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The ALICE collaboration has measured the production of K$^{0}_{\rm S}$ and $\Xi^{\pm}$ in pp collisions at $\sqrt{s}=13$\,TeV in the direction of the leading charged particle and in the direction transverse to it. The $\Xi^{\pm}$ yield normalized to the K$^{0}_{\rm S}$ yield is found to increase with the charged particle multiplicity for both the transverse-to-leading and the toward-leading (jet-like) regions. Although, the enhancement in the transverse-to-leading region which is sensitive to the underlying event can be understood as due to medium(-like) effects, the result for the jet-like region is striking. The effect in the jet-like region is qualitatively reproduced by PYTHIA8 with rope hadronization and EPOS LHC. The medium(-like) effects in the leading charged particle $p_{\rm T}$ spectrum using different Monte Carlo models (AMPT, EPOS4 and PYTHIA8 with the color ropes mechanism) is studied. A medium(-like)-free $p_{\rm T}$-leading threshold for angular correlation studies involving high-$p_{\rm T}$ hadrons is reported, where the leading particle $p_{\rm T}$ spectrum is unaffected by medium(-like) effects. Since the measurements reported by ALICE were performed considering a significantly lower $p_{\rm T}$ leading threshold, the apparent strangeness enhancement in the jet-like region can be explained in terms of a bias due to the misidentification of the leading particle.
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