Balanced Energy/Time Optimal Defibrillation

The synthesis of a cardiac defibrillating pulse is cast as a standard optimal feedback control problem that minimizes a weighted measure of consumed energy and elapsed time to reach a nominal defibrillated state. The solution is developed for a general first-order system that includes the widely used parallel resistor/capacitor circuit and energy source as a special case. The novel optimal pulse comprises an exponentially ascending and a rectangular component; it is agile and energy conscious; and it therefore outperforms the waveforms developed thus far that minimize energy or time expenditures alone. Explicit time-domain expressions are derived which may be used for comparing against other commonly studied defibrillating functions. The analytic formulas and computer simulations may be useful to implement performance improvements in defibrillating devices.

Trace and Density Results on Regular Trees

The boundary of a regular tree can be viewed as a Cantor-type set. We equip our tree with a weighted distance and a weighted measure via the Euclidean arc-length and consider the associated first-order Sobolev spaces. We give characterizations for the existence of traces and for the density of compactly supported functions.

Evaluating Rank-Coherence of Crowd Rating in Customer Satisfaction

Crowd rating is a continuous and public process of data gathering that allows the display of general quantitative opinions on a topic from online anonymous networks as they are crowds. Online platforms leveraged these technologies to improve predictive tasks in marketing. However, we argue for a different employment of crowd rating as a tool of public utility to support social contexts suffering to adverse selection, like tourism. This aim needs to deal with issues in both method of measurement and analysis of data, and with common biases associated to public disclosure of rating information. We propose an evaluative method to investigate fairness of common measures of rating procedures with the peculiar perspective of assessing linearity of the ranked outcomes. This is tested on a longitudinal observational case of 7 years of customer satisfaction ratings, for a total amount of 26.888 reviews. According to the results obtained from the sampled dataset, analysed with the proposed evaluative method, there is a trade-off between loss of (potentially) biased information on ratings and fairness of the resulting rankings. However, computing an ad hoc unbiased ranking case, the ranking outcome through the time-weighted measure is not significantly different from the ad hoc unbiased case.

Some isoperimetric inequalities with respect to monomial weights

We solve a class of isoperimetric problems on $\mathbb{R}^2_+ $ with respect to monomial weights. Let $\alpha $ and $\beta $ be real numbers such that $0\le \alpha <\beta+1$, $\beta\le 2 \alpha$. We show that, among all smooth sets $\Omega$ in $\mathbb{R} ^2_+$ with fixed weighted measure $\iint_{\Omega } y^{\beta} dxdy$, the weighted perimeter $\int_{\partial \Omega } y^\alpha \, ds$ achieves its minimum for a smooth set which is symmetric w.r.t. to the $y$--axis, and is explicitly given. Our results also imply an estimate of a weighted Cheeger constant and a bound for eigenvalues of some nonlinear problems.

Casein haplotype diversity in seven dairy goat breeds

Selection, drift, gene flow and breeding have extensively shaped the genomic variability of domestic animals. In goat species, several mutations identified within the casein genes have been shown to affect the level of gene expression of milk production traits. The four casein genes – CSN1S1, CSN2, CSN1S2 and CSN3 – are organized in a cluster of 250 kb located in chromosome 6, and due to tight linkage, their genetic variability is well depicted by haplotypes which are transmitted to the progeny. Thirty single nucleotide polymorphisms (SNPs) located within the casein gene cluster were used to characterize the haplotype variability of six southern Italian goat breeds (Girgentana, Maltese, Rossa Mediterranea, Argentata dell'Etna, Messinese, Capra dell'Aspromonte). A representative sample of the Norwegian dairy goat breed (Norsk melkegeit) has been used as an out-group to obtain a weighted measure of genetic diversity in the metapopulation. A total of 54 haplotypes were detected among the seven breeds: 26, 9, 8 and 11 haplotypes were found at CSN1S1, CSN2, CSN1S2 and CSN3 respectively. The number of haplotypes per breed was 14 (Norwegian), 26 (Messinese), 27 (Rossa Mediterranea and Girgentana) and 31 (Maltese, Argentata dell'Etna and Capra dell'Aspromonte). The Maltese breed showed the highest number of private haplotypes, whereas the Norwegian goat recorded the highest number of shared haplotypes. The linkage disequilibrium analysis showed higher levels of association for the SNP pairs within casein loci than SNP pairs between casein loci, likely reflecting low levels of intra-genic recombination. The highest linkage disequilibrium values were found in CSN1S1 and CSN2 genes in all the breeds, except for Argentata dell'Etna and Rossa Mediterranea. The resolution of the haplotype diversity at the casein cluster can be exploited both for selective and conservative plans.

Relevance of Education to Occupation: A New Empirical Approach Based on College Courses

We introduce a new approach to measuring the match between education and occupation by using the number of college courses related to one’s occupation. Previous studies have only considered the match between college “major” and occupation. This approach ignores the content of education and the courses taken in college. We find that taking courses in college that are relevant to one’s occupation is significantly associated with higher wages, which can be taken as evidence against the notion that returns to college are principally a matter of signaling. We further find that performing well in these courses is associated with an even higher wage premium. A student’s wage increases, on average, by 1.6–2.9 percent for each matched course. This effect increases to 2.3–3.8 percent when we use a grade weighted measure of match.

On the Limiting Weak-type Behaviors for Maximal Operators Associated with Power Weighted Measure

Let $\unicode[STIX]{x1D6FD}\geqslant 0$ , let $e_{1}=(1,0,\ldots ,0)$ be a unit vector on $\mathbb{R}^{n}$ , and let $d\unicode[STIX]{x1D707}(x)=|x|^{\unicode[STIX]{x1D6FD}}dx$ be a power weighted measure on $\mathbb{R}^{n}$ . For $0\leqslant \unicode[STIX]{x1D6FC}<n$ , let $M_{\unicode[STIX]{x1D707}}^{\unicode[STIX]{x1D6FC}}$ be the centered Hardy-Littlewood maximal function and fractional maximal functions associated with measure $\unicode[STIX]{x1D707}$ . This paper shows that for $q=n/(n-\unicode[STIX]{x1D6FC})$ , $f\in L^{1}(\mathbb{R}^{n},d\unicode[STIX]{x1D707})$ , $$\begin{eqnarray}\displaystyle \lim _{\unicode[STIX]{x1D706}\rightarrow 0+}\unicode[STIX]{x1D706}^{q}\unicode[STIX]{x1D707}(\{x\in \mathbb{R}^{n}:M_{\unicode[STIX]{x1D707}}^{\unicode[STIX]{x1D6FC}}f(x)>\unicode[STIX]{x1D706}\})=\frac{\unicode[STIX]{x1D714}_{n-1}}{(n+\unicode[STIX]{x1D6FD})\unicode[STIX]{x1D707}(B(e_{1},1))}\Vert f\Vert _{L^{1}(\mathbb{R}^{n},d\unicode[STIX]{x1D707})}^{q}, &amp; &amp; \displaystyle \nonumber\\ \displaystyle \lim _{\unicode[STIX]{x1D706}\rightarrow 0+}\unicode[STIX]{x1D706}^{q}\unicode[STIX]{x1D707}\left(\left\{x\in \mathbb{R}^{n}:\left|M_{\unicode[STIX]{x1D707}}^{\unicode[STIX]{x1D6FC}}f(x)-\frac{\Vert f\Vert _{L^{1}(\mathbb{R}^{n},d\unicode[STIX]{x1D707})}}{\unicode[STIX]{x1D707}(B(x,|x|))^{1-\unicode[STIX]{x1D6FC}/n}}\right|>\unicode[STIX]{x1D706}\right\}\right)=0, &amp; &amp; \displaystyle \nonumber\end{eqnarray}$$ which is new and stronger than the previous result even if $\unicode[STIX]{x1D6FD}=0$ . Meanwhile, the corresponding results for the un-centered maximal functions as well as the fractional integral operators with respect to measure $\unicode[STIX]{x1D707}$ are also obtained.