Boij-S\"{o}derberg Decompositions of Lex-segment Ideals

Boij-S\"oderberg theory describes the scalar multiples of Betti diagrams of graded modules over a polynomial ring as a linear combination of pure diagrams with positive coefficients. There are a few results that describe Boij-S\"oderberg decompositions explicitly. In this paper, we focus on the Betti diagrams of lex-segment ideals and describe the Boij-S\"oderberg decomposition of a lex-segment ideal in terms of Boij-S\"oderberg decompositions of some other related lex-segment ideals.Comment: The proof of Theorem 1.2 is improve

Observed intra-cluster correlation coefficients in a cluster survey sample of patient encounters in general practice in Australia

BACKGROUND: Cluster sample study designs are cost effective, however cluster samples violate the simple random sample assumption of independence of observations. Failure to account for the intra-cluster correlation of observations when sampling through clusters may lead to an under-powered study. Researchers therefore need estimates of intra-cluster correlation for a range of outcomes to calculate sample size. We report intra-cluster correlation coefficients observed within a large-scale cross-sectional study of general practice in Australia, where the general practitioner (GP) was the primary sampling unit and the patient encounter was the unit of inference. METHODS: Each year the Bettering the Evaluation and Care of Health (BEACH) study recruits a random sample of approximately 1,000 GPs across Australia. Each GP completes details of 100 consecutive patient encounters. Intra-cluster correlation coefficients were estimated for patient demographics, morbidity managed and treatments received. Intra-cluster correlation coefficients were estimated for descriptive outcomes and for associations between outcomes and predictors and were compared across two independent samples of GPs drawn three years apart. RESULTS: Between April 1999 and March 2000, a random sample of 1,047 Australian general practitioners recorded details of 104,700 patient encounters. Intra-cluster correlation coefficients for patient demographics ranged from 0.055 for patient sex to 0.451 for language spoken at home. Intra-cluster correlations for morbidity variables ranged from 0.005 for the management of eye problems to 0.059 for management of psychological problems. Intra-cluster correlation for the association between two variables was smaller than the descriptive intra-cluster correlation of each variable. When compared with the April 2002 to March 2003 sample (1,008 GPs) the estimated intra-cluster correlation coefficients were found to be consistent across samples. CONCLUSIONS: The demonstrated precision and reliability of the estimated intra-cluster correlations indicate that these coefficients will be useful for calculating sample sizes in future general practice surveys that use the GP as the primary sampling unit

Spin-orbit interaction in symmetric wells with two subbands

We investigate the spin-orbit (s-o) interaction in two-dimensional electron gases (2DEGs) in quantum wells with two subbands. From the $8\times 8$ Kane model, we derive a new inter-subband-induced s-o term which resembles the functional form of the Rashba s-o -- but is non-zero even in \emph{symmetric} structures. This follows from the distinct parity of the confined states (even/odd) which obliterates the need for asymmetric potentials. We self-consistently calculate the new s-o coupling strength for realistic wells and find it comparable to the usual Rashba constant. Our new s-o term gives rise to a non-zero ballistic spin-Hall conductivity, which changes sign as a function of the Fermi energy ($\epsilon_F$), and can induce an unusual \emph{zitterbewegung} with cycloidal trajectories \textit{without} magnetic fields.Comment: v2: 4 two-column pages, 3 figures (added spin Hall conductivity and self-consistent calculation

Micrometeoroid velocity-and-trajectory analyzer

By adding potential energy of charged capacitor to kinetic energy of impacting particle, new technique causes major fraction of atoms in microscopic particle impacting on particle-receiving surface to be ionized. Chemical constituents of impacting particle are represented by generated ion mass spectrum in approximately correct proportions

Swimming Rhythm Generation in The Caudal Hindbrain of The Lamprey

The spinal cord has been well established as the site of generation of the locomotor rhythm in vertebrates, but studies have suggested that the caudal hindbrain in larval fish and amphibians can also generate locomotor rhythms. Here, we investigated whether the caudal hindbrain of the adult lamprey (Petromyzon marinus and Ichthyomyzon unicuspis) has the ability to generate the swimming rhythm. The hindbrain-spinal cord transition zone of the lamprey contains a bilateral column of somatic motoneurons that project via the spino-occipital (S-O) nerves to several muscles of the head. In the brainstem-spinal cord-muscle preparation, these muscles were found to burst and contract rhythmically with a left-right alternation when swimming activity was evoked with a brief electrical stimulation of the spinal cord. In the absence of muscles, the isolated brainstem-spinal cord preparation also produced alternating left-right bursts in S-O nerves (i.e., fictive swimming), and the S-O nerve bursts preceded the bursts occurring in the first ipsilateral spinal ventral root. After physical isolation of the S-O region using transverse cuts of the nervous system, the S-O nerves still exhibited rhythmic bursting with left-right alternation when glutamate was added to the bathing solution. We conclude that the S-O region of the lamprey contains a swimming rhythm generator that produces the leading motor nerve bursts of each swimming cycle, which then propagate down the spinal cord to produce forward swimming. The S-O region of the hindbrain-spinal cord transition zone may play a role in regulating speed, turning, and head orientation during swimming in lamprey

Diffractoid grating configuration for X-ray and ultraviolet focusing

An aspheric grating is described which is operable to image local or distant point sources sharply in a designated wavelength, i.e., produce a perfectly stigmatic image in the given wavelength at grazing angles of incidence. The grating surface comprises a surface of revolution defined by a curve which does not have a constant radius of curvature but is defined by a nonlinear differential equation