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The Identity Correspondence Problem and its Applications

In this paper we study several closely related fundamental problems for words and matrices. First, we introduce the Identity Correspondence Problem (ICP): whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. We prove that ICP is undecidable by a reduction of Post's Correspondence Problem via several new encoding techniques. In the second part of the paper we use ICP to answer a long standing open problem concerning matrix semigroups: "Is it decidable for a finitely generated semigroup S of square integral matrices whether or not the identity matrix belongs to S?". We show that the problem is undecidable starting from dimension four even when the number of matrices in the generator is 48. From this fact, we can immediately derive that the fundamental problem of whether a finite set of matrices generates a group is also undecidable. We also answer several question for matrices over different number fields. Apart from the application to matrix problems, we believe that the Identity Correspondence Problem will also be useful in identifying new areas of undecidable problems in abstract algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the published journal version of this article, see footnote 3 on page 1

Midpoint ratings on personal constructs : constriction or the middle way?

Original article can be found at: http://www.informaworld.com/ Copyright Taylor and FrancisMidpoint ratings of elements on personal constructs have been given various interpretations, and the placement of the ideal self at the midpoint of a construct has been viewed as violating Kelly's (1955) dichotomy and choice corollaries. This article reports analyses, using a mixed models approach, of repertory grids completed by 80 clients referred to a clinical psychology service at up to five assessment points both pre- and posttherapy. A larger than expected number of ideal self ratings at the midpoint was found, and consideration of the content of several of the constructs concerned elucidated why it might have been that neither pole was preferred. Midpoint ratings of the ideal self increased over the course of therapy and were not associated with depression or anxiety. Midpoint ratings of the ideal self and self now were also related to various structural measures of construing. Theoretical and clinical implications of the findings are discussed.Peer reviewedFinal Accepted Versio

Hierarchical relationships in dependency grids : explorations in survivors of childhood sexual abuse

Original article can be found at: http://www.informaworld.com/ Copyright Informa / Taylor & FrancisA methodology for representing the patterns of dependency in a dependency grid using partial order scalogram analysis by coordinates (POSAC) is presented. The technique, devised by Shye (1985), shows these patterns as hierarchical relationships that indicate superordinate and subordinate resources. An index of depth of resource support is calculated in addition to an index of breadth of resource (which is shown to correspond to an index of dispersion of dependency). The procedure was applied to data from 54 survivors of child sexual abuse and a similar number of control subjects who all completed both an adult and child dependency grid. There was significantly less breadth of resource in the abuse group, more so for the child version than the adult, but there was significantly more depth of resource in the dependency grids from the child sexual abuse survivors.Peer reviewe

The Potential of Omega-3 Supplementation to Reduce Muscle-Inflammation after Muscle-Damaging Exercise

Muscle Damaging exercise (EIMD) induces inflammation and relates to strength loss, muscle-soreness and impaired recovery. Overall, this means a performance impairment which might be relevant for those who engages in competitions or strenuous physical activities. It remains unclear whether Omega-3 fatty acids (O-3) supplementation blunts the exercise-induced inflammation associated with EIMD and therefore prevents performance impairment. PURPOSE: Following a three-week supplementation with O-3, indirect markers of muscle damage were examined after a bout of EIMD to determine if supplementation had any beneficial effect in maintaining leg-strength levels. METHODS: Eight healthy, recreationally active caucasian males (28.13 ± 3.4 yr) were randomly allocated to a supplementation group (SUP, n = 4) to receive 2.85g/day O-3 supplementation or a control group (CON, n = 4) for three weeks. Following supplementation, participants performed a bout of EIMD, which consisted of performing 10 sets of 15 repetitions of leg extension at a self-assessed intensity of 7/10 on the Rate of Perceived Exertion scale. Creatine Kinase (CK) from venous blood samples, isometric right-leg strength, squat-jump test and perceived soreness were determined, as indirect markers of muscle-damage at Baseline, immediately after EIMD (POST) and 48 hours after EIMD to coincide with the delayed muscle inflammatory response. RESULTS: No statistically significant differences were found between Baseline and POST. There was a trend for smaller increase of CK levels (pre vs 48-h post EIMD) on the SUP group (38.8% increase) compared with the CON group (105.6% increase; P = 0.051). There was no significant effect (baseline vs. 48-h post EIMD) on muscle strength between SUP and CON group (P > 0.05), however, CON showed a larger decrease in strength compared to SUP (> 6.3% vs SUP). No differences in jump height were found between SUP and CON (P > 0.05). There was no significant difference in muscle soreness at 48-h post EIMD between SUP and CON group (P = 0.171). CONCLUSION: Three weeks of O-3 supplementation might decrease exercise-induced muscle inflammation after eccentric exercise. The lack of statistical significance may be adduced to the limitations of the study design and sample size. Supplementation with O-3 can be beneficial in athletes undergoing heavy exercise regimes and in sedentary individuals restarting physical activity, decreasing the exercise related muscle inflammation. The encouraging results from this pilot study have led to designing further work related to this topic

Genome-wide and Mendelian randomisation studies of liver MRI yield insights into the pathogenesis of steatohepatitis

Background A non-invasive method to grade the severity of steatohepatitis and liver fibrosis is magnetic resonance imaging (MRI) based corrected T1 (cT1). We aimed to identify genetic variants influencing liver cT1 and use genetics to understand mechanisms underlying liver fibroinflammatory disease and its link with other metabolic traits and diseases. Methods First, we performed a genome-wide association study (GWAS) in 14,440 Europeans in UK Biobank with liver cT1 measures. Second, we explored the effects of the cT1 variants on liver blood tests, and a range of metabolic traits and diseases. Third, we used Mendelian randomisation to test the causal effects of 24 predominantly metabolic traits on liver cT1 measures. Results We identified six independent genetic variants associated with liver cT1 that reached GWAS significance threshold (p<5x10-8). Four of the variants (rs75935921 in SLC30A10, rs13107325 in SLC39A8, rs58542926 in TM6SF2, rs738409 in PNPLA3) were also associated with elevated transaminases and had variable effects on liver fat and other metabolic traits. Insulin resistance, type 2 diabetes, non-alcoholic fatty liver and BMI were causally associated with elevated cT1 whilst favourable adiposity (instrumented by variants associated with higher adiposity but lower risk of cardiometabolic disease and lower liver fat) was found to be protective. Conclusion The association between two metal ion transporters and cT1 indicates an important new mechanism in steatohepatitis. Future studies are needed to determine whether interventions targeting the identified transporters might prevent liver disease in at risk individuals

Mining the Local Volume

After recent systematic optical, IR, and HI surveys, the total number of known galaxies within 10 Mpc has increased from 179 to 550. About half this Local Volume (LV) sample is now been imaged with HST, yielding the galaxy distances with an accuracy of about 8%. For the majority of the LV galaxies we currently have H-alpha fluxes that allow us to reconstruct the star formation history of our neighbourhood. For the late-type LV galaxies their HI masses and angular momentum follow the linear relation in the range of 4 orders, which is expected for rotating gaseous disks being near the gravitational instability threshold. The data obtained on the LV galaxies imply important cosmological parameters, in particular, the mean local matter density and HI mass density, as well as SFR density. Surprisingly, the local Hubble flow around the LV groups is very quiet, with 1D rms deviations of 25 km/s,which is a signature of the Universe vacuum-dominated on small scales. The cold infall pattern around nearby groups provides us with a new method to determine the total mass of the groups independent from virial mass estimates.Comment: 10 pages, 6 figures, proceedings Symposium "Galaxies in the Local Volume", Sydney, 8 - 13 July 2007, B. Koribalski and H. Jerjen, ed

A Note on the Integral Formulation of Einstein's Equations Induced on a Braneworld

We revisit the integral formulation (or Green's function approach) of Einstein's equations in the context of braneworlds. The integral formulation has been proposed independently by several authors in the past, based on the assumption that it is possible to give a reinterpretation of the local metric field in curved spacetimes as an integral expression involving sources and boundary conditions. This allows one to separate source-generated and source-free contributions to the metric field. As a consequence, an exact meaning to Mach's Principle can be achieved in the sense that only source-generated (matter fields) contributions to the metric are allowed for; universes which do not obey this condition would be non-Machian. In this paper, we revisit this idea concentrating on a Randall-Sundrum-type model with a non-trivial cosmology on the brane. We argue that the role of the surface term (the source-free contribution) in the braneworld scenario may be quite subtler than in the 4D formulation. This may pose, for instance, an interesting issue to the cosmological constant problem.Comment: 10 pages, no figures, accepted for publication in the General Relativity and Gravitation Journa

On the multiplicity of the O-star Cyg OB2 #8A and its contribution to the gamma-ray source 3EG J2033+4118

We present the results of an intensive spectroscopic campaign in the optical waveband revealing that Cyg OB2 #8A is an O6 + O5.5 binary system with a period of about 21.9 d. Cyg OB2 #8A is a bright X-ray source, as well as a non-thermal radio emitter. We discuss the binarity of this star in the framework of a campaign devoted to the study of non-thermal emitters, from the radio waveband to gamma-rays. In this context, we attribute the non-thermal radio emission from this star to a population of relativistic electrons, accelerated by the shock of the wind-wind collision. These relativistic electrons could also be responsible for a putative gamma-ray emission through inverse Compton scattering of photospheric UV photons, thus contributing to the yet unidentified EGRET source 3EG J2033+4118.Comment: 8 pages, 4 figures, conference on "The Multiwavelength Approach to Gamma-Ray Sources", to appear in Ap&S

On the Resolution of the Time-Like Singularities in Reissner-Nordstrom and Negative-Mass Schwarzschild

Certain time-like singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are formulated. The Reissner-Nordstrom singularity allows for communication through the singularity and can be termed "beam splitter" since the transmission probability of a suitably prepared high energy wave packet is 25%. The high frequency dependence of the cross section is w^{-4/3}. However, smooth geometries arbitrarily close to the singular one require a finite amount of negative energy matter. The negative-mass Schwarzschild has a qualitatively different resolution interpreted to be fully reflecting. These 4d results are similar to the 2d black hole and are generalized to an arbitrary dimension d>4.Comment: 47 pages, 5 figures. v2: See end of introduction for an important note adde