Projective Ring Line Encompassing Two-Qubits

The projective line over the (non-commutative) ring of two-by-two matrices with coefficients in GF(2) is found to fully accommodate the algebra of 15 operators - generalized Pauli matrices - characterizing two-qubit systems. The relevant sub-configuration consists of 15 points each of which is either simultaneously distant or simultaneously neighbor to (any) two given distant points of the line. The operators can be identified with the points in such a one-to-one manner that their commutation relations are exactly reproduced by the underlying geometry of the points, with the ring geometrical notions of neighbor/distant answering, respectively, to the operational ones of commuting/non-commuting. This remarkable configuration can be viewed in two principally different ways accounting, respectively, for the basic 9+6 and 10+5 factorizations of the algebra of the observables. First, as a disjoint union of the projective line over GF(2) x GF(2) (the "Mermin" part) and two lines over GF(4) passing through the two selected points, the latter omitted. Second, as the generalized quadrangle of order two, with its ovoids and/or spreads standing for (maximum) sets of five mutually non-commuting operators and/or groups of five maximally commuting subsets of three operators each. These findings open up rather unexpected vistas for an algebraic geometrical modelling of finite-dimensional quantum systems and give their numerous applications a wholly new perspective.Comment: 8 pages, three tables; Version 2 - a few typos and one discrepancy corrected; Version 3: substantial extension of the paper - two-qubits are generalized quadrangles of order two; Version 4: self-dual picture completed; Version 5: intriguing triality found -- three kinds of geometric hyperplanes within GQ and three distinguished subsets of Pauli operator

Constitutional Law - Due Process - Dismissal of Appeal as Exercise of Contempt Power

A superior court of the state of Washington rendered a $475,000 judgment against the petitioner union for the circulation of a libelous letter. The union filed an appeal to the Washington Supreme Court but obtained no stay of proceedings in the lower court because it made no offer of the required supersedeas bond. In a supplemental proceeding it was learned that the union had no substantial assets in Washington but did have$298,000 of United States bonds in its possession in California. The Superior Court ordered the union to deliver these bonds to the court\u27s receiver to protect the judgment creditors pending the appeal of the main action. Upon failure to comply with the court order, the union was held in contempt. The Washington Supreme Court affirmed the contempt and ordered the appeal in the main action dismissed if the union did not purge itself of contempt within fifteen days. The condition was not met and the appeal was dismissed. On certiorari to the United States Supreme Court, held, affirmed, two justices dissenting. The dismissal of the union\u27s appeal was a reasonable action taken to sustain the effectiveness of the state\u27s judicial process and did not violate due process of law. National Union of Marine Cooks and Stewards v. Arnold, 348 U.S. 37, 75 S.Ct. 92 (1954)

Conflict of Laws - Full Faith and Credit - Exclusive-Remedy Provision of Foreign Workmen\u27s Compensation Law

Plaintiff, a resident of Missouri, entered into an employment contract there with a Missouri painting company. He was injured while working in Arkansas on a job his employer had subcontracted from the defendant, a Louisiana contractor. The Missouri employer\u27s insurer voluntarily began weekly payments to the plaintiff pursuant to the Missouri workmen\u27s compensation law, although there had been no formal proceeding or award. Payments under the Missouri act were exclusive of all other rights and remedies. After receiving thirty-four payments, the plaintiff sued the defendant for negligence in the Arkansas courts. The defendant had the case removed to the federal district court, where judgment was rendered for the plaintiff. The court of appeals reversed. On certiorari to the United States Supreme Court, held, reversed, three justices dissenting. Arkansas\u27 interests in the case were substantial in light of possible problems following in the wake of the injury. Therefore, her courts were not bound by the full faith and credit clause to subserve these interests to those of Missouri, despite the exclusive remedy provision of the Missouri law. Carroll v. Lanza, 349 U.S. 408, 75 S.Ct. 804 (1955)

Corporations - Stockholders - Fiduciary Relationship in Sale of Controlling Stock Interest

This comment is concerned with the duty owed by the controlling stockholders to the non-controlling stockholders when there is a sale of the controlling interest. Recently this question was considered by the United States Court of Appeals for the Second Circuit in Perlman v. Feldmann, and the opinion, reversing the lower court and accompanied by a vigorous dissent by Judge Swan, deserves careful consideration

Fluorescence lifetime imaging microscopy (FLIM) to demonstrate the nuclear binding of flavanols and (--epigallocatechin gallate

The use of light microscopy and DMACA staining strongly suggested that plant and animal cell nuclei act as sinks for flavanols [1, 2]. Detailed uv-vis spectroscopic titration experiments indicated that histone proteins are the likely binding sites in the nucleus [2]. Here we report the development of a multi-photon excitation microscopy technique combined with fluorescent lifetime measurements of flavanols. Using this technique, (+) catechin, (-) epicatechin and (-) epigallocatechin gallate (EGCG) showed strikingly different excited state lifetimes in solution. Interaction of histone proteins with flavanols was indicated by the appearance of a significant τ2-component of 1.7 to 4.0ns. Tryptophan interference could be circumvented in the in vivo fluorescence lifetime imaging microscopy (FLIM) experiments with 2-photon excitation at 630nm. This enabled visualisation and semi-quantitative measurements that demonstrated unequivocally the absorption of (+)catechin, (-)epicatechin and EGCG by nuclei of onion cells. 3D FLIM revealed for the first time that externally added EGCG penetrated the whole nucleus in onion cells. The relative proportions of EGCG in cytoplasm: nucleus: nucleoli were ca. 1:10:100. FLIM experiments may therefore facilitate probing the health effects of EGCG, which is the major constituent of green tea

Stac Proteins Suppress Ca2+-Dependent Inactivation of Neuronal L-type Ca2+ Channels

Stac protein (named for its SH3-and cysteine-rich domains) was first identified in brain 20 years ago and is currently known to have three isoforms. Stac2, Stac1, and Stac3 transcripts are found at high, modest, and very low levels, respectively, in the cerebellum and forebrain, but their neuronal functions have been little investigated. Here, we tested the effects of Stac proteins on neuronal, high-voltage-activated Ca2+ channels. Overexpression of the three Stac isoforms eliminated Ca2+-dependent inactivation (CDI) ofL-type current in rat neonatal hippocampal neurons (sex unknown), but not CDI of non-L-type current. Using heterologous expression in tsA201 cells (together with β and α2-δ1 auxiliary subunits), we found that CDI for CaV1.2 and CaV1.3 (the predominant, neuronalL-type Ca2+ channels) was suppressed by all three Stac isoforms, whereas CDI for the P/Q channel, CaV2.1, was not. For CaV1.2, the inhibition of CDI by the Stac proteins appeared to involve their direct interaction with the channel’s C terminus. Within the Stac proteins, a weakly conserved segment containing ~100 residues and linking the structurally conserved PKC C1 and SH3_1 domains was sufficient to fully suppress CDI. The presence of CDI forL-type current in control neonatal neurons raised the possibility that endogenous Stac levels are low in these neurons and Western blotting indicated that the expression of Stac2 was substantially increased in adult forebrain and cerebellum compared with neonate. Together, our results indicate that one likely function of neuronal Stac proteins is to tune Ca2+ entry via neuronal L-type channels. © 2018 the authors

On Invariant Notions of Segre Varieties in Binary Projective Spaces

Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains \Segrem(2) and is invariant under its projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into \PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under \Stab{m}{2} as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according as $m$ is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m - 1, 2). This spread is also related with a \Stab{m}{2}-invariant non-singular Hermitian variety. The case $m=3$ is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7, 2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and Cryptograph

Increasing pattern recognition accuracy for chemical sensing by evolutionary based drift compensation

Artificial olfaction systems, which mimic human olfaction by using arrays of gas chemical sensors combined with pattern recognition methods, represent a potentially low-cost tool in many areas of industry such as perfumery, food and drink production, clinical diagnosis, health and safety, environmental monitoring and process control. However, successful applications of these systems are still largely limited to specialized laboratories. Sensor drift, i.e., the lack of a sensor's stability over time, still limits real in dustrial setups. This paper presents and discusses an evolutionary based adaptive drift-correction method designed to work with state-of-the-art classification systems. The proposed approach exploits a cutting-edge evolutionary strategy to iteratively tweak the coefficients of a linear transformation which can transparently correct raw sensors' measures thus mitigating the negative effects of the drift. The method learns the optimal correction strategy without the use of models or other hypotheses on the behavior of the physical chemical sensors