A compact olfactometer for IMS measurements and testing human perception

Production of easily controllable and measurable odor stimuli is needed when studying human olfaction, olfaction-related physiology and psychological reactions to odors. Controlled odor producing instruments are called olfactometers. For testing and calibrating new olfactometers or sensor arrays, a reliable input signal has to be produced to verify their accurate functionality. A common input signal in various olfactometers has been the use of volatile organic compounds (VOCs) in gaseous form. We present a compact olfactometer able to produce controlled continuous odor stimuli from three individual channels. For measuring the output gas flow, we used a ChemPro 100i (Environics, Finland) device that is based on aspiration ion mobility spectrometry (aIMS). IMS is a robust and sensitive method for measuring VOCs and is used especially in detecting toxic industrial chemicals and chemical warfare agents, but the technology is also suitable for other olfactory-related applications. The olfactometer was used to produce synthetic jasmine scent using three main odor components from jasmine oil and all the components were diluted using propylene glycol. The dilutions were supplied to the system using programmable syringe pumps, which guided the dilutions to individual evaporation units. We conducted experiments to verify the functionality of our olfactometer. Analysis of the ChemPro100i data showed that olfactometer can use different odor components to produce continuous, stable output flows with controlled concentrations.     

Packing dimension and Ahlfors regularity of porous sets in metric spaces

Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dim_p(A) ￡ s-cr^s{{\rm {dim}_p}(A)\le s-c\varrho^s} where dim_p is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that dim_p(A) ￡ dim_p(X)-c(log\tfrac1r)^-1r^t{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} .     

A Note on Toeplitz’ Conjecture

In 1911, Toeplitz made a conjecture asserting that every Jordan curve in $\mathbb{R}^{2}$ contains four points forming the corners of a square. Here Conjecture C is presented, which states that the side length of the largest square on a closed curve that consists of edges of an n×n grid is at least $1/\sqrt{2}$ times the side length of the largest axis-aligned square contained inside the curve. Conjecture C implies Toeplitz’ conjecture and is verified computationally for n≤13.     

Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity

In this paper we give several global characterisations of the Hörmander class \(\Psi ^m(G)\) of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.     

Scale factor local search in differential evolution

This paper proposes the scale factor local search differential evolution (SFLSDE). The SFLSDE is a differential evolution (DE) based memetic algorithm which employs, within a self-adaptive scheme, two local search algorithms. These local search algorithms aim at detecting a value of the scale factor corresponding to an offspring with a high performance, while the generation is executed. The local search algorithms thus assist in the global search and generate offspring with high performance which are subsequently supposed to promote the generation of enhanced solutions within the evolutionary framework. Despite its simplicity, the proposed algorithm seems to have very good performance on various test problems. Numerical results are shown in order to justify the use of a double local search instead of a single search. In addition, the SFLSDE has been compared with a standard DE and three other modern DE based metaheuristic for a large and varied set of test problems. Numerical results are given for relatively low and high dimensional cases. A statistical analysis of the optimization results has been included in order to compare the results in terms of final solution detected and convergence speed. The efficiency of the proposed algorithm seems to be very high especially for large scale problems and complex fitness landscapes.     

Enumerating Perfect Matchings in n-Cubes

The perfect matchings in the n-cube have earlier been enumerated for n?≤?6. A dynamic programming approach is here used to obtain the total number of perfect matchings in the 7-cube, which is 391 689 748 492 473 664 721 077 609 089. The number of equivalence classes of perfect matchings is further shown to be 336 in the 5-cube, 356 788 059 in the 6-cube and 607 158 046 495 120 886 820 621 in the 7-cube. The techniques used can be generalized to arbitrary bipartite and general graphs.     

Functional magnetic resonance imaging reference phantom

Functional magnetic resonance imaging (fMRI) is widely used to pinpoint active brain areas. Changes in neuronal activity modulate the local blood oxygenation level, and the associated modulation of the magnetic field homogeneity can be detected with magnetic resonance imaging. Thus, the blood oxygenation level-dependent (BOLD) fMRI indirectly measures neuronal activity. Similar modulation of magnetic field homogeneity was here elicited by other means to generate a BOLD-like change in a new phantom constructed to provide reference activations during fMRI. Magnetic inhomogeneities were produced by applying current to coils located near the phantom containing 1.5 ml of Gd-doped water. The signal-to-noise ratio of the images, produced by gradient-recalled echo-planar imaging, varied between 104 and 107 at a selected voxel when the field was and was not inhomogenized, respectively. The contrast of signals between homogeneous and inhomogeneous conditions was generally stable, except in 3% of time points. During the periods of greatest deviations an observable change would have been detected in a simultaneously measured BOLD signal. Such changes could result from the imaging method or occur through glitches in hardware or alterations in the measurement environment. With identical measurement setups, the phantom could allow comparing intersession or intersubject brain activations.     

Synthesis and NMR characterization of the cis and trans isomers of [Pt(II)(N9-adeH)2(pz)2] and X-ray crystallography of the trans isomer

The reaction of tetrapyrazine Pt(II) with adenine under basic conditions yielded two products both disubstituted by adenine and bound in all cases to the N-9 nitrogen of adenine. Crystals amenable to X-crystallographic analysis were obtained for one product which was consequently identified as trans-[Pt(II)(N9-adeH)2(pz)2](NO3)(4).H2O. The other product, though, was identified as the cis isomer based on extensive and comparative NMR structural studies whereby the two compounds were examined as both neutral and tetraprotonated species in solution. The major product of the reaction was unexpectedly the cis isomer, thus obtained in contrast to the trans effect, and the reason for this result is speculated on. Computational calculations using DFT at the B3LYP/TZVP-MARI-J level of theory provided the head-to-tail conformer as the overwhelmingly more stable species over the head-to-head conformer for both compounds whilst the trans product was found to be more stable than the cis. Thus the reaction does not follow a thermodynamic course and rather is kinetically controlled in concert with the speculated mode of reaction.     

Wavelet formulation of the polarizable continuum model

The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF‐PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N^1.5 scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010