Complex Hermite functions as Fourier-Wigner transform

We prove that the complex Hermite polynomials H_{m,n} on the complex plane $\mathbb{C}$ can be realized as the Fourier-Wigner transform $\mathcal{V}$ of the well-known real Hermite functions $h_n$ on real line $\mathbb{R}$. This reduces considerably the Wong's proof giving the explicit expression of $\mathcal{V}(h_m,h_n)$ in terms of the Laguerre polynomials. Moreover, we derive a new generating function for the H_{m,n} as well as some new integral identities.Comment: 6 pages. Mistakes and misprints are correcte

VARIwise: a general-purpose adaptive control simulation framework for spatially and temporally varied irrigation at sub-field scale

Irrigation control strategies may be used to improve the site-specific irrigation of cotton via lateral move and centre pivot irrigation machines. A simulation framework ‘VARIwise’ has been created to aid the development, evaluation and management of spatially and temporally varied site-specific irrigation control strategies. VARIwise accommodates sub-field scale variations in all input parameters using a 1 m2 cell size, and permits application of differing control strategies within the field, as well as differing irrigation amounts down to this scale. In this paper the motivation and objectives for the creation of VARIwise are discussed, the structure of the software is outlined and an example of the use and utility of VARIwise is presented. Three irrigation control strategies have been simulated in VARIwise using a cotton model with a range of input parameters including spatially variable soil properties, non-uniform irrigation application, three weather profiles and two crop varieties. The simulated yield and water use efficiency were affected by the combination of input parameters and the control strategy implemented

Modelling of crystal structure of cis-1,2,3,6 and 3,4,5,6-tetrahydrophthalic anhydrides using lattice energy calculations

Lattice energy calculations using a model potential were performed to model the crystal structures of cis-1,2,3,6- and 3,4,5,6-tetrahydrophthalic (THP) anhydrides. The optimized molecular models using the DFT method at the B3LYP/6-31G** level were found consistent with the available experimental evidence and allowed all differences observed in crystal packing between cis-1,2,3,6- and 3,4,5,6-THP anhydrides to be reproduced. Calculations provide evidence for the presence of dipole–dipole C=O?C=O intermolecular interactions and support the idea that the molecules distort from their ideal geometries, improving packing in both crystals. The search for minima in the lattice energy of both crystals amongst the more common space groups with Z’?=?1, using a simulated annealing crystal structure prediction procedure followed by lattice energy minimization showed that the observed structure of 3,4,5,6-THP anhydride (Z’?=?2) is the thermodynamically most stable, and allowed us to justify why 3,4,5,6-THP anhydride crystallizes in such a complex structure with 16 molecules in the unit cell. The computational model was successful in predicting the second observed form at 173 K for cis-1,2,3,6-THP anhydride as a polymorph, and could predict several hypothetical structures with Z’?=?1 that appear competitive with the observed structures. The results of phonon estimates of zero point intermolecular vibrational energy and entropy suggest that crystal structures of cis-1,2,3,6-THP anhydride cannot be predicted solely on the basis of lattice energy; factors other than thermodynamics favor the observed structures

Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinu-ous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results

AN ARTIFICIAL IMMUNE SYSTEM FOR PUBLIC TRANSPORT REGULATION

International audienc

Energy reconstruction on the LHC ATLAS TileCal upgraded front end: feasibility study for a sROD co-processing unit

Dissertation presented in ful lment of the requirements for the degree of: Master of Science in Physics 2016The Phase-II upgrade of the Large Hadron Collider at CERN in the early 2020s will enable an order of magnitude increase in the data produced, unlocking the potential for new physics discoveries. In the ATLAS detector, the upgraded Hadronic Tile Calorimeter (TileCal) Phase-II front end read out system is currently being prototyped to handle a total data throughput of 5.1 TB/s, from the current 20.4 GB/s. The FPGA based Super Read Out Driver (sROD) prototype must perform an energy reconstruction algorithm on 2.88 GB/s raw data, or 275 million events per second. Due to the very high level of pro ciency required and time consuming nature of FPGA rmware development, it may be more e ective to implement certain complex energy reconstruction and monitoring algorithms on a general purpose, CPU based sROD co-processor. Hence, the feasibility of a general purpose ARM System on Chip based co-processing unit (PU) for the sROD is determined in this work. A PCI-Express test platform was designed and constructed to link two ARM Cortex-A9 SoCs via their PCI-Express Gen-2 x1 interfaces. Test results indicate that the latency of the PCI-Express interface is su ciently low and the data throughput is superior to that of alternative interfaces such as Ethernet, for use as an interconnect for the SoCs to the sROD. CPU performance benchmarks were performed on ve ARM development platforms to determine the CPU integer, oating point and memory system performance as well as energy e ciency. To complement the benchmarks, Fast Fourier Transform and Optimal Filtering (OF) applications were also tested. Based on the test results, in order for the PU to process 275 million events per second with OF, within the 6 s timing budget of the ATLAS triggering system, a cluster of three Tegra-K1, Cortex-A15 SoCs connected to the sROD via a Gen-2 x8 PCI-Express interface would be suitable. A high level design for the PU is proposed which surpasses the requirements for the sROD co-processor and can also be used in a general purpose, high data throughput system, with 80 Gb/s Ethernet and 15 GB/s PCI-Express throughput, using four X-Gene SoCs

Explicit and implicit attitudes, and discriminatory behavior in a Lebanese student sample :an ERP study using the ultimatum game -

Thesis. M.A. American University of Beirut. Department of Psychology, 2014. T:6131Advisor : Dr. Arne Dietrich, Professor, Psychology ; Members of Committee : Dr. Charles Harb, Associate Professor, Psychology ; Dr. Nadiya Slobodenyuk, Assistant Professor, Psychology.Includes bibliographical references (leaves 83-94)Lebanese youth claim to have positive social emotions towards their own sect. However, explicit self-reports of such attitudes may not be in line with implicit attitudes that might lead to discriminatory behavior. Several studies supported the idea that there are discrepancies between explicit and implicit attitudes. The following study examined the discrepancies between implicit attitudes, behavior and explicit beliefs on one kind of intergroup interaction: ingroup favoritism. We turned to the ultimatum game, which is a widely used decision-making task. We tested for possible reflection of implicit attitudes at the electrophysiological level. We also explored discriminatory behaviors by examining the rejection rates of different kinds of offers (fair, moderately unfair and strongly unfair) in different conditions. Explicit attitudes were measured using self-report sectarianism scale. The study recruited 45 participants to play as responders in this game while having their electrophysiological activity recorded using EEG. A 3x3 mixed design was implemented. The within-group factor was the fairness of the offer. Each participant received fair, moderately unfair and strongly unfair offers. The second between-group factor was group interaction. We manipulated three different group interactions, those with someone from the same sect, interaction with someone from a different sect and a condition where the sect was not mentioned. Separate mixed ANOVAs of behavioral and electrophysiological results were carried out. For the behavioral results, there was no significant effect of the group interaction. However, as expected, the fairness of the offers affected rejection rates. For the electrophysiological results, the observed effect was on the kind of offer where the MFN elicited more negativity as the offers became more unfair. P300 was significant in all the different condition with no within-group difference. Results also showed that LPP did not reflect implicit sectarian attitudes. The limitations of this study ar