Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

We study the continuity of an abstract generalization of the maximum-entropy inference - a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for $3\times 3$ matrices.Comment: 27 page

Compressions of linearly independent selfadjoint operators

The following question is considered: What is the smallest number gamma(k) with the property that for every family {X-1,..., X-k} of k selfadjoint and linearly independent operators on a real or complex Hilbert space H there exists a subspace H-0 subset of H of dimension gamma(k) such that the compressions of X-1,..., X-k to H-0 are still linearly independent? Upper and lower bounds for gamma(k) are established for any k, and the exact value is found for k = 2, 3. It is also shown that the set of all gamma(k)-dimensional subspaces H-0 with the desired property is open and dense in the respective Grassmannian. The k = 3 case is used to prove that the ratio numerical range W(A/B) of a pair of operators on a Hilbert space either has a non-empty interior, or lies in a line or a circle. (C) 2011 Elsevier Inc. All rights reserved

On common invariant cones for families of matrices

The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable matrices of any size. Families of matrices with a shared dominant eigenvector are considered under some additional conditions

Jordan Forms of Real and Complex Matrices Under Rank One Perturbations

New perturbation results for the behavior of eigenvalues and Jordan forms of real and complex matrices under generic rank one perturbations are discussed. Several results that are available in the complex case are proved as well for the real case and the assumptions on the genericity are weakened. Rank one perturbations that lead to maximal algebraic multiplicities of the new eigenvalues are also discussed

Demonstration of Photonic Integrated RAU for Millimetre-wave Gigabit Wireless Transmission

This work reports the performance of a wireless transmission link based on a radio access unit (RAU) implemented in photonic integrated circuit (PIC) form. The PIC contains a high speed photodiode for direct optical to RF conversion, monolithically integrated with a semiconductor laser, used as an optical local oscillator for up-conversion of the incoming 16-QAM-OFDM signal through heterodyning. Wireless transmission was demonstrated with a spectral efficiency as high as 3 bits/s/Hz at 60 GHz carrier and with 1.2 Gb/s transmission rate. Moreover, the RAU based on a broad bandwidth photodiode integrated with a tuneable laser allowed for a compact unit that could operate at carrier frequencies up to 100 GHz

Treatment Options in Cushing’s Disease

Endogenous Cushing’s syndrome is a grave disease that requires a multidisciplinary and individualized treatment approach for each patient. Approximately 80% of all patients harbour a corticotroph pituitary adenoma (Cushing’s disease) with excessive secretion of adrenocorticotropin-hormone (ACTH) and, consecutively, cortisol. The goals of treatment include normalization of hormone excess, long-term disease control and the reversal of comorbidities caused by the underlying pathology. The treatment of choice is neurosurgical tumour removal of the pituitary adenoma. Second-line treatments include medical therapy, bilateral adrenalectomy and radiation therapy. Drug treatment modalities target at the hypothalamic/pituitary level, the adrenal gland and at the glucocorticoid receptor level and are commonly used in patients in whom surgery has failed. Bilateral adrenalectomy is the second-line treatment for persistent hypercortisolism that offers immediate control of hypercortisolism. However, this treatment option requires a careful individualized evaluation, since it has the disadvantage of permanent hypoadrenalism which requires lifelong glucocorticoid and mineralocorticoid replacement therapy and bears the risk of developing Nelson’s syndrome. Although there are some very promising medical therapy options it clearly remains a second-line treatment option. However, there are numerous circumstances where medical management of CD is indicated. Medical therapy is frequently used in cases with severe hypercortisolism before surgery in order to control the metabolic effects and help reduce the anestesiological risk. Additionally, it can help to bridge the time gap until radiotherapy takes effect. The aim of this review is to analyze and present current treatment options in Cushing’s disease

Eigenvalue perturbation theory of structured real matrices and their sign characteristics under generic structured rank-one perturbations

An eigenvalue perturbation theory under rank-one perturbations is developed for classes of real matrices that are symmetric with respect to a non-degenerate bilinear form, or Hamiltonian with respect to a non-degenerate skew-symmetric form. In contrast to the case of complex matrices, the sign characteristic is a crucial feature of matrices in these classes. The behavior of the sign characteristic under generic rank-one perturbations is analyzed in each of these two classes of matrices. Partial results are presented, but some questions remain open. Applications include boundedness and robust boundedness for solutions of structured systems of linear differential equations with respect to general perturbations as well as with respect to structured rank perturbations of the coefficients