How unprovable is Rabin's decidability theorem?

We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical core of typical proofs of Rabin's theorem, is equivalent over the moderately strong second-order arithmetic theory $\mathsf{ACA}_0$ to a determinacy principle implied by the positional determinacy of all parity games and implying the determinacy of all Gale-Stewart games given by boolean combinations of ${\bf \Sigma^0_2}$ sets. It follows that complementation for tree automata is provable from $\Pi^1_3$- but not $\Delta^1_3$-comprehension. We then use results due to MedSalem-Tanaka, M\"ollerfeld and Heinatsch-M\"ollerfeld to prove that over $\Pi^1_2$-comprehension, the complementation theorem for tree automata, decidability of the MSO theory of the infinite binary tree, positional determinacy of parity games and determinacy of $\mathrm{Bool}({\bf \Sigma^0_2})$ Gale-Stewart games are all equivalent. Moreover, these statements are equivalent to the $\Pi^1_3$-reflection principle for $\Pi^1_2$-comprehension. It follows in particular that Rabin's decidability theorem is not provable in $\Delta^1_3$-comprehension.Comment: 21 page

Effects of Frontal Transcranial Direct Current Stimulation on Emotional State and Processing in Healthy Humans

The prefrontal cortex is involved in mood and emotional processing. In patients suffering from depression, the left dorsolateral prefrontal cortex (DLPFC) is hypoactive, while activity of the right DLPFC is enhanced. Counterbalancing these pathological excitability alterations by repetitive transcranial magnetic stimulation (rTMS) or transcranial direct current stimulation (tDCS) improves mood in these patients. In healthy subjects, however, rTMS of the same areas has no major effect, and the effects of tDCS are mixed. We aimed to evaluate the effects of prefrontal tDCS on emotion and emotion-related cognitive processing in healthy humans. In a first study, we administered excitability-enhancing anodal, excitability-diminishing cathodal, and placebo tDCS to the left DLPFC, combined with antagonistic stimulation of the right frontopolar cortex, and tested acute emotional changes by an adjective checklist. Subjective emotions were not influenced by tDCS. Emotional face identification, however, which was explored in a second experiment, was subtly improved by a tDCS-driven excitability modulation of the prefrontal cortex, markedly by anodal tDCS of the left DLPFC for positive emotional content. We conclude that tDCS of the prefrontal cortex improves emotion processing in healthy subjects, but does not influence subjective emotional state

Constitutive upregulation of the transforming growth factor-β pathway in rheumatoid arthritis synovial fibroblasts

Genome-wide gene expression was comparatively investigated in early-passage rheumatoid arthritis (RA) and osteoarthritis (OA) synovial fibroblasts (SFBs; n = 6 each) using oligonucleotide microarrays; mRNA/protein data were validated by quantitative PCR (qPCR) and western blotting and immunohistochemistry, respectively. Gene set enrichment analysis (GSEA) of the microarray data suggested constitutive upregulation of components of the transforming growth factor (TGF)-β pathway in RA SFBs, with 2 hits in the top 30 regulated pathways. The growth factor TGF-β1, its receptor TGFBR1, the TGF-β binding proteins LTBP1/2, the TGF-β-releasing thrombospondin 1 (THBS1), the negative effector SkiL, and the smad-associated molecule SARA were upregulated in RA SFBs compared to OA SFBs, whereas TGF-β2 was downregulated. Upregulation of TGF-β1 and THBS1 mRNA (both positively correlated with clinical markers of disease activity/severity) and downregulation of TGF-β2 mRNA in RA SFBs were confirmed by qPCR. TGFBR1 mRNA (only numerically upregulated in RA SFBs) and SkiL mRNA were not differentially expressed. At the protein level, TGF-β1 showed a slightly higher expression, and the signal-transducing TGFBR1 and the TGF-β-activating THBS1 a significantly higher expression in RA SFBs than in OA SFBs. Consistent with the upregulated TGF-β pathway in RA SFBs, stimulation with TGF-β1 resulted in a significantly enhanced expression of matrix-metalloproteinase (MMP)-11 mRNA and protein in RA SFBs, but not in OA SFBs. In conclusion, RA SFBs show broad, constitutive alterations of the TGF-β pathway. The abundance of TGF-β, in conjunction with an augmented mRNA and/or protein expression of TGF-β-releasing THBS1 and TGFBR1, suggests a pathogenetic role of TGF-β-induced effects on SFBs in RA, for example, the augmentation of MMP-mediated matrix degradation/remodeling

Differential clinical efficacy of anti-CD4 monoclonal antibodies in rat adjuvant arthritis is paralleled by differential influence on NF-κB binding activity and TNF-α secretion of T cells

The aim of this study was to analyze the differential effects of three anti-CD4 monoclonal antibodies (mAbs) (with distinct epitope specifities) in the treatment of rat adjuvant arthritis (AA) and on T-cell function and signal transduction. Rat AA was preventively treated by intraperitoneal injection of the anti-CD4 mAbs W3/25, OX35, and RIB5/2 (on days -1, 0, 3, and 6, i.e. 1 day before AA induction, on the day of induction [day 0], and thereafter). The effects on T-cell reactivity in vivo (delayed-type hypersensitivity), ex vivo (ConA-induced proliferation), and in vitro (mixed lymphocyte culture) were assessed. The in vitro effects of anti-CD4 preincubation on T-cell receptor (TCR)/CD3-induced cytokine production and signal transduction were also analyzed. While preventive treatment with OX35 and W3/25 significantly ameliorated AA from the onset, treatment with RIB5/2 even accelerated the onset of AA by approximately 2 days (day 10), and ameliorated the arthritis only in the late phase (day 27). Differential clinical effects at the onset of AA were paralleled by a differential influence of the mAbs on T-cell functions, i.e. in comparison with OX35 and W3/25, the 'accelerating' mAb RIB5/2 failed to increase the delayed-type hypersentivity (DTH) to Mycobacterium tuberculosis, increased the in vitro tumor necrosis factor (TNF)-α secretion, and more strongly induced NF-κB binding activity after anti-CD4 preincubation and subsequent TCR/CD3-stimulation. Depending on their epitope specificity, different anti-CD4 mAbs differentially influence individual proinflammatory functions of T cells. This fine regulation may explain the differential efficacy in the treatment of AA and may contribute to the understanding of such treatments in other immunopathologies

Expression of cytokine mRNA and protein in joints and lymphoid organs during the course of rat antigen-induced arthritis

Cytokine expression was assessed during antigen-induced arthritis (AIA) in synovial membrane (SM), inguinal lymph node (LN), and spleen using competitive RT-PCR and sandwich ELISA. In the SM, early elevations of IL-1β and IL-6 mRNA (by 6 hours; 450- and 200-fold, respectively) correlated with the joint swelling; a 6-fold increase in tumor necrosis factor α (TNFα) was not significant. Not only IL-2 and IFN-γ (which increased 10,000-fold and 200-fold, respectively), but also IL-5 and IL-10, increased acutely (6 hours – day 1; 3-fold and 35-fold, respectively) in the SM. In general, the protein levels in the SM for IL-1β, IL-6, TNFα, IFN-γ, IL-4, and IL-10 (increase from 4-fold to 15-fold) matched the course of mRNA expression. In the inguinal LN, there were early mRNA elevations of IL-6 (a 2.5-fold increase by 6 hours, which correlated positively with the joint swelling) and IL-2 (4-fold by 6 hours), as well as later rises of IL-4 and IL-5 (2.5- and 4-fold, respectively, by day 3). No significant elevations of the corresponding proteins in this tissue were observed, except for IL-1β (by day 6) and IL-10 (by day 1). In the spleen, there were significant mRNA elevations at 6 hours of IL-1β (1.5-fold), IL-6 (4-fold; positively correlated with the joint swelling), IFN-γ (3-fold), and IL-2 (7- to 10-fold). IL-5 and IL-10 (2- and 3-fold, respectively) peaked from 6 hours to day 3 in the spleen. Increases of the corresponding proteins were significant in comparison with day 0 only in the case of IL-2 (day 6). By day 6 (transition to the chronic phase), the mRNA for cytokines declined to or below prearthritis levels in all the tissues studied except for IL-1β in the SM and IL-6 in the spleen. AIA is thus characterized by four phenomena: early synovial activation of macrophages, T helper (Th)1-like, and Th2-like cells; late, well-segregated Th2-like responses in the inguinal LN; late, overlapping Th1-like/Th2-like peaks in the spleen; and chronic elevation of synovial IL-1β mRNA and spleen IL-6 mRNA

Association of Human FOS Promoter Variants with the Occurrence of Knee-Osteoarthritis in a Case Control Association Study

Our aim was to analyse (i) the presence of single nucleotide polymorphisms (SNPs) in the JUN and FOS core promoters in patients with rheumatoid arthritis (RA), knee-osteoarthritis (OA), and normal controls (NC); (ii) their functional influence on JUN/FOS transcription levels; and (iii) their associations with the occurrence of RA or knee-OA. JUN and FOS promoter SNPs were identified in an initial screening population using the Non-Isotopic RNase Cleavage Assay (NIRCA); their functional influence was analysed using reporter gene assays. Genotyping was done in RA (n = 298), knee-OA (n = 277), and NC (n = 484) samples. For replication, significant associations were validated in a Finnish cohort (OA: n = 72, NC: n = 548). Initially, two SNPs were detected in the JUN promoter and two additional SNPs in the FOS promoter in perfect linkage disequilibrium (LD). JUN promoter SNP rs4647009 caused significant downregulation of reporter gene expression, whereas reporter gene expression was significantly upregulated in the presence of the FOS promoter SNPs. The homozygous genotype of FOS promoter SNPs showed an association with the susceptibility for knee-OA (odds ratio (OR) 2.12, 95% confidence interval (CI) 1.2-3.7, p = 0.0086). This association was successfully replicated in the Finnish Health 2000 study cohort (allelic OR 1.72, 95% CI 1.2-2.5, p = 0.006). FOS Promoter variants may represent relevant susceptibility markers for knee-OA.Peer reviewe

Measuring the intelligence of an idealized mechanical knowing agent

We define a notion of the intelligence level of an idealized mechanical knowing agent. This is motivated by efforts within artificial intelligence research to define real-number intelligence levels of compli- cated intelligent systems. Our agents are more idealized, which allows us to define a much simpler measure of intelligence level for them. In short, we define the intelligence level of a mechanical knowing agent to be the supremum of the computable ordinals that have codes the agent knows to be codes of computable ordinals. We prove that if one agent knows certain things about another agent, then the former necessarily has a higher intelligence level than the latter. This allows our intelligence no- tion to serve as a stepping stone to obtain results which, by themselves, are not stated in terms of our intelligence notion (results of potential in- terest even to readers totally skeptical that our notion correctly captures intelligence). As an application, we argue that these results comprise evidence against the possibility of intelligence explosion (that is, the no- tion that sufficiently intelligent machines will eventually be capable of designing even more intelligent machines, which can then design even more intelligent machines, and so on)