Cycle packings in graphs and digraphs

AbstractA cycle packing in a (directed) multigraph is a vertex disjoint collection of (directed) elementary cycles. If D is a demiregular multidigraph we show that the arcs of D can be partitioned into Δin cycle packings — where δin is the maximum indegree of a vertex in D. We then show that the maximum length cycle packings in any digraph contain a common vertex

The Fermion-Boson Transformation in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a single flux quantum oriented opposite to the applied magnetic field. When the mean field approximation is made in the Haldane spherical geometry, the Fermion angular momentum $l_F$ is replaced by $l_B= l_F-{1\over2}(N-1)$. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical if and only if the pseudopotential is ``harmonic'' in form. However, similar low energy bands of states with Laughlin correlations occur in the two spectra if the interaction has short range. The transformation is used to clarify the relation between Boson and Fermion descriptions of the hierarchy of condensed fractional quantum Hall states.Comment: 5 pages, 4 figures, submitted to Physica

Recounting Fibonacci and Lucas Identities

No abstract provided in this article

The Fibonacci Numbers -- Exposed More Discretely

No abstract provided in this article

An Alternate Approach to Alternating Sums: A Method to DIE for

No abstract provided in this article

Unevening the Odds of Even Up

No abstract provided in this article

Transformation of Statistics in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane's spherical geometry, the Fermion angular momentum l_F is replaced by l_B=l_F-(N-1)/2. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular momentum L_12) increases as L_12(L_12+1). Similar bands of low energy states occur in the two spectra if V increases more quickly than this.Comment: 4 pages, 1 figure, poster at ARW in Queenstown, New Zealand (2001

Summing Cubes by Counting Rectangles

No abstract provided in this article

Evaluation of delirium screening tools in geriatric medical inpatients: a diagnostic test accuracy study

Introduction: screening all unscheduled older adults for delirium is recommended in national guidelines, but there is no consensus on how to perform initial assessment. Aim: to evaluate the test accuracy of five brief cognitive assessment tools for delirium diagnosis in routine clinical practice. Methods: a consecutive cohort of non-elective, elderly care (older than 65 years) hospital inpatients admitted to a geriatric medical assessment unit of an urban teaching hospital. Reference assessments were clinical diagnosis of delirium performed by elderly care physicians. Routine screening tests were: Abbreviated Mental Test (AMT-10, AMT-4), 4 A's Test (4AT), brief Confusion Assessment Method (bCAM), months of the year backwards (MOTYB) and informant Single Question in Delirium (SQiD). Results: we assessed 500 patients, mean age 83 years (range = 66−101). Clinical diagnoses were: 93 of 500 (18.6%) definite delirium, 104 of 500 (20.8%) possible delirium and 277 of 500 (55.4%) no delirium; 266 of 500 (53.2%) were identified as definite or possible dementia. For diagnosis of definite delirium, AMT-4 (cut-point < 3/4) had a sensitivity of 92.7% (95% confidence interval (CI): 84.8–97.3), with a specificity of 53.7% (95% CI: 48.1–59.2); AMT-10 (<4/10), MOTYB (<4/12) and SQiD showed similar performance. bCAM had a sensitivity of 70.3% (95% CI: 58.5–80.3) with a specificity of 91.4% (95% CI: 87.7–94.3). 4AT (>4/12) had a sensitivity of 86.7% (95% CI: 77.5–93.2) and specificity of 69.5% (95% CI: 64.4–74.3). Conclusions: short screening tools such as AMT-4 or MOTYB have good sensitivity for definite delirium, but poor specificity; these tools may be reasonable as a first stage in assessment for delirium. The 4AT is feasible and appears to perform well with good sensitivity and reasonable specificity