Abstract:
We prove some epsilon regularity results for n-dimensional minimal two-valued Lipschitz graphs. The main theorems imply uniqueness of tangent cones and regularity of the singular set in a neighbourhood of any point at which at least one tangent cone is equal to a pair of transversely intersecting multiplicity one n-dimensional planes, and in a neighbourhood of any point at which at which at least one tangent cone is equal to a union of four distinct multiplicity one n-dimensional half-planes that meet along an (n-1) - dimensional axis. The key ingredient is a new Excess Improvement Lemma obtained via a blow-up method (inspired by the work of L. Simon on the singularities of `multiplicity one' classes of minimal submanifolds) and which can be iterated unconditionally. We also show that any tangent cone to an n-dimensional minimal two-valued Lipschitz graph that is translation invariant along an (n-1) or (n-2)- dimensional subspace is indeed a cone of one of the two aforementioned forms, which yields a global decomposition result for the singular set

Abstract:
Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H^2, the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.

Abstract:
We study two weight inequalities in the recent innovative language of `entropy' due to Treil-Volberg. The inequalities are extended to $ L ^{p}$, for $ 1< p \neq 2 < \infty $, with new short proofs. A result proved is as follows. Let $ \varepsilon $ be a monotonic increasing function on $ (1, \infty)$ which satisfy $ \int _{1} ^{\infty} \frac {dt} {\varepsilon (t) t} = 1$. Let $ \sigma $ and $ w$ be two weights on $ \mathbb R ^{d}$. If this supremum is finite, for a choice of $ 1< p < \infty $, $$ \sup _{Q} \biggl[ \frac {\sigma (Q)} {\lvert Q\rvert} \biggr]^{p-1} \frac {\int _{Q} M (\sigma \chi_{Q})} {\sigma (Q)} \cdot \frac {w (Q)} {\lvert Q\rvert}\biggl[ \frac {\int _{Q} M (w \chi_{Q})} {w (Q)}\biggr]^{p-1} < \infty, $$ then any Calder\'on-Zygmund operator $ T$ satisfies the bound $ \lVert T _{\sigma} f \rVert _{L ^{p} (w)} \lesssim \lVert f\rVert _{L ^{p} (\sigma)} $.

Abstract:
Hemorrhage during trauma occurred in emergency situations is a significant challenge.
It may be life threatening if it is not treated swiftly. A new device which can
effectively stop bleeding to save life of injured person, especially in battlefield situations
and accidents, is presented. A plasma generator is designed to generate a low
temperature air plasma spray for treating wounds. The spectral spike at 777.4 nm in
the emission spectrum of the plasma plume and the spatial distribution of this emission
line’s spectral intensity indicate that abundant atomic oxygen is generated and
sprays out of the generator by about 25 mm. Atomic oxygen carried by the plasma
spray can quickly activate the cascading of coagulation processes and works as dry
disinfectant to advance healing. Tests on blood droplets reveal the strong dependence
of blood clotting on the amount of atomic oxygen applied in the plasma treatment,
which is maneuvered by increasing the plasma treatment time or decreasing the exposure
distance; in both approaches, the degree of blood clotting increases. Treated
smeared blood samples show that an increase of the erythrocyte concentration and a
drastic decrease of the platelet count are also correlated to the increase of atomic
oxygen dose applied in the plasma treatment. The results reveal the mechanisms of
air plasma blood coagulation and wound healing. As animal models, pigs were used
in the tests of stopping wound bleeding from a cross cut in the ham area, from a hole
in an ear’s saphenous vein, and from cuts to arteries in an ear and in a real leg, all
stopped swiftly. Moreover, both artery cuts were secure to remove tourniquet; downgrade
of tourniquet necessary wound in under 2 minutes was demonstrated. The
healing progress of cross cut wounds was observed. The healing time was shortened
to about half. This battery power plasma spray can be carried to or placed at anywhere
available for first aid applications. It stops bleeding swiftly to save life, and also
downgrades tourniquet necessary wound to extend the golden period of saving the
remaining part below tourniquet.

Abstract:
The efficacy and mechanism of a cold atmospheric-pressure air plasma (CAAP), which carries abundant atomic oxygen (OI), on blood coagulation are studied. The tests on sodium citrate mixed
blood-droplet samples show that 1) The heat delivered by the CAAP has no impact on the observed clot formation, 2) Plasma effluent activates platelets to promote coagulation state and cascade, and 3) The degree of clotting increases with the OI flux delivered by the CAAP. The full clotting time is shortened from about 25 minutes of the natural clotting timeto about 16s of the CAAP treatment time. The tests on smeared blood samples show that the reduction of the platelet count and the increase of RBC count are proportional to the applied OI flux. In vivo tests, using swine as nimal model, swift hemostasis of large and deep cut wounds on the back by the CAAP treatment was demonstrated. A cut artery was sealed completely with 25 s treatment. The pressure applied by a finger on the cut artery could be removed immediately after the treatment and there was no re-bleed. Based on the in vitro test results and the animal model trials, CAAP coagulation mechanism is presented.

Abstract:
Shortly after eye opening, initially disorganized visual cortex circuitry is rapidly refined to form smooth retinotopic maps. This process asymptotes long before adulthood, but it is unknown whether further refinement is possible. Prior work from our lab has shown that the retinotopic map of the non-dominant ipsilateral eye develops faster when the dominant contralateral eye is removed. We examined whether input from the contralateral eye might also limit the ultimate refinement of the ipsilateral eye retinotopic map in adults. In addition, we examined whether the increased refinement involved the recruitment of adjacent cortical area.

Abstract:
Consistent with our hypothesis, flanker interference effects were found on the N2c event-related brain potential and error rate for LH-biased individuals in the Attend-LVF condition. The error rate effect was correlated with the degree of hemispheric utilization bias for the LH-Bias group.We conclude that hemispheric utilization bias can enhance a hemisphere's contralateral attentional bias, at least for individuals with a LH utilization bias. Hemispheric utilization bias may play an important and largely unrecognized role in visuospatial attention.In this study we investigated the hypothesis that the control of spatial attention is influenced by hemispheric utilization bias, a characteristic bias of individuals to utilize one hemisphere more than the other for information processing [1]. Spatial selective attention is commonly thought to be mediated by a network in which attentional control systems based in prefrontal and posterior parietal areas modulate processing in perceptual areas [2,3]. Each of the cerebral hemispheres contains a set of mechanisms for attentional control and perceptual representation [4,5], which may be capable of operating independently in the intact brain [6]. These hemispheric attention systems appear to have mutually inhibitory biases that compete to direct attention to contralateral space, with the left hemisphere (LH) having a stronger and/or more focused intrinsic bias than the right hemisphere (RH) [7].Evidence for interhemispheric attentional competition comes from studies showing asymmetrical gradients in spatial attention in healthy individuals [8,9], split-brain patients [10-12], and neglect patients [13,14]. Also in neglect patients, disruption of the contralesional hemisphere by a subsequent stroke [15] or transcranial magnetic stimulation (TMS) [16] can cause recovery from neglect symptoms, consistent with the lesioned hemisphere being released from inhibition by the contralesional hemisphere. Furthermore, in healthy individual

Abstract:
A collaborative expedition between Khaled bin Sultan Living Oceans Foundation, Cambridge Coastal Research Unit and Seychelles Centre for Marine Research and Technology – Marine Parks Authority (SCMRT-MPA) was conducted to the southern Seychelles, western Indian Ocean, in January 2005. This resulted in a series of habitat maps of the reefs and reef islands of the Amirantes Archipelago, derived from remotely-sensed Compact Airborne Spectrographic Imager (CASI) data. The procedures used in map development, image processing techniques and field survey methods are outlined. Habitat classification, and regional-scale comparisons of relative habitat composition are described. The study demonstrates the use of remotesensing data to construct digital habitat maps for the comparison of regional habitat coverage, a key function for coastal management.

Abstract:
The standard period life table is based entirely on the death probabilities of the given period. Popular (not expert) usage of life expectancies from a period table typically ignores the fact that the expectancies make no allowance for future declines in mortality rates. But the historical record provides overwhelming evidence to suggest that declines will continue, and the period expectancies can therefore be misleading, in a practical context. We propose a "dynamic" extension of the period table that draws out the implications, for survivorship and life expectancy, of observed rates of change of death probabilities.