Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

Interfaces, strings, and a soft mode in the square lattice quantum dimer model

The quantum dimer model on the square lattice is a U(1) gauge theory that addresses aspects of the physics of high-Tc superconductors. Using a quantum Monte Carlo method, we show that the theory exists in a confining columnar valence bond solid phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static “electric” charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux ¼. A soft pseudo-Goldstone mode (which becomes exactly massless at the Rokhsar-Kivelson point) extends deep into the columnar phase, with potential implications for high-Tc physics.

Indications for a protective function of beta2-glycoprotein I in thrombotic thrombocytopenic purpura

It has been shown that β(2) -glycoprotein I (β(2) GPI) interacts with von Willebrand factor (VWF) in a glycoprotein (GP)Ib binding state. Given the presence of active VWF multimers in thrombotic thrombocytopenic purpura (TTP), we speculated that β(2) GPI might play a role in TTP. We found that β(2) GPI plasma levels were significantly lower in acute and remission TTP patients than in normal controls, showing a direct correlation with ADAMTS 13 levels and an inverse correlation with the extent of VWF activation. In vitro flow experiments demonstrated that β(2) GPI can block platelet adhesion to endothelial cell-derived VWF strings. We confirmed the direct binding of β(2) GPI to VWF by surface plasmon resonance, and determined that domain I of β(2) GPI is the binding site of VWF A1 domain. Adhesion of β(2) GPI to erythrocytes and platelets was increased in the presence of active VWF, indicating that β(2) GPI may be cleared from the circulation during TTP episodes together with blood cells. Our findings suggest that β(2) GPI may protect from the effects of hyper-functional VWF by inhibiting its interaction with platelets.

Analysis of gene order data supports vertical inheritance of the leukotoxin operon and genome rearrangements in the 5' flanking region in genus Mannheimia

BACKGROUND: The Mannheimia subclades belong to the same bacterial genus, but have taken divergent paths toward their distinct lifestyles. For example, M. haemolytica + M. glucosida are potential pathogens of the respiratory tract in the mammalian suborder Ruminantia, whereas M. ruminalis, the supposed sister group, lives as a commensal in the ovine rumen. We have tested the hypothesis that vertical inheritance of the leukotoxin (lktCABD) operon has occurred from the last common ancestor of genus Mannheimia to any ancestor of the diverging subclades by exploring gene order data. RESULTS: We examined the gene order in the 5' flanking region of the leukotoxin operon and found that the 5' flanking gene strings, hslVU-lapB-artJ-lktC and xylAB-lktC, are peculiar to M. haemolytica + M. glucosida and M. granulomatis, respectively, whereas the gene string hslVU-lapB-lktC is present in M. ruminalis, the supposed sister group of M. haemolytica + M. glucosida, and in the most ancient subclade M. varigena. In M. granulomatis, we found remnants of the gene string hslVU-lapB-lktC in the xylB-lktC intergenic region. CONCLUSION: These observations indicate that the gene string hslVU-lapB-lktC is more ancient than the hslVU-lapB-artJ-lktC and xylAB-lktC gene strings. The presence of (remnants of) the ancient gene string hslVU-lapB-lktC among any subclades within genus Mannheimia supports that it has been vertically inherited from the last common ancestor of genus Mannheimia to any ancestor of the diverging subclades, thus reaffirming the hypothesis of vertical inheritance of the leukotoxin operon. The presence of individual 5' flanking regions in M. haemolytica + M. glucosida and M. granulomatis reflects later genome rearrangements within each subclade. The evolution of the novel 5' flanking region in M. haemolytica + M. glucosida resulted in transcriptional coupling between the divergently arranged artJ and lkt promoters. We propose that the chimeric promoter have led to high level expression of the leukotoxin operon which could explain the increased potential of certain M. haemolytica + M. glucosida strains to cause a particular type of infection.

VH1-69 germline encoded antibodies directed towards ADAMTS13 in patients with acquired thrombotic thrombocytopenic purpura

BACKGROUND: Autoantibodies directed towards ADAMTS13 are present in the majority of patients with acquired thrombotic thrombocytopenic purpura (TTP). Analysis of a set of antibodies derived from two patients with acquired TTP revealed frequent use of the VH1-69 heavy chain gene segment for the assembly of anti-ADAMTS13 antibodies. OBJECTIVE: We explored the ability of two VH1-69 germline gene-encoded antibodies to inhibit the von Willebrand factor (VWF)-processing activity of ADAMTS13 under different experimental conditions. Furthermore, the presence of VH1-69 encoded anti-ADAMTS13 antibodies in 40 patients with acquired TTP was monitored using monoclonal antibody G8, which specifically reacts with an idiotype expressed on VH1-69 encoded antibodies. METHODS AND RESULTS: Binding of the two VH1-69 encoded monoclonal antibodies was dependent on the presence of the spacer domain. Both antibodies inhibited ADAMTS13 activity under static conditions, as measured by cleavage of FRETS-VWF73 substrate and cleavage of VWF multimers. The recombinant antibodies were also capable of inhibiting the processing of UL-VWF strings on the surface of endothelial cells. G8-reactive antibodies directed towards ADAMTS13 were present in plasma of all patients containing anti ADAMTS13 antibodies. CONCLUSIONS: These results suggest that VH1-69 derived antibodies directed towards ADAMTS13 develop in the majority of patients with acquired TTP.

Language Boxes: Bending the Host Language with Modular Language Changes

As domain-specific modeling begins to attract widespread acceptance, pressure is increasing for the development of new domain-specific languages. Unfortunately these DSLs typically conflict with the grammar of the host language, making it difficult to compose hybrid code except at the level of strings; few mechanisms (if any) exist to control the scope of usage of multiple DSLs; and, most seriously, existing host language tools are typically unaware of the DSL extensions, thus hampering the development process. Language boxes address these issues by offering a simple, modular mechanism to encapsulate (i) compositional changes to the host language, (ii) transformations to address various concerns such as compilation and highlighting, and (iii) scoping rules to control visibility of language extensions. We describe the design and implementation of language boxes, and show with the help of several examples how modular extensions can be introduced to a host language and environment.

Monitoring the Time Course of Perception without Awareness: A Comparison of Mirror Masked Words and Nonwords

Mirror masked words are embedded into a context that makes them appear as senseless patterns or as strings of unfamiliar letters. Thus, mirror masked words can be shown for several hundreds of milliseconds without being recognised as words. We sought to further investigate effects of nonsconscious reading by monitoring event-related brain potentials (ERPs) while participants observed mirror masked letter strings. ERPs were recorded while participants observed mirror masked words and nonwords. Data of 15 participants was segmented into periods of quasi-stable field topography (microstates). Microstates for masked words and nonwords were compared using randomization tests, statistical parametric scalp maps and Low Resolution Electromagnetic Tomography (LORETA). ERPs to masked words and nonwords showed significant topographic differences between 136 and 256 ms, indicating that stimuli were nonconsciously discriminated. A LORETA model localised sources of activation discriminating between masked words and nonwords in left operculum, the right superior parietal lobe and right superior temporal gyrus indicating higher current density for nonwords than for words in these areas. ERPs of mirror masked stimuli can indicate unconscious discrimination even in cases where behavioural priming is unreliable. This approach might be useful for investigating differences in early, nonconscious stages of word perception.

Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

Black probes of Schrödinger spacetimes

We consider black probes of Anti-de Sitter and Schrödinger spacetimes embedded in string theory and M-theory and construct perturbatively new black hole geometries. We begin by reviewing black string configurations in Anti-de Sitter dual to finite temperature Wilson loops in the deconfined phase of the gauge theory and generalise the construction to the confined phase. We then consider black strings in thermal Schrödinger, obtained via a null Melvin twist of the extremal D3-brane, and construct three distinct types of black string configurations with spacelike as well as lightlike separated boundary endpoints. One of these configurations interpolates between the Wilson loop operators, with bulk duals defined in Anti-de Sitter and another class of Wilson loop operators, with bulk duals defined in Schrödinger. The case of black membranes with boundary endpoints on the M5-brane dual to Wilson surfaces in the gauge theory is analysed in detail. Four types of black membranes, ending on the null Melvin twist of the extremal M5-brane exhibiting the Schrödinger symmetry group, are then constructed. We highlight the differences between Anti-de Sitter and Schrödinger backgrounds and make some comments on the properties of the corresponding dual gauge theories.

Crystalline Confinement

We show that exotic phases arise in generalized lattice gauge theories known as quantum link models in which classical gauge fields are replaced by quantum operators. While these quantum models with discrete variables have a finite-dimensional Hilbert space per link, the continuous gauge symmetry is still exact. An efficient cluster algorithm is used to study these exotic phases. The (2+1)-d system is confining at zero temperature with a spontaneously broken translation symmetry. A crystalline phase exhibits confinement via multi stranded strings between chargeanti-charge pairs. A phase transition between two distinct confined phases is weakly first order and has an emergent spontaneously broken approximate SO(2) global symmetry. The low-energy physics is described by a (2 + 1)-d RP(1) effective field theory, perturbed by a dangerously irrelevant SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. This model is an ideal candidate to be implemented in quantum simulators to study phenomena that are not accessible using Monte Carlo simulations such as the real-time evolution of the confining string and the real-time dynamics of the pseudo-Goldstone boson.