The centrality-dependence of forward jet production in \pA\ collisions at the LHC has been found to grossly violate the Glauber model prediction in a way that depends on the $x$ in the proton. We argue that this modification pattern provides the first experimental evidence for $x$-dependent proton color fluctuation effects. On average, parton configurations in the projectile proton containing a parton with large $x$ interact with a nuclear target with a significantly smaller than average cross section and have smaller than average size. Implementing the effects of fluctuations of the interaction strength and using the ATLAS analysis of how hadron production at backward rapidities depends on the number of wounded nucleons, we make quantitative predictions for the centrality dependence of the jet production rate as a function of the $x$-dependent interaction strength $\sigma(x)$. We find a good description of the data in a wide range of x. In particular we find $\sigma(x)\sim 0.6 ~\left<\sigma\right>$. We also analyze the d-Au data with production of large x jet obtained at RHIC. A good consistency of $\sigma(x)/\sigma_{in}$ with the LHC data is observed.

We model color fluctuations (CFs) in the photon wave function and for the first time make predictions for the distribution over the number of wounded nucleons $\nu$ in the inelastic photon--nucleus scattering. We show that CFs lead to a dramatic enhancement of this distribution at $\nu=1$ and large $\nu > 10$. We also study the implications of different scales and CFs in the photon wave function on the total transverse energy $\Sigma E_T$ and other observables in inelastic $\gamma A$ scattering with different triggers. Our predictions can be tested in proton--nucleus and nucleus--nucleus ultraperipheral collisions at the LHC.