Expansive actions on uniform spaces and surjunctive maps

We present a uniform version of a result of M. Gromov on the surjunctivity of maps commuting with expansive group actions and discuss several applications. We prove in particular that for any group $\Gamma$ and any field \K, the space of $\Gamma$-marked groups $G$ such that the group algebra \K[G] is stably finite is compact.Comment: 21 page

Il gruppo di Grigorchuk di crescita intermedia

An explicit description of the 2-group of intermediate growth found by Grigorchuk is given. We also give a few preliminary notions concerning finitely generated groups and their growth functions. © 2001 Springer

Von Neumann Regular Cellular Automata

For any group $G$ and any set $A$, a cellular automaton (CA) is a transformation of the configuration space $A^G$ defined via a finite memory set and a local function. Let $\text{CA}(G;A)$ be the monoid of all CA over $A^G$. In this paper, we investigate a generalisation of the inverse of a CA from the semigroup-theoretic perspective. An element $\tau \in \text{CA}(G;A)$ is von Neumann regular (or simply regular) if there exists $\sigma \in \text{CA}(G;A)$ such that $\tau \circ \sigma \circ \tau = \tau$ and $\sigma \circ \tau \circ \sigma = \sigma$, where $\circ$ is the composition of functions. Such an element $\sigma$ is called a generalised inverse of $\tau$. The monoid $\text{CA}(G;A)$ itself is regular if all its elements are regular. We establish that $\text{CA}(G;A)$ is regular if and only if $\vert G \vert = 1$ or $\vert A \vert = 1$, and we characterise all regular elements in $\text{CA}(G;A)$ when $G$ and $A$ are both finite. Furthermore, we study regular linear CA when $A= V$ is a vector space over a field $\mathbb{F}$; in particular, we show that every regular linear CA is invertible when $G$ is torsion-free elementary amenable (e.g. when $G=\mathbb{Z}^d, \ d \in \mathbb{N}$) and $V=\mathbb{F}$, and that every linear CA is regular when $V$ is finite-dimensional and $G$ is locally finite with $\text{Char}(\mathbb{F}) \nmid o(g)$ for all $g \in G$.Comment: 10 pages. Theorem 5 corrected from previous versions, in A. Dennunzio, E. Formenti, L. Manzoni, A.E. Porreca (Eds.): Cellular Automata and Discrete Complex Systems, AUTOMATA 2017, LNCS 10248, pp. 44-55, Springer, 201

The multifactorial pathways towards resistance to the cytosine analogues emtricitabine and lamivudine: Evidences from literature

The article by Bulteel et al.,1 published in the September issue of the journal, has investigated the rate of M184V emergence in patients receiving HAART combinations containing efavirenz (EFV), tenofovir (TDF) and lamivudine (3 TC) or emtricitabine (FTC) within the UK Collaborative HIV Cohort. By analyzing 304 genotypic resistance tests, the authors asserted that, although patients receiving 3 TC-based regimens were more likely to develop M184V than those receiving FTC-based regimens (event rate: 0.55 [95%CI: 0.28–0.96] for 3 TC versus 0.34 [95%CI: 0.21–0.46] for FTC), this association was not statistically significant in both univariable and multivariable models. These results are different from those reported in previous studies from our and other groups2, 3 and 4 showing a significant decrease in M184V emergence in patients failing FTC + TDF-based compared to 3 TC + TDF-based HAART (Table 1). The lower prevalence of M184V in FTC-containing regimen was also supported by a recently published letter showing a strong trend (P = 0.051) towards higher rates of resistance to the 3 TC containing regimen 5.5 (1.8–12.8) per 1000 patient years when compared with the FTC containing regimens 1.7 (0.8–3.2) per 1000 patient year

Computational analysis of Human Immunodeficiency Virus (HIV) Type-1 reverse transcriptase crystallographic models based on significant conserved residues found in Highly Active Antiretroviral Therapy (HAART)-treated patients.

Reverse transcription of the viral single-stranded (+) RNA genome into double-stranded DNA is an essential step in the human immunodeficiency virus' (HIV) life-cycle. Although several viral proteins are involved in the regulation and/or efficiency of reverse transcription, the process of retroviral DNA synthesis is entirely dependent on the enzymatic activities of the retroviral reverse transcriptase enzyme (RT). Due to its crucial role in the HIV life-cycle, RT is a primary target for anti-HIV drug development. Nonetheless, drug resistance is the major problem affecting the clinical efficacy of antiretroviral agents. Incomplete pharmacological pressure represents the logical cause and not the consequence of different mutation pathways in RT associated with approved inhibitors resistance. In this review we have analyzed RT Protein Data Bank (PDB) models using our innovative computational approach “GRID Based Pharmacophore Model” (GBPM). This method was applied to clinically relevant RT conserved residues found in a large cohort of HAART treated patients. The PDB entries have been selected among the unbound and the complexed models with DNA and/or inhibitors. Such an approach has revealed itself useful to highlight the mutation effects in the drug-RT recognition as well as in the heterodimer stabilization of the enzyme. Most of the clinical and biochemical evidences already reported in the literature have been rationalized at molecular level via the GBPM computational approach. A definite future application of this method will be the identification of conserved regions of critical macromolecules, such as the HIV-1 RT, to be targeted for the development of innovative therapeutic agents

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

Effect of the human immunodeficiency virus type 1 reverse transcriptase polymorphism Leu-214 on replication capacity and drug susceptibility

A negative association between polymorphism Leu-214 and type-1 thymidine analogue mutations (TAM1) and a positive association with a clinically favorable virological response to thymidine analogue-based combination antiretroviral therapy have been described. In this study, the impact of Leu-214 on replication capacity and resistance to zidovudine (ZDV) of viruses containing TAM1 or TAM2 was determined. Leu-214 decreased the growth rate of viruses bearing Tyr-215, as well as their resistance to ZDV. This observation was confirmed by structural and molecular modeling data, suggesting a regulatory role for Leu-214 in the emergence and phenotypic resistance of TAM1

Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called configuration shift-symmetry is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration. Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.Comment: 22 pages, 9 figures, 2 appendice

Using the latest resistance score to predict etravirine (ETV) resistance in naïve and NNRTI-failing patients

Methods A set of 17 mutations (V90I, A98G, L100I, K101E/H/P, V106I, E138A, V179D/F/T, Y181C/I/V, G190A/S, M230L) were found associated with ETV resistance in the Phase III DUET-1 and DUET-2 trials. Recently, a different score was assigned to each mutation (i.e. Y181C/I have the highest score: 3). An overall score of ≤4 was associated with reduced response and a score between 2.5–3.5 with intermediate response (reference). ETV resistance was calculated from a large database of patients undergoing genotypic resistance test