Measuring Topological Chaos

The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a chaotic flow, the braid generated by the motion of three or more fluid particles is computed. A ``braiding exponent'' is then defined to characterize the complexity of the braid. This exponent is proportional to the usual Lyapunov exponent of the flow, associated with separation of nearby trajectories. Measuring chaos in this manner has several advantages, especially from the experimental viewpoint, since neither nearby trajectories nor derivatives of the velocity field are needed.Comment: 4 pages, 6 figures. RevTeX 4 with PSFrag macro

Heavy Flavor Enhancement as a Signal of Color Deconfinement

We argue that the color deconfinement in heavy ion collisions may lead to enhanced production of hadrons with open heavy flavor (charm or bottom). We estimate the upper bound of this enhancement.Comment: 7 pages, LaTeX, 3 PS-figure

On Invariant Notions of Segre Varieties in Binary Projective Spaces

Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains \Segrem(2) and is invariant under its projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into \PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under \Stab{m}{2} as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according as $m$ is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m - 1, 2). This spread is also related with a \Stab{m}{2}-invariant non-singular Hermitian variety. The case $m=3$ is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7, 2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and Cryptograph

Equation of state at FAIR energies and the role of resonances

Two microscopic models, UrQMD and QGSM, are used to extract the effective equation of state (EOS) of locally equilibrated nuclear matter produced in heavy-ion collisions at energies from 11.6 AGeV to 160 AGeV. Analysis is performed for the fixed central cubic cell of volume V = 125 fm**3 and for the expanding cell that followed the growth of the central area with uniformly distributed energy. For all reactions the state of local equilibrium is nearly approached in both models after a certain relaxation period. The EOS has a simple linear dependence P/e = c_s**2 with 0.12 < c_s**2 < 0.145. Heavy resonances are shown to be responsible for deviations of the c_s**2(T) and c_s**2(mu_B) from linear behavior. In the T-mu_B and T-mu_S planes the EOS has also almost linear dependence and demonstrates kinks related not to the deconfinement phase transition but to inelastic freeze-out in the system.Comment: SQM2008 proceedings, 6 page

Topological entropy and secondary folding

A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is exactly equal to the growth induced by the map on the fundamental group of the torus. However, in many situations the numerically-computed topological entropy is greater than the bound implied by this action. We associate this gap between the bound and the true entropy with 'secondary folding': material lines undergo folding which is not homologically forced. We examine this phenomenon both for physical rod-stirring devices and toral linked twist maps, and show rigorously that for the latter secondary folds occur.Comment: 13 pages, 8 figures. pdfLaTeX with RevTeX4 macro

Open charm and charmonium production at relativistic energies

We calculate open charm and charmonium production in $Au+Au$ reactions at $\sqrt{s}$ = 200 GeV within the hadron-string dynamics (HSD) transport approach employing open charm cross sections from $pN$ and $\pi N$ reactions that are fitted to results from PYTHIA and scaled in magnitude to the available experimental data. Charmonium dissociation with nucleons and formed mesons to open charm ($D+\bar{D}$ pairs) is included dynamically. The 'comover' dissociation cross sections are described by a simple phase-space model including a single free parameter, i.e. an interaction strength $M_0^2$, that is fitted to the $J/\Psi$ suppression data for $Pb+Pb$ collisions at SPS energies. As a novel feature we implement the backward channels for charmonium reproduction by $D \bar{D}$ channels employing detailed balance. From our dynamical calculations we find that the charmonium recreation is comparable to the dissociation by 'comoving' mesons. This leads to the final result that the total $J/\Psi$ suppression at $\sqrt{s}$ = 200 GeV as a function of centrality is slightly less than the suppression seen at SPS energies by the NA50 Collaboration, where the 'comover' dissociation is substantial and the backward channels play no role. Furthermore, even in case that all directly produced $J/\Psi$ mesons dissociate immediately (or are not formed as a mesonic state), a sizeable amount of charmonia is found asymptotically due to the $D+\bar{D} \to J/\Psi$ + meson channels in central collisions of $Au+Au$ at $\sqrt{s}$ = 200 GeV which, however, is lower than the $J/\Psi$ yield expected from binary scaling of $pp$ collisions.Comment: 42 pages, including 14 eps figures, discussions extended and references added, to be published in Phys. Rev.

The role of GDNF family ligand signalling in the differentiation of sympathetic and dorsal root ganglion neurons

The diversity of neurons in sympathetic ganglia and dorsal root ganglia (DRG) provides intriguing systems for the analysis of neuronal differentiation. Cell surface receptors for the GDNF family ligands (GFLs) glial cell-line-derived neurotrophic factor (GDNF), neurturin and artemin, are expressed in subpopulations of these neurons prompting the question regarding their involvement in neuronal subtype specification. Mutational analysis in mice has demonstrated the requirement for GFL signalling during embryonic development of cholinergic sympathetic neurons as shown by the loss of expression from the cholinergic gene locus in ganglia from mice deficient for ret, the signal transducing subunit of the GFL receptor complex. Analysis in mutant animals and transgenic mice overexpressing GFLs demonstrates an effect on sensitivity to thermal and mechanical stimuli in DRG neurons correlating at least partially with the altered expression of transient receptor potential ion channels and acid-sensitive cation channels. Persistence of targeted cells in mutant ganglia suggests that the alterations are caused by differentiation effects and not by cell loss. Because of the massive effect of GFLs on neurite outgrowth, it remains to be determined whether GFL signalling acts directly on neuronal specification or indirectly via altered target innervation and access to other growth factors. The data show that GFL signalling is required for the specification of subpopulations of sensory and autonomic neurons. In order to comprehend this process fully, the role of individual GFLs, the transduction of the GFL signals, and the interplay of GFL signalling with other regulatory pathways need to be deciphered

Factoring Products of Braids via Garside Normal Form

Braid groups are infinite non-abelian groups naturally arising from geometric braids. For two decades they have been proposed for cryptographic use. In braid group cryptography public braids often contain secret braids as factors and it is hoped that rewriting the product of braid words hides individual factors. We provide experimental evidence that this is in general not the case and argue that under certain conditions parts of the Garside normal form of factors can be found in the Garside normal form of their product. This observation can be exploited to decompose products of braids of the form ABC when only B is known. Our decomposition algorithm yields a universal forgery attack on WalnutDSA™, which is one of the 20 proposed signature schemes that are being considered by NIST for standardization of quantum-resistant public-key cryptography. Our attack on WalnutDSA™ can universally forge signatures within seconds for both the 128-bit and 256-bit security level, given one random message-signature pair. The attack worked on 99.8% and 100% of signatures for the 128-bit and 256-bit security levels in our experiments. Furthermore, we show that the decomposition algorithm can be used to solve instances of the conjugacy search problem and decomposition search problem in braid groups. These problems are at the heart of other cryptographic schemes based on braid groups.SCOPUS: cp.kinfo:eu-repo/semantics/published22nd IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2019; Beijing; China; 14 April 2019 through 17 April 2019ISBN: 978-303017258-9Volume Editors: Sako K.Lin D.Publisher: Springer Verla