On the expressiveness of subset-sum representations

We develop a general theory for representing information as sums of elements in a subset of the basic set A of numbers of cardinality n, often refered to as a “knapsack vector”. How many numbers can be represented in this way depends heavily on n. The lower, resp. upper, bound for the cardinality of the set of representable numbers is quadratic, resp. exponential, in terms of n. We give an algorithm for the construction of a knapsack vector of any prescribed expressiveness (that is, the cardinality of the set of representable numbers), provided it falls within the range possible for expressiveness. Received: 13 March 1997 / 18 November 1999     

Characterizing the generalized lambda distribution by L-moments

The generalized lambda distribution (GLD) is a flexible four parameter distribution with many practical applications. L-moments of the GLD can be expressed in closed form and are good alternatives for the central moments. The L-moments of the GLD up to an arbitrary order are presented, and a study of L-skewness and L-kurtosis that can be achieved by the GLD is provided. The boundaries of L-skewness and L-kurtosis are derived analytically for the symmetric GLD and calculated numerically for the GLD in general. Additionally, the contours of L-skewness and L-kurtosis are presented as functions of the GLD parameters. It is found that with an exception of the smallest values of L-kurtosis, the GLD covers all possible pairs of L-skewness and L-kurtosis and often there are two or more distributions that share the same L-skewness and the same L-kurtosis. Examples that demonstrate situations where there are four GLD members with the same L-skewness and the same L-kurtosis are presented. The estimation of the GLD parameters is studied in a simulation example where method of L-moments compares favorably to more complicated estimation methods. The results increase the knowledge on the distributions that belong to the GLD family and can be utilized in model selection and estimation.     

Geometric solution strategy of Laplace problems with free boundary

This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Michromatic scope for enhancement of color difference

A michromatic (microscope plus chromatic) scope is a device that enhances the color discrimination between two spectral color datasets. Three spectral filters are required, instead of the conventional red, green, and blue filters, for the implementation of a michromatic camera. In this study, we describe two approaches to the design of these filters: in the first case, the design is based on the direct optimization of the filter characteristics (transmittance), whereas in the second case, the design is based on the nonnegative tensor factorization (NTF) of the spectral datasets. A michromatic camera can be implemented using these filters along with compatible postprocessing in‐camera firmware. Here, we performed experiments with two color datasets: one comprising skin and vein colors, and one comprising skin and cosmetics colors. These were further divided into a training set and a test set. The filters were defined using the training set, and the operation of the filters was tested and magnified using the test set. Our experiments demonstrated that the proposed approaches are suitable for color discrimination. For the first color dataset, the enhancement produced using the optimized filters was up to 252% of the original value, and the average color difference ΔE was increased from 2.82 to 9.93. NTF and preprocessing further enhanced the ΔE up to 21.84. For the second color dataset, NTF and postprocessing enhanced the ΔE from 4.33 to 29.19. The proposed discrimination enhancement could be physically implemented in a designated digital charge‐coupled device camera with proper filter installation and compatible postprocessing. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Urgent need for new approach to energy policy: The case of Finland

The process of climate change is already under way and is a serious threat facing the planet. Our response to this threat will irrevocably transform the energy sector and the priorities within it. The trend in emissions over the next decade will largely determine whether the process of climate change can be kept at a moderate level. This literature-based study focuses on Finland as an example case. Oil price fluctuations, economic development and changes in consumer values and attitudes are key forces that will drive change in the energy sector. A greater diversity of energy sources is vital if we are to avoid a catastrophic warming of the climate. The use of renewable energy sources must be increased, and the efficiency of producing, transmitting and distributing energy must be improved. The energy sector must also exploit the potential of nuclear energy, wind, solar and hydro power, afforestation measures, biomass resources, carbon capture and storage (CCS) technology and the nano-bio sector. National policies and measures must be set out in detail and global cooperation enhanced. The presence and impact of factors that impede the work to curb climate change must also be taken into account in energy strategies if these strategies are to be successful.     

Breath figure templated semifluorinated block copolymers with tunable surface properties and binding capabilities

Patterning of functionalized polymeric surfaces enables the adjustment of their characteristics and use in novel applications. We prepared breath figure (BF) films from three semifluorinated diblock copolymers, which all are composed of a polystyrene block and a semifluorinated one to compare their surface properties. “Click” chemistry was employed to one of the polymers, containing a poly(pentafluorostyrene) block to incorporate hydrophilic sugar or carboxylic acid moieties. The structure of the polymer alters the obtained porous morphology of the films. Contact angle (CA) analyses of the BF films reveals that the surface porosity increases water CAs compared with solvent cast films, and, in the case of hydrophobic polymers, leads to significant increase in the CAs of dodecane. The hydrophobicity of the BF films is further amplified by the removal of the topmost layer which leads in some cases to superhydrophobic surfaces. BF films containing glucose units are hydrophilic exhibiting water CAs below 90°. These glycosylated porous surfaces are shown to bind lectin Con A‐FITC or can be labelled with isothiocyanate marker. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41225.     

Multiple heat pulses during PCR extension enabling amplification of GC-rich sequences and reducing amplification bias

PCR amplification over GC-rich and/or long repetitive sequences is challenging because of thermo-stable structures resulting from incomplete denaturation, reannealing, and self-annealing of target sequences. These structures block the DNA polymerase during the extension step, leading to formation of incomplete extension products and favoring amplification of nonspecific products rather than specific ones. We have introduced multiple heat pulses in the extension step of a PCR cycling protocol to temporarily destabilize such blocking structures, in order to enhance DNA polymerase extension over GC-rich sequences. With this novel type of protocol, we were able to amplify all expansions of CGG repeats in five Fragile X cell lines, as well as extremely GC-rich nonrepetitive segments of the GNAQ and GP1BB genes. The longest Fragile X expansion contained 940 CGG repeats, corresponding to about 2.8 kilo bases of 100% GC content. For the GNAQ and GP1BB genes, different length PCR products in the range of 700 bases to 2 kilobases could be amplified without addition of cosolvents. As this technique improves the balance of amplification efficiencies between GC-rich target sequences of different length, we were able to amplify all of the allelic expansions even in the presence of the unexpanded allele.     

Criteria for the matrix equivalence of words

This paper investigates the criteria for deciding whether two words are matrix equivalent. Certain upper diagonal matrices, generally referred to as the Parikh matrices, have been widely investigated because of their usefulness in computing the numbers of subword occurrences and thereby characterizing words by numbers. However, apart from the binary alphabet, not much is known about the properties of the matrix equivalent words, that is, words possessing the same matrix. The paper investigates both the general criteria, as well as the criteria valid in natural special cases. An exhaustive solution is obtained for ternary alphabets.     

Transposition invariant words

We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out that transposition invariant words have a simple interpretation by means of elementary group theory. This leads us to investigate some properties of the ring of integers modulo n$n$ and primitive roots. In particular, we show that there are infinitely many prime numbers p$p$ with a primitive root dividing p+1$p+1$ and infinitely many prime numbers p$p$ without a primitive root dividing p+1$p+1$. We also consider the orbit of a word under transposition.     

Chemoenzymatic Preparation of Enantiopure Homoadamantyl β‐Amino Acid and β‐Lactam Derivatives

Racemic cis‐10‐azatetracyclo[7.2.0.1^2,6.1^4,8]tridecan‐11‐one was prepared from homoadamant‐4‐ene by chlorosulfonyl isocyanate addition. The transformation of the β‐lactam to the corresponding β‐amino ester followed by Candida antarctica lipase A‐catalyzed enantioselective (E>>200) N‐acylation with 2,2,2‐trifluoroethyl butanoate afforded methyl (1R,4R,5S,8S)‐5‐aminotricyclo[4.3.1.1^3,8]undecane‐4‐carboxylate and the (1S,4S,5R,8R)‐butanamide with>99% ee at 50% conversion. Alternatively, transformation of the β‐lactam to the corresponding N‐hydroxymethyl‐β‐lactam and the following Pseudomonas cepacia (currently Burkholderia cepacia) lipase‐catalyzed enantioseletive O‐acylation provided the (1S,4S,6R,9R)‐alcohol (ee=87%) and the corresponding (1R,4R,6S,9S)‐butanoate (ee>99%). In the latter method, competition for the enzyme between the (1R,4R,6S,9S)‐butanoate, 2,2,2‐trifluoroethyl butanoate and the hydrolysis product, butanoic acid, tended to stop the reaction at about 45% conversion and finally gave racemization in the (1S,4S,6R,9R)‐alcohol with time.