Peak reduction technique in commutative algebra

The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well. In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative algebra and affine algebraic geometry.Comment: survey; 10 page

Single-stranded genomic architecture constrains optimal codon usage

Viral codon usage is shaped by the conflicting forces of mutational pressure and selection to match host patterns for optimal expression. We examined whether genomic architecture (single- or double-stranded DNA) influences the degree to which bacteriophage codon usage differ from their primary bacterial hosts and each other. While both correlated equally with their hosts' genomic nucleotide content, the coat genes of ssDNA phages were less well adapted than those of dsDNA phages to their hosts' codon usage profiles due to their preference for codons ending in thymine. No specific biases were detected in dsDNA phage genomes. In all nine of ten cases of codon redundancy in which a specific codon was overrepresented, ssDNA phages favored the NNT codon. A cytosine to thymine biased mutational pressure working in conjunction with strong selection against non-synonymous mutations appears be shaping codon usage bias in ssDNA viral genomes

Nucleosomes in serum of patients with early cerebral stroke

Background: Nucleosomes are cell death products that are elevated in serum of patients with diseases that are associated with massive cell destruction. We investigated the kinetics of circulating nucleosomes after cerebral stroke and their correlation with the clinical status. Methods: In total, we analyzed nucleosomes by ELISA in sera of 63 patients with early stroke daily during the first week after onset. For correlation with the clinical pathology, patients were grouped into those with medium to slight functional impairment (Barthel Index BI >= 50) and those with severe functional impairment (BI = 50 showed a continuous increase in nucleosomes until day 5 (median: 523 arbitrary units, AU) followed by a slow decline. In contrast, patients with BI = 50 (497 AU; p = 0.031). Concerning the infarction volume, nucleosomes showed significant correlations for the concentrations on day 3 (r = 0.43; p = 0.001) and for the area under the curve (r = 0.34; p = 0.016). Conclusion: Even if nucleosomes are nonspecific cell death markers, their release into serum after cerebral stroke correlates with the gross functional status as well as with the infarction volume and can be considered as biochemical correlative to the severity of stroke. Copyright (c) 2006 S. Karger AG, Basel

Shock waves in strongly coupled plasmas

Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong shocks are discontinuous within hydrodynamics and therefore probe the microscopics of the theory. In this paper we consider the case of the strongly coupled N=4 plasma whose microscopic description, applicable for scales smaller than the inverse temperature, is given in terms of gravity in an asymptotically $AdS_5$ space. In the gravity approximation, weak and strong shocks should be described by smooth metrics with no discontinuities. For weak shocks we find the dual metric in a derivative expansion and for strong shocks we use linearized gravity to find the exponential tail that determines the width of the shock. In particular we find that, when the velocity of the fluid relative to the shock approaches the speed of light $v\to 1$ the penetration depth $\ell$ scales as $\ell\sim (1-v^2)^{1/4}$. We compare the results with second order hydrodynamics and the Israel-Stewart approximation. Although they all agree in the hydrodynamic regime of weak shocks, we show that there is not even qualitative agreement for strong shocks. For the gravity side, the existence of shock waves implies that there are disturbances of constant shape propagating on the horizon of the dual black holes.Comment: 47 pages, 8 figures; v2:typos corrected, references adde

The homotopy type of the loops on (n−1)(n-1)-connected (2n+1)(2n+1)-manifolds

For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are determined by the rank of the free Abelian part of the homology. Moreover, we show that these $p$-local homotopy groups can be expressed as a direct sum of $p$-local homotopy groups of spheres. The integral homotopy type of the loop space is also computed and shown to depend only on the rank of the free Abelian part and the torsion subgroup.Comment: Trends in Algebraic Topology and Related Topics, Trends Math., Birkhauser/Springer, 2018. arXiv admin note: text overlap with arXiv:1510.0519

Quarkonium dissociation by anisotropy

We compute the screening length for quarkonium mesons moving through an anisotropic, strongly coupled N=4 super Yang-Mills plasma by means of its gravity dual. We present the results for arbitrary velocities and orientations of the mesons, as well as for arbitrary values of the anisotropy. The anisotropic screening length can be larger or smaller than the isotropic one, and this depends on whether the comparison is made at equal temperatures or at equal entropy densities. For generic motion we find that: (i) mesons dissociate above a certain critical value of the anisotropy, even at zero temperature; (ii) there is a limiting velocity for mesons in the plasma, even at zero temperature; (iii) in the ultra-relativistic limit the screening length scales as $(1-v^2)^\epsilon$ with \epsilon =1/2, in contrast with the isotropic result \epsilon =1/4.Comment: 39 pages, 26 figures; v2: minor changes, added reference

Probing strongly coupled anisotropic plasma

We calculate the static potential, the drag force and the jet quenching parameter in strongly coupled anisotropic N=4 super Yang-Mills plasma. We find that the jet quenching is in general enhanced in presence of anisotropy compared to the isotropic case and that its value depends strongly on the direction of the moving quark and the direction along which the momentum broadening occurs. The jet quenching is strongly enhanced for a quark moving along the anisotropic direction and momentum broadening happens along the transverse one. The parameter gets lower for a quark moving along the transverse direction and the momentum broadening considered along the anisotropic one. Finally, a weaker enhancement is observed when the quark moves in the transverse plane and the broadening occurs on the same plane. The drag force for quark motion parallel to the anisotropy is always enhanced. For motion in the transverse space the drag force is enhanced compared to the isotropic case only for quarks having velocity above a critical value. Below this critical value the force is decreased. Moreover, the drag force along the anisotropic direction is always stronger than the force in the transverse space. The diffusion time follows exactly the inverse relations of the drag forces. The static potential is decreased and stronger decrease observed for quark-antiquark pair aligned along the anisotropic direction than the transverse one. We finally comment on our results and elaborate on their similarities and differences with the weakly coupled plasmas.Comment: 1+44 pages, 18 Figures; Added results on static force; Added references; version published in JHE

Single-inclusive production of large-pT charged particles in hadronic collisions at TeV energies and perturbative QCD predictions

The single inclusive spectrum of charged particles with transverse momenta pT=3-150 GeV/c measured at midrapidity by the CDF experiment in proton-antiproton (p-pbar) collisions at sqrt(s)=1.96 TeV is compared to next-to-leading order (NLO) perturbative QCD calculations using the most recent parametrizations of the parton distributions and parton-to-hadron fragmentation functions. Above pT~20 GeV/c, there is a very sizeable disagreement of the Tevatron data compared to the NLO predictions and to xT-scaling expectations, suggesting a problem in the experimental data. We also present the predictions for the pT-differential charged hadron spectra and the associated theoretical uncertainties for proton-proton (p-p) collisions at LHC energies (sqrt(s)=0.9-14 TeV). Two procedures to estimate the charged hadron spectra at LHC heavy-ion collision energies (sqrt(s)=2.76,5.5 TeV) from p-p measurements are suggested.Comment: 23 pages, 9 figures. A few text additions. Accepted for publication in JHE