Pattern Matching in Multiple Streams

We investigate the problem of deterministic pattern matching in multiple streams. In this model, one symbol arrives at a time and is associated with one of s streaming texts. The task at each time step is to report if there is a new match between a fixed pattern of length m and a newly updated stream. As is usual in the streaming context, the goal is to use as little space as possible while still reporting matches quickly. We give almost matching upper and lower space bounds for three distinct pattern matching problems. For exact matching we show that the problem can be solved in constant time per arriving symbol and O(m+s) words of space. For the k-mismatch and k-difference problems we give O(k) time solutions that require O(m+ks) words of space. In all three cases we also give space lower bounds which show our methods are optimal up to a single logarithmic factor. Finally we set out a number of open problems related to this new model for pattern matching.Comment: 13 pages, 1 figur

Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity

We study hydrodynamic fluctuations in a non-relativistic fluid. We show that in three dimensions fluctuations lead to a minimum in the shear viscosity to entropy density ratio $\eta/s$ as a function of the temperature. The minimum provides a bound on $\eta/s$ which is independent of the conjectured bound in string theory, $\eta/s \geq \hbar/(4\pi k_B)$, where $s$ is the entropy density. For the dilute Fermi gas at unitarity we find \eta/s\gsim 0.2\hbar. This bound is not universal -- it depends on thermodynamic properties of the unitary Fermi gas, and on empirical information about the range of validity of hydrodynamics. We also find that the viscous relaxation time of a hydrodynamic mode with frequency $\omega$ diverges as $1/\sqrt{\omega}$, and that the shear viscosity in two dimensions diverges as $\log(1/ \omega)$.Comment: 26 pages, 5 figures; final version to appear in Phys Rev

On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

Newly formed black holes are expected to emit characteristic radiation in the form of quasi-normal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multi-mode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black hole spin and the energy emitted in each mode, will affect our ability to do black hole spectroscopy.Comment: 44 pages, 21 figures, 10 tables. Minor changes to match version in press in Phys. Rev.

Stellar Dynamics of Extreme-Mass-Ratio Inspirals

Inspiral of compact stellar remnants into massive black holes (MBHs) is accompanied by the emission of gravitational waves at frequencies that are potentially detectable by space-based interferometers. Event rates computed from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due to uncertaintities about the rate coefficients. Here we present results from direct integration of the post-Newtonian N-body equations of motion descrbing dense clusters of compact stars around Schwarzschild MBHs. These simulations embody an essentially exact (at the post-Newtonian level) treatment of the interplay between stellar dynamical relaxation, relativistic precession, and gravitational-wave energy loss. The rate of capture of stars by the MBH is found to be greatly reduced by relativistic precession, which limits the ability of torques from the stellar potential to change orbital angular momenta. Penetration of this "Schwarzschild barrier" does occasionally occur, resulting in capture of stars onto orbits that gradually inspiral due to gravitational wave emission; we discuss two mechanisms for barrier penetration and find evidence for both in the simulations. We derive an approximate formula for the capture rate, which predicts that captures would be strongly disfavored from orbits with semi-major axes below a certain value; this prediction, as well as the predicted rate, are verified in the N-body integrations. We discuss the implications of our results for the detection of extreme-mass-ratio inspirals from galactic nuclei with a range of physical properties.Comment: 28 pages, 16 figures. Version 2 is significantly revised to reflect new insights into J and Q effects, to be published late

Selective deletion of cochlear hair cells causes rapid age-dependent changes in spiral ganglion and cochlear nucleus neurons

During nervous system development, critical periods are usually defined as early periods during which manipulations dramatically change neuronal structure or function, whereas the same manipulations in mature animals have little or no effect on the same property. Neurons in the ventral cochlear nucleus (CN) are dependent on excitatory afferent input for survival during a critical period of development. Cochlear removal in young mammals and birds results in rapid death of target neurons in the CN. Cochlear removal in older animals results in little or no neuron death. However, the extent to which hair-cell-specific afferent activity prevents neuronal death in the neonatal brain is unknown. We further explore this phenomenon using a new mouse model that allows temporal control of cochlear hair cell deletion. Hair cells express the human diphtheria toxin (DT) receptor behind the Pou4f3 promoter. Injections of DT resulted in nearly complete loss of organ of Corti hair cells within 1 week of injection regardless of the age of injection. Injection of DT did not influence surrounding supporting cells directly in the sensory epithelium or spiral ganglion neurons (SGNs). Loss of hair cells in neonates resulted in rapid and profound neuronal loss in the ventral CN, but not when hair cells were eliminated at a more mature age. In addition, normal survival of SGNs was dependent on hair cell integrity early in development and less so in mature animals. This defines a previously undocumented critical period for SGN survival

Crystal Structure of (E)-2-[(2- bromo-3-pyridyl)methylidene]-6-methoxy-3,4-dihydronaphthalen-1-one and 3-[(E)-(6- methoxy-3,4-dihydronaphth-2-oylidene)methyl]-1H-pyridin-2-one

The title compounds C17H14BrNO2, (I), and C17H15NO3, (II), were obtained from the reaction of 6-meth­oxy-3,4-di­hydro-2H-naphthalen-1-one and 2-bromo­nicotinaldehyde in ethanol. Compound (I) was the expected product and compound (II) was the oxidation product from air exposure. In the crystal structure of compound (I), there are no short contacts or hydrogen bonds. The structure does display [pi]-[pi] inter­actions between adjacent benzene rings and adjacent pyridyl rings. Compound (II) contains two independent mol­ecules, A and B, in the asymmetric unit; both are non-planar, the dihedral angles between the meth­oxy­benzene and 1H-pyridin-2-one mean planes being 35.07 (9)° in A and 35.28 (9)°in B. In each mol­ecule, the 1H-pyridin-2-one unit participates in inter­molecular N-H...O hydrogen bonding to another mol­ecule of the same type (A to A or B to B). The structure also displays [pi]-[pi] inter­actions between the pyridyl and the benzene rings of non-equivalent mol­ecules (viz., A to B and B to A)

Do pharmacy practice standards effectively describe behaviour? Reviewing practice standards using a behavioural specificity framework

BACKGROUND: Guidelines and practice standards exist to communicate the conduct and behaviour expected of health care professionals and ensure consistent quality practice. It is important that they describe behaviours explicitly so they can be interpreted, enacted and measured with ease. The AACTT framework specifies behaviour in terms of the: Action to be performed, Actor who performs the action, Context where the action occurs, Target who the action is performed with/for and Time when the action is performed (AACTT). It provides the most up to date framework for specifying behaviours and is particularly relevant to complex behavioural problems that involve sequences of behaviours performed by different people. Behavioural specificity within pharmacy practice standards has not been explored. AIM: To determine if behaviours described in the Professional Practice Standards for Australian Pharmacists specify Action, Actor, Context, Target and Time. METHODS: Two researchers independently reviewed the scope and structure of the practice standards and one extracted action statements (behaviours) verbatim. Through an iterative process, the researchers modified and developed the existing AACTT definitions to operationalise them for application to review of the action statements in the practice standards. The operational definitions, decision criteria and curated examples were combined in a codebook. The definitions were consistently applied through a directed content analysis approach to evaluate all extracted action statements by one researcher. For consistency 20% was independently checked for agreement by a second researcher. RESULTS: A novel codebook to apply AACTT criteria to evaluate practice standards was developed. Application of this codebook identified 768 independent behaviours. Of these, 300 (39%) described at least one discrete observable action, none specified an actor, 25 (3%) specified context, 131 (17%) specified target and 88 (11%) specified time. CONCLUSION(S): The behaviours detailed in practice standards for Australian pharmacists do not consistently specify behaviours in terms of Action, Actor, Context, Target and Time. Developers in the pharmacy profession, and beyond, should consider the behavioural specificity of their documents to improve interpretability, usability and adherence to the behaviours detailed. This also has implications for the development and evaluation of interventions to change such behaviours and improve quality of care

Chronic hypokalemia due to excessive cola consumption: a case report

A 52-year-old man was noted to have severe chronic hypokalemia despite discontinuation of diuretic treatment for hypertension and aggressive oral potassium supplementation. His serum potassium normalized temporarily when he was hospitalized, but hypokalemia recurred after discharge. He complained of generalized weakness and fatigue, and occasional loose stools. Physical examination showed mild generalized muscle weakness. Laboratory testing ruled out renal potassium wasting. A dietary history revealed that he was consuming 4 liters of cola per day, with a calculated fructose load of 396 grams per day. Since fructose absorption in the small bowel is relatively inefficient, this probably led to an osmotic diarrhea and GI potassium wasting. Physicians should ask their patients about soft drink consumption when they encounter unexplained hypokalemia