A Concrete View of Rule 110 Computation

Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values are updated in the following way: 0s are changed to 1s at all positions where the value to the right is a 1, while 1s are changed to 0s at all positions where the values to the left and right are both 1. Though trivial to define, the behavior exhibited by Rule 110 is surprisingly intricate, and in (Cook, 2004) we showed that it is capable of emulating the activity of a Turing machine by encoding the Turing machine and its tape into a repeating left pattern, a central pattern, and a repeating right pattern, which Rule 110 then acts on. In this paper we provide an explicit compiler for converting a Turing machine into a Rule 110 initial state, and we present a general approach for proving that such constructions will work as intended. The simulation was originally assumed to require exponential time, but surprising results of Neary and Woods (2006) have shown that in fact, only polynomial time is required. We use the methods of Neary and Woods to exhibit a direct simulation of a Turing machine by a tag system in polynomial time

AN EXTENSION OF SOME RESULTS DUE TO JARDEN

This paper defines some generalized Fibonacci and Lucas sequences which satisfy arbitrary order linear recurrence relations and which answer a problem posed by Jarden in 1966 about generalizing an elegant result for a connection between even and odd subscripted Fibonacci and Lucas numbers

Some aspects of Fibonacci polynomial congruences

This paper formulates a definition of Fibonacci polynomials which is slightly different from the traditional definitions, but which is related to the classical polynomials of Bernoulli, Euler and Hermite. Some related congruence properties are developed and some unanswered questions are outlined. Keywords: Congruences, recurrence relations, Fibonacci sequence, Lucas sequences, umbral calculus

ARBITRARY ORDER RECURSIVE SEQUENCES AND ASSOCIATED CONTINUED FRACTIONS

The essential idea in this paper it to generalize and synthesize some of the pioneering ideas of Bernstein, Lucas and Horadam on generalizations of basic and primordial Fibonacci numbers and their arbitrary order generalizations and their relation to generalized continued fractions with matrices as the unifying elements

On acceptance conditions for membrane systems: characterisations of L and NL

In this paper we investigate the affect of various acceptance conditions on recogniser membrane systems without dissolution. We demonstrate that two particular acceptance conditions (one easier to program, the other easier to prove correctness) both characterise the same complexity class, NL. We also find that by restricting the acceptance conditions we obtain a characterisation of L. We obtain these results by investigating the connectivity properties of dependency graphs that model membrane system computations

A Fibreoptic Endoscopic Study of Upper Gastrointestinal Bleeding at Bugando Medical Centre in Northwestern Tanzania: a Retrospective Review of 240 Cases.

Upper gastrointestinal (GI) bleeding is recognized as a common and potentially life-threatening abdominal emergency that needs a prompt assessment and aggressive emergency treatment. A retrospective study was undertaken at Bugando Medical Centre in northwestern Tanzania between March 2010 and September 2011 to describe our own experiences with fibreoptic upper GI endoscopy in the management of patients with upper gastrointestinal bleeding in our setting and compare our results with those from other centers in the world. A total of 240 patients representing 18.7% of all patients (i.e. 1292) who had fibreoptic upper GI endoscopy during the study period were studied. Males outnumbered female by a ratio of 2.1:1. Their median age was 37 years and most of patients (60.0%) were aged 40 years and below. The vast majority of the patients (80.4%) presented with haematemesis alone followed by malaena alone in 9.2% of cases. The use of non-steroidal anti-inflammatory drugs, alcohol and smoking prior to the onset of bleeding was recorded in 7.9%, 51.7% and 38.3% of cases respectively. Previous history of peptic ulcer disease was reported in 22(9.2%) patients. Nine (3.8%) patients were HIV positive. The source of bleeding was accurately identified in 97.7% of patients. Diagnostic accuracy was greater within the first 24 h of the bleeding onset, and in the presence of haematemesis. Oesophageal varices were the most frequent cause of upper GI bleeding (51.3%) followed by peptic ulcers in 25.0% of cases. The majority of patients (60.8%) were treated conservatively. Endoscopic and surgical treatments were performed in 30.8% and 5.8% of cases respectively. 140 (58.3%) patients received blood transfusion. The median length of hospitalization was 8 days and it was significantly longer in patients who underwent surgical treatment and those with higher Rockall scores (P < 0.001). Rebleeding was reported in 3.3% of the patients. The overall mortality rate of 11.7% was significantly higher in patients with variceal bleeding, shock, hepatic decompensation, HIV infection, comorbidities, malignancy, age > 60 years and in patients with higher Rockall scores and those who underwent surgery (P < 0.001). Oesophageal varices are the commonest cause of upper gastrointestinal bleeding in our environment and it is associated with high morbidity and mortality. The diagnostic accuracy of fibreoptic endoscopy was related to the time interval between the onset of bleeding and endoscopy. Therefore, it is recommended that early endoscopy should be performed within 24 h of the onset of bleeding

Reliability of upright posture measurements in primary school children

BACKGROUND: Correct upright posture is considered to be a measure of good musculoskeletal health. Little is known about the usual variability of children's upright standing posture. The aim of this study was to assess differences between repeated measures of upright posture in a group of primary school children. METHODS: Sagittal plane photographs of usual, relaxed upright standing posture of 38 boys and girls aged 5–12 years were taken twice within an hour. Reflective markers were placed over the canthus, tragus, C7 spinous process, greater trochanter and lateral malleolus. Digitising software was used to calculate the x,y plane coordinates, from which five postural angles were calculated (trunk, neck, gaze, head on neck, lower limb). Height, weight, motor control estimates (as measured by the Brace Tests) and presence of recent pain were recorded for each child, and the association between the first test measure of posture angles and these factors was assessed using linear regression and ANOVA models. Multiple ANOVA models were applied to analyse the effect of repeated testing, and significant predictors on the angles. RESULTS: Four of the five postural angles (trunk, neck, head on neck, lower limb) were significantly influenced by age. As age was strongly associated with height (r(2 )= 0.84) and moderately associated with weight and motor control (r(2 )= 0.67, 0.56 respectively), these developmental parameters may well explain the age effect on angles. There was no relationship between age and pain reported on either the testing day, or recently, and there was no gender influence on any angle. There was no significant effect of repeated testing on any angle (ICC>0.93). None of the hypothesized predictors were associated with differences in angles from repeated testing. CONCLUSION: This study outlined the variability of relaxed upright standing posture of children aged 5–12 years, when measured twice in an hour. Age influenced the size of the angles but not the variability. While the subject numbers in this study are small, the findings provide useful information on which further studies in posture and its development in pre-adolescent children can be based

Circulating gluten-specific FOXP3 + CD39 + regulatory T cells have impaired suppressive function in patients with celiac disease

Background Celiac disease is a chronic immune-mediated inflammatory disorder of the gut triggered by dietary gluten. Although the effector T-cell response in patients with celiac disease has been well characterized, the role of regulatory T (Treg) cells in the loss of tolerance to gluten remains poorly understood. Objective We sought to define whether patients with celiac disease have a dysfunction or lack of gluten-specific forkhead box protein 3 (FOXP3)+ Treg cells. Methods Treated patients with celiac disease underwent oral wheat challenge to stimulate recirculation of gluten-specific T cells. Peripheral blood was collected before and after challenge. To comprehensively measure the gluten-specific CD4+ T-cell response, we paired traditional IFN-γ ELISpot with an assay to detect antigen-specific CD4+ T cells that does not rely on tetramers, antigen-stimulated cytokine production, or proliferation but rather on antigen-induced coexpression of CD25 and OX40 (CD134). Results Numbers of circulating gluten-specific Treg cells and effector T cells both increased significantly after oral wheat challenge, peaking at day 6. Surprisingly, we found that approximately 80% of the ex vivo circulating gluten-specific CD4+ T cells were FOXP3+CD39+ Treg cells, which reside within the pool of memory CD4+CD25+CD127lowCD45RO+ Treg cells. Although we observed normal suppressive function in peripheral polyclonal Treg cells from patients with celiac disease, after a short in vitro expansion, the gluten-specific FOXP3+CD39+ Treg cells exhibited significantly reduced suppressive function compared with polyclonal Treg cells. Conclusion This study provides the first estimation of FOXP3+CD39+ Treg cell frequency within circulating gluten-specific CD4+ T cells after oral gluten challenge of patients with celiac disease. FOXP3+CD39+ Treg cells comprised a major proportion of all circulating gluten-specific CD4+ T cells but had impaired suppressive function, indicating that Treg cell dysfunction might be a key contributor to disease pathogenesis