Derivatives and Credit Contagion in Interconnected Networks

The importance of adequately modeling credit risk has once again been highlighted in the recent financial crisis. Defaults tend to cluster around times of economic stress due to poor macro-economic conditions, {\em but also} by directly triggering each other through contagion. Although credit default swaps have radically altered the dynamics of contagion for more than a decade, models quantifying their impact on systemic risk are still missing. Here, we examine contagion through credit default swaps in a stylized economic network of corporates and financial institutions. We analyse such a system using a stochastic setting, which allows us to exploit limit theorems to exactly solve the contagion dynamics for the entire system. Our analysis shows that, by creating additional contagion channels, CDS can actually lead to greater instability of the entire network in times of economic stress. This is particularly pronounced when CDS are used by banks to expand their loan books (arguing that CDS would offload the additional risks from their balance sheets). Thus, even with complete hedging through CDS, a significant loan book expansion can lead to considerably enhanced probabilities for the occurrence of very large losses and very high default rates in the system. Our approach adds a new dimension to research on credit contagion, and could feed into a rational underpinning of an improved regulatory framework for credit derivatives.Comment: 26 pages, 7 multi-part figure

A magnetic quadrupole pick-up for the CERN PS

In the LHC era, there will be a need to monitor and correct betatron mismatch between machines in a non-destructive way. For this purpose, a quadrupole pick-up has been designed for the CERN PS. Originally, the PS was built for much larger beam sizes than now required when generating the LHC beam, but its large physical aperture should be maintained. Because of this large aperture to beam-size ratio, the quadrupole signal component in a standard pick-up design is strongly suppressed with respect to the common-mode signal, and thus demands a very high common-mode rejection in the signal processing. A magnetic quadrupole pick-up has been designed, in which the common-mode rejection is incorporated in the pick-up itself, by virtue of its geometry. The rejection is thus limited only by mechanical tolerances and can therefore be very large. Without the common-mode component, the dominating signal is dipolar, and small when the beam is centred in the pick-up. The dipole and quadrupole signals can thus be separated using a hybrid circuit with only moderate demands on common-mode rejection. Another advantage with a magnetic pick-up is the low output impedance, allowing the use of passive components when forming the quadrupole signal, which is highly desirable in the radiation environment of the PS ring. Simulations and tests of the pick-up and read-out electronics, as well as the first results with real beam are presented

Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices

We study XY spin systems on small world lattices for a variety of graph structures, e.g. Poisson and scale-free, superimposed upon a one dimensional chain. In order to solve this model we extend the cavity method in the one pure-state approximation to deal with real-valued dynamical variables. We find that small-world architectures significantly enlarge the region in parameter space where synchronization occurs. We contrast the results of population dynamics performed on a truncated set of cavity fields with Monte Carlo simulations and find excellent agreement. Further, we investigate the appearance of replica symmetry breaking in the spin-glass phase by numerically analyzing the proliferation of pure states in the message passing equations.Comment: 10 pages, 3 figure

Replica symmetry breaking in the `small world' spin glass

We apply the cavity method to a spin glass model on a `small world' lattice, a random bond graph super-imposed upon a 1-dimensional ferromagnetic ring. We show the correspondence with a replicated transfer matrix approach, up to the level of one step replica symmetry breaking (1RSB). Using the scheme developed by M\'ezard & Parisi for the Bethe lattice, we evaluate observables for a model with fixed connectivity and $\pm J$ long range bonds. Our results agree with numerical simulations significantly better than the replica symmetric (RS) theory.Comment: 21 pages, 3 figure

Solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction

We describe a solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction. We derive self-consistent equations of the order parameters and obtain three non-trivial solutions characterized by the rotation number. We also derive relevant characteristics such as the location-dependent distributions of the resultant frequencies of desynchronized oscillators. Simulation results closely agree with the theoretical ones

Dynamical replica theoretic analysis of CDMA detection dynamics

We investigate the detection dynamics of the Gibbs sampler for code-division multiple access (CDMA) multiuser detection. Our approach is based upon dynamical replica theory which allows an analytic approximation to the dynamics. We use this tool to investigate the basins of attraction when phase coexistence occurs and examine its efficacy via comparison with Monte Carlo simulations.Comment: 18 pages, 2 figure

Theory of agent-based market models with controlled levels of greed and anxiety

We use generating functional analysis to study minority-game type market models with generalized strategy valuation updates that control the psychology of agents' actions. The agents' choice between trend following and contrarian trading, and their vigor in each, depends on the overall state of the market. Even in `fake history' models, the theory now involves an effective overall bid process (coupled to the effective agent process) which can exhibit profound remanence effects and new phase transitions. For some models the bid process can be solved directly, others require Maxwell-construction type approximations.Comment: 30 pages, 10 figure

Survey propagation for the cascading Sourlas code

We investigate how insights from statistical physics, namely survey propagation, can improve decoding of a particular class of sparse error correcting codes. We show that a recently proposed algorithm, time averaged belief propagation, is in fact intimately linked to a specific survey propagation for which Parisi's replica symmetry breaking parameter is set to zero, and that the latter is always superior to belief propagation in the high connectivity limit. We briefly look at further improvements available by going to the second level of replica symmetry breaking.Comment: 14 pages, 5 figure

Registration of ‘Hallam’ Wheat

‘Hallam’ (Reg. no. CV-983, PI 638790) is a hard red winter wheat (Triticum aestivum L.) cultivar developed cooperatively by the Nebraska Agricultural Experiment Station and the USDA-ARS and released in 2005 by the developing institutions. Hallam was released primarily for its superior adaptation to rainfed wheat production systems in eastern Nebraska. The name Hallam was chosen to honor Hallam, NE, a town and its people rebuilding after a tornado. Hallam was selected from the cross ‘Brule’ (Schmidt et al., 1983)/‘Bennett’ (Schmidt et al., 1981)//‘Niobrara’ (Baenziger et al., 1996) that was made in 1992. The F1 generation was grown in the greenhouse and the F2 to F3 generations were advanced using the bulk breeding method in the field at Mead, NE. In 1995, single F3:4 rows were planted for selection. Hallam was selected in the F4 and there was no further selection thereafter. Hallam was evaluated as NE98471 in Nebraska yield nurseries starting in 1999, in the Northern Regional Performance Nursery in 2001 and 2002, and in Nebraska cultivar performance trials from 2002 to 2004. In the Nebraska cultivar performance trials, it was narrowly adapted and performs best in eastern Nebraska. The average Nebraska rainfed yield of Hallam of 4110 kg ha-1 (41 environments from 2002 to 2004) was greater than the yields of ‘Wahoo’ (4030 kg ha-1; Baenziger et al., 2002), ‘Alliance’ (3880 kg ha-1; Baenziger et al., 1995), and ‘Harry’ (4000 kg ha-1; Baenziger et al., 2004b), but was lower than ‘Millennium’ (4180 kg ha-1; Baenziger et al., 2001) and ‘Wesley’ (4210 kg ha-1; Peterson et al., 2001). In its primary area of adaptation (eastern Nebraska), Hallam has yielded 4540 kg ha-1 (five environments), which was greater than Wesley (4150 kg ha-1), Millennium (4250 kg ha-1), Wahoo (3940 kg ha-1), and Alliance (3900 kg ha21). In the Northern Regional Performance Nursery, Hallam ranked 14th of 30 in 2001 (12 environments) and fourth of 25 entries in 2002 (13 environments) and averaged 100 kg ha-1 more grain yield than ‘Nekota’ (Haley et al., 1996). Hallam is not recommended for use in irrigated production systems where other wheat cultivars with superior performance, especially with better straw strength (described below), would be recommended. Other measurements of performance from comparison trials show that Hallam is moderately early in maturity (142 d after January 1, five environments), about 2.5 d and 1.2 d earlier flowering than Millennium and Wesley, respectively. Hallam is a semidwarf wheat cultivar. Hallam has a medium short coleoptile (46 mm), as expected for a semidwarf wheat cultivar, and is shorter than ‘Goodstreak’ (61 mm; Baenziger et al., 2004a) and slightly longer than semidwarf wheat cultivars such as Harry (36 mm). The mature plant height of Hallam (86 cm) is 3 cm shorter than Millennium and 6 cm taller than Wesley (41 environments). Hallam has moderate straw strength (45% lodged), similar to Wahoo (46% lodged), but worse than Wesley (34% lodged) in those environments (3) where severe lodging was found. The winter hardiness of Hallamis good to very good, similar to ‘Abilene’ (PI 511307) and comparable to other winter wheat cultivars adapted and commonly grown in Nebraska

Registration of ‘Hallam’ Wheat

‘Hallam’ (Reg. no. CV-983, PI 638790) is a hard red winter wheat (Triticum aestivum L.) cultivar developed cooperatively by the Nebraska Agricultural Experiment Station and the USDA-ARS and released in 2005 by the developing institutions. Hallam was released primarily for its superior adaptation to rainfed wheat production systems in eastern Nebraska. The name Hallam was chosen to honor Hallam, NE, a town and its people rebuilding after a tornado. Hallam was selected from the cross ‘Brule’ (Schmidt et al., 1983)/‘Bennett’ (Schmidt et al., 1981)//‘Niobrara’ (Baenziger et al., 1996) that was made in 1992. The F1 generation was grown in the greenhouse and the F2 to F3 generations were advanced using the bulk breeding method in the field at Mead, NE. In 1995, single F3:4 rows were planted for selection. Hallam was selected in the F4 and there was no further selection thereafter. Hallam was evaluated as NE98471 in Nebraska yield nurseries starting in 1999, in the Northern Regional Performance Nursery in 2001 and 2002, and in Nebraska cultivar performance trials from 2002 to 2004. In the Nebraska cultivar performance trials, it was narrowly adapted and performs best in eastern Nebraska. The average Nebraska rainfed yield of Hallam of 4110 kg ha-1 (41 environments from 2002 to 2004) was greater than the yields of ‘Wahoo’ (4030 kg ha-1; Baenziger et al., 2002), ‘Alliance’ (3880 kg ha-1; Baenziger et al., 1995), and ‘Harry’ (4000 kg ha-1; Baenziger et al., 2004b), but was lower than ‘Millennium’ (4180 kg ha-1; Baenziger et al., 2001) and ‘Wesley’ (4210 kg ha-1; Peterson et al., 2001). In its primary area of adaptation (eastern Nebraska), Hallam has yielded 4540 kg ha-1 (five environments), which was greater than Wesley (4150 kg ha-1), Millennium (4250 kg ha-1), Wahoo (3940 kg ha-1), and Alliance (3900 kg ha21). In the Northern Regional Performance Nursery, Hallam ranked 14th of 30 in 2001 (12 environments) and fourth of 25 entries in 2002 (13 environments) and averaged 100 kg ha-1 more grain yield than ‘Nekota’ (Haley et al., 1996). Hallam is not recommended for use in irrigated production systems where other wheat cultivars with superior performance, especially with better straw strength (described below), would be recommended. Other measurements of performance from comparison trials show that Hallam is moderately early in maturity (142 d after January 1, five environments), about 2.5 d and 1.2 d earlier flowering than Millennium and Wesley, respectively. Hallam is a semidwarf wheat cultivar. Hallam has a medium short coleoptile (46 mm), as expected for a semidwarf wheat cultivar, and is shorter than ‘Goodstreak’ (61 mm; Baenziger et al., 2004a) and slightly longer than semidwarf wheat cultivars such as Harry (36 mm). The mature plant height of Hallam (86 cm) is 3 cm shorter than Millennium and 6 cm taller than Wesley (41 environments). Hallam has moderate straw strength (45% lodged), similar to Wahoo (46% lodged), but worse than Wesley (34% lodged) in those environments (3) where severe lodging was found. The winter hardiness of Hallamis good to very good, similar to ‘Abilene’ (PI 511307) and comparable to other winter wheat cultivars adapted and commonly grown in Nebraska