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This paper studies binary linear programming problems in the presence of uncertainties that may cause solution values to change during implementation. This type of uncertainty, termed implementation uncertainty, is modeled explicitly affecting the decision variables rather than model parameters. The binary nature of the decision variables invalidates the use of the existing models for this type of uncertainty. The robust solutions obtained are optimal for a worst-case min-max objective and allow a controlled degree of infeasibility with respect to the associated deterministic problem. Structural properties are used to reformulate the problem as a mixed-integer linear binary program. The degree of solution conservatism is controlled by combining both constraint relaxation and cardinality-constrained parameters. Solutions for optimization problems under implementation uncertainty consist of a set of robust solutions; the selection of solutions from this possibly large set is formulated as an optimization problem over the robust set. Results from an experimental study in the context of the knapsack problem suggest the methodology yields solutions that perform well in terms of objective value and feasibility. Furthermore, the selection approach can identify robust solutions that possess desirable implementation characteristics., Comment: 31 pages, 5 figures, 6 tables

We argue that in theories of quantum gravity with discrete gauge symmetries, e.g. $\textbf{Z}_k$, the gauge couplings of U$(1)$ gauge symmetries become weak in the limit of large $k$, as $g\to k^{-\alpha}$ with $\alpha$ a positive order 1 coefficient. The conjecture is based on black hole arguments combined with the Weak Gravity Conjecture (or the BPS bound in the supersymmetric setup), and the species bound. We provide explicit examples based on type IIB on AdS$_5\times \textbf{S}^5/\textbf{Z}_k$ orbifolds, and M-theory on AdS$_4\times\textbf{S}^7/\textbf{Z}_k$ ABJM orbifolds (and their type IIA reductions). We study AdS$_4$ vacua of type IIA on CY orientifold compactifications, and show that the parametric scale separation in certain infinite families is controlled by a discrete $\textbf{Z}_k$ symmetry for domain walls. We accordingly propose a refined version of the strong AdS Distance Conjecture, including a parametric dependence on the order of the discrete symmetry for 3-forms., Comment: 35 pages + appendices. References added

We show that warped throats of the Klebanov-Strassler kind, regarded as 5d flux compactifications on K\"ahler-Einstein manifolds $\bf{X}_5$ describe fully backreacted solutions of transplanckian axion monodromy. We show that the asymptotic Klebanov-Tseytlin solution features a 5d axion physically rolling through its dependence on an spatial coordinate, and traversing arbitrarily large geodesic distances in field space. The solution includes the backreaction on the breathing mode of the compactification space and on the vacuum energy, which yields a novel form of flattening. We establish the description of the system in terms of an effective 5d theory for the axion, and verify its validity in transplanckian regimes. In this context, rolling axion monodromy configurations with limited field space range would correspond, in the holographic dual field theory, to duality walls, which admit no embedding in string theory so far. We present an identical realization of transplanckian axion monodromy in 4d in fluxed version of AdS$_4\times \bf{X}_7$. We speculate that similar models in which the axion rolls in the time direction naturally correspond to embedding of the same mechanism in de Sitter vacua, thus providing a natural arena for large field inflation, and potentially linking the swampland de Sitter and distance conjectures., Comment: 25 pages. v2: corrected typos, references added. v3: added discussion on consistency with the distance conjecture

Most theoretical and simulation studies on charged particles suspensions are at infinite dilution conditions. Hence these studies have been focused on the electrolyte structure around an isolated central particle (or elctrode), where phenomena as charge reversal, charge inversion and overcharging have been shown to be relevant. However, experimental studiesat finite volume fraction exhibit interesting phenomenology which imply very long-range correlations. Inthis paper we apply an integral equation theory to a simple model for a charged macroions suspension, at finite volume fraction, and find two new effects of long-range overcharging and long-range charge reversal. These new effects are different from the classical overcharging and charge reversal in that they occur at finite macroion's volume fraction, far away from the central macroion, are much more intense, and increase, not decrease, as a function of the distance to the central particle, which is indicative of correlations at large separations. We find our results to be qualitative consistent with existing experimental results, and Monte Carlo simulations., Comment: 6 pages, 4 figures