Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “BP”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Lattice Anisotropy-Driven Reduction of Phonon Velocities in Black Phosphorus

Phonon dynamics and transport determine how heat is utilized and dissipated in materials. In 2D systems for optoelectronics and thermoelectrics, the impact of nanoscale material structure on phonon propagation is central to controlling thermal conduction. Here, we directly observe in-plane coherent acoustic phonon propagation in black phosphorus (BP) using ultrafast electron microscopy. We identify a significant reduction of the group velocities in directions intermediate to the armchair and zigzag lattice directions. Using a machine learning-based model with an >8000 atom supercell, we find that this slowing results from the mixing of in-plane transverse and longitudinal acoustic phonons and is independent of broken symmetries of edge reconstructions. In conclusion, this work demonstrates how coherent phonon transport is sensitive to propagation direction in the lattice plane.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A Conjugated Oligoelectrolyte Exhibiting Room Temperature Spin-Correlated Radical Pair Character for Biological Sensing

We report a water-soluble conjugated oligoelectrolyte (COE) composed of carbazole-benzophenone, COE-CbzBP, that exhibits photogenerated spin-correlated radical pair (SCRP) behavior sensitive to static electric fields from DNA but not from lipid bilayers. The SCRP forms from a thermally activated, spin-polarized state enabled by partial π-conjugation disruption at the donor–acceptor (carbazole-benzophenone) nitrogen–carbon (N–C) junction, which facilitates a twisted intramolecular charge-transfer (TICT) geometry. This state minimizes the singlet–triplet energy gap (ΔE ST = 0.12 eV), radical–pair exchange coupling (J RP ∼ ΔE ST /2), and charge separation free energy (ΔG CS ) in both DNA (−0.19 eV) and lipid bilayers (−0.55 eV). Room-temperature continuous-wave electron paramagnetic resonance (CW-EPR) reveals a photogenerated spin-polarized singlet for COE-CbzBP that splits upon DNA association, consistent with modulation of J RP and hyperfine coupling (A x ), presumably via electric field-spin coupling. No spin-polarized signal was observed under dark, cryogenic conditions, or in liposomes, but was quenched by the spin trap 4-POBN. Transient absorption and spectroelectrochemistry confirmed magnetic-field sensitive long-lived excited-state absorption features attributed to charge-separated states 3 [Cbz •+ -BP •– ]*, which were lengthened by DNA, and quenched in lipid bilayers and 4-POBN. Quantum chemical simulations show that planar geometries (lipid-like) increase ΔE ST by 0.31 eV compared to TICT-optimized structures. This geometry-dependent modulation explains the absence of SCRP signatures in rigid environments, underscoring the importance of TICT states, minimized ΔE ST , and favorable ΔG CS for achieving room-temperature SCRP generation. These findings establish design principles for TICT-enabled molecules exhibiting qubit-like behavior that operate under ambient and biologically relevant conditions, with direct implications for quantum information science (QIS).

Aromatic compounds↗
DOE OSTI2022

Middle to Late Holocene Sea Surface Temperature and Productivity Changes in the Northeast Pacific

Variations of the sea surface temperature (SST) and primary productivity in the northeast Pacific have far‐reaching implications. In addition to influencing the regional and global temperature and hydroclimate, these conditions also control marine ecosystems and their services, which subsequently impact regional economies. Yet, our understanding of the variability and controls of northeast Pacific SST and productivity on timescales exceeding observational records remains limited. Here, we use marine sediment records from seven locations, spanning 25.2°N–59.6°N, in the northeast Pacific to characterize the millennial‐scale variability of SST and productivity from 9,000 to 1,000 years BP. We explore the dynamics of their spatiotemporal evolution and compare these data with transient climate model outputs to identify potential drivers. Through a heat budget analysis and optimal fingerprinting analysis, we characterize the spatial pattern of forcings. We find that SST varied spatially in the northeast Pacific, with higher latitudes exhibiting greater magnitude changes than lower latitudes, which differs from previous work suggesting regional synchronicity and coherence during the Holocene. Our analysis did not find evidence for coherent variability of primary producer community nor carbon export, highlighting the difficulty of identifying the complex interactions between environmental conditions, producers, and carbon export. Model‐proxy disagreement demonstrates the need for higher resolution model frameworks, but shows nonetheless that observed variability in the proxy records can be explained by a combination of greenhouse gas and orbital forcing. Here we suggest that the complex SST variations and marine ecosystem responses to forced changes are important factors that can drive disagreements in model projections.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Tailoring poplar lignin without yield penalty by combining a null and haploinsufficient CINNAMOYL-CoA REDUCTASE2 allele

Lignin causes lignocellulosic biomass recalcitrance to enzymatic hydrolysis. Engineered low-lignin plants have reduced recalcitrance but often exhibit yield penalties, offsetting their gains in fermentable sugar yield. Here, CRISPR/Cas9-generated CCR2(–/*) line 12 poplars have one knockout CCR2 allele while the other contains a 3-bp deletion, resulting in a 114I115A-to-114T conversion in the corresponding protein. Despite having 10% less lignin, CCR2(–/*) line 12 grows normally. On a plant basis, the saccharification efficiency of CCR2(–/*) line 12 is increased by 25–41%, depending on the pretreatment. Analysis of monoallelic CCR2 knockout lines shows that the reduced lignin amount in CCR2(–/*) line 12 is due to the combination of a null and the specific haploinsufficient CCR2 allele. Analysis of another CCR2(–/*) line shows that depending on the specific CCR2 amino-acid change, lignin amount and growth can be affected to different extents. Furthermore, our findings open up new possibilities for stably fine-tuning residual gene function in planta.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Structural basis of R-loop recognition by the S9.6 monoclonal antibody

R-loops are ubiquitous, dynamic nucleic-acid structures that play fundamental roles in DNA replication and repair, chromatin and transcription regulation, as well as telomere maintenance. The DNA-RNA hybrid–specific S9.6 monoclonal antibody is widely used to map R-loops. Here, we report crystal structures of a S9.6 antigen-binding fragment (Fab) free and bound to a 13-bp hybrid duplex. We demonstrate that S9.6 exhibits robust selectivity in binding hybrids over double-stranded (ds) RNA and in categorically rejecting dsDNA. S9.6 asymmetrically recognizes a compact epitope of two consecutive RNA nucleotides via their 2'-hydroxyl groups and six consecutive DNA nucleotides via their backbone phosphate and deoxyribose groups. Recognition is mediated principally by aromatic and basic residues of the S9.6 heavy chain, which closely track the curvature of the hybrid minor groove. These findings reveal the molecular basis for S9.6 recognition of R-loops, detail its binding specificity, identify a new hybrid-recognition strategy, and provide a framework for S9.6 protein engineering.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Mechanistic basis of atypical TERT promoter mutations

Non-coding mutations in the TERT promoter (TERTp), typically at one of two bases -124 and -146 bp upstream of the start codon, are among the most prevalent driver mutations in human cancer. Several additional recurrent TERTp mutations have been reported but their functions and origins remain largely unexplained. Here, we show that atypical TERTp mutations arise secondary to canonical TERTp mutations in a two-step process. Canonical TERTp mutations create de novo binding sites for ETS family transcription factors that induce favourable conditions for DNA damage formation by UV light, thus creating a hotspot effect but only after a first mutational hit. In agreement, atypical TERTp mutations co-occur with canonical driver mutations in large cancer cohorts and arise subclonally specifically on the TERTp driver mutant chromosome homolog of melanoma cells treated with UV light in vitro. Our study gives an in-depth view of TERTp mutations in cancer and provides a mechanistic explanation for atypical TERTp mutations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

The interplay of DNA repair context with target sequence predictably biases Cas9-generated mutations

Abstract Repair of double-stranded breaks generated by CRISPR/Cas9 is highly dependent on the flanking DNA sequence. To learn about interactions between DNA repair and target sequence, we measure frequencies of over 236,000 distinct Cas9-generated mutational outcomes at over 2800 synthetic target sequences in 18 DNA repair deficient mouse embryonic stem cells lines. We classify the outcomes in an unbiased way, finding a specialised role forPrkdc(DNA-PKcs protein) andPolmin creating 1 bp insertions matching the nucleotide on the protospacer-adjacent motif side of the break, a variable involvement ofNbnandPolqin the creation of different deletion outcomes, and uni-directional deletions dependent on both end-protection and end-resection. Using our dataset, we build predictive models of the mutagenic outcomes of Cas9 scission that outperform the current standards. This work improves our understanding of DNA repair gene function, and provides avenues for more precise modulation of Cas9-generated mutations.

Science & Technology - Other Topics↗
DOE OSTI2025

Nickase fidelity drives EvolvR-mediated diversification in mammalian cells

Abstract In vivo genetic diversifiers have previously enabled efficient searches of genetic variant fitness landscapes for continuous directed evolution. However, existing genomic diversification modalities for mammalian genomic loci exclusively rely on deaminases to generate transition mutations within target loci, forfeiting access to most missense mutations. Here, we engineer CRISPR-guided error-prone DNA polymerases (EvolvR) to diversify all four nucleotides within genomic loci in mammalian cells. We demonstrate that EvolvR generates both transition and transversion mutations throughout a mutation window of at least 40 bp and implement EvolvR to evolve previously unreported drug-resistantMAP2K1variants via substitutions not achievable with deaminases. Moreover, we discover that the nickase’s mismatch tolerance limits EvolvR’s mutation window and substitution biases in a gRNA-specific fashion. To compensate for gRNA-to-gRNA variability in mutagenesis, we maximize the number of gRNA target sequences by incorporating a PAM-flexible nickase into EvolvR. Finally, we find a strong correlation between predicted free energy changes underlying R-loop formation and EvolvR’s performance using a given gRNA. The EvolvR system diversifies all four nucleotides to enable the evolution of mammalian cells, while nuclease and gRNA-specific properties underlying nickase fidelity can be engineered to further enhance EvolvR’s mutation rates.

Science & Technology - Other Topics↗
DOE OSTI2020

A robust benchmark for detection of germline large deletions and insertions

New technologies and analysis methods are enabling genomic structural variants (SVs) to be detected with ever-increasing accuracy, resolution and comprehensiveness. To help translate these methods to routine research and clinical practice, we developed a sequence-resolved benchmark set for identification of both false-negative and false-positive germline large insertions and deletions. To create this benchmark for a broadly consented son in a Personal Genome Project trio with broadly available cells and DNA, the Genome in a Bottle Consortium integrated 19 sequence-resolved variant calling methods from diverse technologies. The final benchmark set contains 12,745 isolated, sequence-resolved insertion (7,281) and deletion (5,464) calls ≥50 base pairs (bp). The Tier 1 benchmark regions, for which any extra calls are putative false positives, cover 2.51 Gbp and 5,262 insertions and 4,095 deletions supported by ≥1 diploid assembly. We demonstrate that the benchmark set reliably identifies false negatives and false positives in high-quality SV callsets from short-, linked- and long-read sequencing and optical mapping.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Transposon sequencing analysis of Bradyrhizobium diazoefficiens 110 spc4

Bradyrhizobium diazoefficiens USDA110 is one of the most effective nitrogen-fixing symbionts of soybeans. Here we carried out a large-scale transposon insertion sequencing (Tn-seq) analysis of strain Bd110spc4, which is derived from USDA110, with the goal of increasing available resources for identifying genes crucial for the survival of this plant symbiont under diverse conditions. We prepared two transposon (Tn) insertion libraries of Bd110spc4 with 155,042 unique Tn insertions when the libraries were combined, which is an average of one insertion every 58.7 bp of the reference USDA110 genome. Application of bioinformatic filtering steps to remove genes too small to be expected to have Tn insertions, resulted in a list of genes that were classified as putatively essential. Comparison of this gene set with genes putatively essential for the growth of the closely related alpha-proteobacterium, Rhodopseudomonas palustris, revealed a small set of five genes that may be collectively essential for closely related members of the family Bradyrhizobiaceae. This group includes bacteria with diverse lifestyles ranging from plant symbionts to animal-associated species to free-living species.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Knockout of ABC transporter gene ABCA2 confers resistance to Bt toxin Cry2Ab in Helicoverpa zea

Evolution of pest resistance reduces the benefits of widely cultivated genetically engineered crops that produce insecticidal proteins derived from Bacillus thuringiensis (Bt). Better understanding of the genetic basis of pest resistance to Bt crops is needed to monitor, manage, and counter resistance. Previous work shows that in several lepidopterans, resistance to Bt toxin Cry2Ab is associated with mutations in the gene encoding the ATP-binding cassette protein ABCA2. The results here show that mutations introduced by CRISPR/Cas9 gene editing in the Helicoverpa zea (corn earworm or bollworm) gene encoding ABCA2 (HzABCA2) can cause resistance to Cry2Ab. Disruptive mutations in HzABCA2 facilitated the creation of two Cry2Ab-resistant strains. A multiple concentration bioassay with one of these strains revealed it had > 200-fold resistance to Cry2Ab relative to its parental susceptible strain. All Cry2Ab-resistant individuals tested had disruptive mutations in HzABCA2. We identified five disruptive mutations in HzABCA2 gDNA. The most common mutation was a 4-bp deletion in the expected Cas9 guide RNA target site. The results here indicate that HzABCA2 is a leading candidate for monitoring Cry2Ab resistance in field populations of H. zea.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Molecular and biochemical characterization of rice developed through conventional integration of nDart1-0 transposon gene

Mutations, the genetic variations in genomic sequences, play an important role in molecular biology and biotechnology. During DNA replication or meiosis, one of the mutations is transposons or jumping genes. An indigenous transposon nDart1-0 was successfully introduced into local indica cultivar Basmati-370 from transposon-tagged line viz., GR-7895 (japonica genotype) through conventional breeding technique, successive backcrossing. Plants from segregating populationsshowed variegated phenotypes were tagged as BM-37 mutants. Blast analysis of the sequence data revealed that the GTP-binding protein, located on the BAC clone OJ1781_H11 of chromosome 5, contained an insertion of DNA transposon nDart1-0. The nDart1-0 has “A” at position 254 bp, whereas nDart1 homologs have “G”, which efficiently distinguishes nDart1-0 from its homologs. The histological analysis revealed that the chloroplast of mesophyll cells in BM-37 was disrupted with reduction in size of starch granules and higher number of osmophillic plastoglobuli, which resulted in decreased chlorophyll contents and carotenoids, gas exchange parameters (Pn, g, E, Ci), and reduced expression level of genes associated with chlorophyll biosynthesis, photosynthesis and chloroplast development. Along with the rise of GTP protein, the salicylic acid (SA) and gibberellic acid (GA) and antioxidant contents(SOD) and MDA levels significantly enhanced, while, the cytokinins (CK), ascorbate peroxidase (APX), catalase (CAT), total flavanoid contents (TFC) and total phenolic contents (TPC) significantly reduced in BM-37 mutant plants as compared with WT plants. These results support the notion that GTP-binding proteins influence the process underlying chloroplast formation. Therefore, it is anticipated that to combat biotic or abiotic stress conditions, the nDart1-0 tagged mutant (BM-37) of Basmati-370 would be beneficial.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Mechanochemical synthesis and structural analysis of trivalent lanthanide and uranium diphenylphosphinodiboranates

Phosphinodiboranates (H 3 BPR 2 BH 3 – ) are a class of borohydrides that have merited a reputation as weakly coordinating anions, which is attributed in part to the dearth of coordination complexes known with transition metals, lanthanides, and actinides. We recently reported how K(H 3 BP t Bu 2 BH 3 ) exhibits sluggish salt elimination reactivity with f-metal halides in organic solvents such as Et 2 O and THF. Here we report how this reactivity appears to be further attenuated in solution when the t Bu groups attached to phosphorus are exchanged for R = Ph or H, and we describe how mechanochemistry was used to overcome limited solution reactivity with K(H 3 BPPh 2 BH 3 ). Grinding three equivalents of K(H 3 BPPh 2 BH 3 ) with UI 3 (THF) 4 or LnI 3 (Ln = Ce, Pr, Nd) allowed homoleptic complexes with the empirical formulas U(H 3 BPPh 2 BH 3 ) 3 (1), Ce(H 3 BPPh 2 BH 3 ) 3 (2), Pr(H 3 BPPh 2 BH 3 ) 3 (3), and Nd(H 3 BPPh 2 BH 3 ) 3 (4) to be prepared and subsequently crystallized in good yields (50–80%). Single-crystal XRD studies revealed that all four complexes exist as dimers or coordination polymers in the solid-state, whereas 1 H and 11 B NMR spectra showed that they exist as a mixture of monomers and dimers in solution. Treating 4 with THF breaks up the dimer to yield the monomeric complex Nd(H 3 BPPh 2 BH 3 ) 3 (THF) 3 (4-THF). XRD studies revealed that 4-THF has one chelating and two dangling H 3 BPPh 2 BH 3 – ligands bound to the metal to accommodate binding of THF. In contrast to the results with K(H 3 BPPh 2 BH 3 ), attempting the same mechanochemical reactions with Na(H 3 BPH 2 BH 3 ) containing the simplest phosphinodiboranate were unsuccessful; only the partial metathesis product U(H 3 BPH 2 BH 3 )I 2 (THF) 3 (5) was isolated in poor yields. Here, despite these limitations, our results offer new examples showing how mechanochemistry can be used to rapidly synthesize molecular coordination complexes that are otherwise difficult to prepare using more traditional solution methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Quasars with large proper motions: A selection from the LQAC-5 catalogue combined with Gaia EDR3: Focusing on astrometric and photometric properties

Thanks to the cross-identification between the Gaia EDR3 (E-Data Release 3) catalogue and the quasars’ compiled catalogue LQAC-5 (Large Quasar Astrometric Catalogue-5), accurate astrometric parameters as well as photometric measurements were available for a set of 416 113 quasars. After analysing the astrometric and photometric properties of these quasars, we concentrate our study on objects characterized by significant proper motion, which contradicts the postulate that they are fixed in the celestial sphere. We derived statistical properties of the positions, parallaxes, and proper motions of the quasars cross-matched with Gaia EDR3. We carried out a specific investigation of quasars with a proper motion larger than 10 mas yr -1 , and used colour-colour diagrams in mid-infrared to discriminate these quasars from stellar contamination. We discuss, in detail, a few cases where the abnormal proper motion could be caused by misidentifications. We note that 43% of LQAC-5 quasars were not detected by Gaia EDR3, mainly because of the cut-off magnitude at G = 21. The comparison between r(G) (Gaia) and r (SDSS) shows a normal distribution. The normalized distributions of parallaxes and proper motions are identical to that of the Gaia CRF2, as well as the distribution of the G BP -G RP colour index. We have identified 937 LQAC-5 objects (0.27% of the sample) with Gaia EDR3 proper motion which is significant at the 5σ level. We have clearly shown that below z = 0.35, the integrated magnitude G(r) obtained from SDSS spectra is smaller than G (Gaia), leading to the statement that the quasars are generally resolved under this threshold, which should lead to a bad determination of proper motion. Moreover, to discriminate quasars from stellar contamination, we have plotted them in a mid-infrared colour–colour diagram. Finally, we have made a final selection of 41 objects with μ > 10 mas yr -1 , satisfying drastic constraints, which makes them potential candidates for considering their proper motion as real. In this paper we carried out a complete analysis of the quasars of the LQAC-5 which were cross-identified with Gaia EDR3 ; this serves as an alternative and complementary study with respect to Gaia CRF2, involving a different population of quasars. We selected a set of 41 quasars with a proper motion exceeding 10 mas yr -1 , which can be considered as very high for objects which are a priori fixed in the celestial sphere.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Ultrafast-induced coherent acoustic phonons in the two-dimensional magnet CrSBr

Magnetism in two-dimensional (2D) van der Waals (vdW) crystals offers promising new directions for low-dimensional physics and devices. In this work, mega-electron volt (MeV) ultrafast electron diffraction was employed to investigate the ultrafast atomic dynamics of a novel, 2D vdW magnetic single-crystal CrSBr. Femtosecond (fs) optical pump pulses excited non-equilibrium atomic displacements shown to be coherent acoustic phonons (CAPs). Phonon frequencies were extracted by analyzing oscillations of different Bragg peak (BP) intensities and were determined to be GHz acoustic disturbances that propagated as strain waves. Phonon modes exhibit anisotropy with respect to the a and b crystal axes. Subharmonic phonon frequencies were also observed, and this provided a signature of nonlinear oscillatory coupling between the laser-induced pumping phonon frequency and secondary phonon frequencies. Thus, CrSBr was found to serve as a nonlinear phononic frequency converter. The ultrafast time dependence of the Bragg intensity was simulated by incorporating an oscillating deviation parameter ansatz into expressions for the dynamical scattering intensity yielded excellent modeling of the ultrafast structural dynamics of the photo-excited 2D crystal. Our work provides a foundation for exploring how fs light pulses can influence phonon dynamics in materials with strong spin-lattice coupling. These results suggest that CAPs can match the magnon frequencies and show the promise of CrSBr for use in optical-to-microwave transducers and phononic devices.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Engineering tertiary chirality in helical biopolymers

Tertiary chirality describes the handedness of supramolecular assemblies and relies not only on the primary and secondary structures of the building blocks but also on topological driving forces that have been sparsely characterized. Helical biopolymers, especially DNA, have been extensively investigated as they possess intrinsic chirality that determines the optical, mechanical, and physical properties of the ensuing material. Here, we employ the DNA tensegrity triangle as a model system to locate the tipping points in chirality inversion at the tertiary level by X-ray diffraction. We engineer tensegrity triangle crystals with incremental rotational steps between immobile junctions from 3 to 28 base pairs (bp). We construct a mathematical model that accurately predicts and explains the molecular configurations in both this work and previous studies. Our design framework is extendable to other supramolecular assemblies of helical biopolymers and can be used in the design of chiral nanomaterials, optically active molecules, and mesoporous frameworks, all of which are of interest to physical, biological, and chemical nanoscience.

Science & Technology - Other Topics↗
DOE OSTI2020

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. Here, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

97 MATHEMATICS AND COMPUTING↗