $ξ(E) ~ |\text{ln}|E||$, near the band center $\textit{E}$ = 0 . (This singular behavior is also applicable to random $\textit{XY}$ and Heisenberg spin chains; it was first obtained by Dyson for a specific random harmonic oscillator chain.) Simultaneously, the state at$\textit{E}$ = 0 shows a universal, subexponential decay at large distances $\sim \text{exp}[–\sqrt{r/r_0}]$. In this study, we consider singular, but normalizable, distributions of hopping, whose behavior at small $\textit{t}$ is of the form $\sim 1/[t \text{ln}^{λ+1}(1/t)]$, characterized by a single, continuously tunable parameter λ > 0. We find, using a combination of analytic and numerical methods, that while the universal result applies for λ > 2, it no longer holds in the interval 0 < λ < 2. In particular, we find that the form of the density of states singularity is enhanced (relative to the Dyson result) in a continuous manner depending on the nonuniversal parameter λ; simultaneously, the localization length shows a less divergent form at low energies and ceases to diverge below λ = 1. For λ < 2, the fall-off of the $\textit{E}$ = 0 state at large distances also deviates from the universal result and is of the form $\sim\text{exp}[–(r/r_0)^{1/λ}]$ , which decays faster than an exponential for λ < 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Pyrolysis of bio-derived dioxolane fuels: A ReaxFF molecular dynamics study

Alkyl-substituted 1,3-dioxolanes, including 4,5-dimethyl-2-pentan-3-yl-1,3-dioxolane (Fuel 1), 4,5-dimethyl-2-pentyl-1,3-dioxolane (Fuel 2), and 2-(heptan-3-yl)-4,5-dimethyl-1,3-dioxolane (Fuel 3), have been recently suggested as potential biodiesels. In this paper, we investigate the initial pyrolysis of the alkyl-substituted 1,3-dioxolanes at high temperatures using ReaxFF molecular dynamics (MD) simulations. We analyze the decomposition rate, reaction mechanism, and product distribution in the pyrolysis of the three alkyl 1,3-dioxlanes. The three fuels primarily decompose to 4,5-dimethyl-1,3-dioxolane radical and hydrocarbons derived from the alkyl side-chains. The further decomposition of 4,5-dimethyl-1,3-dioxolane radical primarily leads to 2-C 4 H 8 and CO 2 within a few decomposition steps. The hydrocarbon product distribution is significantly affected by the molecular structure of the alkyl side-chain, which would have a strong influence on the sooting tendency of these fuels. The ReaxFF simulations predict that the order of sooting tendency would be Fuel 3 > Fuel 1 > Fuel 2, which agrees with the measured sooting tendency trend. Based on the pyrolysis mechanism identified by ReaxFF, we propose a new alkyl dioxolane, 4-hexyl-5-methyl-1,3-dioxolane (Fuel 4), which might produce even less soot, by modifying the molecular structure of Fuel 2. Our ReaxFF simulation shows that Fuel 4 produce much less C 4 H 8 , an effective non-aromatic soot precursor, than Fuel 2. Moreover, more carbon atoms are bonded to each oxygen atom in Fuel 4 than Fuel 2, which would help reduce soot yield by removing more carbon atoms from the soot-producing pool of species. The major decomposition pathways identified in this work can be used to develop chemical kinetic models for 1,3-dioxolane based compounds, as biodiesel components, applicable to combustion engine simulations. We also demonstrate that the chemical kinetic insight offered by ReaxFF simulations can be used to design new fuel molecules with more desired properties.

09 BIOMASS FUELS↗
DOE OSTI2022

Behavioral and Population Data-Driven Distribution System Load Modeling

Distribution system residential load modeling and analysis for different geographic areas within a utility or an independent system operator territory are critical for enabling small-scale, aggregated distributed energy resources to participate in grid services under Federal Energy Regulatory Commission Order No. 2222 [1]. In this study, we develop a methodology of modeling residential load profiles in different geographic areas with a focus on human behavior impact. First, we construct a behavior-based load profile model leveraging state-of-the-art appliance models. We simulate human activity and occupancy using Markov chain Monte Carlo methods calibrated with the American Time Use Survey data set. Second, we link our model with cleaned Current Population Survey data from the U.S. Census Bureau. Finally, we populate two sets of 500 households using California and Texas census data, respectively, to perform an initial analysis of the load in different geographic areas with various group features (e.g., different income levels). To distinguish the effect of population behavior differences on aggregated load, we simulate load profiles for both sets assuming fixed physical household parameters and weather data. Analysis shows that average daily load profiles vary significantly by income and income dependency varies by locality.

American Time Use Survey↗
DOE OSTI2021

Effects of Ionic Group Distribution on the Structure and Dynamics of Amorphous Polymer Melts

Ionizable groups tethered to a polymer backbone often associate to form ionic clusters, whose features are determined by the balance of the polymer backbone and electrostatics. These assemblies impact the dynamics of the macromolecules and their ability to transport ions. Here, using fully atomistic molecular dynamics (MD) simulations, we investigate the effects of the distribution of ionizable groups along the polymer backbone on cluster characteristics and the resulting impacts on the structure and dynamics of amorphous polymers. Particularly, we probe polystyrene sulfonates (PSS) with random, precise, and block configurations of the SO 3 – sulfonate groups along the backbone with Na + as the counterion. We find that the distribution of the ionic groups affects the shape and distribution of the clusters as well as the internal packing of the ionizable groups in the cluster and the number of unique chains that participate in each cluster, affecting the structure and the dynamics of the polymers. Furthermore, the signature of ionic clusters, observed in the static structure factor S(q) for all three distributions, is significantly more pronounced for the precise and blocky polymers compared to the random one. Remarkably, we find that the local mobility of the polymer segments is not only affected by the number and size of the clusters but also by the number of polymer chains associated with clusters.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Bridging the gap between NMR measured mean silicate chain length and nano-scale silicate polymorphism of calcium silicate hydrates

Variable stoichiometry and silicate polymorphism in calcium-silicate-hydrates (C-S-H) has impeded the revelation of point defects distribution in the silicate tetrahedral network of C-S-H, which resembles tobermorite crystal structure with some bridging tetrahedra (BT) and paired tetrahedra (PT) vacancies in dreierketten chains. Here we use a computational approach to characterize silicate polymorphism by introducing the vacancy ratio of BT to PT (α) and establishing a three-term empirical mean chain length (MCL) formula for different calcium-to‑silicon ratios (Ca/Si) ranging from 1.2 to 2.3. The formula identifies BT and PT controls at low and high α respectively and allows an inverse mapping of polymorphic range based on NMR experiments. The proposed computational framework quantitatively describes silicate polymorphs and links NMR-measured MCL to C-S-H atomistic configurations at the molecular level.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Surveying Phase Modifier Functional Groups for Applications to Ln(III) Separations

The application of N,N,N',N'-tetraoctyl diglycolamide (TODGA) in solvent extraction systems for lanthanide (Ln) separations is well understood. In these systems, the formation of a third phase has motivated the use of phase modifiers to enable higher concentrations of H + and Ln common to industrial processes. Several different phase modifiers with applications to diglycolamide (DGA) systems have previously been reported, with a focus on tri-n-butyl phosphate (TBP), N,N'-dihexylactanamide (DHOA), N,N-dioctyl-2-hydroxyacetamide (DOHyA), N,N'-dimethyl-N,N'-dioctylhexylethoxy malonamide (DMDOHEMA), and octanol. While the primary utility of phase modifiers is the increased metal loading, they can have significant effects on the metal distribution ratios, which are well described by the energetics of the extraction process itself. However, the mechanisms by which phase modifiers impact distribution ratios are not generally understood. This work considers the ability of phase modifiers to affect Ln distribution ratios by using phase modifiers with two different functional groups (–Cl and –C≡N) and an octyl alkyl chain in a TODGA and n-dodecane system. Determining the effect of chlorooctane and octane nitrile is important for understanding how phase modifier functional groups and their hydrogen bonding interactions affect Ln extraction. Through combining distribution ratio measurements with organic phase spectroscopic investigations, the impact of chlorooctane and octane nitrile on Ln extraction and their inner-sphere complexes is reported. The addition of either chlorooctane or octane nitrile to TODGA in n-dodecane decreases Ln extraction while maintaining the same inner-sphere Ln complex. The lack of change in inner-sphere Ln-TODGA coordination upon incorporation of phase modifiers and the significant impact of these phase modifiers on distribution ratios suggest the importance of a supramolecular structure. Understanding the role of chlorooctane and octane nitrile on the organic phase structure at longer length scales has been identified as an avenue for future investigations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Beyond the universal Dyson singularity for 1-D chains with hopping disorder

We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain — that of random walks and diffusion with anomalous exponents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Size-Controlled Nanoparticles Embedded in a Mesoporous Architecture Leading to Efficient and Selective Hydrogenolysis of Polyolefins

A catalytic architecture, comprising a mesoporous silica shell surrounding platinum nanoparticles (NPs) supported on a solid silica sphere (mSiO2/Pt-X/SiO2; X is the mean NP diameter), catalyzes hydrogenolysis of melt-phase polyethylene (PE) into a narrow C23-centered distribution of hydrocarbons in high yield using very low Pt loadings (~10 -5 g Pt/g PE). During catalysis, a polymer chain enters a pore and contacts a Pt NP where the C–C bond cleavage occurs and then the smaller fragment exits the pore. mSiO 2 /Pt/SiO 2 resists sintering or leaching of Pt and provides high yields of liquids; however, many structural and chemical effects on catalysis are not yet resolved. Here, we report the effects of Pt NP size on activity and selectivity in PE hydrogenolysis. Time-dependent conversion and yields and a lumped kinetics model based on the competitive adsorption of long vs short chains reveal that the activity of catalytic material is highest with the smallest NPs, consistent with a structure-sensitive reaction. Remarkably, the three mSiO 2 /Pt-X/SiO 2 catalysts give equivalent selectivity. We propose that mesoscale pores in the catalytic architecture template the C 23 -centered distribution, whereas the active Pt sites influence the carbon–carbon bond cleavage rate. This conclusion provides a framework for catalyst design by separating the C–C bond cleavage activity at catalytic sites from selectivity for chain lengths of the products influenced by the structure of the catalytic architecture. The increased activity, selectivity, efficiency, and lifetime obtained using this architecture highlight the benefits of localized and confined environments for isolated catalytic particles under condensed-phase reaction conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Extending Conformal Prediction to Hidden Markov Models with Exact Validity via de Finetti’s Theorem for Markov Chains

Conformal prediction is a widely used method to quantify uncertainty in settings where the data is independent and identically distributed (IID), or more generally, exchangeable. Conformal prediction takes in a pre-trained classifier and a calibration dataset as inputs, and returns a function which maps feature vectors to subsets of classes. The output of the returned function for a new feature vector is guaranteed to contain the true class with a pre-specified confidence. Despite its success and usefulness in IID settings, extending conformal prediction to non-exchangeable (e.g., Markovian) data in a manner that provably preserves all desirable theoretical properties has largely remained an open problem. As a solution, we extend conformal prediction to the setting of a Hidden Markov Model (HMM) with unknown parameters. The key idea behind the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti’s Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are then viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework and is general enough to be useful in many sequential prediction problems.

Nettasinghe, Don Buddhika Wijayantha↗