PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees

In this article we complete the proof---for a broad class of four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the four-manifold. This article is a revision of sections 4--7 of an earlier version, while a revision of sections 1--3 of that earlier version now appear in a separate companion article (math.DG/0007190). Here, we use our computations of Chern classes for the virtual normal bundles for the Seiberg-Witten strata from the companion article (math.DG/0007190), a comparison of all the orientations, and the PU(2) monopole cobordism to compute pairings with the links of level-zero Seiberg-Witten moduli subspaces of the moduli space of PU(2) monopoles. These calculations then allow us to compute low-degree Donaldson invariants in terms of Seiberg-Witten invariants and provide a partial verification of Witten's conjecture.Comment: Journal fur die Reine und Angewandte Mathematik, to appear; 65 pages. Revision of sections 4-7 of version v1 (December 1997

PU(2) monopoles and a conjecture of Marino, Moore, and Peradze

In this article we show that some of the recent results of Marino, Moore, and Peradze (math.DG/9812042, hep-th/9812055) -- in particular their conjecture that all closed, smooth four-manifolds with b_2^+ > 1 (and Seiberg-Witten simple type) are of `superconformal simple type' -- can be understood using a simple mathematical argument via the PU(2)-monopole cobordism of Pidstrigach and Tyurin (dg-ga/9507004) and results of the first and third authors (dg-ga/9712005, dg-ga/9709022).Comment: 13 pages, 1 figure. Improved exposition, typographical slips corrected, figure and references added. Minor correction on page 2. To appear in Mathematical Research Letter

Decoherence due to XPM-assisted Raman amplification for polarization or wavelength offset pulses in all-normal dispersion supercontinuum generation

We report the importance of cross-phase modulation (XPM) on the coherence of a low-energy probe pulse co-propagating with a high-energy pump pulse that generates incoherent supercontinuum in all-normal dispersion (ANDi) fiber due to Raman amplification of quantum noise. By investigating numerous fiber and pulse parameters, we show consistently that for weak probe pulses, the XPM from the pump is the dominant influence on the degradation of the probe coherence. We show that the faster decoherence at the pump leading edge means that the probe coherence is reduced more significantly when the probe has a higher group velocity, i.e., when an orthogonally polarized probe is aligned to the fast (lower refractive index) axis of the fiber or when a co-polarized probe has a longer central wavelength. Simulations show that this effect occurs for both polarization-maintaining (PM) and non-PM ANDi fibers and can result in a probe decoherence rate that is higher than that of the pump. These previously unreported results extend our earlier scalar simulations showing incoherent supercontinuum within a single pulse

Machine learning differentiates enzymatic and non-enzymatic metals in proteins

Metalloenzymes are 40% of all enzymes and can perform all seven classes of enzyme reactions. Because of the physicochemical similarities between the active sites of metalloenzymes and inactive metal binding sites, it is challenging to differentiate between them. Yet distinguishing these two classes is critical for the identification of both native and designed enzymes. Because of similarities between catalytic and non-catalytic metal binding sites, finding physicochemical features that distinguish these two types of metal sites can indicate aspects that are critical to enzyme function. In this work, we develop the largest structural dataset of enzymatic and non-enzymatic metalloprotein sites to date. We then use a decision-tree ensemble machine learning model to classify metals bound to proteins as enzymatic or non-enzymatic with 92.2% precision and 90.1% recall. Our model scores electrostatic and pocket lining features as more important than pocket volume, despite the fact that volume is the most quantitatively different feature between enzyme and non-enzymatic sites. Finally, we find our model has overall better performance in a side-to-side comparison against other methods that differentiate enzymatic from non-enzymatic sequences. We anticipate that our model’s ability to correctly identify which metal sites are responsible for enzymatic activity could enable identification of new enzymatic mechanisms and de novo enzyme design

Witten's conjecture and Property P

Let K be a non-trivial knot in the 3-sphere and let Y be the 3-manifold obtained by surgery on K with surgery-coefficient 1. Using tools from gauge theory and symplectic topology, it is shown that the fundamental group of Y admits a non-trivial homomorphism to the group SO(3). In particular, Y cannot be a homotopy-sphere.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper7.abs.html Version 5: links correcte

Noise-related polarization dynamics for femto and picosecond pulses in normal dispersion fibers

We report how the complex intra-pulse polarization dynamics of coherent optical wavebreaking and incoherent Raman amplification processes in all-normal dispersion (ANDi) fibers vary for femto and picosecond pump pulses. Using high temporal resolution vector supercontinuum simulations, we identify deterministic polarization dynamics caused by wavebreaking and self-phase modulation for femtosecond pulses and quasi-chaotic polarization evolution driven by Raman amplification of quantum noise for picosecond pulses. In contrast to cross-phase modulation instability, the Raman-based polarization noise has no power threshold and is reduced by aligning the higher energy polarization component with the lower index axis of the fiber. The degree of polarization stability is quantified using new time domain parameters that build on the spectrally averaged degree of coherence used in supercontinuum research to quantify the output spectral stability. We show that the spectral coherence is intrinsically linked to polarization noise, and that the noise will occur in both polarization maintaining (PM) and non-PM fibers, spanning a broad range of pulse energies, durations, and fiber birefringence values. This analysis provides an in-depth understanding of the nonlinear polarization dynamics associated with coherent and incoherent propagation in ANDi fibers

Assessment of Sodium Knowledge and Urinary Sodium Excretion among Regions of the United Arab Emirates: A Cross-Sectional Study

Non-communicable diseases (NCDs) such as cardiovascular disease, cancer and diabetes, are increasing worldwide and cause 65% to 78% of deaths in the Gulf Cooperation Council (GCC). A random sample of 477 healthy adults were recruited in the United Arab Emirates (UAE) in the period March-June 2015. Demographic, lifestyle, medical, anthropometric and sodium excretion data were collected. A questionnaire was used to measure knowledge, attitude and practice regarding salt. Mean sodium and potassium excretion were 2713.4 ± 713 mg/day and 1803 ± 618 mg/day, respectively, significantly higher than the World Health Organization (WHO) recommendations for sodium (2300 mg/day) and lower for potassium (3150 mg/day). Two-thirds (67.4%) exceeded sodium guidelines, with males 2.6 times more likely to consume excessively. The majority of the participants add salt during cooking (82.5%) and whilst eating (66%), and 75% identified processed food as high source of salt. Most (69.1%) were aware that excessive salt could cause disease. Most of the UAE population consumes excess sodium and insufficient potassium, likely increasing the risk of NCDs. Despite most participants being aware that high salt intake is associated with adverse health outcomes, this did not translate into salt reduction action. Low-sodium, high-potassium dietary interventions such as the Mediterranean diet are vital in reducing the impact of NCDs in the UAE

The effect of Gum Arabic (Acacia Senegal) on cardiovascular risk factors and gastrointestinal symptoms in adults at risk of metabolic syndrome: A randomized clinical trial

Gum Arabic (GA) is a widely-used additive in food processing, but is also historically used in a number of traditional therapies. It has been shown to have a broad range of health benefits, particularly in improving important cardiovascular risk indicators. Metabolic syndrome and its associated cardiac outcomes are a significant burden on modern healthcare systems, and complementary interventions to aid in its management are required. We aimed to examine the effect of GA on those with, or at risk of, metabolic syndrome to identify an effect on improving important disease parameters related to cardiovascular outcomes. A single-blind, randomized, placebo-controlled trial was conducted to identify the effects of daily GA supplementation on metabolic and cardiovascular risk factors. A total of 80 participants were randomized to receive 20 g of GA daily (n = 40) or placebo (1 g pectin, n = 40) for 12 weeks. Key endpoints included body-anthropometric indices, diet and physical activity assessment, and blood chemistry (HbA1c, fasting glucose, and blood lipids). Of the 80 enrolled, 61 completed the study (intervention: 31, control: 30) with 19 dropping out due to poor treatment compliance. After 12 weeks, the participants receiving the GA showed significant decreases in systolic and diastolic blood pressure, fat-free body mass, energy and carbohydrate consumption, and fasting plasma glucose, as well as increased intake of dietary fiber. They also reported improvements in self-perceived bloating and quality of bowel movements, as well as a decreased appetite score following GA consumption. These results suggest that GA could be a safe and beneficial adjunct to other treatments for those with, or at risk of, metabolic syndrome

Effect of Calorie Restriction and Exercise on Type 2 Diabetes

Type-2 diabetes (T2D) is a chronic condition, generally regarded as an irreversible, that is among the top 10 causes of death globally. The hallmark of T2D is hyperglycemia, which results from disturbances in insulin sensitivity, insulin secretion, β-cell dysfunction and insulin resistance. Several clinical and lifestyle factors are involved in the progression of T2D, such as obesity and physical inactivity. A high-calorie diet is the main contributor to the development of obesity, which results in T2D, as obesity or increased intra-abdominal adipose tissue is related to insulin resistance. Technological advances have contributed to individuals having a more sedentary lifestyle, leading to obesity and T2D. T2D can be treated with lifestyle interventions, such as diet and exercise. Herein, we highlight the positive impact of a very low-calorie diet (VLCD) and lifestyle modalities in the treatment and prevention of T2D. An inclusion of VLCD 400-800 kcal/day for 8 weeks and ≥ 150 minutes exercise 5 times a week as lifestyle interventions can decrease glucose levels to normal, reduce HbA1c and improve insulin resistance and sensitivity. Therefore, a potential mechanism in maintaining glucose homeostasis and remission of T2D by VLCD and exercise reduces body weight