A Tropical Geometric Approach To Exceptional Points

Non-Hermitian systems have been widely explored in platforms ranging from photonics to electric circuits. A defining feature of non-Hermitian systems is exceptional points (EPs), where both eigenvalues and eigenvectors coalesce. Tropical geometry is an emerging field of mathematics at the interface between algebraic geometry and polyhedral geometry, with diverse applications to science. Here, we introduce and develop a unified tropical geometric framework to characterize different facets of non-Hermitian systems. We illustrate the versatility of our approach using several examples, and demonstrate that it can be used to select from a spectrum of higher-order EPs in gain and loss models, predict the skin effect in the non-Hermitian Su-Schrieffer-Heeger model, and extract universal properties in the presence of disorder in the Hatano-Nelson model. Our work puts forth a new framework for studying non-Hermitian physics and unveils a novel connection of tropical geometry to this field.Comment: Published versio

Primary intracranial myxoma - Report of a rare case and review of literature

Myxomas are benign primary tumors of the heart of mesenchymal origin. Neurological complications attributed to atrial myxoma occurs in 10% to 12% of  patients, with ischemic presentation due to cerebral infarct in 83%-89% of cases. Few case reports are available of multiple metastatic myxomas from primary inthe heart, despite its slow growing and innocuous histological appearance. Primary intracranial myxomas are extremely rare and only six cases have been reported in literature till date, out of which four were supratentorial in location. As on account of its benign nature, complete surgical resection of the tumor is the recommended treatment

Modeling Barkhausen Noise in Magnetic Glasses with Dipole-Dipole Interactions

Long-ranged dipole-dipole interactions in magnetic glasses give rise to magnetic domains having labyrinthine patterns. Barkhausen Noise is then expected to result from the movement of domain boundaries which is supposed to be modeled by the motion of elastic membranes with random pinning. We propose an atomistic model of such magnetic glasses in which we measure the Barkhausen Noise which indeed results from the movement of domain boundaries. Nevertheless the statistics of the Barkhausen Noise is found in striking disagreement with the expectations in the literature. In fact we find exponential statistics without any power law, stressing the fact that Barkhausen Noise can belong to very different universality classes. In this glassy system the essence of the phenomenon is the ability of spin-carrying particles to move and minimize the energy without any spin flip. A theory is offered in excellent agreement with the measured data without any free parameter.Comment: 5 Pages, 5 Figures, Submitted to EP

Expression of estrogen and progesterone receptors in vestibular schwannomas and their clinical significance

<p>Abstract</p> <p>Objective</p> <p>The objective was to determine the expression of estrogen and progesterone receptors in vestibular schwannomas as well as to determine predictive factors for estrogen and progesterone receptor positivity.</p> <p>Materials and methods</p> <p>The study included 100 cases of vestibular schwannomas operated from January 2006 to June 2009. The clinical details were noted from the medical case files. Formaldehyde-fixed parafiin-embedded archival vestibular schwannomas specimens were used for the immunohistochemical assessment of estrogen and progesterone receptors.</p> <p>Results</p> <p>Neither estrogen nor progesterone receptors could be detected in any of our cases by means of well known immunohistochemical method using well documented monoclonal antibodies. In the control specimens, a strongly positive reaction could be seen.</p> <p>Conclusion</p> <p>No estrogen and progesterone receptor could be found in any of our 100 cases of vestibular schwannomas. Hence our study does not support a causative role of estrogen and progesterone in the growth of vestibular schwannoma as well as hormonal manipulation in the treatment of this tumor.</p

Primary spinal melanoma of the cervical leptomeninges: Report of a case with brief review of literature

Central nervous system primary malignant melanoma accounts for approximately 1% of all melanomas. Primary spinal melanomas are even more unusual. We report a patient with primary spinal melanoma of the cervical leptomeninges. The histology of the tumor showed tumor cells arranged in sheets, ill-defined fascicles and nests and displayed a moderate grade of cellular and nuclear pleomorphism and mitoses with abundant pigment in the cytoplasm. The tumor cells were immunoreactive for HMB-45, and for S-100

Characterizing and tuning exceptional points using Newton polygons

The study of non-Hermitian degeneracies—called exceptional points (EPs)—has become an exciting frontier at the crossroads of optics, photonics, acoustics, and quantum physics. Here, we introduce the Newton polygon method as a general algebraic framework for characterizing and tuning EPs. Newton polygons, first described by Isaac Newton, are conventionally used in algebraic geometry, with deep roots in various topics in modern mathematics. We propose and illustrate how the Newton polygon method can enable the prediction of higher-order EPs, using a recently experimentally realized optical system. Using the paradigmatic Hatano-Nelson model, we demonstrate how our method can predict the presence of the non-Hermitian skin effect. As further application of our framework, we show the presence of tunable EPs of various orders in PT -symmetric one-dimensional models. We further extend our method to study EPs in higher number of variables and demonstrate that it can reveal rich anisotropic behaviour around such degeneracies. Our work provides an analytic recipe to understand exceptional physics