Fully differential Vector-Boson Fusion Higgs Pair Production at Next-to-Next-to-Leading Order

We calculate the fully differential next-to-next-to-leading order (NNLO) QCD corrections to vector-boson fusion (VBF) Higgs pair production. This calculation is achieved in the limit in which there is no colored cross-talk between the colliding protons, using the projection-to-Born method. We present differential cross sections of key observables, showing corrections of up to 3-4% at this order after typical VBF cuts, with the total cross section receiving contributions of about 2%. In contrast to single Higgs VBF production, we find that the NNLO corrections are for the most part within the next-to-leading order scale uncertainty bands.Comment: 5 pages, 3 figures, updated to match published versio

New developments in the theory of Groebner bases and applications to formal verification

We present foundational work on standard bases over rings and on Boolean Groebner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems arising from formal verification of digital circuits. In fact, algebraic modelling of formal verification problems is developed on the word-level as well as on the bit-level. The word-level model leads to Groebner basis in the polynomial ring over Z/2n while the bit-level model leads to Boolean Groebner bases. In addition to the theoretical foundations of both approaches, the algorithms have been implemented. Using these implementations we show that special data structures and the exploitation of symmetries make Groebner bases competitive to state-of-the-art tools from formal verification but having the advantage of being systematic and more flexible.Comment: 44 pages, 8 figures, submitted to the Special Issue of the Journal of Pure and Applied Algebr

Observation of Mammalian Similarity Through Allometric Scaling Laws

We discuss the problem of observation of natural similarity in skeletal evolution of terrestrial mammals. Analysis is given by means of testing of the power scaling laws established in long bone allometry, which describe development of bones (of length $L$ and diameter $D$) with body mass in terms of the growth exponents, \QTR{it}{e.g.} $\lambda =d\log L/d\log D$. The bone-size evolution scenario given three decades ago by McMahon was quiet explicit on the geometrical-shape and mechanical-force constraints that predicted $\lambda =2/3$. This remains too far from the mammalian allometric exponent $\lambda ^{(\exp)}=0.80\pm 0.2$, recently revised by Christiansen, that is a chief puzzle in long bone allometry. We give therefore new insights into McMahon's constraints and report on the first observation of the critical-elastic-force, bending-deformation, muscle-induced mechanism that underlies the allometric law with estimated $\lambda =0.80\pm 0.3$. This mechanism governs the bone-size evolution with avoiding skeletal fracture caused by muscle-induced peak stresses and is expected to be unique for small and large mammals.Comment: Keywords: allometric scaling, long bones, muscles, mammals 21 pages, 1 Table, 2 Figure

Vector-Boson Fusion Higgs Pair Production at N3^3LO

We calculate the next-to-next-to-next-to-leading order (N$^3$LO) QCD corrections to vector-boson fusion (VBF) Higgs pair production in the limit in which there is no partonic exchange between the two protons. We show that the inclusive cross section receives negligible corrections at this order, while the scale variation uncertainties are reduced by a factor four. We present differential distributions for the transverse momentum and rapidity of the final state Higgs bosons, and show that there is almost no kinematic dependence to the third order corrections. Finally we study the impact of deviations from the Standard Model in the trilinear Higgs coupling, and show that the structure of the higher order corrections does not depend on the self-coupling. These results are implemented in the latest release of the proVBFH-incl program.Comment: 10 pages, 9 figures, updated to match published versio

Micro-macro transitions in the atomic chain via Whitham's modulation equation

The subject matter of this paper is the thermodynamic description of the nonlinear atomic chain with temperature. For this reason we consider special approximate solutions of Newton's equations, in which the atoms perform microscopic oscillations in form of modulated traveling waves. We start with an existence result for periodic traveling wave with arbitrary large amplitudes, and study several examples including the harmonic chain, the hard sphere model, and the small-amplitude approximation. Then we discuss the thermodynamic properties of traveling waves, and derive the corresponding Gibbs equation. Afterwards we focus on the macroscopic evolution of modulated traveling waves. For this purpose we apply Whitham's modulation theory to the atomic chain, and derive the modulation equation, which turns out to be a system of four macroscopic conservation laws. The last part is devoted to the justification problem: We state a conjecture for the general case, and prove this conjecture for the harmonic chain and the hard sphere model

Continuous Non-Intrusive Hybrid WCET Estimation Using Waypoint Graphs

Traditionally, the Worst-Case Execution Time (WCET) of Embedded Software has been estimated using analytical approaches. This is effective, if good models of the processor/System-on-Chip (SoC) architecture exist. Unfortunately, modern high performance SoCs often contain unpredictable and/or undocumented components that influence the timing behaviour. Thus, analytical results for such processors are unrealistically pessimistic. One possible alternative approach seems to be hybrid WCET analysis, where measurement data together with an analytical approach is used to estimate worst-case behaviour. Previously, we demonstrated how continuous evaluation of basic block trace data can be used to produce detailed statistics of basic blocks in embedded software. In the meantime it has become clear that the trace data provided by modern SoCs delivers a different type of information. In this contribution, we show that even under realistic conditions, a meaningful analysis can be conducted with the trace data

Blow-up versus boundedness in a nonlocal and nonlinear Fokker--Planck equation

We consider a Fokker-Planck equation on a compact interval where, as a constraint, the first moment is a prescribed function of time. Eliminating the associated Lagrange multiplier one obtains nonlinear and nonlocal terms. After establishing suitable local existence results, we use the relative entropy as an energy functional. However, the time-dependent constraint leads to a source term such that a delicate analysis is needed to show that the dissipation terms are strong enough to control the work done by the constraint. We obtain global existence of solutions as long as the prescribed first moment stays in the interior of an interval. If the prescribed moment converges to a constant value inside the interior of the interval, then the solution stabilises to the unique steady state

Blow-up versus boundedness in a nonlocal and nonlinear Fokker-Planck equation

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