Mass problems and intuitionistic higher-order logic

In this paper we study a model of intuitionistic higher-order logic which we call \emph{the Muchnik topos}. The Muchnik topos may be defined briefly as the category of sheaves of sets over the topological space consisting of the Turing degrees, where the Turing cones form a base for the topology. We note that our Muchnik topos interpretation of intuitionistic mathematics is an extension of the well known Kolmogorov/Muchnik interpretation of intuitionistic propositional calculus via Muchnik degrees, i.e., mass problems under weak reducibility. We introduce a new sheaf representation of the intuitionistic real numbers, \emph{the Muchnik reals}, which are different from the Cauchy reals and the Dedekind reals. Within the Muchnik topos we obtain a \emph{choice principle} $(\forall x\,\exists y\,A(x,y))\Rightarrow\exists w\,\forall x\,A(x,wx)$ and a \emph{bounding principle} $(\forall x\,\exists y\,A(x,y))\Rightarrow\exists z\,\forall x\,\exists y\,(y\le_{\mathrm{T}}(x,z)\land A(x,y))$ where $x,y,z$ range over Muchnik reals, $w$ ranges over functions from Muchnik reals to Muchnik reals, and $A(x,y)$ is a formula not containing $w$ or $z$. For the convenience of the reader, we explain all of the essential background material on intuitionism, sheaf theory, intuitionistic higher-order logic, Turing degrees, mass problems, Muchnik degrees, and Kolmogorov's calculus of problems. We also provide an English translation of Muchnik's 1963 paper on Muchnik degrees.Comment: 44 page

Transcutaneous electrical nerve stimulation for cancer pain in adults.

Background Cancer-related pain is complex and multi-dimensional but the mainstay of cancer pain management has predominately used a biomedical approach. There is a need for non-pharmacological and innovative approaches. Transcutaneous Electric Nerve Stimulation (TENS) may have a role for a significant number of patients but the effectiveness of TENS is currently unknown. Objectives The aim of this systematic review was to determine the effectiveness of TENS for cancer-related pain in adults. Search strategy We searched The Cochrane Library, MEDLINE, EMBASE, CINAHL, PsychINFO, AMED and PEDRO databases (11/04/08). Selection criteria Only randomised controlled trials (RCTS) investigating the use of TENS for the management of cancer-related pain in adults were included. Data collection and analysis The search strategy identified 37 possible published studies which were divided between two pairs of review authors that decided on study selection. A study eligibility form was used to screen each abstract and where study eligibility could not be determined from the abstract, the full paper was obtained and assessed by one pair of review authors. A standardised data extraction sheet was used to collect information on the studies and the quality of the studies was assessed independently by two review authors using the validated five-point Oxford Quality Scale. Final scores were discussed and agreed between all four review authors. The small sample sizes and differences in patient study populations of the two included studies prevented meta-analysis. Main results Only two RCTs met the eligibility criteria (64 participants). These studies were heterogenous with respect to study population, sample size, study design, methodological quality, mode of TENS, treatment duration, method of administration and outcome measures used. In one RCT, there were no significant differences between TENS and placebo in women with chronic pain secondary to breast cancer treatment. In the other RCT, there were no significant differences between acupuncture-type TENS and sham in palliative care patients; this study was underpowered. Authors' conclusions The results of this systematic review are inconclusive due to a lack of suitable RCTs. Large multi-centre RCTs are required to assess the value of TENS in the management of cancer-related pain in adults

Some conservation results on weak König's lemma

AbstractBy RCA0, we denote the system of second-order arithmetic based on recursive comprehension axioms and Σ10 induction. WKL0 is defined to be RCA0 plus weak König's lemma: every infinite tree of sequences of 0's and 1's has an infinite path. In this paper, we first show that for any countable model M of RCA0, there exists a countable model M′ of WKL0 whose first-order part is the same as that of M, and whose second-order part consists of the M-recursive sets and sets not in the second-order part of M. By combining this fact with a certain forcing argument over universal trees, we obtain the following result (which has been called Tanaka's conjecture): if WKL0 proves ∀X∃!Yϕ(X,Y) with ϕ arithmetical, so does RCA0. We also discuss several improvements of this results

Permanent Draft Genome Sequences for Two Variants of Frankia sp. Strain CpI1, the First Frankia Strain Isolated from Root Nodules of Comptonia peregrina

Frankia stains CpI1-S and CpI1-P are members of Frankia lineage Ia that are able to reinfect plants of the Betulaceae and Myricaceae families. Here, we report two 7.6-Mbp draft genome sequences with 6,396 and 6,373 candidate protein-coding genes for CpI1-S and CpI1-P, respectively

Permanent draft genome sequences for two variants of Frankia sp. strain CpI1, the first Frankia strain isolated from root nodules of Comptonia peregrina

Frankia stains CpI1-S and CpI1-P are members of Frankia lineage Ia that are able to reinfect plants of the Betulaceae and Myricaceae families. Here, we report two 7.6-Mbp draft genome sequences with 6,396 and 6,373 candidate protein-coding genes for CpI1-S and CpI1-P, respectively

Adaptive Avoidance of Reef Noise

Auditory information is widely used throughout the animal kingdom in both terrestrial and aquatic environments. Some marine species are dependent on reefs for adult survival and reproduction, and are known to use reef noise to guide orientation towards suitable habitat. Many others that forage in food-rich inshore waters would, however, benefit from avoiding the high density of predators resident on reefs, but nothing is known about whether acoustic cues are used in this context. By analysing a sample of nearly 700,000 crustaceans, caught during experimental playbacks in light traps in the Great Barrier Reef lagoon, we demonstrate an auditory capability in a broad suite of previously neglected taxa, and provide the first evidence in any marine organisms that reef noise can act as a deterrent. In contrast to the larvae of species that require reef habitat for future success, which showed an attraction to broadcasted reef noise, taxa with a pelagic or nocturnally emergent lifestyle actively avoided it. Our results suggest that a far greater range of invertebrate taxa than previously thought can respond to acoustic cues, emphasising yet further the potential negative impact of globally increasing levels of underwater anthropogenic noise