An analysis of mixed integer linear sets based on lattice point free convex sets

Split cuts are cutting planes for mixed integer programs whose validity is derived from maximal lattice point free polyhedra of the form $S:=\{x : \pi_0 \leq \pi^T x \leq \pi_0+1 \}$ called split sets. The set obtained by adding all split cuts is called the split closure, and the split closure is known to be a polyhedron. A split set $S$ has max-facet-width equal to one in the sense that $\max\{\pi^T x : x \in S \}-\min\{\pi^T x : x \in S \} \leq 1$. In this paper we consider using general lattice point free rational polyhedra to derive valid cuts for mixed integer linear sets. We say that lattice point free polyhedra with max-facet-width equal to $w$ have width size $w$. A split cut of width size $w$ is then a valid inequality whose validity follows from a lattice point free rational polyhedron of width size $w$. The $w$-th split closure is the set obtained by adding all valid inequalities of width size at most $w$. Our main result is a sufficient condition for the addition of a family of rational inequalities to result in a polyhedral relaxation. We then show that a corollary is that the $w$-th split closure is a polyhedron. Given this result, a natural question is which width size $w^*$ is required to design a finite cutting plane proof for the validity of an inequality. Specifically, for this value $w^*$, a finite cutting plane proof exists that uses lattice point free rational polyhedra of width size at most $w^*$, but no finite cutting plane proof that only uses lattice point free rational polyhedra of width size smaller than $w^*$. We characterize $w^*$ based on the faces of the linear relaxation

W Plus Multiple Jets at the LHC with High Energy Jets

We study the production of a W boson in association with n hard QCD jets (for n>=2), with a particular emphasis on results relevant for the Large Hadron Collider (7 TeV and 8 TeV). We present predictions for this process from High Energy Jets, a framework for all-order resummation of the dominant contributions from wide-angle QCD emissions. We first compare predictions against recent ATLAS data and then shift focus to observables and regions of phase space where effects beyond NLO are expected to be large.Comment: 19 pages, 9 figure

Herbage intake in Danish Jersey and Danish Holstein steers on perennial ryegrass/white clover pasture

The objective of this study was to estimate herbage intake in Danish Friesian and Danish Jersey steers at an age of 8-9 months on ryegrass / white clover pasture. The steers were turned out on pasture in late April and herbage intake was estimated in June in steers of a mean live weight (± S.D.) of 264 ± 14 kg and 185 ± 25 kg for Danish Friesian and Danish Jersey respectively. Faeces and herbage samples were analysed for alkanes to estimate herbage dry matter intake, dry matter digestibility (DMD) and botanical composition of intake. The weight gains at the time of herbage intake estimation in June (kg/day) were 1.142 ± 265 kg/day and 0.927 ± 168 kg/day for Danish Friesian and Danish Jersey respectively. Daily herbage intake (kg dry matter (DM)) estimated by alkanes C32 /C33 was 8.33 ± 0.97 and 6.28 ± 0.61 per day (P<0.001) and 3.15 ± 0.32 and 3.43 ± 0.30 per 100 kg liveweight (LW) (P<0.05) for Danish Friesian and Danish Jersey respectively. The botanical composition of the diet was the same for Danish Friesian and Danish Jersey with about half of the diet being grass leaves and the other half clover leaves. It is concluded that Danish Jersey steers have higher herbage intake per 100 kg LW than Danish Friesian steers of the same age, but herbage intake per kg metabolic LW is not different between the two breeds

Third-generation muffin-tin orbitals

By the example of sp^3-bonded semiconductors, we illustrate what 3rd-generation muffin-tin orbitals (MTOs) are. We demonstrate that they can be downfolded to smaller and smaller basis sets: sp^3d^10,sp^3, and bond orbitals. For isolated bands, it is possible to generate Wannier functions a priori. Also for bands, which overlap other bands, Wannier-like MTOs can be generated a priori. Hence, MTOs have a unique capability for providing chemical understanding.Comment: 13 pages, 8 eps figure

A computer program for anisotropic shallow-shell finite elements using symbolic integration

A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language

Time-Dependent Random Walks and the Theory of Complex Adaptive Systems

Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing boundary. For an unbiased walk the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities. On the other hand, a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability. We use the results to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clustering observed in the evolutionary minority game.Comment: 5 pages, 2 figure

Accuracy control in ultra-large-scale electronic structure calculation

Numerical aspects are investigated in ultra-large-scale electronic structure calculation. Accuracy control methods in process (molecular-dynamics) calculation are focused. Flexible control methods are proposed so as to control variational freedoms, automatically at each time step, within the framework of generalized Wannier state theory. The method is demonstrated in silicon cleavage simulation with 10^2-10^5 atoms. The idea is of general importance among process calculations and is also used in Krylov subspace theory, another large-scale-calculation theory.Comment: 8 pages, 3 figures. To appear in J.Phys. Condens. Matter. A preprint PDF file in better graphics is available at http://fujimac.t.u-tokyo.ac.jp/lses/index_e.htm

Suppression of Dephasing of Optically Trapped Atoms

Ultra-cold atoms trapped in an optical dipole trap and prepared in a coherent superposition of their hyperfine ground states, decohere as they interact with their environment. We demonstrate than the loss in coherence in an "echo" experiment, which is caused by mechanisms such as Rayleigh scattering, can be suppressed by the use of a new pulse sequence. We also show that the coherence time is then limited by mixing to other vibrational levels in the trap and by the finite lifetime of the internal quantum states of the atoms

Raising the critical temperature by disorder in unconventional superconductors mediated by spin fluctuations

We propose a mechanism whereby disorder can enhance the transition temperature Tc of an unconventional superconductor with pairing driven by exchange of spin fluctuations. The theory is based on a self-consistent real space treatment of pairing in the disordered one-band Hubbard model. It has been demonstrated before that impurities can enhance pairing by softening the spin fluctuations locally; here, we consider the competing effect of pair-breaking by the screened Coulomb potential also present. We show that, depending on the impurity potential strength and proximity to magnetic order, this mechanism results in a weakening of the disorder-dependent Tc-suppression rate expected from Abrikosov-Gor'kov theory, or even in disorder-generated Tc enhancements.Comment: 6 pages, 4 figures + Supplementary Materia