A rigorous analysis of high order electromagnetic invisibility cloaks

There is currently a great deal of interest in the invisibility cloaks recently proposed by Pendry et al. that are based in the transformation approach. They obtained their results using first order transformations. In recent papers Hendi et al. and Cai et al. considered invisibility cloaks with high order transformations. In this paper we study high order electromagnetic invisibility cloaks in transformation media obtained by high order transformations from general anisotropic media. We consider the case where there is a finite number of spherical cloaks located in different points in space. We prove that for any incident plane wave, at any frequency, the scattered wave is identically zero. We also consider the scattering of finite energy wave packets. We prove that the scattering matrix is the identity, i.e., that for any incoming wave packet the outgoing wave packet is the same as the incoming one. This proves that the invisibility cloaks can not be detected in any scattering experiment with electromagnetic waves in high order transformation media, and in particular in the first order transformation media of Pendry et al. We also prove that the high order invisibility cloaks, as well as the first order ones, cloak passive and active devices. The cloaked objects completely decouple from the exterior. Actually, the cloaking outside is independent of what is inside the cloaked objects. The electromagnetic waves inside the cloaked objects can not leave the concealed regions and viceversa, the electromagnetic waves outside the cloaked objects can not go inside the concealed regions. As we prove our results for media that are obtained by transformation from general anisotropic materials, we prove that it is possible to cloak objects inside general crystals.Comment: The final version is now published in Journal of Physics A: Mathematical and Theoretical, vol 41 (2008) 065207 (21 pp). Included in IOP-Selec

On Inverse Scattering at a Fixed Energy for Potentials with a Regular Behaviour at Infinity

We study the inverse scattering problem for electric potentials and magnetic fields in \ere^d, d\geq 3, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy.Comment: This is a slightly edited version of the previous pape

Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.Comment: In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some typo

Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is continuous at zero energy. An explicit formula is provided for the scattering matrix at zero energy. The small-energy asymptotics are established also for the corresponding Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems.Comment: This published version has been edited to improve the presentation of the result

Neural networks engaged in tactile object manipulation: patterns of expression among healthy individuals

<p>Abstract</p> <p>Background</p> <p>Somatosensory object discrimination has been shown to involve widespread cortical and subcortical structures in both cerebral hemispheres. In this study we aimed to identify the networks involved in tactile object manipulation by principal component analysis (PCA) of individual subjects. We expected to find more than one network.</p> <p>Methods</p> <p>Seven healthy right-handed male volunteers (aged 22 to 44 yrs) manipulated with their right hand aluminium spheres during 5 s with a repetition frequency of 0.5-0.7 Hz. The correlation coefficients between the principal component temporal expression coefficients and the hemodynamic response modelled by SPM (ecc) determined the task-related components. To establish reproducibility within subjects and similarity of functional connectivity patterns among subjects, regional correlation coefficients (rcc) were computed between task-related component image volumes. By hierarchically categorizing, selecting and averaging the task-related component image volumes across subjects according to the rccs, mean component images (MCIs) were derived describing neural networks associated with tactile object manipulation.</p> <p>Results</p> <p>Two independent mean component images emerged. Each included the primary sensorimotor cortex contralateral to the manipulating hand. The region extended to the premotor cortex in MCI 1, whereas it was restricted to the hand area of the primary sensorimotor cortex in MCI 2. MCI 1 showed bilateral involvement of the paralimbic anterior cingulate cortex (ACC), whereas MCI 2 implicated the midline thalamic nuclei and two areas of the rostral dorsal pons.</p> <p>Conclusions</p> <p>Two distinct networks participate in tactile object manipulation as revealed by the intra- and interindividual comparison of individual scans. Both were employed by most subjects, suggesting that both are involved in normal somatosensory object discrimination.</p

Distinguishing transient from persistent tactile agnosia after partial anterior circulation infarcts - Behavioral and neuroimaging evidence for white matter disconnection.

From a cohort of 36 patients presenting apperceptive tactile agnosia after first cortical ischemic stroke, 14 showed temporary impairment at admission. A previous multi-voxel analysis of the cortical lesions, using as explanatory variable the course of tactile object recognition performance over the recovery period of 9 months, partitioned the cohort into three subgroups. Of the 14 patients constituting two of the subgroups, 7 recovered from their impairment whereas 7 did not. These two subgroups could not be distinguished at admission. The primary aim of the present study is to present two assessments that can do so. The first assessment comprises a pattern of behavioral measures, determined via principal component analysis, encoded in three tests: picking small objects, macrogeometrical discrimination and tactile object recognition. The receiver operating characteristic curve derived from permutation of the behavioral test scores yielded an 80% probability of correct identification of the patient subgroup and an 8% probability for false identification. As done with the permuted scores, the pattern could predict the persistence of affliction of new stroke patients with tactile agnosia. The second predictive assessment extends our previous evaluation of cortical MRI lesion maps to include subcortical regions. Confirming our previous study, the lesions of the persistently impaired subgroup disrupted significantly the anterior arcuatus fasciculus and associated superior longitudinal fasciculus III in the ipsilesional hemisphere, impeding reciprocal information transfer between supramarginal gyrus and both the ventral premotor cortex and Brodmann area 44. Due to the importance of interhemispheric information transfer in tactile agnosia, we performed a supplementary analysis of tactile object recognition scores. It showed that haptic information transfer from the non-affected to the affected hands in the persistent cases partly restored function during the nine months, possibly following restoration of functional interhemispheric haptic information transfer at the border of posterior corpus callosum and splenium. In conclusion, the combined findings of the cortical lesion at subarea PFt of the inferior parietal lobule and the associated subcortical tract lesions permit almost perfect prediction of persistent impairment of tactile object recognition. The study substantiates the need for combined analysis of both cortical lesions and white matter tract disconnections

Prognostic significance of epithelial-mesenchymal transition in malignant pleural mesothelioma

Background: Epithelial-to-mesenchymal transition (EMT) is a morphologic transdifferentiation of carcinomas, conferring increased tumour invasiveness, but may also be applied to the epithelioid versus sarcomatoid histotype of malignant pleural mesothelioma (MPM). Herein, we correlated proteins of a putative MPM-EMT axis, including periostin, epidermal growth factor receptor (EGFR), integrin beta1, phosphatase and tensin homologue (PTEN), integrin-linked kinase (ILK), p21 and p27, with clinico-pathologic parameters, in particular overall survival (OS). Patients and Methods: A retrospective cohort of 352 mostly untreated patients with MPM was investigated by immunohistochemistry of a tissue microarray. Protein expression intensities were semi-quantitatively scored from 0 to 3 in their respective compartments, including peritumoural stroma as well as tumour cell plasma membrane, cytoplasm or nucleus. Data were correlated with histotype and survival outcome. Results: A total of 32% of the tumours were diagnosed as epithelioid, 13% as sarcomatoid and 55% as biphasic histotype. High expression of membranous EGFR and integrin beta1 as well as nuclear p27 correlated with the epithelioid and high expression of cytoplasmic tumoural and stromal periostin with the sarcomatoid histotype. The median survival time of the 128 patients with complete follow-up data was 11.7 months. Univariate survival analysis revealed age, epithelioid histotype and any therapy as prognosticators for better OS. High expression of cytoplasmic PTEN or ILK as well as high expression of nuclear p21 or p27 correlated with increased, whereas high expression of cytoplasmic periostin with decreased OS (all p values <0.05). Multivariate Cox regression revealed any treatment, low cytoplasmic periostin and high cytoplasmic PTEN as independent prognosticators for better OS. Conclusion: Activation of periostin-triggered EMT is associated with the sarcomatoid histotype and has an impact on shorter survival of MPM patients. Finally, only the high expression of PTEN and the low expression of cytosolic periostin could be shown to be independent prognostic factors for longer O

Simplicity of extremal eigenvalues of the Klein-Gordon equation

We consider the spectral problem associated with the Klein-Gordon equation for unbounded electric potentials. If the spectrum of this problem is contained in two disjoint real intervals and the two inner boundary points are eigenvalues, we show that these extremal eigenvalues are simple and possess strictly positive eigenfunctions. Examples of electric potentials satisfying these assumptions are given

Scattering theory for Klein-Gordon equations with non-positive energy

We study the scattering theory for charged Klein-Gordon equations: \{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+ \bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x) \d x. We consider the situation when the energy is not positive. In this case the flow cannot be written as a unitary group on a Hilbert space, and the Klein-Gordon equation may have complex eigenfrequencies. Using the theory of definitizable operators on Krein spaces and time-dependent methods, we prove the existence and completeness of wave operators, both in the short- and long-range cases. The range of the wave operators are characterized in terms of the spectral theory of the generator, as in the usual Hilbert space case