On the density of nice Friedmans

A Friedman number is a positive integer which is the result of an expression combining all of its own digits by use of the four basic operations, exponentiation and digit concatenation. A "nice" Friedman number is a Friedman number for which the expression constructing the number from its own digits can be represented with the original order of the digits unchanged. One of the fundamental questions regarding Friedman numbers, and particularly regarding nice Friedman numbers, is how common they are among the integers. In this paper, we prove that nice Friedman numbers have density 1, when considered in binary, ternary or base four.Comment: 6 page

The RAM equivalent of P vs. RP

One of the fundamental open questions in computational complexity is whether the class of problems solvable by use of stochasticity under the Random Polynomial time (RP) model is larger than the class of those solvable in deterministic polynomial time (P). However, this question is only open for Turing Machines, not for Random Access Machines (RAMs). Simon (1981) was able to show that for a sufficiently equipped Random Access Machine, the ability to switch states nondeterministically does not entail any computational advantage. However, in the same paper, Simon describes a different (and arguably more natural) scenario for stochasticity under the RAM model. According to Simon's proposal, instead of receiving a new random bit at each execution step, the RAM program is able to execute the pseudofunction $\textit{RAND}(y)$, which returns a uniformly distributed random integer in the range $[0,y)$. Whether the ability to allot a random integer in this fashion is more powerful than the ability to allot a random bit remained an open question for the last 30 years. In this paper, we close Simon's open problem, by fully characterising the class of languages recognisable in polynomial time by each of the RAMs regarding which the question was posed. We show that for some of these, stochasticity entails no advantage, but, more interestingly, we show that for others it does.Comment: 23 page

Interaural time difference processing in the mammalian medial superior olive

The dominant cue for localization of low-frequency sounds are microsecond differences in the time-of-arrival of sounds at the two ears [interaural time difference (ITD)]. In mammals, ITD sensitivity is established in the medial superior olive (MSO) by coincidence detection of excitatory inputs from both ears. Hence the relative delay of the binaural inputs is crucial for adjusting ITD sensitivity in MSO cells. How these delays are constructed is, however, still unknown. Specifically, the question of whether inhibitory inputs are involved in timing the net excitation in MSO cells, and if so how, is controversial. These inhibitory inputs derive from the nuclei of the trapezoid body, which have physiological and structural specializations for high-fidelity temporal transmission, raising the possibility that well timed inhibition is involved in tuning ITD sensitivity. Here, we present physiological and pharmacological data from in vivo extracellular MSO recordings in anesthetized gerbils. Reversible blockade of synaptic inhibition by iontophoretic application of the glycine antagonist strychnine increased firing rates and significantly shifted ITD sensitivity of MSO neurons. This indicates that glycinergic inhibition plays a major role in tuning the delays of binaural excitation. We also tonically applied glycine, which lowered firing rates but also shifted ITD sensitivity in a way analogous to strychnine. Hence tonic glycine application experimentally decoupled the effect of inhibition from the timing of its inputs. We conclude that, for proper ITD processing, not only is inhibition necessary, but it must also be precisely timed

Applications of polarography and related techniques in organic analysis

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Tetrahydrobiopterin deficiency and brain nitric oxide metabolism

Tetrahydrobiopterin is an essential cofactor for the aromatic amino acid monooxygenase group of enzymes. Inborn errors of tetrahydrobiopterin metabolism result in hyperphenylalaninaemia and impaired catecholamine and serotonin turnover. Tetrahydrobiopterin is also a cofactor for all known isoforms of nitric oxide synthase (NOS). The effect of tetrahydrobiopterin deficiency on brain nitric oxide metabolism has to date been given little consideration. In this thesis the effect of tetrahydrobiopterin deficiency on brain nitric oxide metabolism has been studied using a mouse model of tetrahydrobiopterin deficiency, the hph-1 mouse. Tetrahydrobiopterin was measured in 10 and 30 day old mice in whole brain and cerebellum. At both age points there was a significant -50% reduction in tetrahydrobiopterin content for whole brain and cerebellum in the hph-1 mouse compared to corresponding control mice. NOS activity was measured in whole brain from 10 and 30 day old hph-1 and control mice. No difference was observed in enzyme activity when tetrahydrobiopterin was included in the incubation medium. However, omission of tetrahydrobiopterin from the reaction buffer resulted in significantly lower NOS activity in the hph-1 mouse group compared to controls. Tetrahy-drobiopterin was also shown to have a potent effect on the affinity of brain NOS for arginine. The Km for arginine was virtually identical for the control and hph-1 mouse when tetrahydrobiopterin was included in the reaction buffer. In the absence of cofactor, the for arginine was three fold greater for control and five fold higher for hph-1 preparations. The accumulation of cGMP from slices prepared from the cerebellum was measured in both groups of mice at both 10 and 30 days using the glutamate analogue, kainate. In the 10 day old hph-1 mouse there was a significant 50% reduction in cGMP levels under basal and stimulated conditions. In the 30 day old hph-1 mouse there was a significant 30% reduction in cGMP accumulation in both basal and activated states. Whole brain amino acid levels were measured. In the 10 day old hph-1 mouse confounding hyperphenylalaninaemia may affect the availability of the NOS substrate, arginine. In the 30 day old hph-1 mouse, which has normal phenylalanine levels, reduced citrulline levels may indicate reduced NOS activity. Reduced levels of tetrahydrobiopterin and also arginine, have been shown to lead to superoxide formation by nitric oxide synthase. Superoxide can react with nitric oxide to form the oxidising species, peroxynitrite, which has been shown to damage of the mitochondrial electron transport chain. Mitochondrial function together with the antioxidant, glutathione, were analysed in both hph-1 and control mice at 10 and 30 days to measure oxidative stress. However, no differences were observed between the two groups. In summary, partial deficiency of tetrahydrobiopterin appears to lead to impaired brain NOS function leading to an impairment of the nitric oxide/cGMP pathway

HOOD : a Higher-Order Object-Oriented Database model and its implementation

Bibliography: pages 133-140.There is no accepted standard for the object-oriented database paradigm at present, which has led to different definitions of features and conformance requirements. HOOD is a Higher-Order Object-Oriented Database system which defines a meta-data model for specifying the requirements of an Object-Oriented Database, which provides uniformity and extensibility. From this specification and by making use of a comprehensive structure system, an exemplar or implementation model is defined. Among the constructs provided by the model are types, instances, objects, values, methods, base types, generic types and metatypes. The mechanisms of instantiation and subtyping allow for relationships between these constructs. Extensibility is provided in the model for types, base types, structures and methods. Uniformity is achieved by defining all constructs as instances and through the use of messages for all operations. There is only one form of object construct which provides persistence and identities. The complex values and extensibility of the model allow it to adapt in order to model the real world instead of adapting the real world to fit the model. We have implemented a subset of the structures and values defined in the model, provided persistence and identities for object, and included the various constructs mentioned above. The method language allows for the specification of methods, the passing of messages, and the use of complex values. The compiler performs type checking and resolution and generates instructions for an abstract machine which manipulates the database

Shocked H2 and Fe+ Dynamics in the Orion Bullets

Observations of H2 velocity profiles in the two most clearly defined Orion bullets are extremely difficult to reconcile with existing steady-state shock models. We have observed [FeII] 1.644um velocity profiles of selected bullets and H2 1-0 S(1) 2.122um velocity profiles for a series of positions along and across the corresponding bow-shaped shock fronts driven into the surrounding molecular cloud. Integrated [FeII] velocity profiles of the brightest bullets are consistent with theoretical bow shock predictions. However, observations of broad, singly-peaked H2 1-0 S(1) profiles at a range of positions within the most clearly resolved bullet wakes are not consistent with molecular shock modelling. A uniform, collisionally broadened background component which pervades the region in both tracers is inconsistent with fluorescence due to the ionizing radiation of the Trapezium stars alone.Comment: 20 pages including 18 figures, published in MNRA