Discovering the roots: Uniform closure results for algebraic classes under factoring

Newton iteration (NI) is an almost 350 years old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. In this form, the process yields a better circuit complexity in the case when the number of roots $r$ is small but the multiplicities are exponentially large. Our method sets up a linear system in $r$ unknowns and iteratively builds the roots as formal power series. For an algebraic circuit $f(x_1,\ldots,x_n)$ of size $s$ we prove that each factor has size at most a polynomial in: $s$ and the degree of the squarefree part of $f$. Consequently, if $f_1$ is a $2^{\Omega(n)}$-hard polynomial then any nonzero multiple $\prod_{i} f_i^{e_i}$ is equally hard for arbitrary positive $e_i$'s, assuming that $\sum_i \text{deg}(f_i)$ is at most $2^{O(n)}$. It is an old open question whether the class of poly($n$)-sized formulas (resp. algebraic branching programs) is closed under factoring. We show that given a polynomial $f$ of degree $n^{O(1)}$ and formula (resp. ABP) size $n^{O(\log n)}$ we can find a similar size formula (resp. ABP) factor in randomized poly($n^{\log n}$)-time. Consequently, if determinant requires $n^{\Omega(\log n)}$ size formula, then the same can be said about any of its nonzero multiples. As part of our proofs, we identify a new property of multivariate polynomial factorization. We show that under a random linear transformation $\tau$, $f(\tau\overline{x})$ completely factors via power series roots. Moreover, the factorization adapts well to circuit complexity analysis. This with allRootsNI are the techniques that help us make progress towards the old open problems, supplementing the large body of classical results and concepts in algebraic circuit factorization (eg. Zassenhaus, J.NT 1969, Kaltofen, STOC 1985-7 \& Burgisser, FOCS 2001).Comment: 33 Pages, No figure

Direct microscopy versus sputum cytology analysis and bleach sedimentation for diagnosis of tuberculosis: a prospective diagnostic study.

ABSTRACT: BACKGROUND: Diagnostic options for pulmonary tuberculosis in resource-poor settings are commonly limited to smear microscopy. We investigated whether bleach concentration by sedimentation and sputum cytology analysis (SCA) increased the positivity rate of smear microscopy for smear-positive tuberculosis. METHODS: We did a prospective diagnostic study in a Medecins Sans Frontieres-supported hospital in Mindouli, Republic of Congo. Three sputum samples were obtained from 280 consecutive pulmonary tuberculosis suspects, and were processed according to WHO guidelines for direct smear microscopy. The remainder of each sputum sample was homogenised with 2.6% bleach, sedimented overnight, smeared, and examined blinded to the direct smear result for acid-fast bacilli (AFB). All direct smears were assessed for quality by SCA. If a patient produced fewer than three good-quality sputum samples, further samples were requested. Sediment smear examination was performed independently of SCA result on the corresponding direct smear. Positivity rates were compared using McNemar's test. RESULTS: Excluding SCA, 43.2% of all patients were diagnosed as positive on direct microscopy of up to three samples. 47.9% were diagnosed on sediment microscopy, with 48.2% being diagnosed on direct microscopy, sediment microscopy, or both. The positivity rate increased from 43.2% to 47.9% with a case definition of one positive smear ([greater than or equal to]1 AFB/100 high power fields) of three, and from 42.1% to 43.9% with two positive smears. SCA resulted in 87.9% of patients producing at least two good-quality sputum samples, with 75.7% producing three or more. Using a case definition of one positive smear, the incremental yield of bleach sedimentation was 14/121, or 11.6% (95% CI 6.5-18.6, p=0.001) and in combination with SCA was 15/121, or 12.4% (95% CI 7.1-19.6, p=0.002). Incremental yields with two positive smears were 5/118, or 4.2% (95% CI 1.4-9.6, p=0.062) and 7/118, or 5.9% (95% CI 2.4-11.8, p=0.016), respectively. CONCLUSIONS: The combination of bleach sedimentation and SCA resulted in significantly increased microscopy positivity rates with a case definition of either one or two positive smears. Implementation of bleach sedimentation led to a significant increase in the diagnosis of smear-positive patients. Implementation of SCA did not result in significantly increased diagnosis of tuberculosis, but did result in improved sample quality. Requesting extra sputum samples based on SCA results, combined with bleach sedimentation, could significantly increase the detection of smear-positive patients if routinely implemented in resource-limited settings where gold standard techniques are not available. We recommend that a pilot phase is undertaken before routine implementation to determine the impact in a particular context

Outputs and cost of HIV prevention programmes for truck drivers in Andhra Pradesh, India

<p>Abstract</p> <p>Background</p> <p>HIV prevention programmes for truck drivers form part of the HIV control efforts, but systematic data on the outputs and cost of providing such services in India are not readily available for further planning and use of resources.</p> <p>Methods</p> <p>Detailed cost and output data were collected from written records and interviews for 2005–2006 fiscal year using standardized methods at six sampled HIV prevention programmes for truck drivers in the Indian state of Andhra Pradesh. The total economic cost for these programmes was computed and the relation of unit cost of services per truck driver with programme scale was assessed using regression analysis.</p> <p>Results</p> <p>A total of 120,436 truck drivers were provided services by the six programmes of which 55.9% were long distance truck drivers. The annual economic cost of providing services to a truck driver varied between programmes from US$1.52 to 4.56 (mean US$ 2.49). There was an inverse relation between unit economic cost of serving a truck driver and scale of the programme (R²= 0.63; p = 0.061). The variation between programmes in the average number of contacts made by the programme staff with truck drivers was 1.3 times versus 5.8 times for contacts by peer educators. Only 1.7% of the truck drivers were referred by the programmes for counseling and HIV testing.</p> <p>Conclusion</p> <p>These data provide information for further planning of HIV prevention programmes for truck drivers and estimating the resources needed for such programmes. The findings suggest the need to strengthen the role of peer educators and increase referral of truck drivers for HIV testing.</p

Lead-free piezoceramics - Where to move on?

Lead-free piezoceramics aiming at replacing the market-dominant lead-based ones have been extensively searched for more than a decade worldwide. Some noteworthy outcomes such as the advent of commercial products for certain applications have been reported, but the goal, i.e., the invention of a lead-free piezocermic, the performance of which is equivalent or even superior to that of PZT-based piezoceramics, does not seem to be fulfilled yet. Nevertheless, the academic effort already seems to be culminated, waiting for a guideline to a future research direction. We believe that a driving force for a restoration of this research field needs to be found elsewhere, for example, intimate collaborations with related industries. For this to be effectively realized, it would be helpful for academic side to understand the interests and demands of the industry side as well as to provide the industry with new scientific insights that would eventually lead to new applications. Therefore, this review covers some of the issues that are to be studied further and deeper, so-to-speak, lessons from the history of piezoceramics, and some technical issues that could be useful in better understanding the industry demands. As well, the efforts made in the industry side will be briefly introduced for the academic people to catch up with the recent trends and to be guided for setting up their future research direction effectively.ope

Mathematical modeling of the West Africa Ebola epidemic

As of November 2015, the Ebola virus disease (EVD) epidemic that began in West Africa in late 2013 is waning. The human toll includes more than 28,000 EVD cases and 11,000 deaths in Guinea, Liberia, and Sierra Leone, the most heavily-affected countries. We reviewed 66 mathematical modeling studies of the EVD epidemic published in the peer-reviewed literature to assess the key uncertainties models addressed, data used for modeling, public sharing of data and results, and model performance. Based on the review, we suggest steps to improve the use of modeling in future public health emergencies. DOI: http://dx.doi.org/10.7554/eLife.09186.00

Scientific Opinion on the re-evaluation of hexamethylene tetramine (E 239) as a food additive

Hexamethylene tetramine (HMT) is a food additive, currently only permitted in EU for use in Provolone cheese. The maximum permitted level is 25 mg/kg residual amount, expressed as formaldehyde, the break down product of HMT under acidic conditions. HMT has been previously evaluated by the Joint Expert Committee on Food Additives (JECFA, 1974) who established an ADI of 0.15 mg/kg bw/day based on a reproductive study with a NOEL of 15 mg/kg bw/day. Due to the limitations in the database the Panel could not identify a critical study and therefore to derive an ADI. However, the Panel noted that the exposure to formaldehyde from HMT of high level consumers of Provolone cheese equalled 18 µg formaldehyde/kg bw/day in adults and could be as high as 87 µg formaldehyde/kg bw/day in children according to a theoretical conservative assumption that all ripened cheese consumed was Provolone cheese. Considering the estimated exposure from the very limited permitted use, the toxicological database on HMT, the data from use of HMT therapeutically, the available oral toxicity and toxicokinetic data of formaldehyde and the magnitude of the potential effect on intracellular formaldehyde levels arising from this use of HMT, the Panel concluded that the use of HMT in Provolone cheese at the MPL of 25 mg/kg residual amount, expressed as formaldehyde, would not be of safety concern. However the Panel considered that any increase in the permitted uses of HMT or increases in the MPL of 25 mg /kg residual amount, expressed as formaldehyde would need detailed assessment which might require new toxicity data as well as use levels and/or an evaluation of its impact on formaldehyde levels in vivo

Food systems as drivers of optimal nutrition and health – Complexities and opportunities for research and implementation

The Sustainable Development Goals (SDGs) are intricately linked to food systems. Addressing challenges in food systems is key to meeting the SDGs in Africa and South Asia, where undernutrition and micronutrient deficiencies persist, alongside increased nutrition transition, overweight and obesity, and related chronic diseases. Suboptimal diets are a key risk factor for mortality and 3 billion people cannot afford a healthy diet; in addition, food systems are not prioritizing environmental sustainability. Optimizing food systems and increasing agricultural productivity beyond calories, to nutrient-rich vegetables and fruits, legumes, and livestock, and sustainable fishing, are required. Strengthening of research around food systems—on pathways, value chains, and development and validation of metrics of diet quality—is required. The development of new technology in crop management and pest control and addressing natural resource degradation is key. Engaging with the public and private sectors, outreach to donors and policymakers, and strengthening cross-disciplinary collaborations are imperative to improving food systems

A review of photovoltaic module technologies for increased performance in tropical climate

The global adoption and use of photovoltaic modules (PVMs) as the main source of energy is the key to realising the UN Millennium Development Goals on Green Energy. The technology – projected to contribute about 20% of world energy supply by 2050, over 60% by 2100 and leading to 50% reduction in global CO2 emissions – is threatened by its poor performance in tropical climate. Such performance discourages its regional acceptance. The magnitude of crucial module performance influencing factors (cell temperature, wind speed and relative humidity) reach critical values of 90 °C, 0.2 m/s and 85%, respectively in tropical climates which negatively impact module performance indices which include power output (PO), power conversion efficiency (PCE) and energy payback time (EPBT). This investigation reviews PVM technologies which include cell, contact and interconnection technologies. It identifies critical technology route(s) with potential to increase operational reliability of PVMs in the tropics when adopted. The cell performance is measured by PO, PCE and EPBT while contacts and interconnections performance is measured by the degree of recombination, shading losses and also the rate of thermo-mechanical degradation. It is found that the mono-crystalline cell has the best PCE of 25% while the Cadmium Telluride (CdTe) cell has the lowest EPBT of 8-months. Results show that the poly-crystalline cell has the largest market share amounting to 54%. The CdTe cell exhibits 0% drop in PCE at high-temperatures and low irradiance operations – demonstrating least affected PO by the conditions. Further results establish that back contacts and back-to-back interconnection technologies produce the least recombination losses and demonstrate absence of shading in addition to possessing longest interconnection fatigue life. Based on these findings, the authors propose a PVM comprising CdTe cell, back contacts and back-to-back interconnection technologies as the technology with latent capacity to produce improved performance in tropical climates