On the threshold branch-point of many-body channels

1963 ◽  
Vol 276 (1367) ◽  
pp. 492-501
Keyword(s):  
Branch Point ◽  
Scattering Amplitude ◽  
Cube Root ◽  
Branch Points ◽  
Many Body ◽  
Realistic Potential ◽  
Break Up ◽  
Analytic Behaviour ◽  
The Masses ◽  
Special Case

The analytic behaviour of the elastic and break-up scattering amplitudes in a soluble one-dimensional model has been examined by Nussenzveig. It was found that the break-up threshold gave rise to rather curious cube-root branch-points in the scattering amplitude. In this paper, we shall examine the scattering amplitude in a soluble model which reduces Nussenzveig’s model to the special case where the incident and ionized particles have equal masses. It will be shown that the threshold branch-point is a function of the ratio of the masses of the two particles and that the cube-root occurs only when the masses are equal. In general, there are an infinite number of Riemann sheets associated with the threshold branch-point. An examination into the physical origin of such a threshold behaviour will also be made to determine if a more complicated branch-point than a simple square-root may exist for a more realistic potential model.

Soluble model of a break-up process

1961 ◽  
Vol 264 (1318) ◽  
pp. 408-430 ◽  
Keyword(s):  
Elastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Impulse Approximation ◽  
Branch Points ◽  
Elastic Scattering Amplitude ◽  
Break Up ◽  
Analytic Behaviour ◽  
Dominant Peak

The exact solution of a one-dimensional problem, representing the scattering of a particle by another particle which is bound to a fixed centre of force, is given. All the interactions have zero range and are described by boundary conditions. The possible processes are elastic scattering and break-up of the bound system. The elastic scattering and break-up amplitudes are explicitly determined, and the behaviour of the corresponding cross-sections is discussed. At high energies, the incident particle tends to transfer its whole momentum to the bound one, giving rise to a strong peak in the break-up cross-section. The analytic behaviour of the amplitudes is examined. The Riemann surface of the elastic scattering amplitude has three sheets. The break-up threshold gives rise to cubic-root branch points. The remaining singularities are a finite number of poles. The exact amplitudes are compared with those given by the impulse approximation (in first and second order) and by Born’s approximation. It is found that these approximations are reliable only at high incident energies and within the width of the dominant peak of the break-up cross-section.

A NUCLEAR MANY-BODY THEORY AT FINITE TEMPERATURE APPLIED TO A PROTONEUTRON STAR

2002 ◽  
Vol 11 (02) ◽  
pp. 83-104 ◽  
Author(s):  
GUILHERME F. MARRANGHELLO ◽  
CESAR A. Z. VASCONCELLOS ◽  
MANFRED DILLIG ◽  
J. A. DE FREITAS PACHECO
Keyword(s):  
Phase Transition ◽  
Nuclear Matter ◽  
Finite Temperature ◽  
Degrees Of Freedom ◽  
Many Body ◽  
Many Body Theory ◽  
The Masses ◽  
Protoneutron Stars ◽  
Protoneutron Star

Thermodynamical properties of nuclear matter are studied in the framework of an effective many-body field theory at finite temperature, considering the Sommerfeld approximation. We perform the calculations by using the nonlinear Boguta and Bodmer model, extended by the inclusion of the fundamental baryon octet and leptonic degrees of freedom. Trapped neutrinos are also included in order to describe protoneutron star properties through the integration of the Tolman–Oppenheimer–Volkoff equations, from which we obtain, beyond the standard relations for the masses and radii of protoneutron stars as functions of the central density, new results of these quantities as functions of temperature. Our predictions include: the determination of an absolute value for the limiting mass of protoneutron stars; new structural aspects on the nuclear matter phase transition via the behavior of the specific heat and, through the inclusion of quark degrees of freedom, the properties of a hadron-quark phase transition and hybrid protoneutron stars

scholarly journals Assessment of branch point prediction tools to predict physiological branch points and their alteration by variants

2019 ◽  
Author(s):  
Raphael Leman ◽  
Hélène Tubeuf ◽  
Sabine Raad ◽  
Isabelle Tournier ◽  
Céline Derambure ◽  
...  
Keyword(s):  
Branch Point ◽  
Mrna Splicing ◽  
Large Set ◽  
Branch Points ◽  
Splice Sites ◽  
Prediction Tools ◽  
Mature Mrna ◽  
Bioinformatics Tools ◽  
The Impact

Abstract Background: Branch points (BPs) map within short motifs upstream of acceptor splice sites (3’ss) and are essential for splicing of pre-mature mRNA. Several BP-dedicated bioinformatics tools, including HSF, SVM-BPfinder, BPP, Branchpointer, LaBranchoR and RNABPS were developed during the last decade. Here, we evaluated their capability to detect the position of BPs, and also to predict the impact on splicing of variants occurring upstream of 3’ss. Results: We used a large set of constitutive and alternative human 3’ss collected from Ensembl (n = 264,787 3’ss) and from in-house RNAseq experiments (n = 51,986 3’ss). We also gathered an unprecedented collection of functional splicing data for 120 variants (62 unpublished) occurring in BP areas of disease-causing genes. Branchpointer showed the best performance to detect the relevant BPs upstream of constitutive and alternative 3’ss (99.48 % and 65.84 % accuracies, respectively). For variants occurring in a BP area, BPP emerged as having the best performance to predict effects on mRNA splicing, with an accuracy of 89.17 %. Conclusions: Our investigations revealed that Branchpointer was optimal to detect BPs upstream of 3’ss, and that BPP was most relevant to predict splicing alteration due to variants in the BP area. Keywords: Branch Point, Prediction, RNA, Benchmark, HSF, SVM-BPfinder, BPP, Branchpointer, LaBranchoR, RNABPS, Variants

scholarly journals An inventory of early branch points in microbial phosphonate biosynthesis

2021 ◽  
Author(s):  
Siwei Li ◽  
Geoff P Horsman
Keyword(s):  
Branch Point ◽  
Sequence Similarity ◽  
Bond Formation ◽  
Branch Points ◽  
Bacterial Genomes ◽  
Naturally Occurring ◽  
Carbon Carbon Bond ◽  
The Common ◽  
Almost All ◽  
Biosynthetic Machinery

Microbial phosphonate biosynthetic machinery has been identified in ~5% of bacterial genomes and encodes natural products like fosfomycin as well as cell surface decorations. Almost all biological phosphonates originate from the rearrangement of phosphoenolpyruvate (PEP) to phosphonopyruvate (PnPy) catalyzed by PEP mutase (Ppm), and PnPy is often converted to phosphonoacetaldehyde (PnAA) by PnAA decarboxylase (Ppd). Seven enzymes are known or likely to act on either PnPy or PnAA as early branch points en route to diverse biosynthetic outcomes, and these enzymes may be broadly classified into three reaction types: hydride transfer, aminotransfer, and carbon-carbon bond formation. However, the relative abundance of these branch points in microbial phosphonate biosynthesis is unknown. Also unknown is the proportion of ppm-containing gene neighborhoods encoding new branch point enzymes and potentially novel phosphonates. In this study we computationally sorted 882 ppm-containing gene neighborhoods based on these seven branch point enzymes. Unsurprisingly, the majority (56%) of these pathways encode for production of the common naturally occurring compound 2-aminoethylphosphonate (AEP) or a hydroxylated derivative. The next most abundant genetically encoded intermediates were phosphonoacetate (PnAc, 16%), phosphonoalanine (PnAla, 10%), and 2-hydroxyethylphosphonate (HEP, 5%). Significantly, about 9% of the gene neighborhoods could not be assigned to any of the seven branch points and may encode novel phosphonates. Sequence similarity network analysis revealed families of unusual gene neighborhoods including possible production of phosphonoacrylate and phosphonofructose, the apparent biosynthetic use of the C-P lyase operon, and a virus-encoded phosphonate. Overall, these results highlight the utility of branch point inventories to identify novel gene neighborhoods and guide future phosphonate discovery efforts.

scholarly journals Dynamic Imaging of Fibrin Network Formation Correlated with Other Measures of Polymerization.

Blood ◽  
2007 ◽  
Vol 110 (11) ◽  
pp. 1757-1757
Author(s):  
John W. Weisel ◽  
Irina N. Chernysh
Keyword(s):  
Branch Point ◽  
Network Formation ◽  
Dynamic Imaging ◽  
Longitudinal Growth ◽  
Gel Point ◽  
Lateral Growth ◽  
Branch Points ◽  
Sequence Of Events ◽  
Fibrin Network ◽  
Length Changes

Abstract The clotting time or gel point is commonly used in a variety of clinical assays, but little has been known about what it represents structurally because of the limitations of imaging technologies. The necessity of fixation and dehydration for electron microscopy means that only final clot structures, often distorted by preparation artifacts, can be observed, and there are severe limitations of image quality for conventional light microscopy. For similar reasons, we know almost nothing about the branching and lateral aggregation of fibrin that are essential for clot or thrombus stability. Turbidity, light scattering, or clot stiffness are useful to follow the time course of polymerization but reflect only overall clot properties. We visualized in real time fibrin network formation in the hydrated state, using deconvolution microscopy, which allows optical sectioning without the bleaching that accompanies confocal microscopy. Thus, the events during polymerization could be followed quantitatively over long periods of time. Videos will demonstrate the major observations. Individual mobile fibers were observed before the gel point. After gelation, an initial fibrin network, or scaffold, was seen, which evolved over time by addition of new fibers and elongation and branching of others. Furthermore, some fibers in the network moved chaotically for some time. A detailed, quantitative morphological analysis of network formation was carried out by superposition of images from different time points colorized to distinguish changes. We quantified network formation by the number of branch points, and longitudinal and lateral growth of fibers as a function of time. The distributions of fibers that reached a maximum of longitudinal growth and branch point formation both had maxima at the gel point but, surprisingly, some longitudinal growth continued and new branch points appeared after the gel point, requiring modification of existing models of fibrin polymerization. The cumulative percentage of fibers reaching their final length and the number of branch points attained maximum values at the time corresponding to that at which the turbidity reached approximately 60% of its maximum. Lateral growth reached a plateau at the same time as turbidity. Measurements of clot mechanical properties revealed that the clots achieved maximum stiffness and minimum plasticity well after branch point, as well as length changes and lateral growth of fibers, were completed. These results provide new information on the time sequence of events during fibrin network formation, which is important to understand both clotting and thrombosis and to allow modulation of clot properties.

scholarly journals Unitarity and Regge Branch Points

1974 ◽  
Vol 27 (6) ◽  
pp. 745
Author(s):  
GC Joshi ◽  
Antonio Pagnamenta
Keyword(s):  
Branch Point ◽  
Branch Points ◽  
End Point

We show how t-channel unitarity imposes constraints on the discontinuity associated with the leading Regge branch point. If the discontinuity across the leading Regge cut does not vanish at the end point it leads to the 'Gribov paradox'.

scholarly journals Widespread separation of the polypyrimidine tract from 3’ AG by G tracts in association with alternative exons in metazoa and plants

2018 ◽  
Author(s):  
Hai Nguyen ◽  
Jiuyong Xie
Keyword(s):  
Alternative Splicing ◽  
Branch Point ◽  
Intron Retention ◽  
Regulatory Elements ◽  
Protein Isoforms ◽  
Model Organisms ◽  
Branch Points ◽  
Splice Sites ◽  
Polypyrimidine Tract ◽  
Whole Genome Analysis

SummaryAt the end of introns, the polypyrimidine tract (Py) is often close to the 3’ AG in a consensus (Y)20NCAGgt in humans. Interestingly, we have found that they could also be separated by purine-rich elements including G tracts in thousands of human genes. These regulatory elements between the Py and 3’AG (REPA) mainly regulate alternative 3’ splice sites (3’SS) and intron retention. Here we show their widespread distribution and special properties across kingdoms. The purine-rich 3’SS are found in up to about 60% of the introns among more than 1000 species/lineages by whole genome analysis, and up to 18% of these introns contain the REPA G tracts in about 2.4 millions of 3’SS in total. In particular, they are significantly enriched over their 3’SS and genome backgrounds in metazoa and plants, and highly associated with alternative splicing of genes in diverse functional clusters. They are also highly enriched (3-6 folds) in the canonical as well as aberrantly used 3’ splice sites in cancer patients carrying mutations of the branch point factor SF3B1 or the 3’AG binding factor U2AF35. Moreover, the REPA G tract-harbouring 3’SS have significantly reduced occurrences of branch point (BP) motifs between the −24 and −4 positions, in particular absent from the −7 - −5 positions in several model organisms examined. The more distant branch points are associated with increased occurrences of alternative splicing in human and zebrafish. The branch points, REPA G tracts and associated 3’SS motifs appear to have emerged differentially in a phylum- or species-specific way during evolution. Thus, there is widespread separation of the Py and 3’AG by REPA G tracts, likely evolved among different species or branches of life. This special 3’SS arrangement contributes to the generation of diverse transcript or protein isoforms in biological functions or diseases through alternative or aberrant splicing.

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