Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Helium in polygonal nanopores at zero temperature: Density functional theory calculations

We investigate adsorption of helium in nanoscopic polygonal pores at zero temperature using a finite-range density functional theory. The adsorption potential is computed by means of a technique denoted as the elementary source method. We analyze a rhombic pore with Cs walls, where we show the existence of multiple interfacial configurations at some linear densities, which correspond to metastable states. Shape transitions and hysterectic loops appear in patterns which are richer and more complex than in a cylindrical tube with the same transverse area.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Conditional manipulation of sex ratios by ant workers: A test of kin selection theory

Variable queen mating frequencies provide a unique opportunity to study the resolution of worker-queen conflict over sex ratio in social Hymenoptera, because the conflict is maximal in colonies headed by a singly mated queen and is weak or nonexistent in colonies headed by a multiply mated queen. In the wood ant Formica exsecta, workers in colonies with a singly mated queen, but not those in colonies with a multiply mated queen, altered the sex ratio of queen-laid eggs by eliminating males to preferentially raise queens. By this conditional response to queen mating frequency, workers enhance their inclusive fitness.

A new aggregation method for strategic decision making and its application in assignment theory

A new aggregation method for decision making is presented by using induced aggregation operators and the index of maximum and minimum level. Its main advantage is that it can assess complex reordering processes in the aggregation that represent complex attitudinal characters of the decision maker such as psychological or personal factors. A wide range of properties and particular cases of this new approach are studied. A further generalization by using hybrid averages and immediate weights is also presented. The key issue in this approach against the previous model is that we can use the weighted average and the ordered weighted average in the same formulation. Thus, we are able to consider the subjective attitude and the degree of optimism of the decision maker in the decision process. The paper ends with an application in a decision making problem based on the use of the assignment theory.

Predictive analysis and mapping of indoor radon concentrations in a complex environment using kernel estimation: an application to Switzerland.

PURPOSE: The aim of this study was to develop models based on kernel regression and probability estimation in order to predict and map IRC in Switzerland by taking into account all of the following: architectural factors, spatial relationships between the measurements, as well as geological information. METHODS: We looked at about 240,000 IRC measurements carried out in about 150,000 houses. As predictor variables we included: building type, foundation type, year of construction, detector type, geographical coordinates, altitude, temperature and lithology into the kernel estimation models. We developed predictive maps as well as a map of the local probability to exceed 300 Bq/m(3). Additionally, we developed a map of a confidence index in order to estimate the reliability of the probability map. RESULTS: Our models were able to explain 28% of the variations of IRC data. All variables added information to the model. The model estimation revealed a bandwidth for each variable, making it possible to characterize the influence of each variable on the IRC estimation. Furthermore, we assessed the mapping characteristics of kernel estimation overall as well as by municipality. Overall, our model reproduces spatial IRC patterns which were already obtained earlier. On the municipal level, we could show that our model accounts well for IRC trends within municipal boundaries. Finally, we found that different building characteristics result in different IRC maps. Maps corresponding to detached houses with concrete foundations indicate systematically smaller IRC than maps corresponding to farms with earth foundation. CONCLUSIONS: IRC mapping based on kernel estimation is a powerful tool to predict and analyze IRC on a large-scale as well as on a local level. This approach enables to develop tailor-made maps for different architectural elements and measurement conditions and to account at the same time for geological information and spatial relations between IRC measurements.

Quantification of magmatic and hydrothermal processes in a peralkaline syenite-alkali granite complex based on textures, phase equilibria, and stable and radiogenic isotopes

The Puklen complex of the Mid-Proterozoic Gardar Province, South Greenland, consists of various silica-saturated to quartz-bearing syenites, which are intruded by a peralkaline granite. The primary mafic minerals in the syenites are augite +/- olivine + Fe-Ti oxide + amphibole. Ternary feldspar thermometry and phase equilibria among mafic silicates yield T = 950-750degreesC, a(SiO2) = 0.7-1 and an f(O2) of 1-3 log units below the fayalite-magnetite-quartz (FMQ) buffer at 1 kbar. In the granites, the primary mafic minerals are ilmenite and Li-bearing arfvedsonite, which crystallized at temperatures below 750degreesC and at f(O2) values around the FMQ buffer. In both rock types, a secondary post-magmatic assemblage overprints the primary magmatic phases. In syenites, primary Ca-bearing minerals are replaced by Na-rich minerals such as aegirine-augite and albite, resulting in the release of Ca. Accordingly, secondary minerals include ferro-actinolite, (calcite-siderite)(ss), titanite and andradite in equilibrium with the Na-rich minerals. Phase equilibria indicate that formation of these minerals took place over a long temperature interval from near-magmatic temperatures down to similar to300degreesC. In the course of this cooling, oxygen fugacity rose in most samples. For example, late-stage aegirine in granites formed at the expense of arfvedsonite at temperatures below 300degreesC and at an oxygen fugacity above the haematite-magnetite (HM) buffer. The calculated delta(18)O(melt) value for the syenites (+5.9 to +6.3parts per thousand) implies a mantle origin, whereas the inferred delta(18)O(melt) value of <+5.1parts per thousand for the granitic melts is significantly lower. Thus, the granites require an additional low-delta(18)O contaminant, which was not involved in the genesis of the syenites. Rb/Sr data for minerals of both rock types indicate open-system behaviour for Rb and Sr during post-magmatic metasomatism. Neodymium isotope compositions (epsilonNd(1170 Ma) = -3.8 to -6.4) of primary minerals in syenites are highly variable, and suggest that assimilation of crustal rocks occurred to variable extents. Homogeneous epsilon(Nd) values of -5.9 and -6.0 for magmatic amphibole in the granites lie within the range of the syenites. Because of the very similar neodymium isotopic compositions of magmatic and late- to post-magmatic minerals from the same syenite samples a principally closed-system behaviour during cooling is implied. In contrast, for the granites an externally derived fluid phase is required to explain the extremely low epsilon(Nd) values of about -10 and low delta(18)O between +2.0 and +0.5parts per thousand for late-stage aegirine, indicating an open system in the late-stage history. In this study we show that the combination of phase equilibria constraints with stable and radiogenic isotope data on mineral separates can provide much better constraints on magma evolution during emplacement and crystallization than conventional whole-rock studies.

Modeling and control of electromechanical systems

The material presented in the these notes covers the sessions Modelling of electromechanical systems, Passive control theory I and Passive control theory II of the II EURON/GEOPLEX Summer School on Modelling and Control of Complex Dynamical Systems.We start with a general description of what an electromechanical system is from a network modelling point of view. Next, a general formulation in terms of PHDS is introduced, and some of the previous electromechanical systems are rewritten in this formalism. Power converters, which are variable structure systems (VSS), can also be given a PHDS form.We conclude the modelling part of these lectures with a rather complex example, showing the interconnection of subsystems from several domains, namely an arrangement to temporally store the surplus energy in a section of a metropolitan transportation system based on dc motor vehicles, using either arrays of supercapacitors or an electric poweredflywheel. The second part of the lectures addresses control of PHD systems. We first present the idea of control as power connection of a plant and a controller. Next we discuss how to circumvent this obstacle and present the basic ideas of Interconnection and Damping Assignment (IDA) passivity-based control of PHD systems.

Variable queen number in ant colonies: no impact on queen turnover, inbreeding, and population genetic differentiation in the ant Formica selysi.

Variation in queen number alters the genetic structure of social insect colonies, which in turn affects patterns of kin-selected conflict and cooperation. Theory suggests that shifts from single- to multiple-queen colonies are often associated with other changes in the breeding system, such as higher queen turnover, more local mating, and restricted dispersal. These changes may restrict gene flow between the two types of colonies and it has been suggested that this might ultimately lead to sympatric speciation. We performed a detailed microsatellite analysis of a large population of the ant Formica selysi, which revealed extensive variation in social structure, with 71 colonies headed by a single queen and 41 by multiple queens. This polymorphism in social structure appeared stable over time, since little change in the number of queens per colony was detected over a five-year period. Apart from queen number, single- and multiple-queen colonies had very similar breeding systems. Queen turnover was absent or very low in both types of colonies. Single- and multiple-queen colonies exhibited very small but significant levels of inbreeding, which indicates a slight deviation from random mating at a local scale and suggests that a small proportion of queens mate with related males. For both types of colonies, there was very little genetic structuring above the level of the nest, with no sign of isolation by distance. These similarities in the breeding systems were associated with a complete lack of genetic differentiation between single- and multiple-queen colonies, which provides no support for the hypothesis that change in queen number leads to restricted gene flow between social forms. Overall, this study suggests that the higher rates of queen turnover, local mating, and population structuring that are often associated with multiple-queen colonies do not appear when single- and multiple-queen colonies still coexist within the same population, but build up over time in populations consisting mostly of multiple-queen colonies.

Debating the centre : the theory of principal qualificand (mukhyavisesya) in classical Indian philosophy

The theory of language has occupied a special place in the history of Indian thought. Indian philosophers give particular attention to the analysis of the cognition obtained from language, known under the generic name of śābdabodha. This term is used to denote, among other things, the cognition episode of the hearer, the content of which is described in the form of a paraphrase of a sentence represented as a hierarchical structure. Philosophers submit the meaning of the component items of a sentence and their relationship to a thorough examination, and represent the content of the resulting cognition as a paraphrase centred on a meaning element, that is taken as principal qualificand (mukhyaviśesya) which is qualified by the other meaning elements. This analysis is the object of continuous debate over a period of more than a thousand years between the philosophers of the schools of Mimāmsā, Nyāya (mainly in its Navya form) and Vyākarana. While these philosophers are in complete agreement on the idea that the cognition of sentence meaning has a hierarchical structure and share the concept of a single principal qualificand (qualified by other meaning elements), they strongly disagree on the question which meaning element has this role and by which morphological item it is expressed. This disagreement is the central point of their debate and gives rise to competing versions of this theory. The Mïmāmsakas argue that the principal qualificand is what they call bhāvanā ̒bringing into being̒, ̒efficient force̒ or ̒productive operation̒, expressed by the verbal affix, and distinct from the specific procedures signified by the verbal root; the Naiyāyikas generally take it to be the meaning of the word with the first case ending, while the Vaiyākaranas take it to be the operation expressed by the verbal root. All the participants rely on the Pāninian grammar, insofar as the Mimāmsakas and Naiyāyikas do not compose a new grammar of Sanskrit, but use different interpretive strategies in order to justify their views, that are often in overt contradiction with the interpretation of the Pāninian rules accepted by the Vaiyākaranas. In each of the three positions, weakness in one area is compensated by strength in another, and the cumulative force of the total argumentation shows that no position can be declared as correct or overall superior to the others. This book is an attempt to understand this debate, and to show that, to make full sense of the irreconcilable positions of the three schools, one must go beyond linguistic factors and consider the very beginnings of each school's concern with the issue under scrutiny. The texts, and particularly the late texts of each school present very complex versions of the theory, yet the key to understanding why these positions remain irreconcilable seems to lie elsewhere, this in spite of extensive argumentation involving a great deal of linguistic and logical technicalities. Historically, this theory arises in Mimāmsā (with Sabara and Kumārila), then in Nyāya (with Udayana), in a doctrinal and theological context, as a byproduct of the debate over Vedic authority. The Navya-Vaiyākaranas enter this debate last (with Bhattoji Dïksita and Kaunda Bhatta), with the declared aim of refuting the arguments of the Mïmāmsakas and Naiyāyikas by bringing to light the shortcomings in their understanding of Pāninian grammar. The central argument has focused on the capacity of the initial contexts, with the network of issues to which the principal qualificand theory is connected, to render intelligible the presuppositions and aims behind the complex linguistic justification of the classical and late stages of this debate. Reading the debate in this light not only reveals the rationality and internal coherence of each position beyond the linguistic arguments, but makes it possible to understand why the thinkers of the three schools have continued to hold on to three mutually exclusive positions. They are defending not only their version of the principal qualificand theory, but (though not openly acknowledged) the entire network of arguments, linguistic and/or extra-linguistic, to which this theory is connected, as well as the presuppositions and aims underlying these arguments.

CR1Dmod: A Matlab program to model 1D complex resistivity effects in electrical and electromagnetic surveys

We have constructed a forward modelling code in Matlab, capable of handling several commonly used electrical and electromagnetic methods in a 1D environment. We review the implemented electromagnetic field equations for grounded wires, frequency and transient soundings and present new solutions in the case of a non-magnetic first layer. The CR1Dmod code evaluates the Hankel transforms occurring in the field equations using either the Fast Hankel Transform based on digital filter theory, or a numerical integration scheme applied between the zeros of the Bessel function. A graphical user interface allows easy construction of 1D models and control of the parameters. Modelling results are in agreement with other authors, but the time of computation is less efficient than other available codes. Nevertheless, the CR1Dmod routine handles complex resistivities and offers solutions based on the full EM-equations as well as the quasi-static approximation. Thus, modelling of effects based on changes in the magnetic permeability and the permittivity is also possible.

Spatial prediction of monthly wind speeds in complex terrain with adaptive general regression neural networks

This paper presents the general regression neural networks (GRNN) as a nonlinear regression method for the interpolation of monthly wind speeds in complex Alpine orography. GRNN is trained using data coming from Swiss meteorological networks to learn the statistical relationship between topographic features and wind speed. The terrain convexity, slope and exposure are considered by extracting features from the digital elevation model at different spatial scales using specialised convolution filters. A database of gridded monthly wind speeds is then constructed by applying GRNN in prediction mode during the period 1968-2008. This study demonstrates that using topographic features as inputs in GRNN significantly reduces cross-validation errors with respect to low-dimensional models integrating only geographical coordinates and terrain height for the interpolation of wind speed. The spatial predictability of wind speed is found to be lower in summer than in winter due to more complex and weaker wind-topography relationships. The relevance of these relationships is studied using an adaptive version of the GRNN algorithm which allows to select the useful terrain features by eliminating the noisy ones. This research provides a framework for extending the low-dimensional interpolation models to high-dimensional spaces by integrating additional features accounting for the topographic conditions at multiple spatial scales. Copyright (c) 2012 Royal Meteorological Society.

The Mont Collon mafic complex (Austroalpine Dent Blanche nappe) : permian evolution of the Western European mantle

Résumé: Le complexe du Mont Collon (nappe de la Dent Blanche, Austroalpin) est l'un des exemples les mieux préservés du magmatisme mafique permien des Alpes occidentales. Il est composé d'affleurements discontinus et d'une stratification magmatique en son centre (Dents de Bertol) et est composé à 95% de roches mafiques cumulatives (gabbros à olivine et/ou cpx, anorthositiques, troctolites, wehrlites et wehrlites à plagioclase) et localement de quelques gabbros pegmatitiques. Ces faciès sont recoupés par de nombreux filons acides (aphtes, pegmatites quartziques, microgranodiorites et filons anorthositiques) et mafiques tardifs (dikes mélanocrates riches en Fe et Ti). Les calculs thermométriques (équilibre olivine-augite) montrent des températures de 1070-1120 ± 6°C, tandis que le thermomètre amphibole-plagioclase indique une température de 740 ± 40°C à 0.5 GPa pour les amphiboles magmatiques tardives. La geobarométrie sur pyroxène donne des pressions moyennes de 0.3-0.6 GPa, indiquant un emplacement dans la croûte moyenne. De plus, les températures obtenues sur des amphiboles coronitiques indiquent des températures de l'ordre de 700 ± 40°C confirmant que les réactions coronitiques apparaissent dans des conditions subsolidus. Les âges concordants U/Pb sur zircons de 284.2 ± 0.6 et 282.9 ± 0.6 Ma obtenus sur un gabbro pegmatitique et une pegmatitique quartzique, sont interprétés comme des âges de cristallisation. Les datations 40Ar/39Ar sur amphiboles des filons mélanocrates donnent un âge plateau de 260.2 ± 0.7 Ma, qui est probablement très proche de l'âge de cristallisation. Ainsi, cet age 40Ar/39Ar indique un second évènement magmatique au sein du complexe. Les compositions des roches totales en éléments majeurs et traces montrent peu de variations, ainsi que le Mg# (75-80). Les éléments traces enregistrent le caractère cumulatif des roches (anomalie positive en Eu) et révèlent des anomalies négatives systématiques en Nb, Ta, Zr, Hf et Ti dans les faciès basiques. Le manque de corrélation entre éléments majeurs et traces est caractéristique d'un processus de cristallisation in situ impliquant une quantité variable de liquide interstitiel (L) entre les phases cumulus. Les distributions des éléments traces dans les minéraux sont homogènes, indiquant une rééquilibration .subsolidus entre cristaux et liquide interstitiel. Un modèle quantitatif basé sur les équations de cristallisation in situ de Langmuir reproduisent correctement les concentrations en terres rares légères des minéraux cumulatifs montrant la présence de 0 à 35% de liquide interstitiel L pour des degrés de différenciation F de 0 à 45%, par rapport au faciès les moins évolués du complexe. En outre, les valeurs de L sont bien corrélées avec les proportions modales d'amphibole interstitielle et les concentrations en éléments incompatibles des roches (Zr, Nb). Le liquide parental calculé des cumulats du Mont Collon est caractérisé par un enrichissement relatif en terres rares légères et Th, un appauvrissement en terres rares lourdes typique d'une affinité transitionnelle (T-MORB) et une forte anomalie négative en Nb-Ta. Les roches cumulatives montrent des compositions isotopiques en Nd-Sr proches de la terre globale silicatée (BSE), soit 0.6<εNdi<+3.2, 0.7045<87Sr/86Sri<0.7056. Les rapports initiaux en Pb indiquent une source dans le manteau enrichi subcontinental lithosphérique, préalablement contaminé par des sédiments océaniques. Les dikes mélanocrates Fe-Ti sont représentatifs de liquides et ont des spectres de terres rares enrichis, une anomalie positive en Nb-Ta et des εNdi de +7, des 87Sr/86Sri de 0.703 et des rapports initiaux en Pb, similaires à ceux des basaltes d'île océanique, indiquant une source asthénosphérique modérément appauvrie. Ainsi, la fusion partielle du manteau lithosphérique subcontinental est induite par l'amincissement post-orogénique et la remontée de l'asthénosphère. Les filons mélanocrates proviennent, après délamination du manteau lithosphérique, de la fusion de l'asthénosphère. Abstract The early Permian Mont Collon mafic complex (Dent Blanche nappe, Austroalpine nappe system) is one of the best preserved examples of the Permian mafic magmatism in the Western Alps. It is composed of discontinuous exposures and a well-preserved magmatic layering (the Dents de Bertol cliff) crops out in the center part of the complex. It mainly consists of cumulative mafic rocks, which represent 95 vol-% of the mafic complex (ol- and cpx-bearing gabbros and rare anorthositic layers, troctolites, wehrlites and plagioclase-wehrlites) and locally pegmatitic gabbros. All these facies are crosscut by widespread acidic (aplites, quartz-rich pegmatites, microgranodiorites) and late mafic Fe-Ti melanocratic dikes. Olivine-augite thermometric calculations yield a range of 1070-1120 ± 6°C, while amphibole-plagioclase thermometer yields a temperature of 740 ± 40°C at 0.5 GPa. Pyroxene geobarometry points to a pressure of 0.3-0.6 GPa, indicating a middle crustal level of emplacement. Moreover, temperature calculations on the Mont Conon coronitic amphiboles indicate temperatures of 700 ± 40°C, close to those calculated for magmatic amphiboles. These temperatures confirm that coronitic reactions occurred at subsolidus conditions. ID-TIMS U/Pb zircon ages of 284.2 ± 0.6 and 282.9 ± 0.6 Ma obtained on a pegmatitic gabbro and a quartz-pegmatitic dike, respectively, were interpreted as the crystallization ages of these rocks. 40Ar/39Ar dating on amphiboles from Fe-Ti melanocratic dikes yields a plateau age of 260.2 ± 0.7 Ma, which is probably very close to the crystallization age. Consequently, this 40Ar/P39Ar age indicates a second magmatic event. Whole-rock major- and trace-element compositions show little variation across the whole intrusion and Mg-number stays within a narrow range (75-80). Trace-element concentrations record the cumulative nature of the rocks (e.g. positive Eu anomaly) and reveal systematic Nb, Ta, Zr, Hf and Ti negative anomalies for all basic facies. The lack of correlation between major and trace elements is characteristic of an in situ crystallization process involving variable amounts of interstitial liquid (L) trapped between the cumulus mineral phases. LA-ICPMS measurements show that trace-element distributions in minerals are homogeneous, pointing to subsolidus re-equilibration between crystals and interstitial melts. A quantitative modeling based on Langmuir's in situ crystallization equation successfully reproduced the Rare Earth Element (REE) concentrations in cumulitic minerals. The calculated amounts of interstitial liquid L vary between 0 and 35% for degrees of differentiation F of 0 to 45%, relative to the least evolved facies of the intrusion. Furthermore, L values are well correlated with the modal proportions of interstitial amphibole and whole-rock incompatible trace-element concentrations (e.g. Zr, Nb) of the tested samples. The calculated parental melt of the Mont Collon cumulates is characterized by a relative enrichment in Light REE and Th, a depletion in Heavy REE, typical of a transitional affinity (T-MORB), and strong negative Nb-Ta anomaly. Cumulative rocks display Nd-Sr isotopic compositions close to the BSE (-0.6 < εNdi < +3.2, 0.7045 < 87Sr/86Sri < 0.7056). Initial Pb ratios point to an origin from the melting of an enriched subcontinental lithospheric mantle source, previously contaminated at the source by oceanic sediments. The contrasted alkaline Fe-Ti melanocratic dikes are representative of liquids. They display enriched fractionated REE patterns, a positive Nb-Ta anomaly and εNdi of +7, 87Sr/86Sri of 0.703 and initial Pb ratios, all reminiscent of Ocean Island Basalt-type rocks, pointing to a moderately