Hierarchy Theorems for Property Testing

Referring to the query complexity of property testing, we prove the existence of a rich hierarchy of corresponding complexity classes. That is, for any relevant function q, we prove the existence of properties that have testing complexity Θ(q). Such results are proven in three standard domains often considered in property testing: generic functions, adjacency predicates describing (dense) graphs, and incidence functions describing bounded-degree graphs. While in two cases, the proofs are quite straightforward, and the techniques employed in the case of the dense graph model seem significantly more involved. Specifically, problems that arise and are treated in the latter case include (1) the preservation of distances between graph under a blow-up operation and (2) the construction of monotone graph properties that have local structure.     

Optimization-based method for calculating water networks with user specified characteristics

This paper addresses problem of designing water usage network that consists of fixed flow rate water using processes. A design method is founded on the solution of mixed-integer linear programming (MILP) model of network superstructure. The application of optimization to solve basic formulation of network synthesis has been reported in some works. However, this approach applies certain extensions of the standard formulation that allow accounting for several industrial scenarios. In particular, it is possible to apply various performance indices and imposing conditions on continuous variables as well as on network topology. Multiple contaminant case is easily accounted for. At least but not at last, the method is able to generate several solutions of identical values of major performance indices but of different structure and other features. All these possibilities are available within single optimization framework. Several examples are given to illustrate advantages of the approach.     

Water network design with stochastic optimization approach

Water network (called also water allocation) problem has been addressed in more than 200 papers to date – see recent reviews by Je?owski (2010) and Foo (2009). Though various solution methods have been developed they all have some limitations. This paper addresses water usage network with regeneration processes. Multiple contaminants and two types of water using processes are taken into regard. Simultaneous one stage optimization method was developed to synthesize the network. In order to solve complex MINLP formulation we propose to apply meta-heuristic optimization – adaptive random search method.The paper contains detailed solution algorithm. Several examples with specific features are solved to show efficiency and flexibility of the approach.     

Structure, energy, and structural transformations of graphene grain boundaries from atomistic simulations

Domain/grain boundaries are often introduced into graphene during chemical vapor deposition growth processes. Here, we performed a series of hybrid molecular dynamics simulations to study the structures, energies, and structural transformations of symmetric tilt grain boundaries of graphene. The grain boundary comprises an array of edge dislocations, with the dislocation density increasing upon increasing the grain boundary misorientation angle. The dislocation in the zigzag-oriented grain boundary contains an edge-sharing pentagon/heptagon defect, whereas the dislocation in the armchair-oriented grain boundary contains two paired pentagon/heptagon defects. In some grain boundaries, out-of-plane buckling exists due to the presence of dislocations. In the transition region (the region between the zigzag- and armchair-oriented grain boundaries), the grain boundary structures feature complex mixtures of both zigzag and armchair grain boundaries. We also discuss the grain boundary transformations and migrations that occur upon adding or removing carbon atoms at the grain boundaries for all of our investigated types of grain boundaries.     

Simultaneous preferential crystallization in a coupled batch operation mode. Part II: Experimental study and model refinement

In the previous part of this series a parametric study was presented to assess theoretically the performance of a novel crystallizer configuration. Complementary, the present work addresses a comprehensive, systematic experimental examination accompanied by an analysis of some relevant process parameters (mass of seeds, CSD of seeds, starting point for the mother liquor exchange, process duration) of two general concepts for preferential crystallization in which the amino acid threonine dissolved in water was used as a model system. In the first step of investigations, the impact of these process parameters was studied for conventional single batch crystallization. The experimental results are discussed and compared with the theoretical ones. Moreover, a configuration consisting of two coupled crystallization vessels was investigated. The specific manipulation of the concentration profiles of each enantiomer in solution as well as of the temperature profiles was found to be suitable to enhance the process performance. This is reflected by higher achievable process productivities and higher product purities.     

Photoinduced and thermal oxidation of rapeseed and sunflower oils

The aim of the present study was to compare oxidative stability of different sunflower and rapeseed oils. Ultra violet (UV) irradiation was used as an accelerator of the oil oxidation process. After UV irradiation, the formed volatile compounds were extracted by headspace solid‐phase microextraction HS‐SPME (DVB/CAR/PDMS fibre) and analysed by gas chromatography coupled with a flame ionization detector (GC/FID). At the same time, the same oil samples were thermally oxidized. The induction periods were determined on the basis of hexanal to 2‐trans‐nonenal ratio in the analysed samples. Finally, the obtained results were compared with induction period values obtained through the determination of peroxide and anisidine values, and from the Rancimat method, manostatic test and differential scanning calorimetry (DSC) method. The results obtained using the new method were well correlated with those achieved with the well‐established analytical techniques. The values of the induction period obtained after UV/HS‐SPME/GC/FID were up to three times higher than those from Rancimat, but the correlation between these two methods was on a very good level (correlation coefficient R>0.98). Similar correlation was also observed between these new methods and the DSC or manostatic test. In all cases, better results were obtained for rapeseed oils than sunflower oils.     

Heat and mass transfer during microwave‐convective drying

The article presents a mathematical model of drying that describes the kinetics of combined microwave‐convective drying for the process as a whole. Based on this model, the drying curves and the temperature evolutions of the drying body were constructed by a number of computer‐simulated drying programs, which were chosen to follow the respective experimental processes carried out on a cylindrical sample made of kaolin. The experimental data allowed both the estimate of material coefficients arising in the model and the validation of the theory. A very satisfactory correlation of the theoretical predictions with the experimental data is found. The main novelty of this article is the mathematically complete drying model that describes all periods of the microwave‐convective drying process. Application of such a complete model is necessary if we want to optimize drying processes with respect to drying time and consumption of energy via computer simulations. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Interference mitigation in WSN by means of directional antennas and duty cycle control

Network spanning algorithms, such as ZigBee‐native and Stojmenovič, constitute a crucial element in the wireless sensor network design, by determining its potential for reliability and fault‐tolerance. The interconnections between nodes have a great impact on the radio interference level present in such a network and may create a serious electromagnetic compatibility issue in some cases. It can be proved that the total interference incurred by a statistical node can be diminished in two ways: either by using directional antennas or by setting an upper limit on the duty cycle of each network node. Copyright © 2010 John Wiley & Sons, Ltd.     

Proton CSI without solvent suppression with strongly reduced field gradient related sideband artifacts

Object

Non-water-suppressed MRSI (magnetic resonance spectroscopy imaging) offers a number of advantages; however, spectra are hampered by the sideband artifacts. The origin of those is associated with the vibration of the gradient coils, and most of the sidebands are assumed to be related to the crusher gradients. The aim was to examine the dependency between the physical direction of the crushers and the sidebands. Additionally, the possibilities of optimization of the point resolved spectroscopy sequence (PRESS) were investigated.

Materials and methods

For the assessment of the sidebands, spectra at short echo time (TE) were collected at 3 T from standard water phantom. A homemade agar phantom was used to test the optimal strength of the crusher gradients. Optimized PRESS sequence was tested in vivo.

Results

The greatest sidebands were found to be associated with the crusher gradient in x-direction. Agar phantom and in vivo measurements revealed that reduction of the crusher’s strength to 5 mT/m could provide a significant minimization of the sidebands without raising the unwanted signals produced by volume selection.

Conclusion

This study demonstrates that crusher gradients in different directions produce a unique pattern of the sidebands. Moreover, optimization of the strength of crushers has been found to decrease sidebands so, the remaining part could be reduced in postprocessing.