Approximating the Minimum Equivalent Digraph

The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives an approximation algorithm with performance guarantee of pi^2/6 ~ 1.64. The algorithm and its analysis are based on the simple idea of contracting long cycles. (This result is strengthened slightly in ``On strongly connected digraphs with bounded cycle length'' (1996).) The analysis applies directly to 2-Exchange, a simple ``local improvement'' algorithm, showing that its performance guarantee is 1.75.Comment: conference version in ACM-SIAM Symposium on Discrete Algorithms (1994

Information Storage and Retrieval for Probe Storage using Optical Diffraction Patterns

A novel method for fast information retrieval from a probe storage device is considered. It is shown that information can be stored and retrieved using the optical diffraction patterns obtained by the illumination of a large array of cantilevers by a monochromatic light source. In thermo-mechanical probe storage, the information is stored as a sequence of indentations on the polymer medium. To retrieve the information, the array of probes is actuated by applying a bending force to the cantilevers. Probes positioned over indentations experience deflection by the depth of the indentation, probes over the flat media remain un-deflected. Thus the array of actuated probes can be viewed as an irregular optical grating, which creates a data-dependent diffraction pattern when illuminated by laser light. We develop a low complexity modulation scheme, which allows the extraction of information stored in the pattern of indentations on the media from Fourier coefficients of the intensity of the diffraction pattern. We then derive a low-complexity maximum likelihood sequence detection algorithm for retrieving the user information from the Fourier coefficients. The derivation of both the modulation and the detection schemes is based on the Fraunhofer formula for data-dependent diffraction patterns. We show that for as long as the Fresnel number F<0.1, the optimal channel detector derived from Fraunhofer diffraction theory does not suffer any significant performance degradation.Comment: 14 pages, 11 figures. Version 2: minor misprints corrected, experimental section expande

Bacatá: A Language Parametric Notebook Generator (Tool Demo)

\u3cp\u3eInteractive notebooks allow people to communicate and collaborate through a single rich document that might include live code, multimedia, computed results, and documentation, which is persisted as a whole for reproducibility. Notebooks are currently being used extensively in domains such as data science, data journalism, and machine learning. However, constructing a notebook interface for a new language requires a lot of effort. In this tool paper, we present Bacatá, a language parametric notebook generator for domain-specific languages (DSL) based on the Jupyter framework. Bacatá is designed so that language engineers may reuse existing language components (such as parsers, code generators, interpreters, etc.) as much as possible. Moreover, we explain the design of Bacatá and how DSL notebooks can be generated with minimum effort in the context of the Rascal meta programming system and language workbench.\u3c/p\u3

Asynchronous simulation of Boolean networks by monotone Boolean networks

International audienceWe prove that the fully asynchronous dynamics of a Boolean network f : {0, 1}^n → {0, 1}^n without negative loop can be simulated, in a very specific way, by a monotone Boolean network with 2n components. We then use this result to prove that, for every even n, there exists a monotone Boolean network f : {0, 1}^n → {0, 1}^n , an initial configuration x and a fixed point y of f such that: (i) y can be reached from x with a fully asynchronous updating strategy, and (ii) all such strategies contains at least 2^{n/2} updates. This contrasts with the following known property: if f : {0, 1}^n → {0, 1}^n is monotone, then, for every initial configuration x, there exists a fixed point y such that y can be reached from x with a fully asynchronous strategy that contains at most n updates

A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end

It is recommended in the mathematics education literature that pupils be presented with equality statements that can be assessed for numerical balance by attending to notational structure rather than computation. I describe an alternative, diagrammatic approach in which pupils do not assess statements but instead use them to make substitutions of notation. I report on two trials of a computer-based task conducted with pairs of pupils and highlight two findings. First, the pupils found it useful to articulate the distinct substitutive effects of commutative (‘swap’, ‘switch’) and partitional (‘split’, ‘separate’) statements when working on the task. Secondly, the pupils did not notice that some of the statements presented were in fact false, which suggests their substituting activities were independent of numerical equivalence conceptions. This demonstrates that making substitutions offers task designers a mathematical utility for equality statements that is distinct from, but complementary to, assessing numerical balance

Structure of the first representative of Pfam family PF04016 (DUF364) reveals enolase and Rossmann-like folds that combine to form a unique active site with a possible role in heavy-metal chelation.

The crystal structure of Dhaf4260 from Desulfitobacterium hafniense DCB-2 was determined by single-wavelength anomalous diffraction (SAD) to a resolution of 2.01 Å using the semi-automated high-throughput pipeline of the Joint Center for Structural Genomics (JCSG) as part of the NIGMS Protein Structure Initiative (PSI). This protein structure is the first representative of the PF04016 (DUF364) Pfam family and reveals a novel combination of two well known domains (an enolase N-terminal-like fold followed by a Rossmann-like domain). Structural and bioinformatic analyses reveal partial similarities to Rossmann-like methyltransferases, with residues from the enolase-like fold combining to form a unique active site that is likely to be involved in the condensation or hydrolysis of molecules implicated in the synthesis of flavins, pterins or other siderophores. The genome context of Dhaf4260 and homologs additionally supports a role in heavy-metal chelation

Structure of a putative NTP pyrophosphohydrolase: YP_001813558.1 from Exiguobacterium sibiricum 255-15.

The crystal structure of a putative NTPase, YP_001813558.1 from Exiguobacterium sibiricum 255-15 (PF09934, DUF2166) was determined to 1.78 Å resolution. YP_001813558.1 and its homologs (dimeric dUTPases, MazG proteins and HisE-encoded phosphoribosyl ATP pyrophosphohydrolases) form a superfamily of all-α-helical NTP pyrophosphatases. In dimeric dUTPase-like proteins, a central four-helix bundle forms the active site. However, in YP_001813558.1, an unexpected intertwined swapping of two of the helices that compose the conserved helix bundle results in a `linked dimer' that has not previously been observed for this family. Interestingly, despite this novel mode of dimerization, the metal-binding site for divalent cations, such as magnesium, that are essential for NTPase activity is still conserved. Furthermore, the active-site residues that are involved in sugar binding of the NTPs are also conserved when compared with other α-helical NTPases, but those that recognize the nucleotide bases are not conserved, suggesting a different substrate specificity

Structure of the γ-D-glutamyl-L-diamino acid endopeptidase YkfC from Bacillus cereus in complex with L-Ala-γ-D-Glu: insights into substrate recognition by NlpC/P60 cysteine peptidases.

Dipeptidyl-peptidase VI from Bacillus sphaericus and YkfC from Bacillus subtilis have both previously been characterized as highly specific γ-D-glutamyl-L-diamino acid endopeptidases. The crystal structure of a YkfC ortholog from Bacillus cereus (BcYkfC) at 1.8 Å resolution revealed that it contains two N-terminal bacterial SH3 (SH3b) domains in addition to the C-terminal catalytic NlpC/P60 domain that is ubiquitous in the very large family of cell-wall-related cysteine peptidases. A bound reaction product (L-Ala-γ-D-Glu) enabled the identification of conserved sequence and structural signatures for recognition of L-Ala and γ-D-Glu and, therefore, provides a clear framework for understanding the substrate specificity observed in dipeptidyl-peptidase VI, YkfC and other NlpC/P60 domains in general. The first SH3b domain plays an important role in defining substrate specificity by contributing to the formation of the active site, such that only murein peptides with a free N-terminal alanine are allowed. A conserved tyrosine in the SH3b domain of the YkfC subfamily is correlated with the presence of a conserved acidic residue in the NlpC/P60 domain and both residues interact with the free amine group of the alanine. This structural feature allows the definition of a subfamily of NlpC/P60 enzymes with the same N-terminal substrate requirements, including a previously characterized cyanobacterial L-alanine-γ-D-glutamate endopeptidase that contains the two key components (an NlpC/P60 domain attached to an SH3b domain) for assembly of a YkfC-like active site

The structure of BVU2987 from Bacteroides vulgatus reveals a superfamily of bacterial periplasmic proteins with possible inhibitory function.

Proteins that contain the DUF2874 domain constitute a new Pfam family PF11396. Members of this family have predominantly been identified in microbes found in the human gut and oral cavity. The crystal structure of one member of this family, BVU2987 from Bacteroides vulgatus, has been determined, revealing a β-lactamase inhibitor protein-like structure with a tandem repeat of domains. Sequence analysis and structural comparisons reveal that BVU2987 and other DUF2874 proteins are related to β-lactamase inhibitor protein, PepSY and SmpA_OmlA proteins and hence are likely to function as inhibitory proteins