Generalized wordlength patterns and strength

Xu and Wu (2001) defined the \emph{generalized wordlength pattern} $(A_1, ..., A_k)$ of an arbitrary fractional factorial design (or orthogonal array) on $k$ factors. They gave a coding-theoretic proof of the property that the design has strength $t$ if and only if $A_1 = ... = A_t = 0$. The quantities $A_i$ are defined in terms of characters of cyclic groups, and so one might seek a direct character-theoretic proof of this result. We give such a proof, in which the specific group structure (such as cyclicity) plays essentially no role. Nonabelian groups can be used if the counting function of the design satisfies one assumption, as illustrated by a couple of examples

Latest clinical evidence and further development of PARP inhibitors in ovarian cancer

For several decades, the systemic treatment of ovarian cancer has involved chemotherapy, with the relatively recent addition of antiangiogenic strategies given with chemotherapy and in the maintenance setting. In the past decade, numerous poly(ADP-ribose) polymerase (PARP)-inhibiting agents have been assessed. We review key trials that have led to the approval of three PARP inhibitors-olaparib, niraparib and rucaparib-as maintenance therapy for platinum-sensitive recurrent ovarian cancer. We discuss the efficacy and safety of these agents in the populations studied in clinical trials. We then provide an overview of the numerous avenues of ongoing research for PARP inhibitors in different treatment settings: as treatment rather than maintenance strategies and in combination with other anticancer approaches, including antiangiogenic and immunotherapeutic agents. Three phase III trials (NOVA, SOLO2 and ARIEL3) demonstrated remarkable improvement in progression-free survival (PFS) with PARP inhibitors given as maintenance therapy in patients with complete or partial response after platinum-based therapy for platinum-sensitive ovarian cancer. Differences in trial design and patient populations influence the conclusions that can be drawn from these trials. Overall survival data are pending and there is a limited experience regarding long-term safety. PARP inhibitors have transformed the management of ovarian cancer and have changed the course of disease for many patients. Although recent approvals are irrespective of BRCA mutation or homologous repair deficiency status, genetic profiles, as well as dosing schedules, tolerability and affordability, may influence patient selection and the setting in which PARP inhibitors are used. The development and evolution of PARP inhibitors continue, with new agents, strategies, combinations and indications under intensive evaluation

Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting

In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing: given a matrix $X$ formed as the sum of an unknown diagonal matrix and an unknown low rank positive semidefinite matrix, decompose $X$ into these constituents. The second problem we consider is to determine the facial structure of the set of correlation matrices, a convex set also known as the elliptope. This convex body, and particularly its facial structure, plays a role in applications from combinatorial optimization to mathematical finance. The third problem is a basic geometric question: given points $v_1,v_2,...,v_n\in \R^k$ (where $n > k$) determine whether there is a centered ellipsoid passing \emph{exactly} through all of the points. We show that in a precise sense these three problems are equivalent. Furthermore we establish a simple sufficient condition on a subspace $U$ that ensures any positive semidefinite matrix $L$ with column space $U$ can be recovered from $D+L$ for any diagonal matrix $D$ using a convex optimization-based heuristic known as minimum trace factor analysis. This result leads to a new understanding of the structure of rank-deficient correlation matrices and a simple condition on a set of points that ensures there is a centered ellipsoid passing through them.Comment: 20 page

Inhomogeneously doped two-leg ladder systems

A chemical potential difference between the legs of a two-leg ladder is found to be harmful for Cooper pairing. The instability of superconductivity in such systems is analyzed by compairing results of various analytical and numerical methods. Within a strong coupling approach for the t-J model, supplemented by exact numerical diagonalization, hole binding is found unstable beyond a finite, critical chemical potential difference. The spinon-holon mean field theory for the t-J model shows a clear reduction of the the BCS gaps upon increasing the chemical potential difference leading to a breakdown of superconductivity. Based on a renormalization group approach and Abelian bosonization, the doping dependent phase diagram for the weakly interacting Hubbard model with different chemical potentials was determined.Comment: Revtex4, 11 pages, 7 figure

Long-term efficacy, tolerability and overall survival in patients with platinum-sensitive, recurrent high-grade serous ovarian cancer treated with maintenance olaparib capsules following response to chemotherapy

BACKGROUND: In Study 19, maintenance monotherapy with olaparib significantly prolonged progression-free survival vs placebo in patients with platinum-sensitive, recurrent high-grade serous ovarian cancer. METHODS: Study 19 was a randomised, placebo-controlled, Phase II trial enrolling 265 patients who had received at least two platinum-based chemotherapy regimens and were in complete or partial response to their most recent regimen. Patients were randomised to olaparib (capsules; 400 mg bid) or placebo. We present long-term safety and final mature overall survival (OS; 79% maturity) data, from the last data cut-off (9 May 2016). RESULTS: Thirty-two patients (24%) received maintenance olaparib for over 2 years; 15 (11%) did so for over 6 years. No new tolerability signals were identified with long-term treatment and adverse events were generally low grade. The incidence of discontinuations due to adverse events was low (6%). An apparent OS advantage was observed with olaparib vs placebo (hazard ratio 0.73, 95% confidence interval 0.55‒0.95, P = 0.02138) irrespective of BRCA1/2 mutation status, although the predefined threshold for statistical significance was not met. CONCLUSIONS: Study 19 showed a favourable final OS result irrespective of BRCA1/2 mutation status and unprecedented long-term benefit with maintenance olaparib for a subset of platinum-sensitive, recurrent ovarian cancer patients

Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.Comment: 28 pages, to appear in J. Math. Phy

Fermi surface renormalization in Hubbard ladders

We derive the one-loop renormalization equations for the shift in the Fermi-wavevectors for one-dimensional interacting models with four Fermi-points (two left and two right movers) and two Fermi velocities v_1 and v_2. We find the shift to be proportional to (v_1-v_2)U^2, where U is the Hubbard-U. Our results apply to the Hubbard ladder and to the t_1-t_2 Hubbard model. The Fermi-sea with fewer particles tends to empty. The stability of a saddle point due to shifts of the Fermi-energy and the shift of the Fermi-wavevector at the Mott-Hubbard transition are discussed.Comment: 5 pages, 4 Postscript figure