Developing the quantum probability ranking principle

In this work, we summarise the development of a ranking principle based on quantum probability theory, called the Quantum Probability Ranking Principle (QPRP), and we also provide an overview of the initial experiments performed employing the QPRP. The main difference between the QPRP and the classic Probability Ranking Principle, is that the QPRP implicitly captures the dependencies between documents by means of quantum interference". Subsequently, the optimal ranking of documents is not based solely on documents' probability of relevance but also on the interference with the previously ranked documents. Our research shows that the application of quantum theory to problems within information retrieval can lead to consistently better retrieval effectiveness, while still being simple, elegant and tractable.

On the use of complex numbers in quantum models for information retrieval

Quantum-inspired models have recently attracted increasing attention in Information Retrieval. An intriguing characteristic of the mathematical framework of quantum theory is the presence of complex numbers. However, it is unclear what such numbers could or would actually represent or mean in Information Retrieval. The goal of this paper is to discuss the role of complex numbers within the context of Information Retrieval. First, we introduce how complex numbers are used in quantum probability theory. Then, we examine van Rijsbergen’s proposal of evoking complex valued representations of informations objects. We empirically show that such a representation is unlikely to be effective in practice (confuting its usefulness in Information Retrieval). We then explore alternative proposals which may be more successful at realising the power of complex numbers.

Document ranking with quantum probabilities

In this thesis we investigate the use of quantum probability theory for ranking documents. Quantum probability theory is used to estimate the probability of relevance of a document given a user's query. We posit that quantum probability theory can lead to a better estimation of the probability of a document being relevant to a user's query than the common approach, i. e. the Probability Ranking Principle (PRP), which is based upon Kolmogorovian probability theory. Following our hypothesis, we formulate an analogy between the document retrieval scenario and a physical scenario, that of the double slit experiment. Through the analogy, we propose a novel ranking approach, the quantum probability ranking principle (qPRP). Key to our proposal is the presence of quantum interference. Mathematically, this is the statistical deviation between empirical observations and expected values predicted by the Kolmogorovian rule of additivity of probabilities of disjoint events in configurations such that of the double slit experiment. We propose an interpretation of quantum interference in the document ranking scenario, and examine how quantum interference can be effectively estimated for document retrieval. To validate our proposal and to gain more insights about approaches for document ranking, we (1) analyse PRP, qPRP and other ranking approaches, exposing the assumptions underlying their ranking criteria and formulating the conditions for the optimality of the two ranking principles, (2) empirically compare three ranking principles (i. e. PRP, interactive PRP, and qPRP) and two state-of-the-art ranking strategies in two retrieval scenarios, those of ad-hoc retrieval and diversity retrieval, (3) analytically contrast the ranking criteria of the examined approaches, exposing similarities and differences, (4) study the ranking behaviours of approaches alternative to PRP in terms of the kinematics they impose on relevant documents, i. e. by considering the extent and direction of the movements of relevant documents across the ranking recorded when comparing PRP against its alternatives. Our findings show that the effectiveness of the examined ranking approaches strongly depends upon the evaluation context. In the traditional evaluation context of ad-hoc retrieval, PRP is empirically shown to be better or comparable to alternative ranking approaches. However, when we turn to examine evaluation contexts that account for interdependent document relevance (i. e. when the relevance of a document is assessed also with respect to other retrieved documents, as it is the case in the diversity retrieval scenario) then the use of quantum probability theory and thus of qPRP is shown to improve retrieval and ranking effectiveness over the traditional PRP and alternative ranking strategies, such as Maximal Marginal Relevance, Portfolio theory, and Interactive PRP. This work represents a significant step forward regarding the use of quantum theory in information retrieval. It demonstrates in fact that the application of quantum theory to problems within information retrieval can lead to improvements both in modelling power and retrieval effectiveness, allowing the constructions of models that capture the complexity of information retrieval situations. Furthermore, the thesis opens up a number of lines for future research. These include: (1) investigating estimations and approximations of quantum interference in qPRP; (2) exploiting complex numbers for the representation of documents and queries, and; (3) applying the concepts underlying qPRP to tasks other than document ranking.

Tethering for Selective Synthesis of 2,2′-Biphenols : the Acetal Method

2,2'-Biphenols are a large and diverse group of compounds with exceptional properties both as ligands and bioactive agents. Traditional methods for their synthesis by oxidative dimerisation are often problematic and lead to mixtures of ortho- and para-connected regioisomers. To compound these issues, an intermolecular dimerisation strategy is often inappropriate for the synthesis of heterodimers. The ‘acetal method’ provides a solution for these problems: stepwise tethering of two monomeric phenols enables heterodimer synthesis, enforces ortho regioselectivity and allows relatively facile and selective intramolecular reactions to take place. The resulting dibenzo[1,3]dioxepines have been analysed by quantum chemical calculations to obtain information about the activation barrier for ring flip between the enantiomers. Hydrolytic removal of the dioxepine acetal unit revealed the 2,2′-biphenol target.

Accurate placement of a pelvic binder improves reduction of unstable fractures of the pelvic ring

The aim of this study was to assess the accuracy of placement of pelvic binders and to determine whether circumferential compression at the level of the greater trochanters is the best method of reducing a symphyseal diastasis. Patients were identified by a retrospective review of all pelvic radiographs performed at a military hospital over a period of 30 months. We analysed any pelvic radiograph on which the buckle of the pelvic binder was clearly visible. The patients were divided into groups according to the position of the buckle in relation to the greater trochanters: high, trochanteric or low. Reduction of the symphyseal diastasis was measured in a subgroup of patients with an open-book fracture, which consisted of an injury to the symphysis and disruption of the posterior pelvic arch (AO/OTA 61-B/C). We identified 172 radiographs with a visible pelvic binder. Five cases were excluded due to inadequate radiographs. In 83 (50%) the binder was positioned at the level of the greater trochanters. A high position was the most common site of inaccurate placement, occurring in 65 (39%). Seventeen patients were identified as a subgroup to assess the effect of the position of the binder on reduction of the diastasis. The mean gap was 2.8 times greater (mean difference 22 mm) in the high group compared with the trochanteric group (p < 0.01). Application of a pelvic binder above the level of the greater trochanters is common and is an inadequate method of reducing pelvic fractures and is likely to delay cardiovascular recovery in these seriously injured patients.

Unusual cross-ring S(N)2 reactions of M-H (-) ions of methoxyacetanilides

Deprotonated o, m-, and p-methoxyacetanilide show pronounced peaks in their collision-induced tandem mass spectra (MS/MS) produced by losses of the elements of C2H6. It is proposed that this reaction is a 'cross-ring' internal S(N)2 reaction involving an incipient methyl anion. For example, p-CH3O-C6H4-N--CO-CH3--> [(p.CH3O-C6H4-N=C=O)CH3-]--> O---C6H4-N=C=O+C2H6.

Response to “Comment on ‘Indications of energetic consequences of decoherence at short times for scattering from open quantum systems’” [AIP Advances 1, 049101 (2011)]

The Comment by Mayers and Reiter criticizes our work on two counts. Firstly, it is claimed that the quantum decoherence effects that we report in consequence of our experimental analysis of neutron Compton scattering from H in gaseous H2 are not, as we maintain, outside the framework of conventional neutron scatteringtheory. Secondly, it is claimed that we did not really observe such effects, owing to a faulty analysis of the experimental data, which are claimed to be in agreement with conventional theory. We focus in this response on the critical issue of the reliability of our experimental results and analysis. Using the same standard Vesuvio instrument programs used by Mayers et al., we show that, if the experimental results for H in gaseous H2 are in agreement with conventional theory, then those for D in gaseous D2 obtained in the same way cannot be, and vice-versa. We expose a flaw in the calibration methodology used by Mayers et al. that leads to the present disagreement over the behaviour of H, namely the ad hoc adjustment of the measured H peak positions in TOF during the calibration of Vesuvio so that agreement is obtained with the expectation of conventional theory. We briefly address the question of the necessity to apply the theory of open quantum systems.

Indications of energetic consequences of decoherence at short times for scattering from open quantum systems

Decoherence of quantum entangled particles is observed in most systems, and is usually caused by system-environment interactions. Disentangling two subsystems A and B of a quantum systemAB is tantamount to erasure of quantum phase relations between A and B. It is widely believed that this erasure is an innocuous process, which e.g. does not affect the energies of A and B. Surprisingly, recent theoretical investigations by different groups showed that disentangling two systems, i.e. their decoherence, can cause an increase of their energies. Applying this result to the context of neutronCompton scattering from H2 molecules, we provide for the first time experimental evidence which supports this prediction. The results reveal that the neutron-proton collision leading to the cleavage of the H-H bond in the sub-femtosecond timescale is accompanied by larger energy transfer (by about 3%) than conventional theory predicts. It is proposed to interpreted the results by considering the neutron-proton collisional system as an entangled open quantum system being subject to decoherence owing to the interactions with the “environment” (i.e., two electrons plus second proton of H2).

Unusual cross-ring SN2 reactions of [MH]− ions of methoxyacetanilides

Deprotonated o, m-, and p-methoxyacetanilide show pronounced peaks in their collision-induced tandem mass spectra (MS/MS) produced by losses of the elements of C2H6. It is proposed that this reaction is a 'cross-ring' internal S(N)2 reaction involving an incipient methyl anion. For example, p-CH3O-C6H4-N--CO-CH3--> [(p.CH3O-C6H4-N=C=O)CH3-]--> O---C6H4-N=C=O+C2H6.

Total energy shaping of a class of underactuated Port-Hamiltonian Systems using a new set of closed-loop potential shape variables

This paper proposes a method for designing set-point regulation controllers for a class of underactuated mechanical systems in Port-Hamiltonian System (PHS) form. A new set of potential shape variables in closed loop is proposed, which can replace the set of open loop shape variables-the configuration variables that appear in the kinetic energy. With this choice, the closed-loop potential energy contains free functions of the new variables. By expressing the regulation objective in terms of these new potential shape variables, the desired equilibrium can be assigned and there is freedom to reshape the potential energy to achieve performance whilst maintaining the PHS form in closed loop. This complements contemporary results in the literature, which preserve the open-loop shape variables. As a case study, we consider a robotic manipulator mounted on a flexible base and compensate for the motion of the base while positioning the end effector with respect to the ground reference. We compare the proposed control strategy with special cases that correspond to other energy shaping strategies previously proposed in the literature.

The loss of carbon dioxide from activated perbenzoate anions in the gas phase : Unimolecular rearrangement via epoxidation of the benzene ring

The unimolecular reactivities of a range of perbenzoate anions (X-C6H5CO3-), including the perbenzoate anion itself (X=H), nitroperbenzoates (X=para-, meta-, ortho-NO2), and methoxyperbenzoates (X=para-, meta-OCH3) were investigated in the gas phase by electrospray ionization tandem mass spectrometry. The collision-induced dissociation mass spectra of these compounds reveal product ions consistent with a major loss of carbon dioxide requiring unimolecular rearrangement of the perbenzoate anion prior to fragmentation. Isotopic labeling of the perbenzoate anion supports rearrangement via an initial nucleophilic aromatic substitution at the ortho carbon of the benzene ring, while data from substituted perbenzoates indicate that nucleophilic attack at the ipso carbon can be induced in the presence of electron-withdrawing moieties at the ortho and para positions. Electronic structure calculations carried out at the B3LYP/6311++G(d,p) level of theory reveal two competing reaction pathways for decarboxylation of perbenzoate anions via initial nucleophilic substitution at the ortho and ipso positions, respectively. Somewhat surprisingly, however, the computational data indicate that the reaction proceeds in both instances via epoxidation of the benzene ring with decarboxylation resulting-at least initially-in the formation of oxepin or benzene oxide anions rather than the energetically favored phenoxide anion. As such, this novel rearrangement of perbenzoate anions provides an intriguing new pathway for epoxidation of the usually inert benzene ring.

The sphynx's new riddle : how to relate the canonical formula of myth to quantum interaction

We introduce Claude Lévi Strauss' canonical formula (CF), an attempt to rigorously formalise the general narrative structure of myth. This formula utilises the Klein group as its basis, but a recent work draws attention to its natural quaternion form, which opens up the possibility that it may require a quantum inspired interpretation. We present the CF in a form that can be understood by a non-anthropological audience, using the formalisation of a key myth (that of Adonis) to draw attention to its mathematical structure. The future potential formalisation of mythological structure within a quantum inspired framework is proposed and discussed, with a probabilistic interpretation further generalising the formula

Fatty acid synthesis and pyruvate metabolism pathways remain active in dihydroartemisinin induced dormant ring stages of Plasmodium falciparum

Artemisinin (ART) based combination therapy (ACT) is used as the first line treatment of uncomplicated falciparum malaria worldwide. However, despite high potency and rapid action there is a high rate of recrudescence associated with ART monotherapy or ACT long before the recent emergence of ART resistance. ART induced ring stage dormancy and recovery has been implicated as possible cause of recrudescence; however, little is known about the characteristics of dormant parasites including whether dormant parasites are metabolically active. We investigated the transcription of 12 genes encoding key enzymes in various metabolic pathways in P. falciparum during dihydroartemisinin (DHA) induced dormancy and recovery. Transcription analysis showed an immediate down regulation for 10 genes following exposure to DHA, but continued transcription of 2 genes encoding apicoplast and mitochondrial proteins. Transcription of several additional genes encoding apicoplast and mitochondrial proteins, particularly genes encoding enzymes in pyruvate metabolism and fatty acid synthesis pathways, were also maintained. Additions of inhibitors for biotin acetyl CoA carbozylase and enoyl-acyl carrier reductase of the fatty acid synthesis pathways delayed the recovery of dormant parasites by 6 and 4 days, respectively following DHA treatment. Our results demonstrate most metabolic pathways are down regulated in DHA induced dormant parasites. In contrast fatty acid and pyruvate metabolic pathways remain active. These findings highlight new targets to interrupt recovery of parasites from ART-induced dormancy and to reduce the rate of recrudescence following ART treatment.

The Quantum Probability Ranking Principle for Information Retrieval

While the Probability Ranking Principle for Information Retrieval provides the basis for formal models, it makes a very strong assumption regarding the dependence between documents. However, it has been observed that in real situations this assumption does not always hold. In this paper we propose a reformulation of the Probability Ranking Principle based on quantum theory. Quantum probability theory naturally includes interference effects between events. We posit that this interference captures the dependency between the judgement of document relevance. The outcome is a more sophisticated principle, the Quantum Probability Ranking Principle, that provides a more sensitive ranking which caters for interference/dependence between documents’ relevance.

Quantum of damages under the Workcover Queensland Act 1996 - some questions of construction

The decision of Wilson J in Calvert v Nickless Ltd [2004] QSC 449 involves significant questions of interpretation of sections 315 and 317 of the Workcover Queensland Act 1996 (Qld) relating to claims for damages for future economic loss and for gratuitous services.