Formulas vs. Circuits for Small Distance Connectivity

We give the first super-polynomial separation in the power of bounded-depth boolean formulas vs. circuits. Specifically, we consider the problem Distance $k(n)$ Connectivity, which asks whether two specified nodes in a graph of size $n$ are connected by a path of length at most $k(n)$. This problem is solvable (by the recursive doubling technique) on {\bf circuits} of depth $O(\log k)$ and size $O(kn^3)$. In contrast, we show that solving this problem on {\bf formulas} of depth $\log n/(\log\log n)^{O(1)}$ requires size $n^{\Omega(\log k)}$ for all $k(n) \leq \log\log n$. As corollaries: (i) It follows that polynomial-size circuits for Distance $k(n)$ Connectivity require depth $\Omega(\log k)$ for all $k(n) \leq \log\log n$. This matches the upper bound from recursive doubling and improves a previous $\Omega(\log\log k)$ lower bound of Beame, Pitassi and Impagliazzo [BIP98]. (ii) We get a tight lower bound of $s^{\Omega(d)}$ on the size required to simulate size-$s$ depth-$d$ circuits by depth-$d$ formulas for all $s(n) = n^{O(1)}$ and $d(n) \leq \log\log\log n$. No lower bound better than $s^{\Omega(1)}$ was previously known for any $d(n) \nleq O(1)$. Our proof technique is centered on a new notion of pathset complexity, which roughly speaking measures the minimum cost of constructing a set of (partial) paths in a universe of size $n$ via the operations of union and relational join, subject to certain density constraints. Half of our proof shows that bounded-depth formulas solving Distance $k(n)$ Connectivity imply upper bounds on pathset complexity. The other half is a combinatorial lower bound on pathset complexity

Large-p_T Photoproduction of D^*+- Mesons in ep Collisions

The cross section for the inclusive photoproduction of large-p_T D^*+- mesons is calculated at next-to-leading order, adopting different approaches to describe the fragmentation of charm quarks into D^*+- mesons. We treat the charm quark according to the massless factorization scheme, where it is assumed to be one of the active flavours inside the proton and the photon. We present inclusive single-particle distributions in transverse momentum and rapidity, including the contributions due to both direct and resolved photons. We compare and assess the various implementations of fragmentation. We argue that, in the high-p_T regime, a particularly realistic description can be obtained by convoluting the Altarelli-Parisi-evolved fragmentation functions of Peterson et al. with the hard-scattering cross sections of massless partons where the factorization of the collinear singularities associated with final-state charm quarks is converted to the massive-charm scheme. The predictions thus obtained agree well with recent experimental data by the H1 and ZEUS Collaborations at DESY HERA.Comment: 31 pages (Latex), 13 figures (Postscript). This version of the manuscript is identical with the one being printed in Z. Phys.

Cross Sections for Charm Production in epep Collisions: Massive versus Massless Scheme

The next--to--leading order inclusive cross section for large-$p_\perp$ photoproduction of charm quarks at HERA is calculated in two different approaches. In the first approach the charm quarks are treated as massive objects which are strictly external to the proton and the photon while in the second approach the charm mass is neglected and the $c$ quark is assumed to be one of the active flavours in the proton and photon structure functions. We present single-inclusive distributions in transverse momentum and rapidity including direct and resolved photons. The cross section in the massless approach is found to be significantly larger than in the massive scheme. The deviation originates from several contributions which are disentangled. We argue that large-$p_\perp$ photoproduction of charm quarks at HERA will be sensitive to the charm content of the photon structure function.Comment: 11 pages, Latex, epsfig, 6 figures appended as uuencoded file (hardcopy can be obtained upon request from [email protected]

Roots of the derivative of the Riemann zeta function and of characteristic polynomials

We investigate the horizontal distribution of zeros of the derivative of the Riemann zeta function and compare this to the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both cases show a surprising bimodal distribution which has yet to be explained. We show by example that the bimodality is a general phenomenon. For the unitary matrix case we prove a conjecture of Mezzadri concerning the leading order behavior, and we show that the same follows from the random matrix conjectures for the zeros of the zeta function.Comment: 24 pages, 6 figure

QCD Corrections to SUSY Higgs Production: The Role of Squark Loops

We calculate the two-loop QCD corrections to the production of the neutral supersymmetric Higgs bosons via the gluon fusion mechanism at hadron colliders, including the contributions of squark loops. To a good approximation, these additional contributions lead to the same QCD corrections as in the case where only top and bottom quark loops are taken into account. The QCD corrections are large and increase the Higgs production cross sections significantly.Comment: 5 pages, latex, 2 figure

The constancy of global regulation across a species: the concentrations of ppGpp and RpoS are strain-specific in Escherichia coli.

BACKGROUND: Sigma factors and the alarmone ppGpp control the allocation of RNA polymerase to promoters under stressful conditions. Both ppGpp and the sigma factor σS (RpoS) are potentially subject to variability across the species Escherichia coli. To find out the extent of strain variation we measured the level of RpoS and ppGpp using 31 E. coli strains from the ECOR collection and one reference K-12 strain. RESULTS: Nine ECORs had highly deleterious mutations in rpoS, 12 had RpoS protein up to 7-fold above that of the reference strain MG1655 and the remainder had comparable or lower levels. Strain variation was also evident in ppGpp accumulation under carbon starvation and spoT mutations were present in several low-ppGpp strains. Three relationships between RpoS and ppGpp levels were found: isolates with zero RpoS but various ppGpp levels, strains where RpoS levels were proportional to ppGpp and a third unexpected class in which RpoS was present but not proportional to ppGpp concentration. High-RpoS and high-ppGpp strains accumulated rpoS mutations under nutrient limitation, providing a source of polymorphisms. CONCLUSIONS: The ppGpp and σS variance means that the expression of genes involved in translation, stress and other traits affected by ppGpp and/or RpoS are likely to be strain-specific and suggest that influential components of regulatory networks are frequently reset by microevolution. Different strains of E. coli have different relationships between ppGpp and RpoS levels and only some exhibit a proportionality between increasing ppGpp and RpoS levels as demonstrated for E. coli K-12

Radiative Higgs Boson Decays H\to f\bar{f}\gamma Beyond the Standard Model

Neutral Higgs boson radiative decays of the form h_0, H, A \to f\bar{f}\gamma, in the light fermion limit $m_f->0, are calculated in the two Higgs doublet model at one-loop level. Comparisons with the calculation within the standard model are given, which indicates that these two models are distinguishable in the decay mode fermion-antifermion -photon. Our results show that the concerned process may stand as an implement to identify the Higgs belongings in case there is a intermediate mass Higgs detected.Comment: 13 pages in Revtex, version to appear in Phys. Rev.

Production and Two-photon Decay of the MSSM Scalar Higgs Bosons at the LHC

We consider the production and two-photon decay of the $CP$-even Higgs bosons ($h^0$ and $H^0$) of the Minimal Supersymmetric Standard Model (MSSM) at the Large Hadron Collider. We study in detail the dependence of the cross section on various parameters of the MSSM, especially the dependence on the mixing effects in the squark sector due to the Higgs bilinear parameter $\mu$ and the soft supersymmetry breaking parameter $A$. We find that the cross section for the production of these Higgs bosons has a significant dependence on the parameters which determine the chiral mixing in the squark sector. The cross section times the two-photon branching ratio of $h^0$ is of the order of 15--25~fb in much of the parameter space that remains after imposing the present experimental constraints. For the $H^0$ the two-photon branching ratio is only significant if the $H^0$ is light, but then the cross section times the branching ratio may exceed 200~fb. The QCD corrections due to quark loop contributions are known to increase the cross section by 50\%. We find the dependence of the cross section on the gluon distribution function used to be rather insignificant.Comment: 16 pages, LaTex, plus 9 uuencoded figures attached Full ps file available at ftp://vsfys1.fi.uib.no/anonymous/pub/ as nordita-9548.ps or nordita-9548.ps-gz or via http://vsfys1.fi.uib.no/thpubl/publications.htm

Next-to-leading order QCD predictions for Z0H0+jetZ^0 H^0 + {\rm jet} production at LHC

We calculate the complete next-to-leading order (NLO) QCD corrections to the $Z^0H^0$ production in association with a jet at the LHC. We study the impacts of the NLO QCD radiative corrections to the integrated and differential cross sections and the dependence of the cross section on the factorization/renormalization scale. We present the transverse momentum distributions of the final $Z^0$-, Higgs-boson and leading-jet. We find that the NLO QCD corrections significantly modify the physical observables, and obviously reduce the scale uncertainty of the LO cross section. The QCD K-factors can be 1.183 and 1.180 at the $\sqrt{s}=14 TeV$ and $\sqrt{s}=7 TeV$ LHC respectively, when we adopt the inclusive event selection scheme with $p_{T,j}^{cut}=50 GeV$, $m_H=120 GeV$ and $\mu=\mu_r=\mu_f=\mu_0 \equiv 1/2(m_Z+m_H)$. Furthermore, we make the comparison between the two scale choices, $\mu=\mu_0$ and $\mu=\mu_1=1/2(E_{T}^{Z}+E_{T}^{H}+ \sum_{j}E_{T}^{jet})$, and find the scale choice $\mu=\mu_1$ seems to be more appropriate than the fixed scale $\mu=\mu_0$.Comment: 18 pages, 7 figure

Scalar and Pseudoscalar Higgs Boson Plus One Jet Production at the LHC and Tevatron

The production of the Standard Model (SM) Higgs boson (H) in association with a jet is compared with that of the lightest scalar Higgs boson (h^0) and the pseudoscalar Higgs boson (A^0) of the Minimal Supersymmetric Model (MSSM) at both the CERN Large Hadron Collider (LHC) and the Fermilab Tevatron. We include both top and bottom quark loops to lowest order in QCD and investigate the limits of zero quark mass and infinite quark mass.Comment: 14 pages, REVTeX4, 14 eps figures v2: Version accepted for publication in PR