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Impedance-based sensor for potassium ions.
A conductometric sensor for potassium ions in solution is presented. Interdigitated, planar gold electrodes were coated with a potassium-selective polymer membrane composed of a poly(vinyl chloride) matrix with about 65 wt% of plasticiser and 2-5 wt% of a potassium-selective ionophore. The impedance of the membrane was measured, using the electrodes as a transducer, and related to the concentration of potassium in a sample solution in contact with the membrane. Sensitivity was optimised by varying the sensor components, and selectivity for potassium over sodium was also shown. The resulting devices are compact, miniature, robust sensors which, by means of impedance measurements, eliminate the need for a reference electrode. The sensor was tested for potassium concentration changes of 2 mM across the clinically relevant range of 2.7-18.7 mM.Henslow Fellowship, Darwin College, Cambridge
L'Oreal -UNESCO UK & Ireland Fellowship For Women In Scienc
Quantum fingerprinting
Classical fingerprinting associates with each string a shorter string (its
fingerprint), such that, with high probability, any two distinct strings can be
distinguished by comparing their fingerprints alone. The fingerprints can be
exponentially smaller than the original strings if the parties preparing the
fingerprints share a random key, but not if they only have access to
uncorrelated random sources. In this paper we show that fingerprints consisting
of quantum information can be made exponentially smaller than the original
strings without any correlations or entanglement between the parties: we give a
scheme where the quantum fingerprints are exponentially shorter than the
original strings and we give a test that distinguishes any two unknown quantum
fingerprints with high probability. Our scheme implies an exponential
quantum/classical gap for the equality problem in the simultaneous message
passing model of communication complexity. We optimize several aspects of our
scheme.Comment: 8 pages, LaTeX, one figur
Submonolayer Epitaxy Without A Critical Nucleus
The nucleation and growth of two--dimensional islands is studied with Monte
Carlo simulations of a pair--bond solid--on--solid model of epitaxial growth.
The conventional description of this problem in terms of a well--defined
critical island size fails because no islands are absolutely stable against
single atom detachment by thermal bond breaking. When two--bond scission is
negligible, we find that the ratio of the dimer dissociation rate to the rate
of adatom capture by dimers uniquely indexes both the island size distribution
scaling function and the dependence of the island density on the flux and the
substrate temperature. Effective pair-bond model parameters are found that
yield excellent quantitative agreement with scaling functions measured for
Fe/Fe(001).Comment: 8 pages, Postscript files (the paper and Figs. 1-3), uuencoded,
compressed and tarred. Surface Science Letters, in press
From Quantum Query Complexity to State Complexity
State complexity of quantum finite automata is one of the interesting topics
in studying the power of quantum finite automata. It is therefore of importance
to develop general methods how to show state succinctness results for quantum
finite automata. One such method is presented and demonstrated in this paper.
In particular, we show that state succinctness results can be derived out of
query complexity results.Comment: Some typos in references were fixed. To appear in Gruska Festschrift
(2014). Comments are welcome. arXiv admin note: substantial text overlap with
arXiv:1402.7254, arXiv:1309.773
Chromatic number, clique subdivisions, and the conjectures of Haj\'os and Erd\H{o}s-Fajtlowicz
For a graph , let denote its chromatic number and
denote the order of the largest clique subdivision in . Let H(n) be the
maximum of over all -vertex graphs . A famous
conjecture of Haj\'os from 1961 states that for every
graph . That is, for all positive integers . This
conjecture was disproved by Catlin in 1979. Erd\H{o}s and Fajtlowicz further
showed by considering a random graph that for some
absolute constant . In 1981 they conjectured that this bound is tight up
to a constant factor in that there is some absolute constant such that
for all -vertex graphs . In this
paper we prove the Erd\H{o}s-Fajtlowicz conjecture. The main ingredient in our
proof, which might be of independent interest, is an estimate on the order of
the largest clique subdivision which one can find in every graph on
vertices with independence number .Comment: 14 page
How large are the level sets of the Takagi function?
Let T be Takagi's continuous but nowhere-differentiable function. This paper
considers the size of the level sets of T both from a probabilistic point of
view and from the perspective of Baire category. We first give more elementary
proofs of three recently published results. The first, due to Z. Buczolich,
states that almost all level sets (with respect to Lebesgue measure on the
range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states
that the average number of points in a level set is infinite. The third result,
also due to Lagarias and Maddock, states that the average number of local level
sets contained in a level set is 3/2. In the second part of the paper it is
shown that, in contrast to the above results, the set of ordinates y with
uncountably infinite level sets is residual, and a fairly explicit description
of this set is given. The paper also gives a negative answer to a question of
Lagarias and Maddock by showing that most level sets (in the sense of Baire
category) contain infinitely many local level sets, and that a continuum of
level sets even contain uncountably many local level sets. Finally, several of
the main results are extended to a version of T with arbitrary signs in the
summands.Comment: Added a new Section 5 with generalization of the main results; some
new and corrected proofs of the old material; 29 pages, 3 figure
Lower bounds for measurable chromatic numbers
The Lovasz theta function provides a lower bound for the chromatic number of
finite graphs based on the solution of a semidefinite program. In this paper we
generalize it so that it gives a lower bound for the measurable chromatic
number of distance graphs on compact metric spaces.
In particular we consider distance graphs on the unit sphere. There we
transform the original infinite semidefinite program into an infinite linear
program which then turns out to be an extremal question about Jacobi
polynomials which we solve explicitly in the limit. As an application we derive
new lower bounds for the measurable chromatic number of the Euclidean space in
dimensions 10,..., 24, and we give a new proof that it grows exponentially with
the dimension.Comment: 18 pages, (v3) Section 8 revised and some corrections, to appear in
Geometric and Functional Analysi
Time reclaimed: temporality and the experience of meaningful work
The importance of meaningful work has been identified in scholarly writings across a range of disciplines. However, empirical studies remain sparse and the potential relevance of the concept of temporality, hitherto somewhat neglected even in wider sociological studies of organizations, has not been considered in terms of the light that it can shed on the experience of work as meaningful. These two disparate bodies of thought are brought together to generate new accounts of work meaningfulness through the lens of temporality. Findings from a qualitative study of workers in three occupations with ostensibly distinct temporal landscapes are reported. All jobs had the potential to be both meaningful and meaningless; meaningfulness arose episodically through work experiences that were shared, autonomous and temporally complex. Schutz’s notion of the ‘vivid present’ emerged as relevant to understanding how work is rendered meaningful within an individual’s personal and social system of relevances
The Erd\H{o}s-Ko-Rado theorem for twisted Grassmann graphs
We present a "modern" approach to the Erd\H{o}s-Ko-Rado theorem for
Q-polynomial distance-regular graphs and apply it to the twisted Grassmann
graphs discovered in 2005 by van Dam and Koolen.Comment: 5 page
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