Continuous-time histories: observables, probabilities, phase space structure and the classical limit

In this paper we elaborate on the structure of the continuous-time histories description of quantum theory, which stems from the consistent histories scheme. In particular, we examine the construction of history Hilbert space, the identification of history observables and the form of the decoherence functional (the object that contains the probability information). It is shown how the latter is equivalent to the closed-time-path (CTP) generating functional. We also study the phase space structure of the theory first through the construction of general representations of the history group (the analogue of the Weyl group) and the implementation of a histories Wigner-Weyl transform. The latter enables us to write quantum theory solely in terms of phase space quantities. These results enable the implementation of an algorithm for identifying the classical (stochastic) limit of a general quantum system.Comment: 46 pages, latex; in this new version typographical errors have been removed and the presentation has been made cleare

Maximizing the Strong Triadic Closure in Split Graphs and Proper Interval Graphs

In social networks the Strong Triadic Closure is an assignment of the edges with strong or weak labels such that any two vertices that have a common neighbor with a strong edge are adjacent. The problem of maximizing the number of strong edges that satisfy the strong triadic closure was recently shown to be NP-complete for general graphs. Here we initiate the study of graph classes for which the problem is solvable. We show that the problem admits a polynomial-time algorithm for two unrelated classes of graphs: proper interval graphs and trivially-perfect graphs. To complement our result, we show that the problem remains NP-complete on split graphs, and consequently also on chordal graphs. Thus we contribute to define the first border between graph classes on which the problem is polynomially solvable and on which it remains NP-complete

Cluster Deletion on Interval Graphs and Split Related Graphs

In the Cluster Deletion problem the goal is to remove the minimum number of edges of a given graph, such that every connected component of the resulting graph constitutes a clique. It is known that the decision version of Cluster Deletion is NP-complete on (P_5-free) chordal graphs, whereas Cluster Deletion is solved in polynomial time on split graphs. However, the existence of a polynomial-time algorithm of Cluster Deletion on interval graphs, a proper subclass of chordal graphs, remained a well-known open problem. Our main contribution is that we settle this problem in the affirmative, by providing a polynomial-time algorithm for Cluster Deletion on interval graphs. Moreover, despite the simple formulation of the algorithm on split graphs, we show that Cluster Deletion remains NP-complete on a natural and slight generalization of split graphs that constitutes a proper subclass of P_5-free chordal graphs. Although the later result arises from the already-known reduction for P_5-free chordal graphs, we give an alternative proof showing an interesting connection between edge-weighted and vertex-weighted variations of the problem. To complement our results, we provide faster and simpler polynomial-time algorithms for Cluster Deletion on subclasses of such a generalization of split graphs

Spectroscopy of bulk and few-layer superconducting NbSe2_2 with van der Waals tunnel junctions

Tunnel junctions, a well-established platform for high-resolution spectroscopy of superconductors, require defect-free insulating barriers with clean engagement to metals on both sides. Extending the range of materials accessible to tunnel junction fabrication, beyond the limited selection which allows high-quality oxide formation, requires the development of alternative fabrication techniques. Here we show that van-der-Waals (vdW) tunnel barriers, fabricated by stacking layered semiconductors on top of the transition metal dichalcogenide (TMD) superconductor NbSe$_2$, sustain a stable, low noise tunneling current, and exhibit strong suppression of sub-gap tunneling. We utilize the technique to measure the spectra of bulk (20 nm) and ultrathin (3- and 4-layer) devices at 70 mK. The spectra exhibit two distinct energy gaps, the larger of which decreases monotonously with thickness and $T_C$, in agreement with BCS theory. The spectra are analyzed using a two-band model modified to account for depairing. We show that in the bulk, the smaller gap exhibits strong depairing in an in-plane magnetic field, consistent with a high Fermi velocity. In the few-layer devices, depairing of the large gap is negligible, consistent with out-of-plane spin-locking due to Ising spin-orbit coupling. Our results demonstrate the utility of vdW tunnel junctions in mapping the intricate spectral evolution of TMD superconductors over a range of magnetic fields.Comment: This submission contains the first part of arxiv:1703.07677 with the addition of spectra taken on this devices. The second part of 1703.07677 will be published separatel

Pax3 synergizes with Gli2 and Zic1 in transactivating the Myf5 epaxial somite enhancer

AbstractBoth Glis, the downstream effectors of hedgehog signaling, and Zic transcription factors are required for Myf5 expression in the epaxial somite. Here we demonstrate a novel synergistic interaction between members of both families and Pax3, a paired-domain transcription factor that is essential for both myogenesis and neural crest development. We show that Pax3 synergizes with both Gli2 and Zic1 in transactivating the Myf5 epaxial somite (ES) enhancer in concert with the Myf5 promoter. This synergy is dependent on conserved functional domains of the proteins, as well as on a novel homeodomain motif in the Myf5 promoter and the essential Gli motif in the ES enhancer. Importantly, overexpression of Zic1 and Pax3 in the 10T1/2 mesodermal cell model results in enrichment of these factors at the endogenous Myf5 locus and induction of Myf5 expression. In our previous work, we showed that by enhancing nuclear translocation of Gli factors, Zics provide spatiotemporal patterning for Gli family members in the epaxial induction of Myf5 expression. Our current study indicates a complementary mechanism in which association with DNA-bound Pax3 strengthens the ability of both Zic1 and Gli2 to transactivate Myf5 in the epaxial somite

Large family cohorts of lymphoblastoid cells provide a new cellular model for investigating facioscapulohumeral muscular dystrophy

Facioscapulohumeral muscular dystrophy (FSHD) is associated with aberrant epigenetic regulation of the chromosome 4q35 D4Z4 macrosatellite repeat. The resulting DNA hypomethylation and relaxation of epigenetic repression leads to increased expression of the deleterious DUX4-fl mRNA encoded within the distal D4Z4 repeat. With the typical late onset of muscle weakness, prevalence of asymptomatic individuals, and an autosomal dominant mode of inheritance, FSHD is often passed on from one generation to the next and affects multiple individuals within a family. Here we have characterized unique collections of 114 lymphoblastoid cell lines (LCLs) generated from 12 multigenerational FSHD families, including 56 LCLs from large, genetically homogeneous families in Utah. We found robust expression of DUX4-fl in most FSHD LCLs and a good correlation between DNA hypomethylation and repeat length. In addition, DUX4-fl levels can be manipulated using epigenetic drugs as in myocytes, suggesting that some epigenetic pathways regulating DUX4-fl in myocytes are maintained in LCLs. Overall, these FSHD LCLs provide an alternative cellular model in which to study many aspects of D4Z4, DUX4, and FSHD gene regulation in a background of low genetic variation. Significantly, these non-adherent immortal LCLs are amenable for high-throughput screening of potential therapeutics targeting DUX4-fl mRNA or protein expression