Multi-Dimensional Pattern Matching with Dimensional Wildcards: Data Structures and Optimal On-Line Search Algorithms

We introduce a new multidimensional pattern matching problem that is a natural generalization of string matching, a well studied problem[1]. The motivation for its algorithmic study is mainly theoretical. LetA[1:n₁,…,1:n_d] be a text matrix withN = n₁…n_dentries andB[1:m₁,…,1:m_r] be a pattern matrix withM = m₁…m_rentries, whered ≥ r ≥ 1 (the matrix entries are taken from an ordered alphabet Σ). We study the problem of checking whether somer-dimensional submatrix ofAis equal toB(i.e., adecisionquery).Acan be preprocessed andBis given on-line. We define a new data structure for preprocessingAand propose CRCW-PRAM algorithms that build it inO(log N) time withN²/n_maxprocessors, wheren_max = max(n₁,…,n_d), such that the decision query forBtakesO(M) work andO(log M) time. By using known techniques, we would get the same preprocessing bounds but anO((^d_r)M) work bound for the decision query. The latter bound is undesirable since it can depend exponentially ond; our bound, in contrast, is independent ofdand optimal. We can also answer, in optimal work, two further types of queries: (a) anenumerationquery retrieving all ther-dimensional submatrices ofAthat are equal toBand (b) anoccurrencequery retrieving only the distinct positions inAthat correspond to all of these submatrices. As a byproduct, we also derive the first efficient sequential algorithms for the new problem.     

On the problem of the elastic plate on one-sided foundation

Summary Solution existence, uniqueness and regularity are analyzed for the elastic plate on unilateral elastic foundation problem. Some results are also given for the one-sided rigid foundation case.

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Sommario Si studiano l'esistenza, l'unicità e la regolarità delle soluzioni del problema della piastra elastica su fondazione elastica unilaterale. Sono anche dati alcuni risultati per il caso di fondazione rigida unilaterale.

     

Fibrillar Networks of Glycyrrhizic Acid for Hybrid Nanomaterials with Catalytic Features

Self‐assembly of the naturally occurring sweetening agent, glycyrrhizic acid (GA) in water is studied by small‐angle X‐ray scattering and microscopic techniques. Statistical analysis on atomic force microscopy images reveals the formation of ultralong GA fibrils with uniform thickness of 2.5 nm and right‐handed twist with a pitch of 9 nm, independently of GA concentration. Transparent nematic GA hydrogels are exploited to create functional hybrid materials. Two‐fold and three‐fold hybrids are developed by introducing graphene oxide (GO) and in situ‐synthesized gold nanoparticles (Au NPs) in the hydrogel matrix for catalysis applications. In the presence of GO, the catalytic efficiency of Au NPs in the reduction of p‐nitrophenol to p‐aminophenol is enhanced by 2.5 times. Gold microplate single crystals are further synthesized in the GA hydrogel, expanding the scope of these hybrids and demonstrating their versatility in materials design.     

Phase Behavior of a Designed Cyclopropyl Analogue of Monoolein: Implications for Low‐Temperature Membrane Protein Crystallization

Lipidic cubic phases (LCPs) are used in areas ranging from membrane biology to biodevices. Because some membrane proteins are notoriously unstable at room temperature, and available LCPs undergo transformation to lamellar phases at low temperatures, development of stable low‐temperature LCPs for biophysical studies of membrane proteins is called for. Monodihydrosterculin (MDS) is a designer lipid based on monoolein (MO) with a configurationally restricted cyclopropyl ring replacing the olefin. Small‐angle X‐ray scattering (SAXS) analyses revealed a phase diagram for MDS lacking the high‐temperature, highly curved reverse hexagonal phase typical for MO, and extending the cubic phase boundary to lower temperature, thereby establishing the relationship between lipid molecular structure and mesophase behavior. The use of MDS as a new material for LCP‐based membrane protein crystallization at low temperature was demonstrated by crystallizing bacteriorhodopsin at 20 °C as well as 4 °C.     

An exact algorithm to extend lifetime through roles allocation in sensor networks with connectivity constraints

We face the problem of scheduling optimally the activities in a wireless sensor network in order to ensure that, in each instant of time, the activated sensors can monitor all points of interest (targets) and route the collected information to a processing facility. Each sensor is allocated to a role, depending on whether it is actually used to monitor the targets, to forward information or kept idle, leading to different battery consumption ratios. We propose a column generation algorithm that embeds a highly efficient genetic metaheuristic for the subproblem. Moreover, to optimally solve the subproblem, we introduce a new formulation with fewer integer variables than a previous one proposed in the literature. Finally, we propose a stopping criterion to interrupt the optimal resolution of the subproblem as soon as a favorable solution is found. The results of our computational tests show that our algorithm consistently outperforms previous approaches in the literature, and also improves the best results known to date on some benchmark instances.     

Conjugate Direction Methods and Polarity for Quadratic Hypersurfaces

We use some results from polarity theory to recast several geometric properties of Conjugate Gradient-based methods, for the solution of nonsingular symmetric linear systems. This approach allows us to pursue three main theoretical objectives. First, we can provide a novel geometric perspective on the generation of conjugate directions, in the context of positive definite systems. Second, we can extend the above geometric perspective to treat the generation of conjugate directions for handling indefinite linear systems. Third, by exploiting the geometric insight suggested by polarity theory, we can easily study the possible degeneracy (pivot breakdown) of Conjugate Gradient-based methods on indefinite linear systems. In particular, we prove that the degeneracy of the standard Conjugate Gradient on nonsingular indefinite linear systems can occur only once in the execution of the Conjugate Gradient.     

2-(3,5-Dinitrophenyl)-1,3-dithiane carbanion: a benzylic anion with a low energy triplet state

Calculations at the DFT level predict that benzyl anions with strong π-electron-withdrawing groups in the meta position(s) have low energy diradical or triplet electronic states. Specifically, the 2-(3,5-dinitrophenyl)-1,3-dithiane carbanion is predicted to have nearly degenerate singlet and triplet states at the (U)B3LYP level as a free anion. Its lithium ion pair is predicted to be a ground-state triplet with a substantial (26 kcal/mol) singlet-triplet energy gap. Experiments on this anion using chemical trapping, NMR, and the Evans method strongly suggest that this anion is either a triplet or a ground-state singlet with a very low energy triplet state.     

Amyloid-mediated synthesis of giant, fluorescent, gold single crystals and their hybrid sandwiched composites driven by liquid crystalline interactions

We report for the first time on the templating effect of β-lactoglobulin amyloid-like fibrils to synthesize gold single crystals of several decades of μm in dimensions. The gold single crystals were produced by reducing an aqueous solution of chloroauric acid by β-lactoglobulin amyloid protein fibrils. Atomic force microscopy, conventional and scanning transmission electron microscopy, electron diffraction and optical microscopy techniques were combined to characterize the structure of the gold crystals. The single-crystalline features of these macroscopic gold crystals are witnessed by their distinctive hexagonal and triangular shape and are confirmed by selected area electron diffraction (SAED). UV-vis absorption spectrum, recorded after a reaction time of 6h at the heating temperature of 55°C showed a surface plasmon resonance peak at 540 nm. With the increase of reaction time to 24h, the absorption spectrum peaks shift to a very broad and higher wavelength region extending up to near infrared region. Remarkably, these single crystalline gold crystals show auto fluorescence when illuminated to UV lamp. Further increase in β-lactoglobulin amyloid fibrils concentration above the isotropic-nematic transition, drives the formation of gold single crystals microplates stacking together and self-assembling into new hierarchical, layered protein-gold hybrid composites.