Generalized Futaki Invariant of Almost Fano Toric Varieties, Examples

The interpretation, due to T. Mabuchi, of the classical Futaki invariant of Fano toric manifolds is extended to the case of the Generalized Futaki invariant, introduced by W. Ding and G. Tian, of almost Fano toric varieties. As an application it is shown that the real part of the Generalized Futaki invariant is positive for all degenerations of the Fano manifold V_{38}, obtained by intersection of the Veronese embedding of ${\bf P}^3\times{\bf P}^2 \subset {\bf P}^{11}$ with codimension-two hyperplanes.Comment: 22 pages, LaTeX2

What are spin currents in Heisenberg magnets?

We discuss the proper definition of the spin current operator in Heisenberg magnets subject to inhomogeneous magnetic fields. We argue that only the component of the naive "current operator" J_ij S_i x S_j in the plane spanned by the local order parameters and is related to real transport of magnetization. Within a mean field approximation or in the classical ground state the spin current therefore vanishes. Thus, finite spin currents are a direct manifestation of quantum correlations in the system.Comment: 4 pages, 1 figure, published versio

Dynamical Models of Extreme Rolling of Vessels in Head Waves

Rolling of a ship is a swinging motion around its length axis. In particular vessels transporting containers may show large amplitude roll when sailing in seas with large head waves. The dynamics of the ship is such that rolling interacts with heave being the motion of the mass point of the ship in vertical direction. Due to the shape of the hull of the vessel its heave is influenced considerably by the phase of the wave as it passes the ship. The interaction of heave and roll can be modeled by a mass-spring-pendulum system. The effect of waves is then included in the system by a periodic forcing term. In first instance the damping of the spring can be taken infinitely large making the system a pendulum with an in vertical direction periodically moving suspension. For a small angular deflection the roll motion is then described by the Mathieu equation containing a periodic forcing. If the period of the solution of the equation without forcing is about twice the period of the forcing then the oscillation gets unstable and the amplitude starts to grow. After describing this model we turn to situation that the ship is not anymore statically fixed at the fluctuating water level. It may move up and down showing a motion modeled by a damped spring. One step further we also allow for pitch, a swinging motion around a horizontal axis perpendicular to the ship. It is recommended to investigate the way waves may directly drive this mode and to determine the amount of energy that flows along this path towards the roll mode. Since at sea waves are a superposition of waves with different wavelengths, we also pay attention to the properties of such a type of forcing containing stochastic elements. It is recommended that as a measure for the occurrence of large deflections of the roll angle one should take the expected time for which a given large deflection may occur instead of the mean amplitude of the deflection

What are the reasons for the strikingly different approaches to the use of ACTH in infants with West syndrome?

A large body of experience has been compiled in different countries, documenting the efficacy of adenocorticotropic hormone (ACTH) for infantile spasms. This is important, because it may serve as a key for understanding this disorder, as well as for designing better medicines. However, significant discrepancies exist among studies originating in different countries regarding the relative efficacy of small or large ACTH doses. These differences may be caused by a number of factors, including potential genetic or environmental-related differences in the biology of the disorder or associated genetic components that determine responsiveness to ACTH. In addition, striking differences in the preparations used around the world may be responsible. These include bio-availability and extent of blood brain barrier penetration, efficacy in activating the efficacy-mediating 'ACTH receptors', the presence in certain preparations of competing analogs, and others. These issues should not detract from the overall agreement that ACTH might be the most useful medication currently available to treat WS

Anticipating Daily Intention using On-Wrist Motion Triggered Sensing

Anticipating human intention by observing one's actions has many applications. For instance, picking up a cellphone, then a charger (actions) implies that one wants to charge the cellphone (intention). By anticipating the intention, an intelligent system can guide the user to the closest power outlet. We propose an on-wrist motion triggered sensing system for anticipating daily intentions, where the on-wrist sensors help us to persistently observe one's actions. The core of the system is a novel Recurrent Neural Network (RNN) and Policy Network (PN), where the RNN encodes visual and motion observation to anticipate intention, and the PN parsimoniously triggers the process of visual observation to reduce computation requirement. We jointly trained the whole network using policy gradient and cross-entropy loss. To evaluate, we collect the first daily "intention" dataset consisting of 2379 videos with 34 intentions and 164 unique action sequences. Our method achieves 92.68%, 90.85%, 97.56% accuracy on three users while processing only 29% of the visual observation on average

Ontogeny of somatostatin gene expression in rat diencephalon.

Somatostatin gene expression is first detectable, using in situ hybridization, on the 14th fetal day in rat diencephalon. Other structures expressing somatostatin messenger RNA include the anterior basal periventricular nucleus, amygdalo-hippocampal complex, dorsolateral thalamus and distinct areas in the parieto-frontal cortex. Semiquantitative analysis reveals that somatostatin synthesis increases progressively throughout the last third of fetal life and onto postnatal life