On the duration of negative surplus

Doutoramento em Matemática

The average mixing matrix signature

Laplacian-based descriptors, such as the Heat Kernel Signature and the Wave Kernel Signature, allow one to embed the vertices of a graph onto a vectorial space, and have been successfully used to find the optimal matching between a pair of input graphs. While the HKS uses a heat di↵usion process to probe the local structure of a graph, the WKS attempts to do the same through wave propagation. In this paper, we propose an alternative structural descriptor that is based on continuoustime quantum walks. More specifically, we characterise the structure of a graph using its average mixing matrix. The average mixing matrix is a doubly-stochastic matrix that encodes the time-averaged behaviour of a continuous-time quantum walk on the graph. We propose to use the rows of the average mixing matrix for increasing stopping times to develop a novel signature, the Average Mixing Matrix Signature (AMMS). We perform an extensive range of experiments and we show that the proposed signature is robust under structural perturbations of the original graphs and it outperforms both the HKS and WKS when used as a node descriptor in a graph matching task.

Keeping Variables within Bounds: Using Information between Observations

This research develops an econometric framework to analyze time series processes with bounds. The framework is general enough that it can incorporate several different kinds of bounding information that constrain continuous-time stochastic processes between discretely-sampled observations. It applies to situations in which the process is known to remain within an interval between observations, by way of either a known constraint or through the observation of extreme realizations of the process. The main statistical technique employs the theory of maximum likelihood estimation. This approach leads to the development of the asymptotic distribution theory for the estimation of the parameters in bounded diffusion models. The results of this analysis present several implications for empirical research. The advantages are realized in the form of efficiency gains, bias reduction and in the flexibility of model specification. A bias arises in the presence of bounding information that is ignored, while it is mitigated within this framework. An efficiency gain arises, in the sense that the statistical methods make use of conditioning information, as revealed by the bounds. Further, the specification of an econometric model can be uncoupled from the restriction to the bounds, leaving the researcher free to model the process near the bound in a way that avoids bias from misspecification. One byproduct of the improvements in model specification is that the more precise model estimation exposes other sources of misspecification. Some processes reveal themselves to be unlikely candidates for a given diffusion model, once the observations are analyzed in combination with the bounding information. A closer inspection of the theoretical foundation behind diffusion models leads to a more general specification of the model. This approach is used to produce a set of algorithms to make the model computationally feasible and more widely applicable. Finally, the modeling framework is applied to a series of interest rates, which, for several years, have been constrained by the lower bound of zero. The estimates from a series of diffusion models suggest a substantial difference in estimation results between models that ignore bounds and the framework that takes bounding information into consideration.

Price manipulation: theoretical models and empirical investigation

Understanding why market manipulation is conducted, under which conditions it is the most profitable and investigating the magnitude of these practices are crucial questions for financial regulators. Closing price manipulation induced by derivatives’ expiration is the primary subject of this thesis. The first chapter provides a mathematical framework in continuous time to study the incentive to manipulate a set of securities induced by a derivative position. An agent holding a European-type contingent claim, depending on the price of a basket of underlying securities, is considered. The agent can affect the price of the underlying securities by trading on each of them before expiration. The elements of novelty are at least twofold: (1) a multi-asset market is considered; (2) the problem is solved by means of both classic optimisation and stochastic control techniques. Both linear and option payoffs are considered. In the second chapter an empirical investigation is conducted on the existence of expiration day effects on the UK equity market. Intraday data on FTSE 350 stocks over a six-year period from 2015-2020 are used. The results show that the expiration of index derivatives is associated with a rise in both trading activity and volatility, together with significant price distortions. The expiration of single stock options appears to have little to no impact on the underlying securities. The last chapter examines the existence of patterns in line with closing price manipulation of UK stocks on option expiration days. The main contributions are threefold: (1) this is one of the few empirical studies on manipulation induced by the options market; (2) proprietary equity orderbook and transaction data sets are used to define manipulation proxies, providing a more detailed analysis; (3) the behaviour of proprietary trading firms is studied. Despite the industry concerns, no evidence is found of this type of manipulative behaviour.

A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.

An optimal control tool for trajectory generation of autonomous drones

In the recent years, autonomous aerial vehicles gained large popularity in a variety of applications in the field of automation. To accomplish various and challenging tasks the capability of generating trajectories has assumed a key role. As higher performances are sought, traditional, flatness-based trajectory generation schemes present their limitations. In these approaches the highly nonlinear dynamics of the quadrotor is, indeed, neglected. Therefore, strategies based on optimal control principles turn out to be beneficial, since in the trajectory generation process they allow the control unit to best exploit the actual dynamics, and enable the drone to perform quite aggressive maneuvers. This dissertation is then concerned with the development of an optimal control technique to generate trajectories for autonomous drones. The algorithm adopted to this end is a second-order iterative method working directly in continuous-time, which, under proper initialization, guarantees quadratic convergence to a locally optimal trajectory. At each iteration a quadratic approximation of the cost functional is minimized and a decreasing direction is then obtained as a linear-affine control law, after solving a differential Riccati equation. The algorithm has been implemented and its effectiveness has been tested on the vectored-thrust dynamical model of a quadrotor in a realistic simulative setup.

Modulation of Mediotemporal and Ventrostriatal Function in Humans by Delta 9-Tetrahydrocannabinol A Neural Basis for the Effects of Cannabis sativa on Learning and Psychosis

Context: Cannabis sativa use can impair verbal learning, provoke acute psychosis, and increase the risk of schizophrenia. It is unclear where C sativa acts in the human brain to modulate verbal learning and to induce psychotic symptoms. Objectives: To investigate the effects of 2 main psychoactive constituents of C sativa, Delta 9-tetrahydrocannabinol (Delta 9-THC) and cannabidiol, on regional brain function during verbal paired associate learning. Design: Subjects were studied on 3 separate occasions using a block design functional magnetic resonance imaging paradigm while performing a verbal paired associate learning task. Each imaging session was preceded by the ingestion of Delta 9-THC (10 mg), cannabidiol (600 mg), or placebo in a double-blind, randomized, placebo-controlled, repeated-measures, within-subject design. Setting: University research center. Participants: Fifteen healthy, native English-speaking, right-handed men of white race/ethnicity who had used C sativa 15 times or less and had minimal exposure to other illicit drugs in their lifetime. Main Outcome Measures: Regional brain activation ( blood oxygen level-dependent response), performance in a verbal learning task, and objective and subjective ratings of psychotic symptoms, anxiety, intoxication, and sedation. Results: Delta 9-Tetrahydrocannabinol increased psychotic symptoms and levels of anxiety, intoxication, and sedation, whereas no significant effect was noted on these parameters following administration of cannabidiol. Performance in the verbal learning task was not significantly modulated by either drug. Administration of Delta 9-THC augmented activation in the parahippocampal gyrus during blocks 2 and 3 such that the normal linear decrement in activation across repeated encoding blocks was no longer evident. Delta 9-Tetrahydrocannabinol also attenuated the normal time-dependent change in ventrostriatal activation during retrieval of word pairs, which was directly correlated with concurrently induced psychotic symptoms. In contrast, administration of cannabidiol had no such effect. Conclusion: The modulation of mediotemporal and ventrostriatal function by Delta 9-THC may underlie the effects of C sativa on verbal learning and psychotic symptoms, respectively.

Fronts with continuous waiting-time distributions: Theory and application to virus infections

We generalize to arbitrary waiting-time distributions some results which were previously derived for discrete distributions. We show that for any two waiting-time distributions with the same mean delay time, that with higher dispersion will lead to a faster front. Experimental data on the speed of virus infections in a plaque are correctly explained by the theoretical predictions using a Gaussian delay-time distribution, which is more realistic for this system than the Dirac delta distribution considered previously [J. Fort and V. Méndez, Phys. Rev. Lett.89, 178101 (2002)]

Molecular analysis of Sigma-1 receptor modulation of the dopamine transporter

Sigma (σ) receptors are well established as a non-opioid, non-phencyclidine, and haloperidol-sensitive receptor family with its own binding profile and a characteristic distribution in the central nervous system (CNS) as well as in endocrine, immune, and some peripheral tissues. Two σ receptors subtypes, termed σ1 and σ2, have been pharmacologically characterized, but, to date, only the σ1 has also been cloned. Activation of σ1 receptors alter several neurotransmitter systems and dopamine (DA) neurotrasmission has been often shown to constitute an important target of σ receptors in different experimental models; however the exact role of σ1 receptor in dopaminergic neurotransmission remains unclear. The DA transporter (DAT) modulates the spatial and temporal aspects of dopaminergic synaptic transmission and interprer the primary mechanism by wich dopaminergic neurons terminate the signal transmission. For this reason present studies have been focused in understanding whether, in cell models, the human subtype of σ1 (hσ1) receptor is able to directly modulate the human DA transporter (hDAT). In the first part of this thesis, HEK-293 and SH-SY5Y cells were permanently transfected with the hσ1 receptor. Subsequently, they were transfected with another plasmid for transiently expressing the hDAT. The hDAT activity was estimated using the described [3H]DA uptake assay and the effects of σ ligands were evaluated by measuring the uptaken [3H]DA after treating the cells with known σ agonists and antagonists. Results illustrated in this thesis demonstrate that activation of overexpressed hσ1 receptors by (+)-pentazocine, the σ1 agonist prototype, determines an increase of 40% of the extracellular [3H]DA uptake, in comparison to non-treated controls and the σ1 antagonists BD-1047 and NE-100 prevent the positive effect of (+)-pentazocine on DA reuptake DA is likely to be considered a neurotoxic molecule. In fact, when levels of intracellular DA abnormally invrease, vescicles can’t sequester the DA which is metabolized by MAO (A and B) and COMT with consequent overproduction of oxygen reactive species and toxic catabolites. Stress induced by these molecules leads cells to death. Thus, for the second part of this thesis, experiments have been performed in order to investigate functional alterations caused by the (+)-pentazocine-mediated increase of DA uptake; particularly it has been investigated if the increase of intracellular [DA] could affect cells viability. Results obtained from this study demonstrate that (+)-pentazocine alone increases DA cell toxicity in a concentration-dependent manner only in cells co-expressing hσ1 and hDAT and σ1 antagonists are able to revert the (+)-pentazocine-induced increase of cell susceptibility to DA toxicity. In the last part of this thesis, the functional cross-talking between hσ1 receptor and hDAT has been further investigated using confocal microscopy. From the acquired data it could be suggested that, following exposure to (+)-pentazocine, the hσ1 receptors massively translocate towards the plasma membrane and colocalize with the hDATs. However, any physical interaction between the two proteins remains to be proved. In conclusion, the presented study shows for the first time that, in cell models, hσ1 receptors directly modulate the hDAT activity. Facilitation of DA uptake induced by (+)-pentazocine is reflected on the increased cell susceptibility to DA toxicity; these effects are prevented by σ1 selective antagonists. Since numerous compounds, including several drugs of abuse, bind to σ1 receptors and activating them could facilitate the damage of dopaminergic neurons, the reported protective effect showed by σ1 antagonists would represent the pharmacological basis to test these compounds in experimental models of dopaminergic neurodegenerative diseases (i.e. Parkinson’s Disease).

Temperature, water level and bathymetry of thermokarst lakes in the continuous permafrost zone of northern Siberia - Lena River Delta, Siberia

Thermokarst lakes are typical features of the northern permafrost ecosystems, and play an important role in the thermal exchange between atmosphere and subsurface. The objective of this study is to describe the main thermal processes of the lakes and to quantify the heat exchange with the underlying sediments. The thermal regimes of five lakes located within the continuous permafrost zone of northern Siberia (Lena River Delta) were investigated using hourly water temperature and water level records covering a 3-year period (2009-2012), together with bathymetric survey data. The lakes included thermokarst lakes located on Holocene river terraces that may be connected to Lena River water during spring flooding, and a thermokarst lake located on deposits of the Pleistocene Ice Complex. Lakes were covered by ice up to 2 m thick that persisted for more than 7 months of the year, from October until about mid-June. Lake-bottom temperatures increased at the start of the ice-covered period due to upward-directed heat flux from the underlying thawed sediment. Prior to ice break-up, solar radiation effectively warmed the water beneath the ice cover and induced convective mixing. Ice break-up started at the beginning of June and lasted until the middle or end of June. Mixing occurred within the entire water column from the start of ice break-up and continued during the ice-free periods, as confirmed by the Wedderburn numbers, a quantitative measure of the balance between wind mixing and stratification that is important for describing the biogeochemical cycles of lakes. The lake thermal regime was modeled numerically using the FLake model. The model demonstrated good agreement with observations with regard to the mean lake temperature, with a good reproduction of the summer stratification during the ice-free period, but poor agreement during the ice-covered period. Modeled sensitivity to lake depth demonstrated that lakes in this climatic zone with mean depths > 5 m develop continuous stratification in summer for at least 1 month. The modeled vertical heat flux across the bottom sediment tends towards an annual mean of zero, with maximum downward fluxes of about 5 W/m**2 in summer and with heat released back into the water column at a rate of less than 1 W/m**2 during the ice-covered period. The lakes are shown to be efficient heat absorbers and effectively distribute the heat through mixing. Monthly bottom water temperatures during the ice-free period range up to 15 °C and are therefore higher than the associated monthly air or ground temperatures in the surrounding frozen permafrost landscape. The investigated lakes remain unfrozen at depth, with mean annual lake-bottom temperatures of between 2.7 and 4 °C.

Simultaneous determination of delta(33) SV-CDT and delta S-34(V-CDT) using masses 48, 49 and 50 on a continuous flow isotope ratio mass spectrometer

A new, fast, continuous flow technique is described for the simultaneous determination of 633 S and delta(34)S using SO masses 48, 49 and 50. Analysis time is similar to5min/sample with measurement precision and accuracy better than +/-0.3parts per thousand. This technique, which has been set up using IAEA Ag2S standards S-1, S-2 and S-3, allows for the fast determination of mass-dependent or mass-independent fractionation (MIF) effects in sulfide, organic sulfur samples and possibly sulfate. Small sample sizes can be analysed directly, without chemical pre-treatment. Robustness of the technique for natural versus artificial standards was demonstrated by analysis of a Canon Diablo troilite, which gave a delta(33)S of 0.04parts per thousand and a delta(34)S of -0.06parts per thousand compared to the values obtained for S-1 of 0.07parts per thousand and -0.20parts per thousand, respectively. Two pyrite samples from a banded-iron formation from the 3710 Ma Isua Greenstone Belt were analysed using this technique and yielded MIF (Delta(33)S of 2.45 and 3.31parts per thousand) comparable to pyrite previously analysed by secondary ion probe. Copyright (C) 2004 John Wiley Sons, Ltd.

Facies, delta(13)C, delta(15)N and C/N analyses in a late Quaternary compound estuarine fill, northern Brazil and relation to sea level

The present work integrates sedimentary facies, (14)C dating, delta(13)C, delta(15)N, and C/N with geologic and geomorphologic data available from literature. The aim was to characterize the depositional settings of a late Quaternary estuary in northeastern Marajo Island and analyze its evolution within the context of relative sea level fluctuations. The data derive from four continuous cores along a proximal-to-distal transect of a paleoestuary, previously recognized using remote sensing information. Fifteen sediment samples recorded ages ranging from 42,580 +/- 1430 to 3184 +/- 37 (14)C yr B.P. Fades analysis indicated fine- to coarse-grained sands with parallel lamination or cross stratification, massive or laminated muds and heterolithic deposits. delta(13)C (-28.1 parts per thousand to -19.7 parts per thousand, mean = -23.0 parts per thousand), delta(15)N (+ 14.8 parts per thousand to + 4.7 parts per thousand, mean = + 9.2 parts per thousand) and C/N (14.5 to 1.5, mean = 7.9) indicate mostly marine and freshwater phytoplankton sources for the organic matter. The results confirm a large late Quaternary paleoestuary in northeastern Marajo Island. The distribution of delta(13)C, delta(15)N, and C/N, together with fades associations, led to identify depositional settings related to fluvial channel, floodplain, tidal channel/tidal flat, central basin, tidal delta, and tidal inlet/sand barrier. These deposits are consistent with a wave-dominated estuary. Variations in stratigraphy and geochemistry are controlled by changes in relative sea level, revealing a main transgression from an undetermined time around 42,000 (14)C yr B.P. and 29,340 (+/- 200) (14)C yr B.P., which is synchronous to the overall drop in sea level after the last interglacial. Following this period, and probably until 9110 +/- 37 (14)C yr B.P., i.e., during a time interval encompassing two glacial episodes including the Last Glacial and the Younger Dryas, there was a pronounced drop in sea level, recorded by the development of a major erosional discontinuity due to valley re-incision. Sea level rose again until 5464 +/- 40 (14)C yr B.P, just before the main worldwide mid-Holocene transgressive peak. Mid to late Holocene coastal progradation ended the Marajo paleoestuarine history, and promoted the establishment of continental conditions throughout the island. The divergence comparing the Marajo sea level behavior with the eustatic curve allows hypothesizing that post-rifting tectonics along the Brazilian Equatorial margin influenced the sedimentary evolution of the studied paleoestuary. Considering that sedimentary facies in estuarine settings are highly variable both laterally and vertically, the present integration of facies with isotope and elemental analyses was crucial to provide a more precise interpretation of the Late Pleistocene and Holocene Marajo paleoestuary, and analyze its sea level history within the eustatic and tectonic context. (C) 2010 Elsevier B.V. All rights reserved.

Tonal Modulation and Subjective Time

This work investigated listeners` sense of the temporal expression of tonal modulation. One experiment described the effects on retrospective reproductions of sudden and gradual modulations to close and distant keys. The results showed that modulations elicit time underestimations as an inverse function of interkey distances, with a major impact for sudden modulations. A proposed vectorial model - ""Expected Development Fraction"" (EDF) - describes the development of expectations when an interkey distance is traversed during a certain time interval. This expected development is longer than the perceived duration, leading to underestimation of the time.

Qualitative and Quantitative Real Time Myocardial Contrast Echocardiography for Detecting Hibernating Myocardium

Background: Real time myocardial contrast echocardiography (RTMCE) is an emerging imaging modality for assessing myocardial perfusion that allows for noninvasive quantification of regional myocardial blood flow (MBF). Aim: We sought to assess the value of qualitative analysis of myocardial perfusion and quantitative assessment of myocardial blood flow (MBF) by RTMCE for predicting regional function recovery in patients with ischemic heart disease who underwent coronary artery bypass grafting (CABG). Methods: Twenty-four patients with coronary disease and left ventricular systolic dysfunction (ejection fraction < 45%) underwent RTMCE before and 3 months after CABG. RTMCE was performed using continuous intravenous infusion of commercially available contrast agent with low mechanical index power modulation imaging. Viability was defined by qualitative assessment of myocardial perfusion as homogenous opacification at rest in >= 2 segments of anterior or >= 1 segment of posterior territory. Viability by quantitative assessment of MBF was determined by receiver-operating characteristics curve analysis. Results: Regional function recovery was observed in 74% of territories considered viable by qualitative analysis of myocardial perfusion and 40% of nonviable (P = 0.03). Sensitivity, specificity, positive and negative predictive values of qualitative RTMCE for detecting regional function recovery were 74%, 60%, 77%, and 56%, respectively. Cutoff value of MBF for predicting regional function recovery was 1.76 (AUC = 0.77; 95% CI = 0.62-0.92). MBF obtained by RTMCE had sensitivity of 91%, specificity of 50%, positive predictive value of 75%, and negative predictive value of 78%. Conclusion: Qualitative and quantitative RTMCE provide good accuracy for predicting regional function recovery after CABG. Determination of MBF increases the sensitivity for detecting hibernating myocardium. (Echocardiography 2011;28:342-349).