Conjugacy in Baumslag's group, generic case complexity, and division in power circuits

The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} = y in G. The conjugacy problem is more difficult than the word problem, in general. We investigate the complexity of the conjugacy problem for two prominent groups: the Baumslag-Solitar group BS(1,2) and the Baumslag(-Gersten) group G(1,2). The conjugacy problem in BS(1,2) is TC^0-complete. To the best of our knowledge BS(1,2) is the first natural infinite non-commutative group where such a precise and low complexity is shown. The Baumslag group G(1,2) is an HNN-extension of BS(1,2). We show that the conjugacy problem is decidable (which has been known before); but our results go far beyond decidability. In particular, we are able to show that conjugacy in G(1,2) can be solved in polynomial time in a strongly generic setting. This means that essentially for all inputs conjugacy in G(1,2) can be decided efficiently. In contrast, we show that under a plausible assumption the average case complexity of the same problem is non-elementary. Moreover, we provide a lower bound for the conjugacy problem in G(1,2) by reducing the division problem in power circuits to the conjugacy problem in G(1,2). The complexity of the division problem in power circuits is an open and interesting problem in integer arithmetic.Comment: Section 5 added: We show that an HNN extension G = < H, b | bab^-1 = {\phi}(a), a \in A > has a non-amenable Schreier graph with respect to the base group H if and only if A \neq H \neq

Harmonisation and diagnostics of MIPAS ESA CH4 and N2O profiles using data assimilation

This paper discusses assimilation experiments of methane (CH4) and nitrous oxide (N2O) profiles retrieved from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). Here we focus on data versions 6 and 7 provided by the ESA processor. These data sets have been assimilated by the Belgian Assimilation System for Chemical ObsErvations (BASCOE). The CH4 and N2O retrieved profiles can oscillate, especially in the tropical lower stratosphere. Using the averaging kernels of the observations and a background error covariance matrix, which has previously been calibrated, allows the system to partly remedy this issue and provide assimilated fields that are more regular vertically. In general, there is a good agreement between the BASCOE analyses and independent observations from ACE–FTS (CH4 and N2O) and MLS (N2O), demonstrating the general good quality of CH4 and N2O retrievals provided by MIPAS ESA. Nevertheless, this study also identifies two issues in these data sets. First, time series of the observations show unexpected discontinuities due to an abrupt change in the gain of MIPAS band B, generally occurring after the instrument decontamination. Since the calibration is performed weekly, the abrupt change in the gain affects the measurements until the subsequent calibration is performed. Second, the correlations between BASCOE analyses and independent observations are poor in the lower stratosphere, especially in the tropics, probably due to the presence of outliers in the assimilated data. In this region, we recommend using MIPAS CH4 and N2O retrievals with caution

Comparative replication capacity of raltegravir-resistant strains and antiviral activity of the new-generation integrase inhibitor dolutegravir in human primary macrophages and lymphocytes

To evaluate the replication capacity and phenotypic susceptibility to dolutegravir and raltegravir of wild-type and raltegravir-resistant HIV-1 strains in several cellular systems

C60_{60} in intense femtosecond laser pulses: nonlinear dipole response and ionization

We study the interaction of strong femtosecond laser pulses with the C$_{60}$ molecule employing time-dependent density functional theory with the ionic background treated in a jellium approximation. The laser intensities considered are below the threshold of strong fragmentation but too high for perturbative treatments such as linear response. The nonlinear response of the model to excitations by short pulses of frequencies up to 45eV is presented and analyzed with the help of Kohn-Sham orbital resolved dipole spectra. In femtosecond laser pulses of 800nm wavelength ionization is found to occur multiphoton-like rather than via excitation of a ``giant'' resonance.Comment: 14 pages, including 1 table, 5 figure

Prevalence of resistance mutations related to integrase inhibitor S/GSK1349572 in HIV-1 subtype B raltegravir-naive and -treated patients

Objectives To compare the frequency of previously in vitro-selected integrase mutations (T124A, T124A/S153F, S153Y, T124A/S153Y and L101I/T124A/S153Y) conferring resistance to S/GSK1349572 between HIV-1 subtype B integrase inhibitor (INI)-naive and raltegravir-treated patients. Methods Integrase sequences from 650 INI-naive patients and 84 raltegravir-treated patients were analysed. Results The T124A mutation alone and the combination T124A/L101I were more frequent in raltegravir-failing patients than in INI-naive patients (39.3% versus 24.5%, respectively, P = 0.005 for T124A and 20.2% versus 10.0%, respectively, P = 0.008 for T124A/L101I). The S153Y/F mutations were not detected in any integrase sequence (except for S153F alone, only detected in one INI-naive patient). Conclusions T124A and T124A/L101I, more frequent in raltegravir-treated patients, could have some effect on raltegravir response and their presence could play a role in the selection of other mutations conferring S/GSK1349572 resistance. The impact of raltegravir-mediated changes such as these on the virological response to S/GSK1349572 should be studied further

Electron correlation vs. stabilization: A two-electron model atom in an intense laser pulse

We study numerically stabilization against ionization of a fully correlated two-electron model atom in an intense laser pulse. We concentrate on two frequency regimes: very high frequency, where the photon energy exceeds both, the ionization potential of the outer {\em and} the inner electron, and an intermediate frequency where, from a ``single active electron''-point of view the outer electron is expected to stabilize but the inner one is not. Our results reveal that correlation reduces stabilization when compared to results from single active electron-calculations. However, despite this destabilizing effect of electron correlation we still observe a decreasing ionization probability within a certain intensity domain in the high-frequency case. We compare our results from the fully correlated simulations with those from simpler, approximate models. This is useful for future work on ``real'' more-than-one electron atoms, not yet accessible to numerical {\em ab initio} methods.Comment: 8 pages, 8 figures in an extra ps-file, submitted to Phys. Rev. A, updated references and shortened introductio

Effectiveness of dolutegravir-based regimens as either first-line or switch antiretroviral therapy: data from the Icona cohort

Introduction: Concerns about dolutegravir (DTG) tolerability in the real-life setting have recently arisen. We aimed to estimate the risk of treatment discontinuation and virological failure of DTG-based regimens from a large cohort of HIV-infected individuals. Methods: We performed a multicentre, observational study including all antiretroviral therapy (ART)-naïve and virologically suppressed treatment-experienced (TE) patients from the Icona (Italian Cohort Naïve Antiretrovirals) cohort who started, for the first time, a DTG-based regimen from January 2015 to December 2017. We estimated the cumulative risk of DTG discontinuation regardless of the reason and for toxicity, and of virological failure using Kaplan–Meier curves. We used Cox regression model to investigate predictors of DTG discontinuation. Results: About 1679 individuals (932 ART-naïve, 747 TE) were included. The one- and two-year probabilities (95% CI) of DTG discontinuation were 6.7% (4.9 to 8.4) and 11.5% (8.7 to 14.3) for ART-naïve and 6.6% (4.6 to 8.6) and 7.6% (5.4 to 9.8) for TE subjects. In both ART-naïve and TE patients, discontinuations of DTG were mainly driven by toxicity with an estimated risk (95% CI) of 4.0% (2.6 to 5.4) and 2.5% (1.3 to 3.6) by one year and 5.6% (3.8 to 7.5) and 4.0% (2.4 to 5.6) by two years respectively. Neuropsychiatric events were the main reason for stopping DTG in both ART-naïve (2.1%) and TE (1.7%) patients. In ART-naïve, a concomitant AIDS diagnosis predicted the risk of discontinuing DTG for any reason (adjusted relative hazard (aRH)&nbsp;=&nbsp;3.38, p&nbsp;=&nbsp;0.001), whereas starting DTG in combination with abacavir (ABC) was associated with a higher risk of discontinuing because of toxicity (aRH&nbsp;=&nbsp;3.30, p&nbsp;=&nbsp;0.009). TE patients starting a DTG-based dual therapy compared to a triple therapy had a lower risk of discontinuation for any reason (adjusted hazard ratio (aHR)&nbsp;=&nbsp;2.50, p&nbsp;=&nbsp;0.037 for ABC-based triple-therapies, aHR&nbsp;=&nbsp;3.56, p&nbsp;=&nbsp;0.012 for tenofovir-based) and for toxicity (aHR&nbsp;=&nbsp;5.26, p&nbsp;=&nbsp;0.030 for ABC-based, aHR&nbsp;=&nbsp;6.60, p&nbsp;=&nbsp;0.024 for tenofovir-based). The one- and two-year probabilities (95% CI) of virological failure were 1.2% (0.3 to 2.0) and 4.6% (2.7 to 6.5) in the ART naïve group and 2.2% (1.0 to 3.3) and 2.9% (1.5 to 4.3) in the TE group. Conclusions: In this large cohort, DTG showed excellent efficacy and optimal tolerability both as first-line and switching ART. The low risk of treatment-limiting toxicities in ART-naïve as well as in treated individuals reassures on the use of DTG in everyday clinical practice

Branch Rings, Thinned Rings, Tree Enveloping Rings

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).Comment: 35 pages; small changes wrt previous versio

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht