Mixture Selection, Mechanism Design, and Signaling

We pose and study a fundamental algorithmic problem which we term mixture selection, arising as a building block in a number of game-theoretic applications: Given a function $g$ from the $n$-dimensional hypercube to the bounded interval $[-1,1]$, and an $n \times m$ matrix $A$ with bounded entries, maximize $g(Ax)$ over $x$ in the $m$-dimensional simplex. This problem arises naturally when one seeks to design a lottery over items for sale in an auction, or craft the posterior beliefs for agents in a Bayesian game through the provision of information (a.k.a. signaling). We present an approximation algorithm for this problem when $g$ simultaneously satisfies two smoothness properties: Lipschitz continuity with respect to the $L^\infty$ norm, and noise stability. The latter notion, which we define and cater to our setting, controls the degree to which low-probability errors in the inputs of $g$ can impact its output. When $g$ is both $O(1)$-Lipschitz continuous and $O(1)$-stable, we obtain an (additive) PTAS for mixture selection. We also show that neither assumption suffices by itself for an additive PTAS, and both assumptions together do not suffice for an additive FPTAS. We apply our algorithm to different game-theoretic applications from mechanism design and optimal signaling. We make progress on a number of open problems suggested in prior work by easily reducing them to mixture selection: we resolve an important special case of the small-menu lottery design problem posed by Dughmi, Han, and Nisan; we resolve the problem of revenue-maximizing signaling in Bayesian second-price auctions posed by Emek et al. and Miltersen and Sheffet; we design a quasipolynomial-time approximation scheme for the optimal signaling problem in normal form games suggested by Dughmi; and we design an approximation algorithm for the optimal signaling problem in the voting model of Alonso and C\^{a}mara

Honest signaling in zero-sum games is hard, and lying is even harder

We prove that, assuming the exponential time hypothesis, finding an \epsilon-approximately optimal symmetric signaling scheme in a two-player zero-sum game requires quasi-polynomial time. This is tight by [Cheng et al., FOCS'15] and resolves an open question of [Dughmi, FOCS'14]. We also prove that finding a multiplicative approximation is NP-hard. We also introduce a new model where a dishonest signaler may publicly commit to use one scheme, but post signals according to a different scheme. For this model, we prove that even finding a (1-2^{-n})-approximately optimal scheme is NP-hard

Entanglement, intractability and no-signaling

We consider the problem of deriving the no-signaling condition from the assumption that, as seen from a complexity theoretic perspective, the universe is not an exponential place. A fact that disallows such a derivation is the existence of {\em polynomial superluminal} gates, hypothetical primitive operations that enable superluminal signaling but not the efficient solution of intractable problems. It therefore follows, if this assumption is a basic principle of physics, either that it must be supplemented with additional assumptions to prohibit such gates, or, improbably, that no-signaling is not a universal condition. Yet, a gate of this kind is possibly implicit, though not recognized as such, in a decade-old quantum optical experiment involving position-momentum entangled photons. Here we describe a feasible modified version of the experiment that appears to explicitly demonstrate the action of this gate. Some obvious counter-claims are shown to be invalid. We believe that the unexpected possibility of polynomial superluminal operations arises because some practically measured quantum optical quantities are not describable as standard quantum mechanical observables.Comment: 17 pages, 2 figures (REVTeX 4

UNC93B1 recruits syntenin-1 to dampen TLR7 signalling and prevent autoimmunity.

At least two members of the Toll-like receptor (TLR) family, TLR7 and TLR9, can recognize self-RNA and self-DNA, respectively. Despite the structural and functional similarities between these receptors, their contributions to autoimmune diseases such as systemic lupus erythematosus can differ. For example, TLR7 and TLR9 have opposing effects in mouse models of systemic lupus erythematosus-disease is exacerbated in TLR9-deficient mice but attenuated in TLR7-deficient mice1. However, the mechanisms of negative regulation that differentiate between TLR7 and TLR9 are unknown. Here we report a function for the TLR trafficking chaperone UNC93B1 that specifically limits signalling of TLR7, but not TLR9, and prevents TLR7-dependent autoimmunity in mice. Mutations in UNC93B1 that lead to enhanced TLR7 signalling also disrupt binding of UNC93B1 to syntenin-1, which has been implicated in the biogenesis of exosomes2. Both UNC93B1 and TLR7 can be detected in exosomes, suggesting that recruitment of syntenin-1 by UNC93B1 facilitates the sorting of TLR7 into intralumenal vesicles of multivesicular bodies, which terminates signalling. Binding of syntenin-1 requires phosphorylation of UNC93B1 and provides a mechanism for dynamic regulation of TLR7 activation and signalling. Thus, UNC93B1 not only enables the proper trafficking of nucleic acid-sensing TLRs, but also sets the activation threshold of potentially self-reactive TLR7

Inhibition of IRE1α-mediated XBP1 mRNA cleavage by XBP1 reveals a novel regulatory process during the unfolded protein response

Background: The mammalian endoplasmic reticulum (ER) continuously adapts to the cellular secretory load by the activation of an unfolded protein response (UPR).  This stress response results in expansion of the ER, upregulation of proteins involved in protein folding and degradation, and attenuation of protein synthesis.  The response is orchestrated by three signalling pathways each activated by a specific signal transducer, either inositol requiring enzyme α (IRE1α), double-stranded RNA-activated protein kinase-like ER kinase (PERK) or activating transcription factor 6 (ATF6).  Activation of IRE1α results in its oligomerisation, autophosphorylation and stimulation of its ribonuclease activity.  The ribonuclease initiates the splicing of an intron from mRNA encoding the transcription factor, X-box binding protein 1 (XBP1), as well as degradation of specific mRNAs and microRNAs. Methods: To investigate the consequence of expression of exogenous XBP1, we generated a stable cell-line expressing spliced XBP1 mRNA under the control of an inducible promotor. Results: Following induction of expression, high levels of XBP1 protein were detected, which allowed upregulation of target genes in the absence of induction of the UPR.  Remarkably under stress conditions, the expression of exogenous XBP1 repressed splicing of endogenous XBP1 mRNA without repressing the activation of PERK. Conclusions: These results illustrate that a feedback mechanism exists to attenuate Ire1α ribonuclease activity in the presence of XBP1

A general strategy for discovery of inhibitors and activators of RING and U-box E3 ligases with ubiquitin variants

RING and U-box E3 ubiquitin ligases regulate diverse eukaryotic processes and have been implicated in numerous diseases, but targeting these enzymes remains a major challenge. We report the development of three ubiquitin variants (UbVs), each binding selectively to the RING or U-box domain of a distinct E3 ligase: monomeric UBE4B, phosphorylated active CBL, or dimeric XIAP. Structural and biochemical analyses revealed that UbVs specifically inhibited the activity of UBE4B or phosphorylated CBL by blocking the E2∼Ub binding site. Surprisingly, the UbV selective for dimeric XIAP formed a dimer to stimulate E3 activity by stabilizing the closed E2∼Ub conformation. We further verified the inhibitory and stimulatory functions of UbVs in cells. Our work provides a general strategy to inhibit or activate RING/U-box E3 ligases and provides a resource for the research community to modulate these enzymes