Generating cryptographically-strong random lattice bases and recognizing rotations of Zn\mathbb{Z}^n

Lattice-based cryptography relies on generating random bases which are difficult to fully reduce. Given a lattice basis (such as the private basis for a cryptosystem), all other bases are related by multiplication by matrices in $GL(n,\mathbb{Z})$. How can one sample random elements from $GL(n,\mathbb{Z})$? We consider various methods, finding some are stronger than others with respect to the problem of recognizing rotations of the $\mathbb{Z}^n$ lattice. In particular, the standard algorithm of multiplying unipotent generators together (as implemented in Magma's RandomSLnZ command) generates instances of this last problem which can be efficiently broken, even in dimensions nearing 1,500. Similar weaknesses for this problem are found with the random basis generation method in one of the NIST Post-Quantum Cryptography competition submissions (DRS). Other algorithms are described which appear to be much stronger.Comment: 24 pages, 2 figure

Reconstruction of cell surface densities of ion pumps, exchangers, and channels from mRNA expression, conductance kinetics, whole-cell calcium, and current-clamp voltage recordings, with an application to human uterine smooth muscle cells

Uterine smooth muscle cells remain quiescent throughout most of gestation, only generating spontaneous action potentials immediately prior to, and during, labor. This study presents a method that combines transcriptomics with biophysical recordings to characterise the conductance repertoire of these cells, the ‘conductance repertoire’ being the total complement of ion channels and transporters expressed by an electrically active cell. Transcriptomic analysis provides a set of potential electrogenic entities, of which the conductance repertoire is a subset. Each entity within the conductance repertoire was modeled independently and its gating parameter values were fixed using the available biophysical data. The only remaining free parameters were the surface densities for each entity. We characterise the space of combinations of surface densities (density vectors) consistent with experimentally observed membrane potential and calcium waveforms. This yields insights on the functional redundancy of the system as well as its behavioral versatility. Our approach couples high-throughput transcriptomic data with physiological behaviors in health and disease, and provides a formal method to link genotype to phenotype in excitable systems. We accurately predict current densities and chart functional redundancy. For example, we find that to evoke the observed voltage waveform, the BK channel is functionally redundant whereas hERG is essential. Furthermore, our analysis suggests that activation of calcium-activated chloride conductances by intracellular calcium release is the key factor underlying spontaneous depolarisations

Labor-associated gene expression in the human uterine fundus, lower segment, and cervix

Background Preterm labor, failure to progress, and postpartum hemorrhage are the common causes of maternal and neonatal mortality or morbidity. All result from defects in the complex mechanisms controlling labor, which coordinate changes in the uterine fundus, lower segment, and cervix. We aimed to assess labor-associated gene expression profiles in these functionally distinct areas of the human uterus by using microarrays. Methods and Findings Samples of uterine fundus, lower segment, and cervix were obtained from patients at term (mean +/- 6 SD = 39.1 +/- 0.5 wk) prior to the onset of labor (n = 6), or in active phase of labor with spontaneous onset (n = 7). Expression of 12,626 genes was evaluated using microarrays ( Human Genome U95A; Affymetrix) and compared between labor and non-labor samples. Genes with the largest labor-associated change and the lowest variability in expression are likely to be fundamental for parturition, so gene expression was ranked accordingly. From 500 genes with the highest rank we identified genes with similar expression profiles using two independent clustering techniques. Sets of genes with a probability of chance grouping by both techniques less than 0.01 represented 71.2%, 81.8%, and 79.8% of the 500 genes in the fundus, lower segment, and cervix, respectively. We identified 14, 14, and 12 those sets of genes in the fundus, lower segment, and cervix, respectively. This enabled networks of coregulated and co-expressed genes to be discovered. Many genes within the same cluster shared similar functions or had functions pertinent to the process of labor. Conclusions Our results provide support for many of the established processes of parturition and also describe novel-to-labor genes not previously associated with this process. The elucidation of these mechanisms likely to be fundamental for controlling labor is an important prerequisite to the development of effective treatments for major obstetric problems - including prematurity, with its long-term consequences to the health of mother and offspring

Towards understanding the myometrial physiome: approaches for the construction of a virtual physiological uterus

Premature labour (PTL) is the single most significant factor contributing to neonatal morbidity in Europe with enormous attendant healthcare and social costs. Consequently, it remains a major challenge to alleviate the cause and impact of this condition. Our ability to improve the diagnosis and treatment of women most at risk of PTL is, however, actually hampered by an incomplete understanding of the ways in which the functions of the uterine myocyte are integrated to effect an appropriate biological response at the multicellular whole organ system. The level of organization required to co-ordinate labouring uterine contractile effort in time and space can be considered immense. There is a multitude of what might be considered mini-systems involved, each with their own regulatory feedback cycles, yet they each, in turn, will influence the behaviour of a related system. These include, but are not exclusive to, gestational-dependent regulation of transcription, translation, post-translational modifications, intracellular signaling dynamics, cell morphology, intercellular communication and tissue level morphology. We propose that in order to comprehend how these mini-systems integrate to facilitate uterine contraction during labour (preterm or term) we must, in concert with biological experimentation, construct detailed mathematical descriptions of our findings. This serves three purposes: firstly, providing a quantitative description of series of complex observations; secondly, proferring a database platform that informs further testable experimentation; thirdly, advancing towards the establishment of a virtual physiological uterus and in silico clinical diagnosis and treatment of PTL

Myometrial transcriptional signatures of human parturition

The process of parturition involves the transformation of the quiescent myometrium (uterine smooth muscle) to the highly contractile laboring state. This is thought to be driven by changes in gene expression in myometrial cells. Despite the existence of multiple myometrial gene expression studies, the transcriptional programs that initiate labor are not known. Here, we integrated three transcriptome datasets, one novel (NCBI Gene Expression Ominibus: GSE80172) and two existing, to characterize the gene expression changes in myometrium associated with the onset of labor at term. Computational analyses including classification, singular value decomposition, pathway enrichment, and network inference were applied to individual and combined datasets. Outcomes across studies were integrated with multiple protein and pathway databases to build a myometrial parturition signaling network. A high-confidence (significant across all studies) set of 126 labor genes were identified and machine learning models exhibited high reproducibility between studies. Labor signatures included both known (interleukins, cytokines) and unknown (apoptosis, , cell proliferation/differentiation) pathways while cyclic AMP signaling and muscle relaxation were associated with non-labor. These signatures accurately classified and characterized the stages of labor. The data-derived parturition signaling networks provide new genes/signaling interactions to understand phenotype-specific processes and aid in future studies of parturition

Mammography screening: views from women and primary care physicians in Crete

Background: Breast cancer is the most commonly diagnosed cancer among women and a leading cause of death from cancer in women in Europe. Although breast cancer incidence is on the rise worldwide, breast cancer mortality over the past 25 years has been stable or decreasing in some countries and a fall in breast cancer mortality rates in most European countries in the 1990s was reported by several studies, in contrast, in Greece have not reported these favourable trends. In Greece, the age-standardised incidence and mortality rate for breast cancer per 100.000 in 2006 was 81,8 and 21,7 and although it is lower than most other countries in Europe, the fall in breast cancer mortality that observed has not been as great as in other European countries. There is no national strategy for screening in this country. This study reports on the use of mammography among middleaged women in rural Crete and investigates barriers to mammography screening encountered by women and their primary care physicians. Methods: Design: Semi-structured individual interviews. Setting and participants: Thirty women between 45–65 years of age, with a mean age of 54,6 years, and standard deviation 6,8 from rural areas of Crete and 28 qualified primary care physicians, with a mean age of 44,7 years and standard deviation 7,0 serving this rural population. Main outcome measure: Qualitative thematic analysis. Results: Most women identified several reasons for not using mammography. These included poor knowledge of the benefits and indications for mammography screening, fear of pain during the procedure, fear of a serious diagnosis, embarrassment, stress while anticipating the results, cost and lack of physician recommendation. Physicians identified difficulties in scheduling an appointment as one reason women did not use mammography and both women and physicians identified distance from the screening site, transportation problems and the absence of symptoms as reasons for non-use. Conclusion: Women are inhibited from participating in mammography screening in rural Crete. The provision of more accessible screening services may improve this. However physician recommendation is important in overcoming women's inhibitions. Primary care physicians serving rural areas need to be aware of barriers preventing women from attending mammography screening and provide women with information and advice in a sensitive way so women can make informed decisions regarding breast caner screening

Breast cancer incidence and mortality in Tyrol/Austria after fifteen years of opportunistic mammography screening

<p>Abstract</p> <p>Background</p> <p>The aim of this study was to analyse breast cancer incidence and mortality in Tyrol from 1970 to 2006, namely after performing more than a decade of opportunistic mammography screening and just before piloting an organised screening programme. Our investigation was conducted on a population level.</p> <p>Methods</p> <p>To study time trends in breast cancer incidence and mortality, we applied the age-period-cohort model by Poisson regression to the official mortality data covering more than three decades from 1970 to 2006 and to the incidence data ranging from 1988 to 2006. In addition, for incidence data we analysed data on breast cancer staging and compared these with EU guidelines.</p> <p>Results</p> <p>For the analysis of time trend in breast cancer mortality in age groups 40-79, an age-period-cohort model fits well and shows for years 2002-2006 a statistically significant reduction of 26% (95% CI 13%-36%) in breast cancer mortality as compared to 1992-1996.</p> <p>We see only slight non-significant increases in breast cancer incidence. For the past five years, incidence data show a 10% proportion of in situ cases, and of 50% for cases in stages II+.</p> <p>Conclusions</p> <p>The opportunistic breast cancer screening programme in Tyrol has only in part exploited the mortality reduction known for organised screening programmes. There seems to be potential for further improvement, and we recommend that an organised screening programme and a detailed screening database be introduced to collect all information needed to analyse the quality indicators suggested by the EU guidelines.</p

Quantification of the effect of mammographic screening on fatal breast cancers: The Florence Programme 1990–96

Breast cancer cases diagnosed in women aged 50–69 since 1990 to 1996 in the City of Florence were partitioned into those who had been invited to screening prior to diagnosis and those who had not. All cases were followed up for vital status until 31 December 1999. The cumulative number of breast cancer deaths among the cases were divided by screening and invitation status, to give the rates of cancers proving fatal within a period of 8 years of observation (incidence-based mortality). We used the incidence-based mortality rates for two periods (1985–86, 1990–96), pre and during screening. The incidence-based mortality ratio comparing 1990–96 and 1985–86 was 0.50 (95% CI : 0.38–0.66), a significant 50% reduction. For noninvited women, compared to 1985-86, there was a 41% significant mortality reduction (RR=0.59, 95% CI : 0.42–0.82). The comparable reduction in those invited was a significant 55% (RR=0.45, 95% CI : 0.32–0.61). The incidence ratio of rates of cancers stage II or worse was close to one when the noninvited in 1990–96 were compared with 1985–86 (RR=0.97, 95% CI : 0.78–1.21). Excluding prevalent cases, the rate of stage II+ breast cancer cases was 42% lower in Screened women compared with the noninvited (RR=0.58, 95% CI : 0.45–0.74). This study confirmed that new treatments and the first rounds of the screening programme contributed to reducing mortality from breast cancer