On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String Vacua

Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the pdf is not yet known. As a first result of this work, an explicit analytic expression for the density of the sum of two gamma random variables is derived. Then a computationally efficient algorithm to numerically calculate the linear combination of chi square random variables is developed. An explicit expression for the error bound is obtained. The proposed technique is shown to be computationally efficient, i.e. only polynomial in growth in the number of terms compared to the exponential growth of most other methods. It provides a vast improvement in accuracy and shows only logarithmic growth in the required precision. In addition, it is applicable to a much greater number of terms and currently the only way of computing the distribution for hundreds of terms. As an application, the exponential dependence of the eigenvalue fluctuation probability of a random matrix model for 4d supergravity with N scalar fields is found to be of the asymptotic form exp(-0.35N).Comment: 21 pages, 19 figures. 3rd versio

Third-order neurons in the lateral horn enhance bilateral contrast of odor inputs through contralateral inhibition in Drosophila

The survival and reproduction of Drosophila melanogaster depends heavily on its ability to determine the location of an odor source and either to move towards or away from it. Despite the very small spatial separation between the two antennae and the redundancy in sensory neuron projection to both sides of the brain, Drosophila can resolve the concentration gradient by comparing the signal strength between the two antennae. When an odor stimulates the antennae asymmetrically, ipsilateral projection neurons from the first olfactory center are more strongly excited compared to the contralateral ones. However, it remains elusive how higher-order neurons process such asymmetric or lateralized odor inputs. Here, we monitored and analyzed for the first time the activity patterns of a small cluster of third-order neurons (so-called VLP neurons) to asymmetric olfactory stimulation using two-photon calcium imaging. Our data demonstrate that lateralized odors evoke distinct activation of these neurons in the left and right brain hemisphere as a result of contralateral inhibition. Moreover, using laser transection experiments we show that this contralateral inhibition is mediated by presynaptic neurons most likely located in the lateral horn. Finally, we propose that this inhibitory interaction between higher-order neurons facilitates odor lateralization and plays a crucial role in olfactory navigation behavior of Drosophila, a theory that needs to be experimentally addressed in future studies

{S-Benzyl 3-[(6-methyl­pyridin-2-yl)­methyl­idene]dithio­carbazato}nickel(II) monohydrate

The structure of the title compound, [Ni(C15H14N3S2)2]·H2O, has one mol­ecule in the asymmetric unit, along with a solvent water mol­ecule. The two different Schiff base moieties coordinate to the central NiII ion as tridentate N,N′,S-chelating ligands, creating a six-coordinate distorted octa­hedral environment [the smallest angle being 77.43 (7)° and the widest angle being 169.99 (7)°]. The mean planes of the two ligands are nearly orthogonal to each other with an angle of 89.53 (6)°. The packing of the complex is supported by O—H⋯N and O—H⋯S hydrogen bonding between the solvent water mol­ecule and the uncoordinated N and S atoms of neighbouring ligands

Bis{S-benzyl 3-[(phen­yl)(pyridin-2-yl)methyl­idene]dithio­carbazato}zinc acetonitrile monosolvate

In the title compound, [Zn(C20H16N3S2)2]·CH3CN, two different Schiff base moieties coordinate to the central ZnII ion as tridentate N,N′,S-chelating ligands, creating a distorted octa­hedral environment [the smallest angle being 73.24 (6)° and the widest angle being 155.73 (7)°], with the two S atoms in cis positions. The dihedral angle between the mean planes of the two coordinating ligands is 83.65 (5)°. The crystal packing is consolidated by weak C—H⋯N hydrogen-bonding inter­actions

Chemical Polymerization Kinetics of Poly-O-Phenylenediamine and Characterization of the Obtained Polymer in Aqueous Hydrochloric Acid Solution Using K 2

The oxidative chemical polymerization of o-phenylenediamine (OPDA) was studied in hydrochloric acid solution using potassium dichromate as oxidant at 5°C. The effects of potassium dichromate, hydrochloric acid, and monomer concentrations on the polymerization reaction were investigated. The order of reaction with respect to potassium dichromate, hydrochloric acid, and monomer concentration was found to be 1.011, 0.954, and 1.045, respectively. Also, the effect of temperature on the polymerization rate was studied and the apparent activation energy of the polymerization reaction was found to be 63.658 kJ/mol. The obtained polymer was characterized using XPS, IR, UV-visible, and elemental analysis. The surface morphology of the obtained polymers was characterized by X-ray diffraction and transmission electron microscopy (TEM). The TGA analysis was used to confirm the proposed structure and number of water molecules in each polymeric chain unit. The ac conductivity (σac) of (POPDA) was investigated as a function of frequency and temperature. The ac conductivity was interpreted as a power law of frequency. The frequency exponent (s) was found to be less than unity and decreased with the increase of temperature, which confirms that the correlated barrier hopping model was the dominant charge transport mechanism

Growth and nutritional value of a Tropical Green Alga, Ankistrodesmus convolutus corda, in Agro-industrialeffluents

Use of agro-industrial effluents for microalgal culture was investigated using a tropical freshwater green alga, Ankistrodesmus convolutus cultured in various dilutions of latex concentrate effluent (LCRE), standard Malaysian rubber effluent (SMRE) and digested palm oil mill effluent (POMED). Ankistrodesmus convolutus grown in 40%and 60%LCRE, 60%SMRE and 10% POMED showed significantly higher (P < 0.05) specific growth rate in terms of cell number and chlorophyll a than that grown in other effluent media and inorganic fertiliser (N:P:K = 1:1:0.5) as control. Total biomass of this microalgae grown in 60%LCRE, 60%SMRE and 10% POMED was significantly higher (P < 0.05) than that cultured in other effluent media and the control. Ankistrodesmus convolutus cultured in 40% and 60% LCRE, 60% SMRE and 10% POMED showed significantly (P < 0.05) higher amount of crude protein and lipid than that grown in other effluent media and the control. Significantly higher (P < 0.05) amount of most of the essential amino acids (EAAs) except a few were found in A. convolutus cultured in 60% LCRE and 60% SMRE than that grown in other effluent media and control. Ankistrodesmus convolutus cultured in 10% POMED resulted in significantly higher (P < 0.05) amount of all the EAAs except threonine and tyrosine that were grown in other POMED media and control. Ankistrodesmus convolutus grown in 40% and 60% LCRE, contained significantly higher (P < 0.05) amounts of all the C18 and C20 polyunsaturated fatty acids (PDFAs) than that cultured in other SMRE media and control, except eicosadienoic acid (20: 2n-11). A similar trend of PUFAs was recorded in A. convolutus cultured in 60% SMRE except eicosatrienoic acid (20:3n-6) and arachidonic acid (20:4n-6). It was found that A. convolutus contained significantly (P < 0.05) higher amount of PUFAs such as linoleic acid (l8:2n-6), linolenic acid (18:3n-3) and arachidonic acid (20:4n-6) when grown in 10% POMED than that cultured in other POMED media and control. This study showed that A. convolutus grown in 40-60% rubber and 10% POMED has higher nutritional value that that cultured in other effluent media and inogranic fertilizer