Metric Embedding via Shortest Path Decompositions

We study the problem of embedding shortest-path metrics of weighted graphs into $\ell_p$ spaces. We introduce a new embedding technique based on low-depth decompositions of a graph via shortest paths. The notion of Shortest Path Decomposition depth is inductively defined: A (weighed) path graph has shortest path decomposition (SPD) depth $1$. General graph has an SPD of depth $k$ if it contains a shortest path whose deletion leads to a graph, each of whose components has SPD depth at most $k-1$. In this paper we give an $O(k^{\min\{\frac{1}{p},\frac{1}{2}\}})$-distortion embedding for graphs of SPD depth at most $k$. This result is asymptotically tight for any fixed $p>1$, while for $p=1$ it is tight up to second order terms. As a corollary of this result, we show that graphs having pathwidth $k$ embed into $\ell_p$ with distortion $O(k^{\min\{\frac{1}{p},\frac{1}{2}\}})$. For $p=1$, this improves over the best previous bound of Lee and Sidiropoulos that was exponential in $k$; moreover, for other values of $p$ it gives the first embeddings whose distortion is independent of the graph size $n$. Furthermore, we use the fact that planar graphs have SPD depth $O(\log n)$ to give a new proof that any planar graph embeds into $\ell_1$ with distortion $O(\sqrt{\log n})$. Our approach also gives new results for graphs with bounded treewidth, and for graphs excluding a fixed minor

Metabolomics of Muscle-specific Beef Color Stability

Inherent metabolite differences in muscles can significantly affect biochemical properties and meat color. The objective was to compare metabolite profile differences between beef longissimus and psoas muscles during display. Beef short loins were collected 3 d postmortem (n = 10). Steaks were cut from each longissimus lumborum (LL) and psoas major (PM) muscles and displayed under retail conditions for 7 d. Surface color, biochemical properties, and metabolomics were analyzed during display. Psoas major discolored (P < 0.05) by d 3 compared with longissimus lumborum. There were significant differences in metabolite concentrations (P < 0.05) for each muscle type at each time point. Sugars, amino acids, Tricarboxylic acid cycle substrates and glycolytic substrates were detected in both muscles. Glycolytic metabolites like pyruvic acid, glucose–6–phosphate and, fructose were greater in LL at all display times. TCA metabolites, citric acid, and succinic acid, which were lower in concentration on d0, in LL, became overabundant in LL by d 7. The amino acid carnitine was lower in LL at all display times. The results suggest that in addition to muscle - specific differences in mitochondrial and enzyme activities, inherent metabolite differences also can contribute to muscle color stability.Animal Scienc

Achieving Privacy

Is privacy a luxury for the rich? Remarkably, there is a dearth of literature evaluating whether data privacy is too costly for companies to implement or too expensive for governments to enforce. This paper is the first to offer a review of the costs of compliance and to summarize national budgets for enforcement. Our study suggests that, while privacy may indeed prove costly for companies to implement and may present a special burden for small and medium-sized businesses, it is not too costly for governments to enforce. Indeed, the European Union, seen as a global champion of privacy, expends less than a dollar a year per citizen on data protection enforcement. Effective data protection agencies are not prohibitively costly, even for small administrations, especially if they collaborate through regional bodies. This study will help inform governments as they fashion and implement privacy laws to address the “privacy enforcement gap”—the disparity between privacy on the books and privacy on the ground

Achieving Privacy: Costs of Compliance and Enforcement of Data Protection Regulation

Is privacy a luxury for the rich world? Remarkably, there is a dearth of literature evaluating whether data privacy is too costly for companies to implement, or too expensive for governments to enforce. This paper is the first to offer a review of surveys of costs of compliance, and to summarize national budgets for enforcement. The study shows that while privacy may indeed prove costly for companies to implement, it is not too costly for governments to enforce. This study will help inform governments as they fashion and implement privacy laws to address the “privacy enforcement gap”—the disparity between the privacy on the books, and the privacy on the ground

Development of Learning Resources within Higher Education in Response to the Challenges of COVID 19

This brief paper describes how additional learning resources can be developed at a module level within higher education. The context to further meet the requirements of a rapidly changing environment within the higher education context and to meet different trends and challenges such as employers’ expectations and challenges facing graduates to secure appropriate employment considering their disciplines. The case study reflects key considerations to ensure further students’ success as universities in the UK shifted from face-to-face delivery to quick online delivery due to the challenges presented by the Covid-19 virus spreading in the UK and Globally. In addition, the case study provides key considerations during the curriculum development process, such as constructive alignment, students’ backgrounds and diversity, and utilization of additional resources at the organizational level, such as Library Services and I

Comparative Anatomy of Chromosomal Domains with Imprinted and Non-Imprinted Allele-Specific DNA Methylation

Allele-specific DNA methylation (ASM) is well studied in imprinted domains, but this type of epigenetic asymmetry is actually found more commonly at non-imprinted loci, where the ASM is dictated not by parent-of-origin but instead by the local haplotype. We identified loci with strong ASM in human tissues from methylation-sensitive SNP array data. Two index regions (bisulfite PCR amplicons), one between the C3orf27 and RPN1 genes in chromosome band 3q21 and the other near the VTRNA2-1 vault RNA in band 5q31, proved to be new examples of imprinted DMRs (maternal alleles methylated) while a third, between STEAP3 and C2orf76 in chromosome band 2q14, showed non-imprinted haplotype-dependent ASM. Using long-read bisulfite sequencing (bis-seq) in 8 human tissues we found that in all 3 domains the ASM is restricted to single differentially methylated regions (DMRs), each less than 2kb. The ASM in the C3orf27-RPN1 intergenic region was placenta-specific and associated with allele-specific expression of a long non-coding RNA. Strikingly, the discrete DMRs in all 3 regions overlap with binding sites for the insulator protein CTCF, which we found selectively bound to the unmethylated allele of the STEAP3-C2orf76 DMR. Methylation mapping in two additional genes with non-imprinted haplotype-dependent ASM, ELK3 and CYP2A7, showed that the CYP2A7 DMR also overlaps a CTCF site. Thus, two features of imprinted domains, highly localized DMRs and allele-specific insulator occupancy by CTCF, can also be found in chromosomal domains with non-imprinted ASM. Arguing for biological importance, our analysis of published whole genome bis-seq data from hES cells revealed multiple genome-wide association study (GWAS) peaks near CTCF binding sites with ASM

Different Rho GTPase–dependent signaling pathways initiate sequential steps in the consolidation of long-term potentiation

The releasable factor adenosine blocks the formation of long-term potentiation (LTP). These experiments used this observation to uncover the synaptic processes that stabilize the potentiation effect. Brief adenosine infusion blocked stimulation-induced actin polymerization within dendritic spines along with LTP itself in control rat hippocampal slices but not in those pretreated with the actin filament stabilizer jasplakinolide. Adenosine also blocked activity-driven phosphorylation of synaptic cofilin but not of synaptic p21-activated kinase (PAK). A search for the upstream origins of these effects showed that adenosine suppressed RhoA activity but only modestly affected Rac and Cdc42. A RhoA kinase (ROCK) inhibitor reproduced adenosine's effects on cofilin phosphorylation, spine actin polymerization, and LTP, whereas a Rac inhibitor did not. However, inhibitors of Rac or PAK did prolong LTP's vulnerability to reversal by latrunculin, a toxin which blocks actin filament assembly. Thus, LTP induction initiates two synaptic signaling cascades: one (RhoA-ROCK-cofilin) leads to actin polymerization, whereas the other (Rac-PAK) stabilizes the newly formed filaments