Continuous slice functional calculus in quaternionic Hilbert spaces

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic $C^*$--algebras and to define, on each of these $C^*$--algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews in Mathematical Physic

Neoadjuvant eribulin mesylate following anthracycline and taxane in triple negative breast cancer: Results from the HOPE study

Background Eribulin mesylate (E) is indicated for metastatic breast cancer patients previously treated with anthracycline and taxane. We argued that E could also benefit patients eligible for neoadjuvant chemotherapy. Methods Patients with primary triple negative breast cancer 2 cm received doxorubicin 60 mg/m2 and paclitaxel 200 mg/m2 x 4 cycles (AT) followed by E 1.4 mg/m2 x 4 cycles. Primary endpoint was pathological complete response (pCR) rate; secondary and explorative endpoints included clinical/metabolic response rates and safety, and biomarker analysis, respectively. Using a two-stage Simon design, 43 patients were to be included provided that 4 of 13 patients had achieved pCR in the first stage of the study. Results In stage I of the study 13 women were enrolled, median age 43 years, tumor size 2–5 cm in 9/13 (69%), positive nodal status in 8/13 (61%). Main grade 3 adverse event was neutropenia (related to AT and E in 4 and 2 cases, respectively). AT followed by E induced clinical complete + partial responses in 11/13 patients (85%), pCR in 3/13 (23%). Median measurements of maximum standardized uptake value (SUVmax) resulted 13, 3, and 1.9 at baseline, after AT and E, respectively. Complete metabolic response (CMR) occurred after AT and after E in 2 and 3 cases, respectively. Notably, 2 of the 5 (40%) patients with CMR achieved pCR at surgery. Immunostaining of paired pre-/post-treatment tumor specimens showed a reduction of β-catenin, CyclinD1, Zeb-1, and c-myc expression, in the absence of N-cadherin modulation. The study was interrupted at stage I due to the lack of the required patients with pCR. Conclusions Despite the early study closure, preoperative E following AT showed clinical and biological activity in triple negative breast cancer patients. Furthermore, the modulation of β-catenin pathway core proteins, supposedly outside the domain of epithelial–mesenchymal transition, claims for further investigation. Trial registration EU Clinical Trial Register, EudraCT number 2012-004956-12

Spin-density-functional theory: some open problems and application to inhomogeneous Heisenberg models

Spin-density-functional theory (SDFT) is the most widely implemented and applied formulation of density-functional theory. However, it is still finding novel applications, and occasionally encounters unexpected problems. In this paper we first briefly describe a few of the latter, related to issues such as nonuniqueness, noncollinearity, and currents. In the main part we then turn to an example of the former, namely SDFT for the Heisenberg model. It is shown that time-honored concepts of Coulomb DFT, such as the local-density approximation, can be applied to this (and other) model Hamiltonians, too, once the concept of 'density' has been suitably reinterpreted. Local-density-type approximations for the inhomogeneous Heisenberg model are constructed. Numerical applications to finite-size and impurity systems demonstrate that DFT is a computationally efficient and reasonably accurate alternative to conventional methods of statistical mechanics for the Heisenberg model.Comment: 15 pages, 1 figure, 1 tabl

Kinematic analysis of reaching movements of the upper limb after total or reverse shoulder arthroplasty

Studies have analyzed three-dimensional complex motion of the shoulder in healthy subjects or patients undergoing total shoulder arthroplasty (TSA) or reverse shoulder arthroplasty (RSA). No study to date has assessed the reaching movements in patients with TSA or RSA. Twelve patients with TSA (Group A) and 12 with RSA (Group B) underwent kinematic analysis of reaching movements directed at four targets. The results were compared to those of 12 healthy subjects (Group C). The assessed parameters were hand-to-target distance, target-approaching velocity, humeral-elevation angular velocity, normalized jerk (indicating motion fluidity), elbow extension and humeral elevation angles. Mean Constant score increased by 38 points in Group A and 47 in Group B after surgery. In three of the tasks, there were no significant differences between healthy subjects and patients in the study groups. Mean target-approaching velocity and humeral-elevation angular velocity were significantly greater in the control group than in study groups and, overall, greater in Group A than Group B. Movement fluidity was significantly greater in the controls, with patients in Group B showing greater fluidity than those in Group A. Reaching movements in the study groups were comparable, in three of the tasks, to those in the control group. However, the latter performed significantly better with regard to target-approaching velocity, humeral-elevation angular velocity and movement fluidity, which are the most representative characteristics of reaching motion. These differences, that may be related to deterioration of shoulder proprioception after prosthetic implant, might possibly be decreased with appropriate rehabilitation

Hadamard state in Schwarzschild-de Sitter spacetime

We construct a state in the Schwarzschild-de Sitter spacetime which is invariant under the action of its group of symmetries. Our state is not defined in the whole Kruskal extension of this spacetime, but rather in a subset of the maximally extended conformal diagram. The construction is based on a careful use of the bulk-to-boundary technique. We will show that our state is Hadamard and that it is not a KMS state, differently from the case of states constructed in spacetimes containing only one event horizon.Comment: More emphasis put on the result. 41 pages. Uses natbib and iopart. This version is going to be published in Classical and Quantum Gravity. PACS numbers: 04.62.+v,04.70.Dy,03.65.Fd. arXiv admin note: text overlap with arXiv:0907.1034 by other author

Free space optical system performance for a Gaussian beam propagating through non Kolmogorov weak turbulence

Atmospheric turbulence has been described for many years by Kolmogorov's power spectral density model because of its simplicity. Unfortunately several experiments have been reported recently that show Kolmogorov theory is sometimes incomplete to describe atmospheric statistics properly, in particular in portions of the troposphere and stratosphere. It is known that free space laser system performance is limited by atmospheric turbulence. In this paper we use a non-Kolmogorov power spectrum which uses a generalized exponent instead of constant standard exponent value 11/3 and a generalized amplitude factor instead of constant value 0.033. Using this spectrum in weak turbulence, we carry out, for a Gaussian beam propagating along a horizontal path, analysis of long term beam spread, scintillation, probability of fade, mean signal to noise ratio and mean bit error rate as variation of the spectrum exponent. Our theoretical results show that for alpha values lower than 11/3 , but not for alpha close to 3 , there is a remarkable increase of scintillation and consequently a major penalty on the system performance. However when alpha assumes values close to 3 or for alpha values higher than 11/3 scintillation decreases leading to an improvement on the system performanc