Maximal entanglement versus entropy for mixed quantum states

Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy. Along the way, we determine the states that, for a given value of entropy, achieve maximal violation of Bell's inequality

Existence of Least-perimeter Partitions

We prove the existence of a perimeter-minimizing partition of R^n into regions of unit volume. We conclude with a short tribute to the late Manuel A. Fortes.Comment: 5 pages; for submission to Fortes memorial isue of Philosphical Magazine Letter

On fractionality of the path packing problem

In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing each edge does not exceed 1. Well-known fractional path packing problem consists of maximizing the total weight of paths with ends in a subset S of TxT over all fractional multiflows. Together, G,T and S form a network. A network is an Eulerian network if all nodes in N\T have even degrees. A term "fractionality" was defined for the fractional path packing problem by A. Karzanov as the smallest natural number D so that there exists a solution to the problem that becomes integer-valued when multiplied by D. A. Karzanov has defined the class of Eulerian networks in terms of T and S, outside which D is infinite and proved that whithin this class D can be 1,2 or 4. He conjectured that D should be 1 or 2 for this class of networks. In this paper we prove this conjecture.Comment: 18 pages, 5 figures in .eps format, 2 latex files, main file is kc13.tex Resubmission due to incorrectly specified CS type of the article; no changes to the context have been mad

The Epidemics of Donations: Logistic Growth and Power-Laws

This paper demonstrates that collective social dynamics resulting from individual donations can be well described by an epidemic model. It captures the herding behavior in donations as a non-local interaction between individual via a time-dependent mean field representing the mass media. Our study is based on the statistical analysis of a unique dataset obtained before and after the tsunami disaster of 2004. We find a power-law behavior for the distributions of donations with similar exponents for different countries. Even more remarkably, we show that these exponents are the same before and after the tsunami, which accounts for some kind of universal behavior in donations independent of the actual event. We further show that the time-dependent change of both the number and the total amount of donations after the tsunami follows a logistic growth equation. As a new element, a time-dependent scaling factor appears in this equation which accounts for the growing lack of public interest after the disaster. The results of the model are underpinned by the data analysis and thus also allow for a quantification of the media influence

Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem

phenix.mr_rosetta: molecular replacement and model rebuilding with Phenix and Rosetta.

The combination of algorithms from the structure-modeling field with those of crystallographic structure determination can broaden the range of templates that are useful for structure determination by the method of molecular replacement. Automated tools in phenix.mr_rosetta simplify the application of these combined approaches by integrating Phenix crystallographic algorithms and Rosetta structure-modeling algorithms and by systematically generating and evaluating models with a combination of these methods. The phenix.mr_rosetta algorithms can be used to automatically determine challenging structures. The approaches used in phenix.mr_rosetta are described along with examples that show roles that structure-modeling can play in molecular replacement

Aurora kinase A drives the evolution of resistance to third-generation EGFR inhibitors in lung cancer.

Although targeted therapies often elicit profound initial patient responses, these effects are transient due to residual disease leading to acquired resistance. How tumors transition between drug responsiveness, tolerance and resistance, especially in the absence of preexisting subclones, remains unclear. In epidermal growth factor receptor (EGFR)-mutant lung adenocarcinoma cells, we demonstrate that residual disease and acquired resistance in response to EGFR inhibitors requires Aurora kinase A (AURKA) activity. Nongenetic resistance through the activation of AURKA by its coactivator TPX2 emerges in response to chronic EGFR inhibition where it mitigates drug-induced apoptosis. Aurora kinase inhibitors suppress this adaptive survival program, increasing the magnitude and duration of EGFR inhibitor response in preclinical models. Treatment-induced activation of AURKA is associated with resistance to EGFR inhibitors in vitro, in vivo and in most individuals with EGFR-mutant lung adenocarcinoma. These findings delineate a molecular path whereby drug resistance emerges from drug-tolerant cells and unveils a synthetic lethal strategy for enhancing responses to EGFR inhibitors by suppressing AURKA-driven residual disease and acquired resistance

Ribosomal oxygenases are structurally conserved from prokaryotes to humans

2-Oxoglutarate (2OG)-dependent oxygenases have important roles in the regulation of gene expression via demethylation of N-methylated chromatin components1,2 and in the hydroxylation of transcription factors3 and splicing factor proteins4. Recently, 2OG-dependent oxygenases that catalyse hydroxylation of transfer RNA5,6,7 and ribosomal proteins8 have been shown to be important in translation relating to cellular growth, TH17-cell differentiation and translational accuracy9,10,11,12. The finding that ribosomal oxygenases (ROXs) occur in organisms ranging from prokaryotes to humans8 raises questions as to their structural and evolutionary relationships. In Escherichia coli, YcfD catalyses arginine hydroxylation in the ribosomal protein L16; in humans, MYC-induced nuclear antigen (MINA53; also known as MINA) and nucleolar protein 66 (NO66) catalyse histidine hydroxylation in the ribosomal proteins RPL27A and RPL8, respectively. The functional assignments of ROXs open therapeutic possibilities via either ROX inhibition or targeting of differentially modified ribosomes. Despite differences in the residue and protein selectivities of prokaryotic and eukaryotic ROXs, comparison of the crystal structures of E. coli YcfD and Rhodothermus marinus YcfD with those of human MINA53 and NO66 reveals highly conserved folds and novel dimerization modes defining a new structural subfamily of 2OG-dependent oxygenases. ROX structures with and without their substrates support their functional assignments as hydroxylases but not demethylases, and reveal how the subfamily has evolved to catalyse the hydroxylation of different residue side chains of ribosomal proteins. Comparison of ROX crystal structures with those of other JmjC-domain-containing hydroxylases, including the hypoxia-inducible factor asparaginyl hydroxylase FIH and histone Nε-methyl lysine demethylases, identifies branch points in 2OG-dependent oxygenase evolution and distinguishes between JmjC-containing hydroxylases and demethylases catalysing modifications of translational and transcriptional machinery. The structures reveal that new protein hydroxylation activities can evolve by changing the coordination position from which the iron-bound substrate-oxidizing species reacts. This coordination flexibility has probably contributed to the evolution of the wide range of reactions catalysed by oxygenases

Protein crystals in adenovirus type 5-infected cells: requirements for intranuclear crystallogenesis, structural and functional analysis

Intranuclear crystalline inclusions have been observed in the nucleus of epithelial cells infected with Adenovirus serotype 5 (Ad5) at late steps of the virus life cycle. Using immuno-electron microscopy and confocal microscopy of cells infected with various Ad5 recombinants modified in their penton base or fiber domains, we found that these inclusions represented crystals of penton capsomers, the heteromeric capsid protein formed of penton base and fiber subunits. The occurrence of protein crystals within the nucleus of infected cells required the integrity of the fiber knob and part of the shaft domain. In the knob domain, the region overlapping residues 489–492 in the FG loop was found to be essential for crystal formation. In the shaft, a large deletion of repeats 4 to 16 had no detrimental effect on crystal inclusions, whereas deletion of repeats 8 to 21 abolished crystal formation without altering the level of fiber protein expression. This suggested a crucial role of the five penultimate repeats in the crystallisation process. Chimeric pentons made of Ad5 penton base and fiber domains from different serotypes were analyzed with respect to crystal formation. No crystal was found when fiber consisted of shaft (S) from Ad5 and knob (K) from Ad3 (heterotypic S5-K3 fiber), but occurred with homotypic S3K3 fiber. However, less regular crystals were observed with homotypic S35-K35 fiber. TB5, a monoclonal antibody directed against the Ad5 fiber knob was found by immunofluorescence microscopy to react with high efficiency with the intranuclear protein crystals in situ. Data obtained with Ad fiber mutants indicated that the absence of crystalline inclusions correlated with a lower infectivity and/or lower yields of virus progeny, suggesting that the protein crystals might be involved in virion assembly. Thus, we propose that TB5 staining of Ad-infected 293 cells can be used as a prognostic assay for the viability and productivity of fiber-modified Ad5 vectors