Optimal densities of packings consisting of highly unequal objects

Let $\Delta$ be the optimal packing density of $\mathbb R^n$ by unit balls. We show the optimal packing density using two sizes of balls approaches $\Delta + (1 - \Delta) \Delta$ as the ratio of the radii tends to infinity. More generally, if $B$ is a body and $D$ is a finite set of bodies, then the optimal density $\Delta_{\{rB\} \cup D}$ of packings consisting of congruent copies of the bodies from $\{rB\} \cup D$ converges to $\Delta_D + (1 - \Delta_D) \Delta_{\{B\}}$ as $r$ tends to zero

Moment methods in energy minimization: New bounds for Riesz minimal energy problems

We use moment methods to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate the infinite dimensional optimization problems in this hierarchy by block diagonal semidefinite programs. For this we develop the necessary harmonic analysis for spaces consisting of subsets of another space, and we develop symmetric sum-of-squares techniques. We compute the second step of our hierarchy for Riesz $s$-energy problems with five particles on the $2$-dimensional unit sphere, where the $s=1$ case known as the Thomson problem. This yields new sharp bounds (up to high precision) and suggests the second step of our hierarchy may be sharp throughout a phase transition and may be universally sharp for $5$-particles on $S^2$. This is the first time a $4$-point bound has been computed for a continuous problem

Lower bounds on matrix factorization ranks via noncommutative polynomial optimization

We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the completely positive rank, and their symmetric analogues: the positive semidefinite rank and the completely positive semidefinite rank. We study the convergence properties of our hierarchies, compare them extensively to known lower bounds, and provide some (numerical) examples

La composición tipográfica de la Políglota

We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive semidefinite rank, and their symmetric analogs: the completely positive rank and the completely positive semidefinite rank. We study convergence properties of our hierarchies, compare them extensively to known lower bounds, and provide some (numerical) examples

Midtrimester preterm prelabour rupture of membranes (PPROM):expectant management or amnioinfusion for improving perinatal outcomes (PPROMEXIL - III trial)

BACKGROUND: Babies born after midtrimester preterm prelabour rupture of membranes (PPROM) are at risk to develop neonatal pulmonary hypoplasia. Perinatal mortality and morbidity after this complication is high. Oligohydramnios in the midtrimester following PPROM is considered to cause a delay in lung development. Repeated transabdominal amnioinfusion with the objective to alleviate oligohydramnios might prevent this complication and might improve neonatal outcome. METHODS/DESIGN: Women with PPROM and persisting oligohydramnios between 16 and 24 weeks gestational age will be asked to participate in a multi-centre randomised controlled trial. Intervention: random allocation to (repeated) abdominal amnioinfusion (intervention) or expectant management (control). The primary outcome is perinatal mortality. Secondary outcomes are lethal pulmonary hypoplasia, non-lethal pulmonary hypoplasia, survival till discharge from NICU, neonatal mortality, chronic lung disease (CLD), number of days ventilatory support, necrotizing enterocolitis (NEC), periventricular leucomalacia (PVL) more than grade I, severe intraventricular hemorrhage (IVH) more than grade II, proven neonatal sepsis, gestational age at delivery, time to delivery, indication for delivery, successful amnioinfusion, placental abruption, cord prolapse, chorioamnionitis, fetal trauma due to puncture. The study will be evaluated according to intention to treat. To show a decrease in perinatal mortality from 70% to 35%, we need to randomise two groups of 28 women (two sided test, β-error 0.2 and α-error 0.05). DISCUSSION: This study will answer the question if (repeated) abdominal amnioinfusion after midtrimester PPROM with associated oligohydramnios improves perinatal survival and prevents pulmonary hypoplasia and other neonatal morbidities. Moreover, it will assess the risks associated with this procedure. TRIAL REGISTRATION: NTR3492 Dutch Trial Register (http://www.trialregister.nl)

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

Causes and consequences of cerebral small vessel disease. The RUN DMC study: a prospective cohort study. Study rationale and protocol

Contains fulltext : 96704.pdf (publisher's version ) (Open Access)BACKGROUND: Cerebral small vessel disease (SVD) is a frequent finding on CT and MRI scans of elderly people and is related to vascular risk factors and cognitive and motor impairment, ultimately leading to dementia or parkinsonism in some. In general, the relations are weak, and not all subjects with SVD become demented or get parkinsonism. This might be explained by the diversity of underlying pathology of both white matter lesions (WML) and the normal appearing white matter (NAWM). Both cannot be properly appreciated with conventional MRI. Diffusion tensor imaging (DTI) provides alternative information on microstructural white matter integrity. The association between SVD, its microstructural integrity, and incident dementia and parkinsonism has never been investigated. METHODS/DESIGN: The RUN DMC study is a prospective cohort study on the risk factors and cognitive and motor consequences of brain changes among 503 non-demented elderly, aged between 50-85 years, with cerebral SVD. First follow up is being prepared for July 2011. Participants alive will be included and invited to the research centre to undergo a structured questionnaire on demographics and vascular risk factors, and a cognitive, and motor, assessment, followed by a MRI protocol including conventional MRI, DTI and resting state fMRI. DISCUSSION: The follow up of the RUN DMC study has the potential to further unravel the causes and possibly better predict the consequences of changes in white matter integrity in elderly with SVD by using relatively new imaging techniques. When proven, these changes might function as a surrogate endpoint for cognitive and motor function in future therapeutic trials. Our data could furthermore provide a better understanding of the pathophysiology of cognitive and motor disturbances in elderly with SVD. The execution and completion of the follow up of our study might ultimately unravel the role of SVD on the microstructural integrity of the white matter in the transition from "normal" aging to cognitive and motor decline and impairment and eventually to incident dementia and parkinsonism

State of the climate in 2018

In 2018, the dominant greenhouse gases released into Earth’s atmosphere—carbon dioxide, methane, and nitrous oxide—continued their increase. The annual global average carbon dioxide concentration at Earth’s surface was 407.4 ± 0.1 ppm, the highest in the modern instrumental record and in ice core records dating back 800 000 years. Combined, greenhouse gases and several halogenated gases contribute just over 3 W m−2 to radiative forcing and represent a nearly 43% increase since 1990. Carbon dioxide is responsible for about 65% of this radiative forcing. With a weak La Niña in early 2018 transitioning to a weak El Niño by the year’s end, the global surface (land and ocean) temperature was the fourth highest on record, with only 2015 through 2017 being warmer. Several European countries reported record high annual temperatures. There were also more high, and fewer low, temperature extremes than in nearly all of the 68-year extremes record. Madagascar recorded a record daily temperature of 40.5°C in Morondava in March, while South Korea set its record high of 41.0°C in August in Hongcheon. Nawabshah, Pakistan, recorded its highest temperature of 50.2°C, which may be a new daily world record for April. Globally, the annual lower troposphere temperature was third to seventh highest, depending on the dataset analyzed. The lower stratospheric temperature was approximately fifth lowest. The 2018 Arctic land surface temperature was 1.2°C above the 1981–2010 average, tying for third highest in the 118-year record, following 2016 and 2017. June’s Arctic snow cover extent was almost half of what it was 35 years ago. Across Greenland, however, regional summer temperatures were generally below or near average. Additionally, a satellite survey of 47 glaciers in Greenland indicated a net increase in area for the first time since records began in 1999. Increasing permafrost temperatures were reported at most observation sites in the Arctic, with the overall increase of 0.1°–0.2°C between 2017 and 2018 being comparable to the highest rate of warming ever observed in the region. On 17 March, Arctic sea ice extent marked the second smallest annual maximum in the 38-year record, larger than only 2017. The minimum extent in 2018 was reached on 19 September and again on 23 September, tying 2008 and 2010 for the sixth lowest extent on record. The 23 September date tied 1997 as the latest sea ice minimum date on record. First-year ice now dominates the ice cover, comprising 77% of the March 2018 ice pack compared to 55% during the 1980s. Because thinner, younger ice is more vulnerable to melting out in summer, this shift in sea ice age has contributed to the decreasing trend in minimum ice extent. Regionally, Bering Sea ice extent was at record lows for almost the entire 2017/18 ice season. For the Antarctic continent as a whole, 2018 was warmer than average. On the highest points of the Antarctic Plateau, the automatic weather station Relay (74°S) broke or tied six monthly temperature records throughout the year, with August breaking its record by nearly 8°C. However, cool conditions in the western Bellingshausen Sea and Amundsen Sea sector contributed to a low melt season overall for 2017/18. High SSTs contributed to low summer sea ice extent in the Ross and Weddell Seas in 2018, underpinning the second lowest Antarctic summer minimum sea ice extent on record. Despite conducive conditions for its formation, the ozone hole at its maximum extent in September was near the 2000–18 mean, likely due to an ongoing slow decline in stratospheric chlorine monoxide concentration. Across the oceans, globally averaged SST decreased slightly since the record El Niño year of 2016 but was still far above the climatological mean. On average, SST is increasing at a rate of 0.10° ± 0.01°C decade−1 since 1950. The warming appeared largest in the tropical Indian Ocean and smallest in the North Pacific. The deeper ocean continues to warm year after year. For the seventh consecutive year, global annual mean sea level became the highest in the 26-year record, rising to 81 mm above the 1993 average. As anticipated in a warming climate, the hydrological cycle over the ocean is accelerating: dry regions are becoming drier and wet regions rainier. Closer to the equator, 95 named tropical storms were observed during 2018, well above the 1981–2010 average of 82. Eleven tropical cyclones reached Saffir–Simpson scale Category 5 intensity. North Atlantic Major Hurricane Michael’s landfall intensity of 140 kt was the fourth strongest for any continental U.S. hurricane landfall in the 168-year record. Michael caused more than 30 fatalities and $25 billion (U.S. dollars) in damages. In the western North Pacific, Super Typhoon Mangkhut led to 160 fatalities and$6 billion (U.S. dollars) in damages across the Philippines, Hong Kong, Macau, mainland China, Guam, and the Northern Mariana Islands. Tropical Storm Son-Tinh was responsible for 170 fatalities in Vietnam and Laos. Nearly all the islands of Micronesia experienced at least moderate impacts from various tropical cyclones. Across land, many areas around the globe received copious precipitation, notable at different time scales. Rodrigues and Réunion Island near southern Africa each reported their third wettest year on record. In Hawaii, 1262 mm precipitation at Waipā Gardens (Kauai) on 14–15 April set a new U.S. record for 24-h precipitation. In Brazil, the city of Belo Horizonte received nearly 75 mm of rain in just 20 minutes, nearly half its monthly average. Globally, fire activity during 2018 was the lowest since the start of the record in 1997, with a combined burned area of about 500 million hectares. This reinforced the long-term downward trend in fire emissions driven by changes in land use in frequently burning savannas. However, wildfires burned 3.5 million hectares across the United States, well above the 2000–10 average of 2.7 million hectares. Combined, U.S. wildfire damages for the 2017 and 2018 wildfire seasons exceeded $40 billion (U.S. dollars)