Searching for extremal PPT entangled states

We study extremality in various sets of states that have positive partial transposes. One of the tools we use for this purpose is the recently formulated criterion allowing to judge if a given state is extremal in the set of PPT states. First we investigate qubit-ququart states and show that the only candidates for extremal PPT entangled states (PPTES) have ranks of the state and its partial transposition (5, 5) or (5, 6) (equivalently (6, 5)). Then, examples of extremal states of (5, 5) type and the so-called edge states of type (5, 6) are provided. We also make an attempt to explore the set of PPT states with ranks (5, 6). Finally, we discuss what are the possible configurations of ranks of density matrices and their respective partial transposition in general three-qubit and four-qubit symmetric states for which there may exist extremal entangled PPT states. For instance in the first case we show that the only possibilities are (4, 4, 4) and (4, 4, 5).     

On some properties of the number of permutations being products of pairwise disjoint d-cycles

Monatshefte für Mathematik - Let $$d\ge 2$$ be an integer. In this paper we study arithmetic properties of the sequence $$(H_d(n))_{n\in \mathbb {N}}$$, where $$H_{d}(n)$$ is the number of...     

Mechanistic insights into dopaminergic and serotonergic neurotransmission – concerted interactions with helices 5 and 6 drive the functional outcome

Brain functions rely on neurotransmitters that mediate communication between billions of neurons. Disruption of this communication can result in a plethora of psychiatric and neurological disorders. In this work, we combine molecular dynamics simulations, live-cell biosensor and electrophysiological assays to investigate the action of the neurotransmitter dopamine at the dopaminergic D₂ receptor (D₂R). The study of dopamine and closely related chemical probes reveals how neurotransmitter binding translates into the activation of distinct subsets of D₂R effectors (i.e.: G_i2, G_oB, G_z and β-arrestin 2). Ligand interactions with key residues in TM5 (S5.42) and TM6 (H6.55) in the D₂R binding pocket yield a dopamine-like coupling signature, whereas exclusive TM5 interaction is typically linked to preferential G protein coupling (in particular G_oB) over β-arrestin. Further experiments for serotonin receptors indicate that the reported molecular mechanism is shared by other monoaminergic neurotransmitter receptors. Ultimately, our study highlights how sequence variation in position 6.55 is used by nature to fine-tune β-arrestin recruitment and in turn receptor signaling and internalization of neurotransmitter receptors.

Neurotransmitter contacts within the receptor binding site differentially contribute to the overall functional response: transmembrane helix (TM) 5 contacts promote G protein coupling whereas concerted TM5–TM6 contacts enhance β-arrestin recruitment.     

Complex algebraic plane curves via Poincaré-Hopf formula. II. Annuli

We give a complete classification of algebraic curves in ℂ² which are homeomorphic with ℂ* and which satisfy a certain natural condition about codimensions of its singularities. In the proof we use the method developed in [BZI]. It relies on estimation of certain invariants of the curve, the so-called numbers of double points hidden at singularities and at infinity. The sum of these invariants is given by the Poincaré-Hopf formula applied to a suitable vector field.     

Heegaard–Floer homologies of (+1) surgeries on torus knots

We compute the Heegaard–Floer homology of $S^{3}_{1}(K)$ (the (+1) surgery on the torus knot T _p,q ) in terms of the semigroup generated by p and q, and we find a compact formula (involving Dedekind sums) for the corresponding Ozsváth–Szabó d-invariant. We relate the result to known knot invariants of T _p,q as the genus and the Levine–Tristram signatures. Furthermore, we emphasize the striking resemblance between Heegaard–Floer homologies of (+1) and (?1) surgeries on torus knots. This relation is best seen at the level of τ functions.     

Strong NP-hardness of scheduling problems with learning or aging effect

Proofs of strong NP-hardness of single machine and two-machine flowshop scheduling problems with learning or aging effect given in Rudek (Computers & Industrial Engineering 61:20–31, 2011; Annals of Operations Research 196(1):491–516, 2012a; International Journal of Advanced Manufacturing Technology 59:299–309, 2012b; Applied Mathematics and Computations 218:6498–6510, 2012c; Applied Mathematical Modelling 37:1523–1536, 2013) contain a common mistake that make them incomplete. We reveal the mistake and provide necessary corrections for the problems in Rudek (Computers & Industrial Engineering 61:20–31, 2011; Annals of Operations Research 196(1):491–516, 2012a; Applied Mathematical Modelling 37:1523–1536, 2013). NP-hardness of problems in Rudek (International Journal of Advanced Manufacturing Technology 59:299–309, 2012b; Applied Mathematics and Computations 218:6498–6510, 2012c) remains unknown because of another mistake which we are unable to correct.     

Mott-insulator States of ultracold atoms in optical resonators

We study the low temperature physics of an ultracold atomic gas in the potential formed inside a pumped optical resonator. Here, the height of the cavity potential, and hence the quantum state of the gas, depends not only on the pump parameters, but also on the atomic density through a dynamical ac-Stark shift of the cavity resonance. We derive the Bose-Hubbard model in one dimension and use the strong coupling expansion to determine the parameter regime in which the system is in the Mott-insulator state. We predict the existence of overlapping, competing Mott-insulator states, and bistable behavior in the vicinity of the shifted cavity resonance, controlled by the pump parameters. Outside these parameter regions, the state of the system is in most cases superfluid.     

Large-Nc confinement and turbulence

We suggest that the transition that occurs at large N_{c} in the eigenvalue distribution of a Wilson loop may have a turbulent origin. We arrived at this conclusion by studying the complex-valued inviscid Burgers-Hopf equation that corresponds to the Makeenko-Migdal loop equation, and we demonstrate the appearance of a shock in the spectral flow of the Wilson loop eigenvalues. This picture supplements that of the Durhuus-Olesen transition with a particular realization of disorder. The critical behavior at the formation of the shock allows us to infer exponents that have been measured recently in lattice simulations by Narayanan and Neuberger in d=2 and d=3. Our analysis leads us to speculate that the universal behavior observed in these lattice simulations might be a generic feature of confinement, also in d=4 Yang-Mills theory.     

C, N CPMAS NMR and GIAO DFT calculations of stereoisomeric oxindole alkaloids from Cat's Claw (Uncaria tomentosa)

Oxindole alkaloids, isolated from the bark of Uncaria tomentosa [Willd. ex Schult.] Rubiaceae, are considered to be responsible for the biological activity of this herb. Five pentacyclic and two tetracyclic alkaloids were studied by solid-state NMR and theoretical GIAO DFT methods. The ¹³C and ¹⁵N CPMAS NMR spectra were recorded for mitraphylline, isomitraphylline, pteropodine (uncarine C), isopteropodine (uncarine E), speciophylline (uncarine D), rhynchophylline and isorhynchophylline. Theoretical GIAO DFT calculations of shielding constants provide arguments for identification of asymmetric centers and proper assignment of NMR spectra. These alkaloids are 7R/7S and 20R/20S stereoisomeric pairs. Based on the ¹³C CP MAS chemical shifts the 7S alkaloids (δ C3 70–71 ppm) can be easily and conveniently distinguished from 7R (δC3 74.5–74.9 ppm), also 20R (δC20 41.3–41.7 ppm) from the 20S (δC20 36.3–38.3 ppm). The epiallo-type isomer (3R, 20S) of speciophylline is characterized by a larger ¹⁵N MAS chemical shift of N4 (64.6 ppm) than the allo-type (3S, 20S) of isopteropodine (δN4 53.3 ppm). ¹⁵N MAS chemical shifts of N1–H in pentacyclic alkaloids are within 131.9–140.4 ppm.