Quantum Dissension: Generalizing Quantum Discord for Three-Qubit States

We introduce the notion of quantum dissension for a three-qubit system as a measure of quantum correlations. We use three equivalent expressions of three-variable mutual information. Their differences can be zero classically but not so in quantum domain. It generalizes the notion of quantum discord to a multipartite system. There can be multiple definitions of the dissension depending on the nature of projective measurements done on the subsystems. As an illustration, we explore the consequences of these multiple definitions and compare them for three-qubit pure and mixed GHZ and W states. We find that unlike discord, dissension can be negative. This is because measurement on a subsystem may enhance the correlations in the rest of the system. This approach can pave a way to generalize the notion of quantum correlations in the multiparticle setting.Comment: 9 pages 6 figures typo fixed and some arguments adde

Role of Decompressive Craniectomy in the Management of Cerebral Venous Sinus Thrombosis

Cerebral venous sinus thrombosis (CVST) is a relatively uncommon cause of stroke more often affecting women and younger individuals. Blockage of the venous outflow rapidly causes edema and space-occupying venous infarctions and it seems intuitive that decompressive craniectomy (DC) can effectively reduce intracranial pressure just like it works for malignant middle cerebral artery infarcts and traumatic brain injury. But because of the relative rarity of this type of stroke, strong evidence from randomized controlled trials that DC is a life-saving procedure is not available unlike in the latter two conditions. There is a possibility that other forms of interventions like endovascular recanalization, thrombectomy, thrombolysis, and anticoagulation, which cannot be used in established middle cerebral artery infarcts and TBI, can reverse the ongoing pathology of increasing edema in CVST. Such interventions, although presently unproven, could theoretically obviate the need for DC when used in early stages. However, in the absence of such evidence, we recommend that DC be considered early as a life-saving measure whenever there are large hemorrhagic infarcts, expanding edema, radiological, and clinical features of impending herniation. This review gives an overview of the etiology and risk factors of CVST in different patient populations and examines the effectiveness of DC and other forms of interventions

Complications of Decompressive Craniectomy

Decompressive craniectomy (DC) has become the definitive surgical procedure to manage medically intractable rise in intracranial pressure due to stroke and traumatic brain injury. With incoming evidence from recent multi-centric randomized controlled trials to support its use, we could expect a significant rise in the number of patients who undergo this procedure. Although one would argue that the procedure reduces mortality only at the expense of increasing the proportion of the severely disabled, what is not contested is that patients face the risk of a large number of complications after the operation and that can further compromise the quality of life. Decompressive craniectomy (DC), which is designed to overcome the space constraints of the Monro Kellie doctrine, perturbs the cerebral blood, and CSF flow dynamics. Resultant complications occur days to months after the surgical procedure in a time pattern that can be anticipated with advantage in managing them. New or expanding hematomas that occur within the first few days can be life-threatening and we recommend CT scans at 24 and 48 h postoperatively to detect them. Surgeons should also be mindful of the myriad manifestations of peculiar complications like the syndrome of the trephined and neurological deterioration due to paradoxical herniation which may occur many months after the decompression. A sufficiently large frontotemporoparietal craniectomy, 15 cm in diameter, increases the effectiveness of the procedure and reduces chances of external cerebral herniation. An early cranioplasty, as soon as the brain is lax, appears to be a reasonable choice to mitigate many of the late complications. Complications, their causes, consequences, and measures to manage them are described in this chapter

Super-A-polynomials for Twist Knots

We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed A-polynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.Comment: 22+16 pages, 16 tables and 5 figures; with a Maple program by Xinyu Sun and a Mathematica notebook in the ancillary files linked on the right; v2 change in appendix B, typos corrected and references added; v3 change in section 3.3; v4 corrections in Ooguri-Vafa polynomials and quantum super-A-polynomials for 7_2 and 8_1 are adde

Many-body perturbation calculation of spherical nuclei with a separable monopole interaction: I. Finite nuclei

We present calculations of ground state properties of spherical, doubly closed-shell nuclei from $^{16}$O to $^{208}$Pb employing the techniques of many-body perturbation theory using a separable density dependent monopole interaction. The model gives results in Hartree-Fock order which are of similar quality to other effective density-dependent interactions. In addition, second and third order perturbation corrections to the binding energy are calculated and are found to contribute small, but non-negligible corrections beyond the mean-field result. The perturbation series converges quickly, suggesting that this method may be used to calculate fully correlated wavefunctions with only second or third order perturbation theory. We discuss the quality of the results and suggest possible methods of improvement.Comment: 20 Pages, 11 figure

Quantum discord evolution of three-qubit states under noisy channels

We investigated the dissipative dynamics of quantum discord for correlated qubits under Markovian environments. The basic idea in the present scheme is that quantum discord is more general, and possibly more robust and fundamental, than entanglement. We provide three initially correlated qubits in pure Greenberger-Horne-Zeilinger (GHZ) or W state and analyse the time evolution of the quantum discord under various dissipative channels such as: Pauli channels $\sigma_{x}$, $\sigma_{y}$, and $\sigma_{z}$, as well as depolarising channels. Surprisingly, we find that under the action of Pauli channel $\sigma_{x}$, the quantum discord of GHZ state is not affected by decoherence. For the remaining dissipative channels, the W state is more robust than the GHZ state against decoherence. Moreover, we compare the dynamics of entanglement with that of the quantum discord under the conditions in which disentanglement occurs and show that quantum discord is more robust than entanglement except for phase flip coupling of the three qubits system to the environment.Comment: 17 pages, 4 figures, accepted for publication in EPJ

Preparation of anti-vicinal amino alcohols: asymmetric synthesis of D-erythro-Sphinganine, (+)-spisulosine and D-ribo-phytosphingosine

Two variations of the Overman rearrangement have been developed for the highly selective synthesis of anti-vicinal amino alcohol natural products. A MOM-ether directed palladium(II)-catalyzed rearrangement of an allylic trichloroacetimidate was used as the key step for the preparation of the protein kinase C inhibitor D-erythro-sphinganine and the antitumor agent (+)-spisulosine, while the Overman rearrangement of chiral allylic trichloroacetimidates generated by asymmetric reduction of an alpha,beta-unsaturated methyl ketone allowed rapid access to both D-ribo-phytosphingosine and L-arabino-phytosphingosine

Spherically symmetric dissipative anisotropic fluids: A general study

The full set of equations governing the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behaviour of such systems, in the context of general relativity. Emphasis is given to the link between the Weyl tensor, the shear tensor, the anisotropy of the pressure and the density inhomogeneity. In particular we provide the general, necessary and sufficient, condition for the vanishing of the spatial gradients of energy density, which in turn suggests a possible definition of a gravitational arrow of time. Some solutions are also exhibited to illustrate the discussion.Comment: 28 pages Latex. To appear in Phys.Rev.

Calorimetric Investigation of Copper Binding in the N-Terminal Region of the Prion Protein at Low Copper Loading: Evidence for an Entropically Favorable First Binding Event

Although the Cu²⁺-binding sites of the prion protein have been well studied when the protein is fully saturated by Cu²⁺, the Cu²⁺-loading mechanism is just beginning to come into view. Because the Cu²⁺-binding modes at low and intermediate Cu²⁺ occupancy necessarily represent the highest-affinity binding modes, these are very likely populated under physiological conditions, and it is thus essential to characterize them in order to understand better the biological function of copper–prion interactions. Besides binding-affinity data, almost no other thermodynamic parameters (e.g., Δ<i>H</i> and Δ<i>S</i>) have been measured, thus leaving undetermined the enthalpic and entropic factors that govern the free energy of Cu²⁺ binding to the prion protein. In this study, isothermal titration calorimetry (ITC) was used to quantify the thermodynamic parameters (<i>K</i>, Δ<i>G</i>, Δ<i>H</i>, and <i>T</i>Δ<i>S</i>) of Cu²⁺ binding to a peptide, PrP­(23–28, 57–98), that encompasses the majority of the residues implicated in Cu²⁺ binding by full-length PrP. Use of the buffer <i>N</i>-(2-acetomido)-aminoethanesulfonic acid (ACES), which is also a well-characterized Cu²⁺ chelator, allowed for the isolation of the two highest affinity binding events. Circular dichroism spectroscopy was used to characterize the different binding modes as a function of added Cu²⁺. The <i>K</i>_d values determined by ITC, 7 and 380 nM, are well in line with those reported by others. The first binding event benefits significantly from a positive entropy, whereas the second binding event is enthalpically driven. The thermodynamic values associated with Cu²⁺ binding by the Aβ peptide, which is implicated in Alzheimer’s disease, bear striking parallels to those found here for the prion protein