The effect of reaction conditions on montmorillonite-catalysed peptide formation

Oligomerization of glycine (gly) and diglycine (gly₂) on montmorillonite was performed as cyclic, drying-wetting process at temperatures below 100°C, under varying reaction conditions. The influence of substrate/clay ratio, temperature and pH was found to be different for amino acid (AA) dimerization, cyclic anhydride (CA) formation and peptide chain elongation. High temperatures and neutral pH favour CA formation over diglycine production. An AA/catalyst ratio of 0.2 mmol/g leads to optimal yields. This supports the assumption that amino acid dimerization and CA formation take place at the edges of clay particles. Peptide chain elongation, starting from gly₂, produces higher yields at higher temperatures and neutral pH.     

Biclustering meets triadic concept analysis

Biclustering numerical data became a popular data-mining task at the beginning of 2000’s, especially for gene expression data analysis and recommender systems. A bicluster reflects a strong association between a subset of objects and a subset of attributes in a numerical object/attribute data-table. So-called biclusters of similar values can be thought as maximal sub-tables with close values. Only few methods address a complete, correct and non-redundant enumeration of such patterns, a well-known intractable problem, while no formal framework exists. We introduce important links between biclustering and Formal Concept Analysis (FCA). Indeed, FCA is known to be, among others, a methodology for biclustering binary data. Handling numerical data is not direct, and we argue that Triadic Concept Analysis (TCA), the extension of FCA to ternary relations, provides a powerful mathematical and algorithmic framework for biclustering numerical data. We discuss hence both theoretical and computational aspects on biclustering numerical data with triadic concept analysis. These results also scale to n-dimensional numerical datasets.     

Three-dimensional automated nanoparticle tracking using Mie scattering in an optical microscope

The forward scattering of light in a conventional inverted optical microscope by nanoparticles ranging in diameter from 10 to 50nm has been used to automatically and quantitatively identify and track their location in three-dimensions with a temporal resolution of 200ms. The standard deviation of the location of nominally stationary 50-nm-diameter nanoparticles was found to be about 50nm along the light path and about 5nm in the plane perpendicular to the light path. The method is based on oscillating the microscope objective along the light path using a piezo actuator and acquiring images with the condenser aperture closed to a minimum to enhance the effects of diffraction. Data processing in the time and spatial domains allowed the location of particles to be obtained automatically so that the technique has potential applications both in the processing of nanoparticles and in their use in a variety of fields including nanobiotechnology, pharmaceuticals and food processing where a simple optical microscope maybe preferred for a variety of reasons.     

On the Power of Las Vegas for One-Way Communication Complexity, OBDDs, and Finite Automata

The study of the computational power of randomized computations is one of the central tasks of complexity theory. The main goal of this paper is the comparison of the power of Las Vegas computation and deterministic respectively nondeterministic computation. We investigate the power of Las Vegas computation for the complexity measures of one-way communication, ordered binary decision diagrams, and finite automata.(i) For the one-way communication complexity of two-party protocols we show that Las Vegas communication can save at most one half of the deterministic one-way communication complexity. We also present a language for which this gap is tight.(ii) The result (i) is applied to show an at most polynomial gap between determinism and Las Vegas for ordered binary decision diagrams.(iii) For the size (i.e., the number of states) of finite automata we show that the size of Las Vegas finite automata recognizing a language L is at least the square root of the size of the minimal deterministic finite automaton recognizing L. Using a specific language we verify the optimality of this lower bound.     

The Power of Nondeterminism and Randomness for Oblivious Branching Programs

Abstract. This paper abstracts and generalizes the known approaches for proving lower bounds on the size of various variants of oblivious branching programs (oblivious BPs for short), providing an easy-to-use technique which works for all nondeterministic and randomized modes of acceptance. The technique is applied to obtain the following results concerning the power of nondeterminism and randomness for oblivious BPs: <p>— Oblivious read-once BPs, better known as OBDDs (ordered binary decision diagrams), are used in many applications and their structure is well understood in the deterministic case. It has been open so far to compare the power of nondeterministic OBDDs with so-called partitioned BDDs which are a variant of nondeterministic branching programs also used in practice. A k -partitioned BDD has a nondeterministic node at the top by which one out of k deterministic OBDDs with possibly different variable orders is chosen. It is proven here that the two models are incomparable as long as k is bounded by a logarithmic function in the input length. <p>— It is shown that deterministic oblivious read-k -times BPs for an explicitly defined function require superpolynomial size, for k logarithmic in the input length, while there are Las Vegas oblivious read-twice BPs of linear size for this function. This is in contrast to the situation for OBDDs, for which the respective size measures are polynomially related. <p>— Furthermore, an explicitly defined function is presented for which randomized oblivious read-k -times BPs with bounded error require exponential size, while the function as well as its complement can be represented in polynomial size by nondeterministic oblivious read-k -times BPs and deterministic oblivious read-(k+1) -times BPs, where k=o(log n) .     

Sketching human character animations by composing sequences from large motion database

Quick creation of 3D character animations is an important task in game design, simulations, forensic animation, education, training, and more. We present a framework for creating 3D animated characters using a simple sketching interface coupled with a large, unannotated motion database that is used to find the appropriate motion sequences corresponding to the input sketches. Contrary to the previous work that deals with static sketches, our input sketches can be enhanced by motion and rotation curves that improve matching in the context of the existing animation sequences. Our framework uses animated sequences as the basic building blocks of the final animated scenes, and allows for various operations with them such as trimming, resampling, or connecting by use of blending and interpolation. A database of significant and unique poses, together with a two-pass search running on the GPU, allows for interactive matching even for large amounts of poses in a template database. The system provides intuitive interfaces, an immediate feedback, and poses very small requirements on the user. A user study showed that the system can be used by novice users with no animation experience or artistic talent, as well as by users with an animation background. Both groups were able to create animated scenes consisting of complex and varied actions in less than 20 minutes.     

Online Coloring of Bipartite Graphs with and without Advice

In the online version of the well-known graph coloring problem, the vertices appear one after the other together with the edges to the already known vertices and have to be irrevocably colored immediately after their appearance. We consider this problem on bipartite, i.e., two-colorable graphs. We prove that at least ?1.13746?log₂(n)?0.49887? colors are necessary for any deterministic online algorithm to be able to color any given bipartite graph on n vertices, thus improving on the previously known lower bound of ?log₂ n?+1 for sufficiently large n. Recently, the advice complexity was introduced as a method for a fine-grained analysis of the hardness of online problems. We apply this method to the online coloring problem and prove (almost) tight linear upper and lower bounds on the advice complexity of coloring a bipartite graph online optimally or using 3 colors. Moreover, we prove that \(O(\sqrt{n})\) advice bits are sufficient for coloring any bipartite graph on n vertices with at most ?log₂ n? colors.