Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation

2000 Mathematics Subject Classification: 54H25, 47H10.

On a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series

MSC 2010: 33C20

Probabilistic Approach to the Neumann Problem for a Symmetric Operator

2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.

Plus-Minus Property as a Generalization of the Daugavet Property

2000 Mathematics Subject Classification: Primary 46B20. Secondary 47A99, 46B42.

Probabilistic topographic information visualisation

The focus of this thesis is the extension of topographic visualisation mappings to allow for the incorporation of uncertainty. Few visualisation algorithms in the literature are capable of mapping uncertain data with fewer able to represent observation uncertainties in visualisations. As such, modifications are made to NeuroScale, Locally Linear Embedding, Isomap and Laplacian Eigenmaps to incorporate uncertainty in the observation and visualisation spaces. The proposed mappings are then called Normally-distributed NeuroScale (N-NS), T-distributed NeuroScale (T-NS), Probabilistic LLE (PLLE), Probabilistic Isomap (PIso) and Probabilistic Weighted Neighbourhood Mapping (PWNM). These algorithms generate a probabilistic visualisation space with each latent visualised point transformed to a multivariate Gaussian or T-distribution, using a feed-forward RBF network. Two types of uncertainty are then characterised dependent on the data and mapping procedure. Data dependent uncertainty is the inherent observation uncertainty. Whereas, mapping uncertainty is defined by the Fisher Information of a visualised distribution. This indicates how well the data has been interpolated, offering a level of ‘surprise’ for each observation. These new probabilistic mappings are tested on three datasets of vectorial observations and three datasets of real world time series observations for anomaly detection. In order to visualise the time series data, a method for analysing observed signals and noise distributions, Residual Modelling, is introduced. The performance of the new algorithms on the tested datasets is compared qualitatively with the latent space generated by the Gaussian Process Latent Variable Model (GPLVM). A quantitative comparison using existing evaluation measures from the literature allows performance of each mapping function to be compared. Finally, the mapping uncertainty measure is combined with NeuroScale to build a deep learning classifier, the Cascading RBF. This new structure is tested on the MNist dataset achieving world record performance whilst avoiding the flaws seen in other Deep Learning Machines.

Specification and quantitative analysis of probabilistic cloud deployment patterns

Cloud computing is a new technological paradigm offering computing infrastructure, software and platforms as a pay-as-you-go, subscription-based service. Many potential customers of cloud services require essential cost assessments to be undertaken before transitioning to the cloud. Current assessment techniques are imprecise as they rely on simplified specifications of resource requirements that fail to account for probabilistic variations in usage. In this paper, we address these problems and propose a new probabilistic pattern modelling (PPM) approach to cloud costing and resource usage verification. Our approach is based on a concise expression of probabilistic resource usage patterns translated to Markov decision processes (MDPs). Key costing and usage queries are identified and expressed in a probabilistic variant of temporal logic and calculated to a high degree of precision using quantitative verification techniques. The PPM cost assessment approach has been implemented as a Java library and validated with a case study and scalability experiments. © 2012 Springer-Verlag Berlin Heidelberg.

Towards probabilistic synchronization of local controllers

The traditional use of global and centralised control methods, fails for large, complex, noisy and highly connected systems, which typify many real world industrial and commercial systems. This paper provides an efficient bottom up design of distributed control in which many simple components communicate and cooperate to achieve a joint system goal. Each component acts individually so as to maximise personal utility whilst obtaining probabilistic information on the global system merely through local message-passing. This leads to an implied scalable and collective control strategy for complex dynamical systems, without the problems of global centralised control. Robustness is addressed by employing a fully probabilistic design, which can cope with inherent uncertainties, can be implemented adaptively and opens a systematic rich way to information sharing. This paper opens the foreseen direction and inspects the proposed design on a linearised version of coupled map lattice with spatiotemporal chaos. A version close to linear quadratic design gives an initial insight into possible behaviours of such networks.

On Probabilistic Rationing Methods

Rationing occurs if the demand for a certain good exceeds its supply. In such situations a rationing method has to be specified in order to determine the allocation of the scarce good to the agents. Moulin (1999) introduced the notion of probabilistic rationing methods for the discrete framework. In this paper we establish a link between classical and probabilistic rationing methods. In particular, we assign to any given classical rationing method a probabilistic rationing method with minimal variance among those probabilistic rationing methods, which result in the same expected distributions as the given classical rationing method.

A generalization of correlated equilibrium: A new protocol

A new correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is introduced for finite games. After randomization over the outcome space, players have the choice either to follow the recommendation of an umpire blindly or freely choose some other action except the one suggested. This scheme can lead to Pareto-better outcomes than the simple extension introduced by [Moulin, H., Vial, J.-P., 1978. Strategically zero-sum games: the class of games whose completely mixed equilibria cannot be improved upon. International Journal of Game Theory 7, 201–221]. The informational and interpretational aspects of soft correlated equilibria are also discussed in detail. The power of the generalization is illustrated in the prisoners’s dilemma and a congestion game.

Determinisztikus és valószínűségi elosztási eljárások (Deterministic and probabilistic rationing methods)

Az életben számtalan olyan esettel találkozunk, amikor egy jószág iránti kereslet meghaladja a rendelkezésre álló kínálatot. Példaként említhetjük a kárpótlási igényeket, egy csődbement cég hitelezőinek igényeit, valamely szerv átültetésére váró betegek sorát stb. Ilyen helyzetekben valamilyen eljárás szerint oszthatjuk el a szűkös mennyiséget a szereplők között. Szokás megkülönböztetni a determinisztikus és a sztochasztikus elosztási eljárásokat, jóllehet sok esetben csak a determinisztikus eljárásokat alkalmazzák. Azonban igazságossági szempontból gyakran használnak sztochasztikus elosztási eljárásokat is, mint például tette azt az Egyesült államok hadserege a második világháború végét követően a külföldön állomásozó katonáinak visszavonásakor, illetve a vietnami háború során behívandó személyek kiválasztásakor. / === / We investigated the minimal variance methods introduced in Tasnádi [6] based on seven popular axioms. We proved that if a deterministic rationing method satisfies demand monotonicity, resource monotonicity, equal treatment of equals and self-duality, than the minimal variance methods associated with the given deterministic rationing method also satisfies demand monotonicity, resource monotonicity, equal treatment of equals and self-duality. Furthermore, we found that the consistency, the lower composition and the upper composition of a deterministic rationing method does not imply the consistency, the lower composition and the upper composition of a minimal variance method associated with the given deterministic rationing method.

Measuring centrality by a generalization of degree

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes in a network, for which purpose a number of centrality measures have been developed. This paper proposes a new parametric family of centrality measures called generalized degree. It is based on the idea that a relationship to a more interconnected node contributes to centrality in a greater extent than a connection to a less central one. Generalized degree improves on degree by redistributing its sum over the network with the consideration of the global structure. Application of the measure is supported by a set of basic properties. A sufficient condition is given for generalized degree to be rank monotonic, excluding counter-intuitive changes in the centrality ranking after certain modifications of the network. The measure has a graph interpretation and can be calculated iteratively. Generalized degree is recommended to apply besides degree since it preserves most favorable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish between their importance.

A probabilistic analysis of the biometrics menagerie existence: case study in fingerprint data

Until recently the use of biometrics was restricted to high-security environments and criminal identification applications, for economic and technological reasons. However, in recent years, biometric authentication has become part of daily lives of people. The large scale use of biometrics has shown that users within the system may have different degrees of accuracy. Some people may have trouble authenticating, while others may be particularly vulnerable to imitation. Recent studies have investigated and identified these types of users, giving them the names of animals: Sheep, Goats, Lambs, Wolves, Doves, Chameleons, Worms and Phantoms. The aim of this study is to evaluate the existence of these users types in a database of fingerprints and propose a new way of investigating them, based on the performance of verification between subjects samples. Once introduced some basic concepts in biometrics and fingerprint, we present the biometric menagerie and how to evaluate them.

A probabilistic analysis of the biometrics menagerie existence: case study in fingerprint data

Until recently the use of biometrics was restricted to high-security environments and criminal identification applications, for economic and technological reasons. However, in recent years, biometric authentication has become part of daily lives of people. The large scale use of biometrics has shown that users within the system may have different degrees of accuracy. Some people may have trouble authenticating, while others may be particularly vulnerable to imitation. Recent studies have investigated and identified these types of users, giving them the names of animals: Sheep, Goats, Lambs, Wolves, Doves, Chameleons, Worms and Phantoms. The aim of this study is to evaluate the existence of these users types in a database of fingerprints and propose a new way of investigating them, based on the performance of verification between subjects samples. Once introduced some basic concepts in biometrics and fingerprint, we present the biometric menagerie and how to evaluate them.

A probabilistic approach to assess hydrate formation and design preventive measures

Formation of hydrates is one of the major flow assurance problems faced by the oil and gas industry. Hydrates tend to form in natural gas pipelines with the presence of water and favorable temperature and pressure conditions, generally low temperatures and corresponding high pressures. Agglomeration of hydrates can result in blockage of flowlines and equipment, which can be time consuming to remove in subsea equipment and cause safety issues. Natural gas pipelines are more susceptible to burst and explosion owing to hydrate plugging. Therefore, a rigorous risk-assessment related to hydrate formation is required, which assists in preventing hydrate blockage and ensuring equipment integrity. This thesis presents a novel methodology to assess the probability of hydrate formation and presents a risk-based approach to determine the parameters of winterization schemes to avoid hydrate formation in natural gas pipelines operating in Arctic conditions. It also presents a lab-scale multiphase flow loop to study the effects of geometric and hydrodynamic parameters on hydrate formation and discusses the effects of geometric and hydrodynamic parameters on multiphase development length of a pipeline. Therefore, this study substantially contributes to the assessment of probability of hydrate formation and the decision making process of winterization strategies to prevent hydrate formation in Arctic conditions.

Deterministic and probabilistic verification of multi-model meteorological forecasts on the subseasonal timescale

In questo studio, un multi-model ensemble è stato implementato e verificato, seguendo una delle priorità di ricerca del Subseasonal to Seasonal Prediction Project (S2S). Una regressione lineare è stata applicata ad un insieme di previsioni di ensemble su date passate, prodotte dai centri di previsione mensile del CNR-ISAC e ECMWF-IFS. Ognuna di queste contiene un membro di controllo e quattro elementi perturbati. Le variabili scelte per l'analisi sono l'altezza geopotenziale a 500 hPa, la temperatura a 850 hPa e la temperatura a 2 metri, la griglia spaziale ha risoluzione 1 ◦ × 1 ◦ lat-lon e sono stati utilizzati gli inverni dal 1990 al 2010. Le rianalisi di ERA-Interim sono utilizzate sia per realizzare la regressione, sia nella validazione dei risultati, mediante stimatori nonprobabilistici come lo scarto quadratico medio (RMSE) e la correlazione delle anomalie. Successivamente, tecniche di Model Output Statistics (MOS) e Direct Model Output (DMO) sono applicate al multi-model ensemble per ottenere previsioni probabilistiche per la media settimanale delle anomalie di temperatura a 2 metri. I metodi MOS utilizzati sono la regressione logistica e la regressione Gaussiana non-omogenea, mentre quelli DMO sono il democratic voting e il Tukey plotting position. Queste tecniche sono applicate anche ai singoli modelli in modo da effettuare confronti basati su stimatori probabilistici, come il ranked probability skill score, il discrete ranked probability skill score e il reliability diagram. Entrambe le tipologie di stimatori mostrano come il multi-model abbia migliori performance rispetto ai singoli modelli. Inoltre, i valori più alti di stimatori probabilistici sono ottenuti usando una regressione logistica sulla sola media di ensemble. Applicando la regressione a dataset di dimensione ridotta, abbiamo realizzato una curva di apprendimento che mostra come un aumento del numero di date nella fase di addestramento non produrrebbe ulteriori miglioramenti.