On the algebra of cornered Floer homology

Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2-algebra, the nilCoxeter sequential 2-algebra, and to a surface with connected boundary an algebra-module over this 2-algebra, such that a natural gluing property is satisfied. Moreover, with a view toward the structure of a potential Floer homology theory of 3-manifolds with codimension-two corners, we present a decomposition theorem for the Floer complex of a planar grid diagram, with respect to vertical and horizontal slicing.Comment: a few minor revision

Gap prediction in hybrid graphene - hexagonal boron nitride nanoflakes using artificial neural networks

The electronic properties graphene nanoflakes (GNFs) with embedded hexagonal boron nitride (hBN) domains are investigated by combined {\it ab initio} density functional theory calculations and machine learning techniques. The energy gaps of the quasi-0D graphene based systems, defined as the differences between LUMO and HOMO energies, depend on the sizes of the hBN domains relative to the size of the pristine graphene nanoflake, but also on the position of the hBN domain. The range of the energy gaps for different configurations is increasing as the hBN domains get larger. We develop two artificial neural network (ANN) models able to reproduce the gap energies with high accuracies and investigate the tunability of the energy gap, by considering a set of GNFs with embedded rectangular hBN domains. In one ANN model, the input is in one-to-one correspondence with the atoms in the GNF, while in the second model the inputs account for basic structures in the GNF, allowing potential use in up-scaled structures. We perform a statistical analysis over different configurations of ANNs to optimize the network structure. The trained ANNs provide a correlation between the atomic system configuration and the magnitude of the energy gaps, which may be regarded as an efficient tool for optimizing the design of nanostructured graphene based materials for specific electronic properties.Comment: 6 pages, 5 figure

Hysteresis effect due to the exchange Coulomb interaction in short-period superlattices in tilted magnetic fields

We calculate the ground-state of a two-dimensional electron gas in a short-period lateral potential in magnetic field, with the Coulomb electron-electron interaction included in the Hartree-Fock approximation. For a sufficiently short period the dominant Coulomb effects are determined by the exchange interaction. We find numerical solutions of the self-consistent equations that have hysteresis properties when the magnetic field is tilted and increased, such that the perpendicular component is always constant. This behavior is a result of the interplay of the exchange interaction with the energy dispersion and the spin splitting. We suggest that hysteresis effects of this type could be observable in magneto-transport and magnetization experiments on quantum-wire and quantum-dot superlattices.Comment: 3 pages, 3 figures, Revtex, to appear in Phys. Rev.

HBV and neurological impairment in HIV-infected patients

Objective: HIV can affect CNS in early stages of disease and determine neurological impairment. HBV DNA was found in CSF of HIV co-infected patients, but little is known about the neurotropic character of this virus. Here we assessed the degree of association between HBV infection and neurological impairment in a large cohort of long-term survivors, HIV-infected patients that experienced multiple therapeutic schemes over time. Methods: A total of 462 HIV-1-infected patients were retrospectively followed up for 10 years for HBV infection and neurological impairment. The patients were tested for immune (flow cytometry) and virological parameters of HIV infection (Roche Amplicor, version 1.5/ COBAS AmpliPrep/COBAS TaqMan HIV-1 test) and for HBV infection markers (HBsAg, anti HBc: Murex Biotech ELISA tests). Many of these patients have experienced between one and six regimens such as: 2 NRTIs, 3 NRTIs, 2 NRTIs+1 NNRTI, 1 NRTI+1 NNRTI+1 PI, 2 NRTIs+2 PIs. Results: After 10 years 29.87% of the patients presented neurological impairment. Out of them 56.52% were HBV-infected. The prevalence of HIV encephalopathy (HE) in our studied cohort was 22.7% and 50.4% of these patients were HBV-infected. The median HIV diagnosis age was 7 and the median age of HE diagnosis was 10. In order to establish a possible correlation between HBV infection and HE we first reviewed and excluded the main risk factors associated with HE at the moment of diagnosis: low weight, anemia, constitutional symptoms, low CD4+count, high plasma HIV-RNA load. No patient was infected with HCV. The groups of patients that presented HE and HBsAg and HE without HBsAg were balanced regarding sex, number of deceased patients, number of class C3 patients, but the patients in first group presented lower CD4 values at HE diagnosis vs patients from second group 2: 44.5 vs 95 cells/µL, p=0.3; lower nadir CD4 count: 38 vs 51 cell/µL, p=0.1; and slightly higher HIV viral load: 5.2 vs 5 log10 copies/mL, p = 0.2. There were only 53 patients that presented at the same time HE and HBV infection and the majority, 78.69%, were first infected with HBV. Conclusions: In our studied cohort HBV infection was associated with HE but further studies are needed to prove HBV neurotropic potential. Absolute CD4 nadir count and class C3 are proved to be strong predictors of HE in HIV-infected patients even after several changes in antiretroviral therapy schemes

Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

Similar to knots in S^3, any knot in a lens space has a grid diagram from which one can combinatorially compute all of its knot Floer homology invariants. We give an explicit description of the generators, differentials, and rational Maslov and Alexander gradings in terms of combinatorial data on the grid diagram. Motivated by existing results for the Floer homology of knots in S^3 and the similarity of the combinatorics presented here, we conjecture that a certain family of knots is characterized by their Floer homology. Coupled with work of the third author, an affirmative answer to this would prove the Berge conjecture, which catalogs the knots in S^3 admitting lens space surgeries.Comment: 27 pages, 8 figures; Expositional improvements, corrected normalization of A grading in proof of Lemma 4.1

Coulomb interaction and transient charging of excited states in open nanosystems

We obtain and analyze the effect of electron-electron Coulomb interaction on the time dependent current flowing through a mesoscopic system connected to biased semi-infinite leads. We assume the contact is gradually switched on in time and we calculate the time dependent reduced density operator of the sample using the generalized master equation. The many-electron states (MES) of the isolated sample are derived with the exact diagonalization method. The chemical potentials of the two leads create a bias window which determines which MES are relevant to the charging and discharging of the sample and to the currents, during the transient or steady states. We discuss the contribution of the MES with fixed number of electrons N and we find that in the transient regime there are excited states more active than the ground state even for N=1. This is a dynamical signature of the Coulomb blockade phenomenon. We discuss numerical results for three sample models: short 1D chain, 2D lattice, and 2D parabolic quantum wire.Comment: 12 pages, 12 figure

Correlated time-dependent transport through a 2D quantum structure

We use a generalized master equation (GME) to describe the nonequilibrium magnetotransport of interacting electrons through a broad finite quantum wire with an embedded ring structure. The finite quantum wire is weakly coupled to two broad leads acting as reservoirs of electrons. The mutual Coulomb interaction of the electrons is described using a configuration interaction method for the many-electron states of the central system. We report some non-trivial interaction effects both at the level of time-dependent filling of states and on the time-dependent transport. We find that the Coulomb interaction in this non-trivial geometry can enhance the correlation of electronic states in the system and facilitate it's charging in certain circumstances in the weak coupling limit appropriate for the GME. In addition, we find oscillations in the current in the leads due to the correlations oscillations caused by the switched-on lead- system coupling. The oscillations are influenced and can be enhanced by the external magnetic field and the Coulomb interaction.Comment: RevTeX (pdf-LaTeX), 10 pages with 15 included jpg figure

Memorization of short-range potential fluctuations in Landau levels

We calculate energy spectra of a two-dimensional electron system in a perpendicular magnetic field and periodic potentials of short periods. The Coulomb interaction is included within a screened Hartree-Fock approximation. The electrostatic screening is poor and the exchange interaction amplifies the energy dispersion. We obtain, by numerical iterations, self-consistent solutions that have a hysteresis-like property. With increasing amplitude of the external potential the energy dispersion and the electron density become periodic, and they remain stable when the external potential is reduced to zero. We explain this property in physical terms and speculate that a real system could memorize short-range potential fluctuations after the potential has been turned off.Comment: 11 pages with 4 included figures, Revte