Witten index of supersymmetric chiral theories

The Witten index can be defined in many supersymmetric theories by formulating them in the space-time R×S3. If the index is nonzero for any value of the radius of S3, it can be shown that the theory does not break supersymmetry in Minkowski space. This approach rules out supersymmetry breaking in a large class of models, chiral and otherwise. The index arguments are consistent with previous instanton calculations which indicate supersymmetry breaking in certain theories.

Approximation of Internal Refractive Index Variation Improves Image Guided Diffuse Optical Tomography of Breast

Effective usage of image guidance by incorporating the refractive index (RI) variation in computational modeling of light propagation in tissue is investigated to assess its impact on optical-property estimation. With the aid of realistic patient breast three-dimensional models, the variation in RI for different regions of tissue under investigation is shown to influence the estimation of optical properties in image-guided diffuse optical tomography (IG-DOT) using numerical simulations. It is also shown that by assuming identical RI for all regions of tissue would lead to erroneous estimation of optical properties. The a priori knowledge of the RI for the segmented regions of tissue in IG-DOT, which is difficult to obtain for the in vivo cases, leads to more accurate estimates of optical properties. Even inclusion of approximated RI values, obtained from the literature, for the regions of tissue resulted in better estimates of optical properties, with values comparable to that of having the correct knowledge of RI for different regions of tissue.

High-precision diode-laser-based temperature measurement for air refractive index compensation

We present a laser-based system to measure the refractive index of air over a long path length. In optical distance measurements it is essential to know the refractive index of air with high accuracy. Commonly, the refractive index of air is calculated from the properties of the ambient air using either Ciddor or Edlén equations, where the dominant uncertainty component is in most cases the air temperature. The method developed in this work utilises direct absorption spectroscopy of oxygen to measure the average temperature of air and of water vapor to measure relative humidity. The method allows measurement of temperature and humidity over the same beam path as in optical distance measurement, providing spatially well matching data. Indoor and outdoor measurements demonstrate the effectiveness of the method. In particular, we demonstrate an effective compensation of the refractive index of air in an interferometric length measurement at a time-variant and spatially non-homogenous temperature over a long time period. Further, we were able to demonstrate 7 mK RMS noise over a 67 m path length using 120 s sample time. To our knowledge, this is the best temperature precision reported for a spectroscopic temperature measurement.

Sedimentary zooplankton remains as indicators of lake ecological quality and trophic structure

To protect and restore lake ecosystems under threats posed by the increasing human population, information on their ecological quality is needed. Lake sediments provide a data rich archive that allows identification of various biological components present prior to anthropogenic alterations as well as a constant record of changes. By providing a longer dimension of time than any ongoing monitoring programme, palaeolimnological methods can help in understanding natural variability and long-term ecological changes in lakes. As zooplankton have a central role in the lake food web, their remains can potentially provide versatile information on past trophic structure. However, various taphonomic processes operating in the lakes still raise questions concerning how subfossil assemblages reflect living communities. This thesis work aimed at improving the use of sedimentary zooplankton remains in the reconstruction of past zooplankton communities and the trophic structure in lakes. To quantify interspecific differences in the accumulation of remains, the subfossils of nine pelagic zooplankton taxa in annually laminated sediments were compared with monitoring results for live zooplankton in Lake Vesijärvi. This lake has a known history of eutrophication and recovery, which resulted from reduced external loading and effective fishing of plankti-benthivorous fish. The response of zooplankton assemblages to these known changes was resolved using annually laminated sediments. The generality of the responses observed in Lake Vesijärvi were further tested with a set of 31 lakes in Southern Finland, relating subfossils in surface sediments to contemporary water quality and fish density, as well as to lake morphometry. The results demonstrated differential preservation and retention of cladoceran species in the sediment. Daphnia, Diaphanosoma and Ceriodaphnia were clearly underrepresented in the sediment samples in comparison to well-preserved Bosmina species, Chydorus, Limnosida and Leptodora. For well-preserved species, the annual net accumulation rate was similar to or above the expected values, reflecting effective sediment focusing and accumulation in the deepest part of the lake. The decreased fish density and improved water quality led to subtle changes in zooplankton community composition. The abundance of Diaphanosoma and Limnosida increased after the reduction in fish density, while Ceriodaphnia and rotifers decreased. The most sensitive indicator of fish density was the mean size of Daphnia ephippia and Bosmina (E.) crassicornis ephippia and carapaces. The concentration of plant-associated species increased, reflecting expanding littoral vegetation along with increasing transparency. Several of the patterns observed in Lake Vesijärvi could also be found within the set of 31 lakes. According to this thesis work, the most useful cladoceran-based indices for nutrient status and planktivorous fish density in Finnish lakes were the relative abundances of certain pelagic taxa, and the mean size of Bosmina spp. carapaces, especially those of Bosmina (E.) cf. coregoni. The abundance of plant-associated species reflected the potential area for aquatic plants. Lake morphometry and sediment organic content, however, explained a relatively high proportion of the variance in the species data, and more studies are needed to quantify lake-specific differences in the accumulation and preservation of remains. Commonly occurring multicollinearity between environmental variables obstructs the cladoceran-based reconstruction of single environmental variables. As taphonomic factors and several direct and indirect structuring forces in lake ecosystems simultaneously affect zooplankton, the subfossil assemblages should be studied in a holistic way before making final conclusions about the trophic structure and the change in lake ecological quality.

A reexamination of the permeability index of clays

The permeability index Ck, similar to the compression index, is the slope of the void ratio – coefficient of permeability relationship. Literature shows that, in general, for sensitive clays it can be related to initial void ratio by Ck = 0.5e0. The possibility of obtaining such a relationship for Cochin marine clays in terms of liquid limit void ratio is indicated in this paper. Analysis of permeability behaviour of Cochin marine clays and the test results available in published literature using generalized state parameter approach show that, in principle, these forms of equations for the permeability index are tenable, even though they were obtained based on experimental observation alone.

Tropical Clays .1. Index Properties And Microstructural Aspects

Soils showing changes in plasticity characteristics upon driving form an important group in tropical soils. These changes are attributed to the grouping of particles into aggregates either due to mineralogy or presence of cementing agents and/or pore fluid characteristics. These changes are found to be permanent. In this paper, the effect of these changes leading to changes in index properties is discussed. The coefficient of permeability has been found to be comparable at liquid limit water content for different soils of varying liquid limit values. Permeability is an indirect reflection of microstructure and indicates the flow rate, which depends upon pore geometry. Other mechanical properties like compressibility and shear strength also depend upon pore geometry. These microstructural aspects of liquid limit as a reference state for the analysis of engineering behavior of tropical soils are examined in detail.

Strength Symmetry Index: A measure of seizure adequacy in ECT

Seizure electroencephalography (EEG) was recorded from two channels-right (Rt) and left (Lt)-during bilateral electroconvulsive therapy (ECT) (n = 12) and unilateral ECT (n = 12). The EEG was also acquired into a microcomputer and was analyzed without knowledge of the clinical details. EEG recordings of both ECT procedures yielded seizures of comparable duration. The Strength Symmetry Index (SSI) was computed from the early- and midseizure phases using the fractal dimension of the EEG. The seizures of unilateral ECT were characterized by significantly smaller SSI in both phases. More unilateral than bilateral ECT seizures had a smaller than median SSI in both phases. The seizures also differed on other measures as reported in the literature. The findings indicate that SSI may be a potential measure of seizure adequacy that remains to be validated in future research.