An Introduction to Closed/Open Neighborhood Sums: Minimax, Maximin, and Spread

For a graph G of order |V(G)| = n and a real-valued mapping f:V(G)?\mathbbR{f:V(G)\rightarrow\mathbb{R}}, if S ì V(G){S\subset V(G)} then f(S)=?_{w ? S} f(w){f(S)=\sum_{w\in S} f(w)} is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, NS[f]=max{f(N[v])|v ? V(G)}{NS[f]={\rm max}\{f(N[v])|v \in V(G)\}} and NS(f)=max{f(N(v))|v ? V(G)}{NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, NS^-[f]=min{f(N[v])|v ? V(G)}{NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}} and NS^-(f)=min{f(N(v))|v ? V(G)}{NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}. For W ì \mathbbR{W\subset \mathbb{R}}, the closed and open neighborhood sum parameters are NS_W[G]=min{NS[f]|f:V(G)? W{NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W} is a bijection} and NS_W(G)=min{NS(f)|f:V(G)? W{NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W} is a bijection}. The lower neighbor sum parameters are NS^-_W[G]=maxNS^-[f]|f:V(G)? W{NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W} is a bijection} and NS^-_W(G)=maxNS^-(f)|f:V(G)? W{NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W} is a bijection}. For bijections f:V(G)? {1,2,?,n}{f:V(G)\rightarrow \{1,2,\ldots,n\}} we consider the parameters NS[G], NS(G), NS ⁻[G] and NS ⁻(G), as well as two parameters minimizing the maximum difference in neighborhood sums.     

On the mechanisms involved in the recovery of envelope information from temporal fine structure

Three experiments were designed to provide psychophysical evidence for the existence of envelope information in the temporal fine structure (TFS) of stimuli that were originally amplitude modulated (AM). The original stimuli typically consisted of the sum of a sinusoidally AM tone and two unmodulated tones so that the envelope and TFS could be determined a priori. Experiment 1 showed that normal-hearing listeners not only perceive AM when presented with the Hilbert fine structure alone but AM detection thresholds are lower than those observed when presenting the original stimuli. Based on our analysis, envelope recovery resulted from the failure of the decomposition process to remove the spectral components related to the original envelope from the TFS and the introduction of spectral components related to the original envelope, suggesting that frequency- to amplitude-modulation conversion is not necessary to recover envelope information from TFS. Experiment 2 suggested that these spectral components interact in such a way that envelope fluctuations are minimized in the broadband TFS. Experiment 3 demonstrated that the modulation depth at the original carrier frequency is only slightly reduced compared to the depth of the original modulator. It also indicated that envelope recovery is not specific to the Hilbert decomposition.     

The enhancement effect: evidence for adaptation of inhibition using a binaural centering task

The enhancement effect is consistently shown when simultaneously masked stimuli are preceded by the masker alone, with a reduction in the amount of masking relative to when that precursor is absent. One explanation for this effect proposed by Viemeister and Bacon [(1982). J. Acoust. Soc. Am. 71, 1502-1507] is the adaptation of inhibition, which predicts that an enhanced component (the "target") will be effectively more intense within the auditory system than one that has not been enhanced. Forward masking studies have indicated this effect of increased gain; however, other explanations of the enhancement effect have also been suggested. In order to provide an alternative measure of the amount of effective gain for an enhanced target, a subjective binaural centering task was used in which listeners matched the intensities of enhanced and unenhanced 2-kHz tones presented to opposite ears to produce a centered stimulus. The results showed that the enhancement effect produces an effective 4-5 dB increase in the level of the enhanced target. The enhancement effect was also measured using other enhancement paradigms which yielded similar results over a range of levels for the target, supporting an account based on adaptation of inhibition.     

Multilayer thin-film inspection through measurements of reflection coefficients

A vibration-insensitive interferometer is described to measure the thickness, refraction index and surface profile of thin-film stack at normal incidence. By satisfying the continuous boundary conditions of electric and magnetic fields at interfaces in a multilayer film stack, the reflection coefficient phase of the thin-film stack can be distinguished from the phase of spatial path difference, thus thickness and refraction index can be extracted. The experiment results showed that the measurement precision is significantly increased after the phase analysis was added into the reflectance analysis.     

EEG topography-specific BOLD changes: a continuous EEG-fMRI study in a patient with focal epilepsy

Blood oxygenation level dependent (BOLD) response related to interictal activity was evaluated in a patient with post-traumatic focal epilepsy at repeated continuous electroencephalogram (EEG)-functional magnetic resonance imaging examinations. Lateralized interictal EEG activity induced a main cluster of activation co-localized with the anatomical lesion. Spreading of EEG interictal activity to both frontal lobes evoked bilateral clusters of activation indicating that topography of BOLD response might depend on the spatial distribution of epileptiform activity.     

The Influence of Ripeness on the Phenolic Content,Antioxidant and Antimicrobial Activities of Pumpkins (Cucurbita moschata Duchesne)

Cucurbita moschata Duchesne (Cucurbitaceae) is a plant food highly appreciated for the content of nutrients and bioactive compounds, including polyphenols and carotenoids, which contribute to its antioxidant and antimicrobial capacities. The purpose of this study was to identify phenolic acids and flavonoids of Cucurbita moschata Duchesne using high-performance liquid chromatography–diode array detection–electrospray ionization tandem mass spectrometry (HPLC–DAD–ESI-MS) at different ripening stages (young, mature, ripened) and determine its antioxidant and antimicrobial activities. According to the results, phenolic acids and flavonoids were dependent on the maturity stage. The mature fruits contain the highest total phenolic and flavonoids contents (97.4 mg GAE. 100 g⁻¹ and 28.6 mg QE. 100 g⁻¹).A total of 33 compounds were identified. Syringic acid was the most abundant compound (37%), followed by cinnamic acid (12%) and protocatechuic acid (11%). Polyphenol extract of the mature fruits showed the highest antioxidant activity when measured by DPPH (0.065 μmol TE/g) and ABTS (0.074 μmol TE/g) assays. In the antimicrobial assay, the second stage of ripening had the highest antibacterial activity. Staphylococcus aureus was the most sensitive strain with an inhibition zone of 12 mm and a MIC of 0.75 mg L⁻¹. The lowest inhibition zone was obtained with Salmonella typhimurium (5 mm), and the MIC value was 10 mg L⁻¹.     

Fluoropropenoates as dienophiles in the Diels-Alder reaction

Several fluorinated alkenes were prepared from known ethyl (R)-2-fluoro-4,5-dihydroxyisopropylidine-2-pentenoate (1). The fluoroalkenoates were tested as dienophiles with several dienes and showed cycloaddition only with the very reactive diene, 1,3-diphenylisobenzofuran (5). Fluorobutenolide 2 reacted with 5 to produce the endo-syn adduct 9 in a highly stereoselective manner.     

An electrochemiluminescence-based competitive displacement immunoassay for the type-2 brevetoxins in oyster extracts

A new competitive electrochemiluminescence-based immunoassay for the type-2 brevetoxins in oyster extracts was developed. The assay was verified by spiking known amounts of PbTx-3 into 80% methanol extracts of Gulf Coast oysters. We also provide preliminary data demonstrating that 100% acetone extracts, aqueous homogenates, and the clinical matrixes urine and serum can also be analyzed without significant matrix interferences. The assay offers the advantages of speed ( 2 h analysis time); simplicity (only 2 additions, one incubation period, and no wash steps before analysis); low limit of quantitation (conservatively, 50 pg/mL = 1 ng/g tissue equivalents); and a stable, nonradioactive label. Due to the variety of brevetoxin metabolites present and the lack of certified reference standards for liquid chromatography-mass spectrometry confirmation, a true validation of brevetoxins in shellfish extracts is not possible at this time. However, our assay correlated well with another brevetoxin immunoassay currently in use in the United States. We believe this assay could be useful as a regulatory screening tool and could support pharmacokinetic studies in animals and clinical evaluation of neurotoxic shellfish poisoning victims.