Supersymmetric Yang-Mills quantum mechanics in various dimensions

Recent analytical and numerical solutions of the above systems are reviewed. Discussed results include: a) exact construction of the supersymmetric vacua in two space-time dimensions, and b) precise numerical calculations of the coexisting continuous and discrete spectra in the four-dimensional system, together with the identification of dynamical supermultiplets and SUSY vacua. New construction of the gluinoless SO(9) singlet state, which is vastly different from the empty state, in the ten-dimensional model is also briefly summarized.Comment: Talk presented at the Eighth Workshop on Non-Perturbative QCD, Paris, June 2004; 8 pages, 4 figure

Some Problems in Probabilistic Tomography

Given probability distributions F1 , F2 , . . ., Fk on R and distinct directions θ1, . . ., θk, one may ask whether there is a probability measure μ on R2 such that the marginal of μ in direction θj is Fj, j = 1, . . ., k. For example for k = 3 we ask what the marginal of μ at 45° can be if the x and y marginals are each say standard normal? In probabilistic language, if X and Y are each standard normal with an arbitrary joint distribution, what can the distribution of X + Y or X - Y be? This type of question is familiar to probabilists and is also familiar (except perhaps in that μ is positive) to tomographers, but is difficult to answer in special cases. The set of distributions for Z = X - Y is a convex and compact set, C, which contains the single point mass Z ≡ 0 since X ≡ Y, standard normal, is possible. We show that Z can be 3-valued, Z=0, ±a for any a, each with positive probability, but Z cannot have any (genuine) two-point distribution. Using numerical linear programming we present convincing evidence that Z can be uniform on the interval [-ε, ε] for ε small and give estimates for the largest such ε. The set of all extreme points of C seems impossible to determine explicitly. We also consider the more basic question of finding the extreme measures on the unit square with uniform marginals on both coordinates, and show that not every such measure has a support which has only one point on each horizontal or vertical line, which seems surprising

Sets Uniquely Determined by Projections on Axes I. Continuous Case

This paper studies sets S in Rn which are uniquely reconstructible from their hyperplane integral projections Pi(xi ;S) = ∬ . . . ∫ΧS ( {x1, . . . ,xi, . . . ,xn) dx1 . . . dxi - 1 dxi + 1 . . .dxn onto the n coordinate axes of Rn. It is shown that any additive set S = {x = (x1, . . .,xn) : ∑i = 1n fi(xi)≧0}, where each fi(xi) is a bounded measurable function, is uniquely reconstructible. In particular, balls are uniquely reconstructible. It is shown that in R2 all uniquely reconstructible sets are additive. For n≧3, Kemperman has shown that there are uniquely reconstructible sets in Rn of bounded measure that are not additive. It is also noted for n≧3 that neither of the properties of being additive and being a set of uniqueness is closed under monotone pointwise limits. A necessary condition for S to be a set of uniqueness is that S contain no bad configuration. A bad configuration is two finite sets of points T1 in Int(S) and T2 in Int(Sc), where Sc=Rn - S, such that T1 and T2 have the same number of points in any hyperplane xi = c for 1≦ i ≦n, and all c ∈ R2. We show that this necessary condition is sufficient for uniqueness for open sets S in R2. The results show that prior information about a density f in R2 to be reconstructed in tomography (namely if f is known to have only values 0 and 1) can sometimes reduce the problem of reconstructing f to knowing only two projections of f. Thus even meager prior information can in principle be of enormous value in tomography

The importance of biotic entrainment for base flow fluvial sediment transport

Sediment transport is regarded as an abiotic process driven by geophysical energy, but zoogeomorphological activity indicates that biological energy can also fuel sediment movements. It is therefore prudent to measure the contribution that biota make to sediment transport, but comparisons of abiotic and biotic sediment flux are rare. For a stream in the UK, the contribution of crayfish bioturbation to suspended sediment flux was compared with the amount of sediment moved by hydraulic forcing. During baseflow periods, biotic fluxes can be isolated because nocturnal crayfish activity drives diel turbidity cycles, such that night-time increases above day-time lows are attributable to sediment suspension by crayfish. On average, crayfish bioturbation contributed at least 36% (430 kg) to monthly baseflow suspended sediment loads; this biotic surcharge added between 4.7 and 13.54 t (0.19 to 0.55 t km-2 yr-1) to the annual sediment yield. As anticipated, most sediment was moved by hydraulic forcing during floods and the biotic contribution from baseflow periods represented between 0.43 and 1.24% of the annual load. Crayfish activity is nonetheless an important impact during baseflow periods and the measured annual contribution may be a conservative estimate because of unusually prolonged flooding during the measurement period. In addition to direct sediment entrainment by bioturbation, crayfish burrowing supplies sediment to the channel for mobilization during floods so that the total biotic effect of crayfish is potentially greater than documented in this study. These results suggest that in rivers, during baseflow periods, bioturbation can entrain significant quantities of fine sediment into suspension with implications for the aquatic ecosystem and baseflow sediment fluxes. Energy from life rather than from elevation can make significant contributions to sediment fluxes

Dietary fat and carbohydrates differentially alter insulin sensitivity during caloric restriction

BACKGROUND AND AIMS: We determined the effects of acute and chronic calorie restriction with either a low-fat, high-carbohydrate diet or a low-carbohydrate diet on hepatic and skeletal muscle insulin sensitivity. METHODS: Twenty-two obese subjects (body-mass index, 36.5±0.8kg/m(2)) were randomized to a high-carbohydrate (>180g/d) or low-carbohydrate (<60g/d) energy-deficit diet. A euglycemic–hyperinsulinemic clamp, muscle biopsies, and magnetic resonance spectroscopy were used to determine insulin action, cellular insulin signaling and intrahepatic triglyceride content before, after 48 h, and after ~11 wks (7% weight loss) of diet therapy. RESULTS: At 48 h, intrahepatic triglyceride content decreased more in the low-carbohydrate than the high-carbohydrate diet group (29.6±4.8% vs. 8.9±1.4%; P<0.05), but was similar in both groups after 7% weight loss (low-carbohydrate diet, 38.0±4.5% vs. high-carbohydrate diet, 44.5±13.5%). Basal glucose production rate decreased more in the low-carbohydrate than the high-carbohydrate diet group at 48 h (23.4±2.2% vs. 7.2±1.4%, P<0.05) and after 7% weight loss (20.0±2.4% vs. 7.9±1.2%, P<0.05). Insulin-mediated glucose uptake did not change at 48 h, but increased similarly in both groups after 7% weight loss (48.4±14.3%, P<0.05). In both groups, insulin-stimulated phosphorylation of Jun N-terminal kinase decreased by 29±13% and phosphorylation of Akt and insulin receptor substrate -1 increased by 35±9% and 36±9%, respectively, after 7% weight loss (all p<0.05). CONCLUSION: Moderate calorie restriction causes temporal changes in liver and skeletal muscle metabolism; 48 h of calorie restriction affects the liver (intrahepatic triglyceride content, hepatic insulin sensitivity, and glucose production), whereas moderate weight loss affects muscle (insulin-mediated glucose uptake and insulin signaling)

The long-term effects of invasive signal crayfish (Pacifastacus leniusculus) on instream macroinvertebrate communities

Non-native species represent a significant threat to indigenous biodiversity and ecosystem functioning worldwide. It is widely acknowledged that invasive crayfish species may be instrumental in modifying benthic invertebrate community structure, but there is limited knowledge regarding the temporal and spatial extent of these effects within lotic ecosystems. This study investigates the long term changes to benthic macroinvertebrate community composition following the invasion of signal crayfish, Pacifastacus leniusculus, into English rivers. Data from long-term monitoring sites on 7 rivers invaded by crayfish and 7 rivers where signal crayfish were absent throughout the record (control sites) were used to examine how invertebrate community composition and populations of individual taxa changed as a result of invasion. Following the detection of non-native crayfish, significant shifts in invertebrate community composition were observed at invaded sites compared to control sites. This pattern was strongest during autumn months but was also evident during spring surveys. The observed shifts in community composition following invasion were associated with reductions in the occurrence of ubiquitous Hirudinea species (Glossiphonia complanata and Erpobdella octoculata), Gastropoda (Radix spp.), Ephemeroptera (Caenis spp.), and Trichoptera (Hydropsyche spp.); although variations in specific taxa affected were evident between regions and seasons. Changes in community structure were persistent over time with no evidence of recovery, suggesting that crayfish invasions represent significant perturbations leading to permanent changes in benthic communities. The results provide fundamental knowledge regarding non-native crayfish invasions of lotic ecosystems required for the development of future management strategies