Solomonoff Induction Violates Nicod's Criterion

Nicod's criterion states that observing a black raven is evidence for the hypothesis H that all ravens are black. We show that Solomonoff induction does not satisfy Nicod's criterion: there are time steps in which observing black ravens decreases the belief in H. Moreover, while observing any computable infinite string compatible with H, the belief in H decreases infinitely often when using the unnormalized Solomonoff prior, but only finitely often when using the normalized Solomonoff prior. We argue that the fault is not with Solomonoff induction; instead we should reject Nicod's criterion.Comment: ALT 201

Cluster and virial expansions for the multi-species tonks gas

We consider a mixture of non-overlapping rods of different lengths ℓk moving in R or Z. Our main result are necessary and sufficient convergence criteria for the expansion of the pressure in terms of the activities zk and the densities ρk. This provides an explicit example against which to test known cluster expansion criteria, and illustrates that for non-negative interactions, the virial expansion can converge in a domain much larger than the activity expansion. In addition, we give explicit formulas that generalize the well-known relation between non-overlapping rods and labelled rooted trees. We also prove that for certain choices of the activities, the system can undergo a condensation transition akin to that of the zero-range process. The key tool is a fixed point equation for the pressure

Beyond ‘significance’:Principles and practice of the analysis of credibility

The inferential inadequacies of statistical significance testing are now widely recognized. There is, however, no consensus on how to move research into a ‘post p < 0.05’ era. We present a potential route forward via the Analysis of Credibility, a novel methodology that allows researchers to go beyond the simplistic dichotomy of significance testing and extract more insight from new findings. Using standard summary statistics, AnCred assesses the credibility of significant and non-significant findings on the basis of their evidential weight, and in the context of existing knowledge. The outcome is expressed in quantitative terms of direct relevance to the substantive research question, providing greater protection against misinterpretation. Worked examples are given to illustrate how AnCred extracts additional insight from the outcome of typical research study designs. Its ability to cast light on the use of p-values, the interpretation of non-significant findings and the so-called ‘replication crisis’ is also discussed

Translation invariant extensions of finite volume measures

We investigate the following questions: Given a measure μΛ on configurations on a subset Λ of a lattice L, where a configuration is an element of ΩΛ for some fixed set Ω, does there exist a measure μ on configurations on all of L, invariant under some specified symme- try group of L, such that μΛ is its marginal on configurations on Λ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L = Zd and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance (LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ ⊂ Z is not an interval, or when Λ ⊂ Zd with d > 1, the LTI condition is necessary but not sufficient for extendibility. For Zd with d > 1, extendibility is in some sense undecidable

Pathogen- and Host-Directed Antileishmanial Effects Mediated by Polyhexanide (PHMB)

BACKGROUND:Cutaneous leishmaniasis (CL) is a neglected tropical disease caused by protozoan parasites of the genus Leishmania. CL causes enormous suffering in many countries worldwide. There is no licensed vaccine against CL, and the chemotherapy options show limited efficacy and high toxicity. Localization of the parasites inside host cells is a barrier to most standard chemo- and immune-based interventions. Hence, novel drugs, which are safe, effective and readily accessible to third-world countries and/or drug delivery technologies for effective CL treatments are desperately needed. METHODOLOGY/PRINCIPAL FINDINGS:Here we evaluated the antileishmanial properties and delivery potential of polyhexamethylene biguanide (PHMB; polyhexanide), a widely used antimicrobial and wound antiseptic, in the Leishmania model. PHMB showed an inherent antileishmanial activity at submicromolar concentrations. Our data revealed that PHMB kills Leishmania major (L. major) via a dual mechanism involving disruption of membrane integrity and selective chromosome condensation and damage. PHMB's DNA binding and host cell entry properties were further exploited to improve the delivery and immunomodulatory activities of unmethylated cytosine-phosphate-guanine oligodeoxynucleotides (CpG ODN). PHMB spontaneously bound CpG ODN, forming stable nanopolyplexes that enhanced uptake of CpG ODN, potentiated antimicrobial killing and reduced host cell toxicity of PHMB. CONCLUSIONS:Given its low cost and long history of safe topical use, PHMB holds promise as a drug for CL therapy and delivery vehicle for nucleic acid immunomodulators

Fast and reliable pricing of American options with local volatility

We present globally convergent multigrid methods for the nonsymmetric obstacle problems as arising from the discretization of Black—Scholes models of American options with local volatilities and discrete data. No tuning or regularization parameters occur. Our approach relies on symmetrization by transformation and data recovery by superconvergence

Critical review of the United Kingdom’s “gold standard” survey of public attitudes to science

Since 2000, the UK government has funded surveys aimed at understanding the UK public’s attitudes toward science, scientists, and science policy. Known as the Public Attitudes to Science series, these surveys and their predecessors have long been used in UK science communication policy, practice, and scholarship as a source of authoritative knowledge about science-related attitudes and behaviors. Given their importance and the significant public funding investment they represent, detailed academic scrutiny of the studies is needed. In this essay, we critically review the most recently published Public Attitudes to Science survey (2014), assessing the robustness of its methods and claims. The review casts doubt on the quality of key elements of the Public Attitudes to Science 2014 survey data and analysis while highlighting the importance of robust quantitative social research methodology. Our analysis comparing the main sample and booster sample for young people demonstrates that quota sampling cannot be assumed equivalent to probability-based sampling techniques

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)