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]

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

NLO corrections to differential cross sections for pseudo-scalar Higgs boson production

We have computed the full next-to-leading (NLO) QCD corrections to the differential distributions $d^2\sigma/(dp_T~dy)$ for pseudo-scalar Higgs (A) production at large hadron colliders. This calculation has been carried out using the effective Lagrangian approach which is valid as long as the mass of the pseudo-scalar Higgs boson $m_{\rm A}$ and its transverse momentum $p_T$ do not exceed the top-quark mass $m_t$. The shape of the distributions hardly differ from those obtained for scalar Higgs (H) production because, apart from the overall coupling constant and mass, there are only small differences between the partonic differential distributions for scalar and pseudo-scalar production. Therefore there are only differences in the magnitudes of the hadronic differential distributions which can be mainly attributed to the unknown mixing angle $\beta$ describing the pseudo-scalar Higgs coupling to the top quarks.Comment: 9 pages, LaTeX, 3 Postscript figures In the previous version we have forgotten to include contributions which arrise from interferences between graphs containing vertices corresponding to the operator $O_2(x)$ in Eq. (3) with graphs originating from the operator $O_1(x)$. These interferences occur because of the prescription for the Levi-Civita tensor given in our paper. These extra contributions are added to Eqs. (19) and (20). Numerically they are completely negligible so that the figures are not altere

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

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

Facilitating Transformation in Workforce Training: Using Clinical Theory to Understand Psychological Self-Sufficiency

Acknowledging the scarcity of a bottom up social work practice model in facilitating the development of success in workforce development programs, this study explores Psychological self-sufficiency (PSS) as an emerging social work practice theory. Phenomenological studies of low-income jobseekers in employment training along with the empirical validation of measures of the core constructs of PSS – employment hope scale (EHS) and perceived employment barrier scale (PEBS) – and testing of the theoretical model resulted in the emergence of a new theory of PSS. PSS was conceptually defined as a dynamic and internal drive that activates the process of transforming cognitively and affectively perceived barriers into hope driven action – the process that enables individuals to move forward toward goals. Based on the evidence of PSS, a participant-centered group intervention model called transforming impossible into possible (TIP) program was developed. This article delineates the trajectory of PSS theory development by critically reviewing various streams of practice theories influencing the PSS theory. Next, the conditions that necessitated the creation of the TIP program and its core principles underlying the functions of PSS are explained. By depicting the TIP program with direct quotes of clients’ experiences, authors exemplify the successful self-discovery process through enhanced PSS skills as a result of participating in the TIP program

NLO QCD corrections to t anti-t H production in hadron collisions

The Higgs boson H of the Standard Model can be searched for in the channels p pbar / pp -> t tbar H + X at the Tevatron and the LHC. The cross sections for these processes and the final-state distributions of the Higgs boson and top quarks are presented at next-to-leading order QCD. To calculate these QCD corrections, a special calculational technique for pentagon diagrams has been developed and the dipole subtraction formalism has been adopted for massive particles. The impact of the corrections on the total cross sections is characterized by K factors, the ratios of the cross sections in next-to-leading order over leading order QCD. At the central scale mu_0 = (2 m_t + M_H)/2 the K factors are found to be slightly below unity for the Tevatron (K \sim 0.8) and slightly above unity for the LHC (K \sim 1.2). Including the corrections significantly stabilizes the theoretical predictions for total cross sections and for the distributions in rapidity and transverse momentum of the Higgs boson and top quarks.Comment: 50 pages, LaTeX, 17 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