Cohomologies of Generalized Complex Manifolds and Nilmanifolds

We study generalized complex cohomologies of generalized complex structures constructed from certain symplectic fiber bundles over complex manifolds. We apply our results in the case of left-invariant generalized complex structures on nilmanifolds and to their space of small deformations.     

Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality

We define the concept of reproducible map and show that, whenever the constraint map defining the quasivariational inequality (QVI) is reproducible then one can characterize the whole solution set of the QVI as a union of solution sets of some variational inequalities (VI). By exploiting this property, we give sufficient conditions to compute any solution of a generalized Nash equilibrium problem (GNEP) by solving a suitable VI. Finally, we define the class of pseudo-Nash equilibrium problems, which are (not necessarily convex) GNEPs whose solutions can be computed by solving suitable Nash equilibrium problems.     

Rapid liquid chromatography–tandem mass spectrometry analysis of 4-hydroxynonenal for the assessment of oxidative degradation and safety of vegetable oils

A novel method for the UHPLC–MS/MS analysis of (E)-4-hydroxynonenal (4-HNE) is described. The method is based on derivatization of 4-HNE with pentafluorophenylhydrazine (1) or 4-trifluoromethylphenylhydrazine (2) in acetonitrile in the presence of trifluoroacetic acid as catalyst at room temperature and allows complete analysis of one sample of vegetable oil in only 21 min, including sample preparation and chromatography. The method involving hydrazine 1, implemented in an ion trap instrument with analysis of the transition m/z 337 → 154 showed LOD = 10.9 nM, average accuracy of 101% and precision ranging 2.5–4.0% RSD intra-day (2.7–4.1% RSD inter-day), with 4-HNE standard solutions. Average recovery from lipid matrices was 96.3% from vaseline oil, 91.3% from sweet almond oil and 105.3% from olive oil. The method was tested on the assessment of safety and oxidative degradation of seven samples of dietary oil (soybean, mixed seeds, corn, peanut, sunflower, olive) and six cosmetic-grade oils (avocado, blackcurrant, apricot kernel, echium, sesame, wheat germ) and effectively detected increased 4-HNE levels in response to chemical (Fenton reaction), photochemical, or thermal stress and aging, aimed at mimicking typical oxidation associated with storage or industrial processing. The method is a convenient, cost-effective and reliable tool to assess quality and safety of vegetable oils.     

Large deviations for generalized Polya urns with arbitrary urn function

We consider a generalized two-color Polya urn (black and white balls) first introduced by Hill et al. (1980), where the urn composition evolves as follows: let $\pi :\left[0,1\right]\to \left[0,1\right]$, and denote by $x_n$ the fraction of black balls after step $n$, then at step $n+1$ a black ball is added with probability $\pi \left(x_n\right)$ and a white ball is added with probability $1?\pi \left(x_n\right)$. Originally introduced to mimic attachment under imperfect information, this model has found applications in many fields, ranging from Market Share modeling to polymer physics and biology.In this work we discuss large deviations for a wide class of continuous urn functions $\pi$. In particular, we prove that this process satisfies a Sample-Path Large Deviations principle, also providing a variational representation for the rate function. Then, we derive a variational representation for the limit

$?\left(s\right)=\underset{n\to \infty }{lim}\frac{1}{n}log\mathbb{P}\left(n{x}_n=?sn?\right),s\in \left[0,1\right],$

where $n{x}_n$ is the number of black balls at time $n$, and use it to give some insight on the shape of $?\left(s\right)$. Under suitable assumptions on $\pi$ we are able to identify the optimal trajectory. We also find a non-linear Cauchy problem for the Cumulant Generating Function and provide an explicit analysis for some selected examples. In particular we discuss the linear case, which embeds the Bagchi–Pal Model [6], giving the exact implicit expression for $?$ in terms of the Cumulant Generating Function.     

A Comparison of Dose Metrics to Predict Local Tumor Control for Photofrin‐mediated Photodynamic Therapy

This preclinical study examines light fluence, photodynamic therapy (PDT) dose and “apparent reacted singlet oxygen,” [¹O₂]_rx, to predict local control rate (LCR) for Photofrin‐mediated PDT of radiation‐induced fibrosarcoma (RIF) tumors. Mice bearing RIF tumors were treated with in‐air fluences (50–250 J cm^?2) and in‐air fluence rates (50–150 mW cm^?2) at Photofrin dosages of 5 and 15 mg kg^?1 and a drug‐light interval of 24 h using a 630‐nm, 1‐cm‐diameter collimated laser. A macroscopic model was used to calculate [¹O₂]_rx and PDT dose based on in vivo explicit dosimetry of the drug concentration, light fluence and tissue optical properties. PDT dose and [¹O₂]_rx were defined as a temporal integral of drug concentration and fluence rate, and singlet oxygen concentration consumed divided by the singlet oxygen lifetime, respectively. LCR was stratified for different dose metrics for 74 mice (66 + 8 control). Complete tumor control at 14 days was observed for [¹O₂]_rx ≥ 1.1 mm or PDT dose ≥1200 μm J cm^?2 but cannot be predicted with fluence alone. LCR increases with increasing [¹O₂]_rx and PDT dose but is not well correlated with fluence. Comparing dosimetric quantities, [¹O₂]_rx outperformed both PDT dose and fluence in predicting tumor response and correlating with LCR.     

Crystal growth of progesterone metastable and stable polymorphs by polymer induced herteronucleation (PIHn) method

The selective crystallization of progesterone polymorphs prepared by Polymer‐Induced Heteronucleation (PIHn) method was investigated. Polyvinyl alcohol (PVA), hydroxypropyl methylcellulose (HPMC), dextran, gelatin, polyisoprene (PI), and acrylonitrile/butadiene copolymer (NBR) were used as heteronucleants. Crystallizations were conducted from 0.5, 10 and 40 mg mL⁻¹ solutions in chloroform at room temperature by solvent evaporation. The samples were characterized by X‐ray powder diffraction, differential scanning calorimetry, infrared spectroscopy and scanning electron microscopy. Form 2 was obtained from 0.5 mg mL⁻¹ solution in almost all polymers. A mixture of both polymorphs crystallized from the three concentrations on gelatine; from 10 and 40mg mL⁻¹ on PVA and HPMC and, from 10 mg mL⁻¹ solutions on NBR. Form 2 crystallized on HPMC was stable for three months under ambient stress conditions (40ºC and 75% RH). These results are good evidence that the tailoring of new formulations and devices with progesterone the metastable and more soluble form 2 is possible.     

Robust optimal quantum gates for Josephson charge qubits

Quantum optimal control theory allows us to design accurate quantum gates. We employ it to design high-fidelity two-bit gates for Josephson charge qubits in the presence of both leakage and noise. Our protocol considerably increases the fidelity of the gate and, more important, it is quite robust in the disruptive presence of 1/f noise. The improvement in the gate performances discussed in this work (errors approximately 10(-3)-10(-4) in realistic cases) allows us to cross the fault tolerance threshold.     

Singing proficiency in the general population

Most believe that the ability to carry a tune is unevenly distributed in the general population. To test this claim, we asked occasional singers (n=62) to sing a well-known song in both the laboratory and in a natural setting (experiment 1). Sung performances were judged by peers for proficiency, analyzed for pitch and time accuracy with an acoustic-based method, and compared to professional singing. The peer ratings for the proficiency of occasional singers were normally distributed. Only a minority of the occasional singers made numerous pitch errors. The variance in singing proficiency was largely due to tempo differences. Occasional singers tended to sing at a faster tempo and with more pitch and time errors relative to professional singers. In experiment 2 15 nonmusicians from experiment 1 sang the same song at a slow tempo. In this condition, most of the occasional singers sang as accurately as the professional singers. Thus, singing appears to be a universal human trait. However, two of the occasional singers maintained a high rate of pitch errors at the slower tempo. This poor performance was not due to impaired pitch perception, thus suggesting the existence of a purely vocal form of tone deafness.