Nonapproximability Results for Partially Observable Markov Decision Processes

We show that for several variations of partially observable Markov decision processes, polynomial-time algorithms for finding control policies are unlikely to or simply don't have guarantees of finding policies within a constant factor or a constant summand of optimal. Here "unlikely" means "unless some complexity classes collapse," where the collapses considered are P=NP, P=PSPACE, or P=EXP. Until or unless these collapses are shown to hold, any control-policy designer must choose between such performance guarantees and efficient computation

Role of goblet cell protein CLCA1 in murine DSS colitis

Background The secreted goblet cell protein CLCA1 (chloride channel regulator, calcium-activated-1) is, in addition to its established role in epithelial chloride conductance regulation, thought to act as a multifunctional signaling protein, including cellular differentiation pathways and induction of mucus production. Specifically, CLCA1 has recently been shown to modulate early immune responses by regulation of cytokines. Here, we analyze the role of CLCA1, which is highly expressed and secreted by colon goblet cells, in the course of murine dextran sodium sulfate-induced colitis. Findings We compared Clca1-deficient and wild type mice under unchallenged and DSS-challenged conditions at various time points, including weight loss, colon weight-length- ratio and histological characterization of inflammation and regeneration. Expression levels of relevant cytokines, trefoil factor 3 and E-cadherin were assessed via quantitative PCR and cytometric bead arrays. Lack of CLCA1 was associated with a more than two-fold increased expression of Cxcl-1- and Il-17-mRNA during DSS colitis. However, no differences were found between Clca1-deficient and wild type mice under unchallenged or DSS-challenged conditions in terms of clinical findings, disease progression, colitis outcome, epithelial defects or regeneration. Conclusions CLCA1 is involved in the modulation of cytokine responses in the colon, albeit differently than what had been observed in the lungs. Obviously, the pathways involved depend on the type of challenge, time point or tissue environment

False-Name Manipulation in Weighted Voting Games is Hard for Probabilistic Polynomial Time

False-name manipulation refers to the question of whether a player in a weighted voting game can increase her power by splitting into several players and distributing her weight among these false identities. Analogously to this splitting problem, the beneficial merging problem asks whether a coalition of players can increase their power in a weighted voting game by merging their weights. Aziz et al. [ABEP11] analyze the problem of whether merging or splitting players in weighted voting games is beneficial in terms of the Shapley-Shubik and the normalized Banzhaf index, and so do Rey and Rothe [RR10] for the probabilistic Banzhaf index. All these results provide merely NP-hardness lower bounds for these problems, leaving the question about their exact complexity open. For the Shapley--Shubik and the probabilistic Banzhaf index, we raise these lower bounds to hardness for PP, "probabilistic polynomial time", and provide matching upper bounds for beneficial merging and, whenever the number of false identities is fixed, also for beneficial splitting, thus resolving previous conjectures in the affirmative. It follows from our results that beneficial merging and splitting for these two power indices cannot be solved in NP, unless the polynomial hierarchy collapses, which is considered highly unlikely

Model Checking CTL is Almost Always Inherently Sequential

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+

Improving exploration in policy gradient search: Application to symbolic optimization

Many machine learning strategies designed to automate mathematical tasks leverage neural networks to search large combinatorial spaces of mathematical symbols. In contrast to traditional evolutionary approaches, using a neural network at the core of the search allows learning higher-level symbolic patterns, providing an informed direction to guide the search. When no labeled data is available, such networks can still be trained using reinforcement learning. However, we demonstrate that this approach can suffer from an early commitment phenomenon and from initialization bias, both of which limit exploration. We present two exploration methods to tackle these issues, building upon ideas of entropy regularization and distribution initialization. We show that these techniques can improve the performance, increase sample efficiency, and lower the complexity of solutions for the task of symbolic regression.Comment: Published in 1st Mathematical Reasoning in General Artificial Intelligence Workshop, ICLR 202

The Goblet Cell Protein Clca1 (Alias mClca3 or Gob-5) Is Not Required for Intestinal Mucus Synthesis, Structure and Barrier Function in Naive or DSS- Challenged Mice

The secreted, goblet cell-derived protein Clca1 (chloride channel regulator, calcium-activated-1) has been linked to diseases with mucus overproduction, including asthma and cystic fibrosis. In the intestine Clca1 is found in the mucus with an abundance and expression pattern similar to Muc2, the major structural mucus component. We hypothesized that Clca1 is required for the synthesis, structure or barrier function of intestinal mucus and therefore compared wild type and Clca1-deficient mice under naive and at various time points of DSS (dextran sodium sulfate)-challenged conditions. The mucus phenotype in Clca1-deficient compared to wild type mice was systematically characterized by assessment of the mucus protein composition using proteomics, immunofluorescence and expression analysis of selected mucin genes on mRNA level. Mucus barrier integrity was assessed in-vivo by analysis of bacterial penetration into the mucus and translocation into sentinel organs combined analysis of the fecal microbiota and ex-vivo by assessment of mucus penetrability using beads. All of these assays revealed no relevant differences between wild type and Clca1-deficient mice under steady state or DSS-challenged conditions in mouse colon. Clca1 is not required for mucus synthesis, structure and barrier function in the murine colon