On the Complexity of Isomorphism Problems for Tensors, Groups, and Polynomials I: Tensor Isomorphism-Completeness

We study the complexity of isomorphism problems for tensors, groups, and polynomials. These problems have been studied in multivariate cryptography, machine learning, quantum information, and computational group theory. We show that these problems are all polynomial-time equivalent, creating bridges between problems traditionally studied in myriad research areas. This prompts us to define the complexity class TI, namely problems that reduce to the Tensor Isomorphism (TI) problem in polynomial time. Our main technical result is a polynomial-time reduction from d-tensor isomorphism to 3-tensor isomorphism. In the context of quantum information, this result gives multipartite-to-tripartite entanglement transformation procedure, that preserves equivalence under stochastic local operations and classical communication (SLOCC)

The Challenges of Leading the Attainment Agenda: Framing the Role and Practices of the New Secondary Headteacher

Scottish institutions within the educational networks, including Government, local authorities, and schools, are entangled in performative activities dedicated to improvements in student attainment. Secondary school performance in Scotland is measured nationally predominantly by the number and level of national qualifications achieved. The thesis makes the case that this attainment agenda places enormous pressures on Headteachers to ensure student outcomes are maximised and that the culture of performativity is a major factor in shaping the roles and practices of Headteachers. The study is based on four new secondary school Headteachers in a single Scottish local authority. It is through an examination of their work practices that the formation of subjectivities within a range of power relations and discursive regimes are explored. Performativity and accountability influence the role and actions of the Headteacher in many ways which are unanticipated. There is an ongoing power struggle engendered by the pressures and controls imposed on new Headteachers which modify and discipline their behaviours. In this thesis, a case study methodology is employed and the concepts of Michel Foucault are applied to provide an alternative means of understanding the practices of Headteachers. A Foucauldian approach also provides a different perspective on the problematic conceptualisation of school leadership. The aim of this study is to make a research-based contribution to our understanding of the complexities and competing priorities negotiated by new Headteachers. The research evidences the dominance of the attainment agenda on the lived lives of the new Headteachers. This study should enable the development of additional ways to assist with Headteacher preparation and the provision of improved support in the early years of Headship

Development of novel methodologies for the identification of unknown compounds in the environment employing non-target screening and high-resolution mass spectrometry

Τα κέντρα επεξεργασίας λυμάτων (ΚΕΛ) δεν απομακρύνουν αποτελεσματικά τους αναδυόμενους ρύπους. Έτσι, οι αναδυόμενοι ρύποι εισάγονται στο υδατικό περιβάλλον και σχηματίζουν πολύπλοκα μίγματα, τα οποία περιέχουν δεκάδες χιλιάδες χημικές ουσίες. Η ανάλυση αυτών των πολύπλοκων δειγμάτων με τεχνικές υψηλής απόδοσης, όπως υγρoχρωματογραφία συζευγμένη με φασματομετρία μαζών υψηλής διακριτικής ικανότητας, παράγουν ένα μεγάλο αριθμό σημάτων. Για την επιτυχή μετάφραση των πολύπλοκων αυτών δεδομένων αλλά και για να επιτευχθεί ένα ολιστικό πρόγραμμα παρακολούθησης του περιβάλλοντος, απαιτείται ολόπλευρη χημική ανάλυση με εφαρμογή στοχευμένης σάρωσης, σάρωσης ύποπτων ενώσεων και μη στοχευμένης σάρωσης. Ο σκοπός της Διατριβής είναι η ανάπτυξη εργαλείων ολόπλευρης χημικής ανάλυσης και η εφαρμογή τους σε σημαντικά Ευρωπαΐκά οικοσυστήματα όπως η λεκάνη απορροής του Δούναβη και η Μάυρη Θάλασσα. Στα πλαίσια του σκοπού αυτού, στο Κεφάλαιο 1 εισάγονται οι αναδυόμενοι ρύποι προτεραιότητας και οι τεχνικές ταυτοποίησης τους, ακολουθούμενοι από λεπτoμερή περιγραφή των στόχων της Διατριβής στο Κεφάλαιο 2. Στο Κεφάλαιο 3 περιγράφεται μια πορεία μη στοχευμένης σάρωσης για την προτεραιοποίηση ουσιών που παρουσιάζουν απότομη μεταβολή στην συγκέντρωση ως προς το χρόνο. Η πορεία αυτή χρησιμοποιήθηκε για την εύρεση φαινομένων απευθείας ρίψης ουσιών στο δίκτυο του ΚΕΛ της Αθήνας. Το Κεφάλαιο 4 περιγράφει την ίδρυση ενός παγκόσμιου δικτύου έγκαιρης προειδοποίησης για την αξιολόγηση της χωρικής και χρονικής κατανομής νέων αναδυόμενων ρύπων. Εξέλιξη αυτού του δικτύου είναι ένα λογισμικό αποθήκευσης δεδομένων LC-HRMS με δυνατότητα εφαρμογής ευρείας αυτόματης σάρωσης ύποπτων ενώσεων, που ενσωματώνει όλα τα έργαλεία που χρησιμοποιούνται στις HRMS μεθόδους (Κεφάλαιο 5). Το λογισμικό χρησιμοποιήθηκε για την ανίχνευση αναδυόμενων ρύπων και χημικών ουσιών της βάσης REACH (i) σε δείγματα από τη Μαύρη θάλασσα (ζωντανοί όργανισμοί, ιζήματα και θαλάσσιο νερό), (ii) σε εξερχόμενα λύματα από τη λεκάνη απορροής του Δούναβη (Κεφάλαιο 6) και (iii) σε εξερχόμενα λύματα που συλλέχθηκαν από τη Γερμανία (Κεφάλαιο 7). Καινοτόμα εργαλεία βιοπαρακολούθησης όπως βιοδοκιμασίες και ανάλυση γονιδίων ανθεκτικών στα αντιβιοτικά συμπλήρωνουν τα αποτελέσματα της ανάλυσης αναδυόμενων ρύπων.Wastewater treatment plants (WWTPs) are unable to remove many contaminants of emerging concern (CECs) efficiently, and therefore introduce them into the aquatic environment, where they form complex chemical mixtures containing typically thousands of individual substances. When analysed by liquid chromatography coupled to high-resolution mass spectrometry (LC-HRMS), these complex mixtures produce a high number of signals. To successfully translate these complex data into information required by environmental monitoring programmes, implementation of wide-scope target, suspect and non-target screening using powerful computational tools and related databases is required. The objective of the thesis was to develop novel workflows employing state-of-the-art target, suspect and non-target screening tools and apply them on samples obtained from important European ecosystems such as the Danube River Basin (DRB) and the Black Sea (BS). In this context, an introduction on CECs, workflows and techniques for their identification is presented in Chapter 1, which is followed by the scope of the thesis in Chapter 2. Chapter 3 describes a non-target screening (NTS) workflow capable to prioritise compounds that exhibit large variation in their signal intensity over time (trend-analysis), which was used to detect events of direct disposal or sudden changes in the use of substances in WWTP of Athens. Chapter 4 describes the establishment of a decentralised global emerging contaminant early-warning network to assess the spatial and temporal distribution using suspect screening. A platform to archive LC-HRMS data and apply wide-scope suspect screening of thousands of CECs, that incorporates all recent development in HRMS screening methods, is presented in Chapter 5. The platform was used to screen antibiotics and REACH chemicals in samples from BS (biota, sediment, seawater), various classes of CECs in wastewater from DRB (Chapter 6) and surfactants in wastewater samples collected within the national monitoring campaign in Germany (Chapter 7). Novel biomonitoring tools such as in vitro bioassays and analysis of antibiotic resistant genes (ARGs) supplemented NTS analyses of wastewater samples

On the complexity of isomorphism problems for tensors, groups, and polynomials I: Tensor isomorphism-completeness

We study the complexity of isomorphism problems for tensors, groups, and polynomials. These problems have been studied in multivariate cryptography, machine learning, quantum information, and computational group theory. We show that these problems are all polynomial-time equivalent, creating bridges between problems traditionally studied in myriad research areas. This prompts us to define the complexity class TI, namely problems that reduce to the Tensor Isomorphism (TI) problem in polynomial time. Our main technical result is a polynomial-time reduction from d-tensor isomorphism to 3-tensor isomorphism. In the context of quantum information, this result gives multipartite-to-tripartite entanglement transformation procedure, that preserves equivalence under stochastic local operations and classical communication (SLOCC)

Practice-Based Design for Professional Learning and Knowledge Sharing: Adapting the ‘Key Situation Model’ for Social Work in England

How can social workers be supported to continuously develop knowledgeable and ethical practice? Acknowledging the dilemmas and uncertainties in social work practice that unfolds in complex environments, this thesis turns to practice-based perspectives in response to the main question. It foregrounds the interplay of humans within physical and social environments with a focus on ‘practices’ and considers the challenges for social workers as practitioners, professionals and knowledge workers. In relation to individual decision-making, the role of research, theory, tools, emotions, experience and reflective deliberation are explored. On an organisational level, evidence-informed and best practice, knowledge transfer, group reflection approaches and the role of technology are examined. The author argues that knowledgeable and ethical practice emerges from knowledge related (epistemic) practices within organisations that are grounded in what professionals do. This requires reflexive and mindful professionals who are able to weave together different forms of knowledge and ethical principles with practice situations and with organisations who will support epistemic practices and environments for reflective learning, knowledge co-production and the sharing of knowledge. Building on earlier work (Tov et al., 2016; Staempfli et al., 2012), the author argues that the Key Situation Model can support both practices and environments. Key situations are the typical practices that social workers regularly encounter and thus reflect what social workers actually do. 116 key situations in social work in England are developed and validated in a modified three-round Delphi study with experienced social workers from diverse sectors from across England (n1= 13, n2= 88 and n3= 41). Based on these and informed by the Activity Centred Analysis and Design (ACAD) framework, this thesis presents design options for social work organisations for the implementation of the Key Situation Model’s blended reflective learning and knowledge sharing. These design options could support the development of knowledgeable and ethical practice