Finite Projective Spaces, Geometric Spreads of Lines and Multi-Qubits

Given a (2N - 1)-dimensional projective space over GF(2), PG(2N - 1, 2), and its geometric spread of lines, there exists a remarkable mapping of this space onto PG(N - 1, 4) where the lines of the spread correspond to the points and subspaces spanned by pairs of lines to the lines of PG(N - 1, 4). Under such mapping, a non-degenerate quadric surface of the former space has for its image a non-singular Hermitian variety in the latter space, this quadric being {\it hyperbolic} or {\it elliptic} in dependence on N being {\it even} or {\it odd}, respectively. We employ this property to show that generalized Pauli groups of N-qubits also form two distinct families according to the parity of N and to put the role of symmetric operators into a new perspective. The N=4 case is taken to illustrate the issue.Comment: 3 pages, no figures/tables; V2 - short introductory paragraph added; V3 - to appear in Int. J. Mod. Phys.

Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators

The commutation relations of the generalized Pauli operators of a qubit-qutrit system are discussed in the newly established graph-theoretic and finite-geometrical settings. The dual of the Pauli graph of this system is found to be isomorphic to the projective line over the product ring Z2xZ3. A "peculiar" feature in comparison with two-qubits is that two distinct points/operators can be joined by more than one line. The multi-line property is shown to be also present in the graphs/geometries characterizing two-qutrit and three-qubit Pauli operators' space and surmised to be exhibited by any other higher-level quantum system.Comment: 8 pages, 6 figures. International Journal of Theoretical Physics (2007) accept\'

Black Hole Entropy and Finite Geometry

It is shown that the $E_{6(6)}$ symmetric entropy formula describing black holes and black strings in D=5 is intimately tied to the geometry of the generalized quadrangle GQ$(2,4)$ with automorphism group the Weyl group $W(E_6)$. The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ$(2,4)$. Different truncations with $15, 11$ and 9 charges are represented by three distinguished subconfigurations of GQ$(2,4)$, well-known to finite geometers; these are the "doily" (i. e. GQ$(2,2)$) with 15, the "perp-set" of a point with 11, and the "grid" (i. e. GQ$(2,1)$) with 9 points, respectively. In order to obtain the correct signs for the terms in the entropy formula, we use a non- commutative labelling for the points of GQ$(2,4)$. For the 40 different possible truncations with 9 charges this labelling yields 120 Mermin squares -- objects well-known from studies concerning Bell-Kochen-Specker-like theorems. These results are connected to our previous ones obtained for the $E_{7(7)}$ symmetric entropy formula in D=4 by observing that the structure of GQ$(2,4)$ is linked to a particular kind of geometric hyperplane of the split Cayley hexagon of order two, featuring 27 points located on 9 pairwise disjoint lines (a distance-3-spread). We conjecture that the different possibilities of describing the D=5 entropy formula using Jordan algebras, qubits and/or qutrits correspond to employing different coordinates for an underlying non-commutative geometric structure based on GQ$(2,4)$.Comment: 17 pages, 3 figures, v2 a new paragraph added, typos correcte

Preclinical toxicology and safety pharmacology of the first-in-class GADD45β/MKK7 inhibitor and clinical candidate, DTP3

Aberrant NF-κB activity drives oncogenesis and cell survival in multiple myeloma (MM) and many other cancers. However, despite an aggressive effort by the pharmaceutical industry over the past 30 years, no specific IκBα kinase (IKK)β/NF-κB inhibitor has been clinically approved, due to the multiple dose-limiting toxicities of conventional NF-κB-targeting drugs. To overcome this barrier to therapeutic NF-κB inhibition, we developed the first-in-class growth arrest and DNA-damage-inducible (GADD45)β/mitogen-activated protein kinase kinase (MKK)7 inhibitor, DTP3, which targets an essential, cancer-selective cell-survival module downstream of the NF-κB pathway. As a result, DTP3 specifically kills MM cells, ex vivo and in vivo, ablating MM xenografts in mice, with no apparent adverse effects, nor evident toxicity to healthy cells. Here, we report the results from the preclinical regulatory pharmacodynamic (PD), safety pharmacology, pharmacokinetic (PK), and toxicology programmes of DTP3, leading to the approval for clinical trials in oncology. These results demonstrate that DTP3 combines on-target-selective pharmacology, therapeutic anticancer efficacy, favourable drug-like properties, long plasma half-life and good bioavailability, with no target-organs of toxicity and no adverse effects preclusive of its clinical development in oncology, upon daily repeat-dose administration in both rodent and non-rodent species. Our study underscores the clinical potential of DTP3 as a conceptually novel candidate therapeutic selectively blocking NF-κB survival signalling in MM and potentially other NF-κB-driven cancers

Differential roles of push and pull factors on escape for travel: Personal and social identity perspectives

© 2020 John Wiley & Sons Ltd This study examines the effects of push and pull motivations linked to an individual\u27s personal and social identities as key antecedents to escape for travel. In terms of push factors, escape for travel is driven from a personal identity perspective by the need for evaluation of self and regression and from a social identity perspective by the need for social interaction but not enhancement of kinship. Cultural motives that reflect personal identity positively influence escape for travel than destination pull factors linked to social identity. Overall, the study contributes to the existing knowledge on push and pull tourist motivations