Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

A pilot welfare assessment of working ponies on Gili Trawangan, Indonesia

Many working equids in developing countries experience poor health and welfare due to environmental and management factors. Collecting baseline data on these populations is essential to inform education projects to improve equid health and welfare. Gili Trawangan is an island in Indonesia that has no motor vehicles and a working pony population of approximately 200. This pilot study sought to determine baseline data on their health, welfare, and husbandry to inform future health and welfare strategies. A cross-sectional study was performed in May 2017 consisting of a pony cart driver questionnaire (n = 33) and a basic pony health examination (n = 38). The body condition scores of ponies were 3/5 (60.5%), 2/5 (31.6%), and 1/5 (7.9%), while 38% and 92% of ponies had lameness and foot pathology, respectively, and 31 ponies (86.1%) had at least one wound. Thirty percent of cart drivers stated they would work their ponies despite evidence of injury or illness. Limited education, poor access to veterinary services, and remoteness pose barriers to improving pony health and welfare. Our results indicate a need for, and can help inform, targeted education programmes to improve the lives of working ponies and protect livelihoods and tourism on Gili Trawangan

Restoration of kTk_T factorization for low pTp_T hadron hadroproduction

We discuss the applicability of the $k_T$ factorization theorem to low-$p_T$ hadron production in hadron-hadron collision in a simple toy model, which involves only scalar particles and gluons. It has been shown that the $k_T$ factorization for high-$p_T$ hadron hadroproduction is broken by soft gluons in the Glauber region, which are exchanged among a transverse-momentum-dependent (TMD) parton density and other subprocesses of the collision. We explain that the contour of a loop momentum can be deformed away from the Glauber region at low $p_T$, so the above residual infrared divergence is factorized by means of the standard eikonal approximation. The $k_T$ factorization is then restored in the sense that a TMD parton density maintains its universality. Because the resultant Glauber factor is independent of hadron flavors, experimental constraints on its behavior are possible. The $k_T$ factorization can also be restored for the transverse single-spin asymmetry in hadron-hadron collision at low $p_T$ in a similar way, with the residual infrared divergence being factorized into the same Glauber factor.Comment: 12 pages, 2 figures, version to appear in EPJ

Wilson Lines off the Light-cone in TMD PDFs

Transverse Momentum Dependent (TMD) parton distribution functions (PDFs) also take into account the transverse momentum ($p_T$) of the partons. The $p_T$-integrated analogues can be linked directly to quark and gluon matrix elements using the operator product expansion in QCD, involving operators of definite twist. TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Taking into account gauge links that no longer are along the light-cone, one finds that new distribution functions arise. They appear at leading order in the description of azimuthal asymmetries in high-energy scattering processes. In analogy to the collinear operator expansion, we define a universal set of TMDs of definite rank and point out the importance for phenomenology.Comment: 12 pages, presented by the first author at the Light-Cone Conference 2013, May 20-24, 2013, Skiathos, Greece. To be published in Few Body System

Qubits from Number States and Bell Inequalities for Number Measurements

Bell inequalities for number measurements are derived via the observation that the bits of the number indexing a number state are proper qubits. Violations of these inequalities are obtained from the output state of the nondegenerate optical parametric amplifier.Comment: revtex4, 7 pages, v2: results identical but extended presentation, v3: published versio

The evolution of compliance in the human lateral mid-foot.

Fossil evidence for longitudinal arches in the foot is frequently used to constrain the origins of terrestrial bipedality in human ancestors. This approach rests on the prevailing concept that human feet are unique in functioning with a relatively stiff lateral mid-foot, lacking the significant flexion and high plantar pressures present in non-human apes. This paradigm has stood for more than 70 years but has yet to be tested objectively with quantitative data. Herein, we show that plantar pressure records with elevated lateral mid-foot pressures occur frequently in healthy, habitually shod humans, with magnitudes in some individuals approaching absolute maxima across the foot. Furthermore, the same astonishing pressure range is present in bonobos and the orangutan (the most arboreal great ape), yielding overlap with human pressures. Thus, while the mean tendency of habitual mechanics of the mid-foot in healthy humans is indeed consistent with the traditional concept of the lateral mid-foot as a relatively rigid or stabilized structure, it is clear that lateral arch stabilization in humans is not obligate and is often transient. These findings suggest a level of detachment between foot stiffness during gait and osteological structure, hence fossilized bone morphology by itself may only provide a crude indication of mid-foot function in extinct hominins. Evidence for thick plantar tissues in Ardipithecus ramidus suggests that a human-like combination of active and passive modulation of foot compliance by soft tissues extends back into an arboreal context, supporting an arboreal origin of hominin bipedalism in compressive orthogrady. We propose that the musculoskeletal conformation of the modern human mid-foot evolved under selection for a functionally tuneable, rather than obligatory stiff structure

Change management: The case of the elite sport performance team

The effective and efficient implementation of change is often required for both successful performance and management survival across a host of contemporary domains. However, although of major theoretical and practical significance, research to date has overlooked the application of change management (hereafter CM) knowledge to the elite sport performance team environment. Considering that the success of ‘off-field’ sports businesses are largely dependent on the performances of their ‘on-field’ team, this article explores the application of current CM theorizing to this specific setting and the challenges facing its utility. Accordingly, we identify the need and importance of developing theory specific to this area, with practical application in both sport and business, through examination of current knowledge and identification of the domain's unique, dynamic and contested properties. Markers of successful change are then suggested to guide initial enquiry before the article concludes with proposed lines of research which may act to provide a valid and comprehensive theoretical account of CM to optimize the research and practice of those working in the field

Azimuthal asymmetries in lepton-pair production at a fixed-target experiment using the LHC beams (AFTER)

A multi-purpose fixed-target experiment using the proton and lead-ion beams of the LHC was recently proposed by Brodsky, Fleuret, Hadjidakis and Lansberg, and here we concentrate our study on some issues related to the spin physics part of this project (referred to as AFTER). We study the nucleon spin structure through $pp$ and $pd$ processes with a fixed-target experiment using the LHC proton beams, for the kinematical region with 7 TeV proton beams at the energy in center-of-mass frame of two nucleons $\sqrt{s}=115$ GeV. We calculate and estimate the $\cos2\phi$ azimuthal asymmetries of unpolarized $pp$ and $pd$ dilepton production processes in the Drell--Yan continuum region and at the $Z$-pole. We also calculate the $\sin(2\phi-\phi_S)$, $\sin(2\phi+\phi_S)$ and $\sin2\phi$ azimuthal asymmetries of $pp$ and $pd$ dilepton production processes with the target proton and deuteron longitudinally or transversally polarized in the Drell--Yan continuum region and around $Z$ resonances region. We conclude that it is feasible to measure these azimuthal asymmetries, consequently the three-dimensional or transverse momentum dependent parton distribution functions (3dPDFs or TMDs), at this new AFTER facility.Comment: 15 pages, 40 figures. Version accepted for publication in EPJ

Lattice theory of trapping reactions with mobile species

We present a stochastic lattice theory describing the kinetic behavior of trapping reactions $A + B \to B$, in which both the $A$ and $B$ particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter of an $A$ particle with any of the $B$ particles, $A$ is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables - "gates", imposed on each $B$ particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the $A$ particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time $t$, the $A$ particle survival probability is always larger in case when $A$ stays immobile, than in situations when it moves.Comment: 12 pages, appearing in PR

pQCD Physics of multiparton interactions

We study production of two pairs of jets in %hard hadron--hadron collisions in view of extracting contribution of {\em double hard interactions} of three and four partons ($3\to4$, $4\to4$). Such interactions, in spite of being power suppressed at the level of the total cross section, become comparable with the standard hard collisions of two partons, $2\to4$, in the {\em back-to-back kinematics} when the transverse momentum imbalances of two pairing jets are relatively small. We express differential and total cross sections for two-dijet production in double parton collisions through the generalized two-parton distributions, $_2$GPDs \cite{BDFS1}, that contain large-distance two-parton correlations of non-perturbative origin as well as small-distance correlations due to parton evolution. We find that these large- and small-distance correlations participate in different manner in 4-jet production, and treat them in the leading logarithmic approximation of pQCD that resums collinear logarithms in all orders. A special emphasis is given to $3\to4$ double hard interaction processes that occur as an interplay between large- and short-distance parton correlations and were not taken into consideration by approaches inspired by the parton model picture. We demonstrate that the $3\to4$ mechanism, being of the same order in \as as the $4\to4$ process, turns out to be {\em geometrically enhanced} compared to the latter and should contribute significantly to 4-jet production. The framework developed here takes into systematic consideration perturbative $Q^2$ evolution of $_2$GPDs. It can be used as a basis for future analysis of NLO corrections to multi-parton interactions (MPI) at LHC and Tevatron colliders, in particular for improving evaluation of QCD backgrounds to new physics searches.Comment: 16 pages,4 figures Improved presentation; list of references reworked; qualitative estimate of the magnitude of different contributions in the beck-to- back region correcte