Locality and Exceptional Points in Pseudo-Hermitian Physics

Pseudo-Hermitian operators generalize the concept of Hermiticity. Included in this class of operators are the quasi-Hermitian operators, which define a generalization of quantum theory with real-valued measurement outcomes and unitary time evolution. This thesis is devoted to the study of locality in quasi-Hermitian theory, the symmetries and conserved quantities associated with non-Hermitian operators, and the perturbative features of pseudo-Hermitian matrices. An implicit assumption of the tensor product model of locality is that the inner product factorizes with the tensor product. Quasi-Hermitian quantum theory generalizes the tensor product model by modifying the Born rule via a metric operator with nontrivial Schmidt rank. Local observable algebras and expectation values are examined in chapter 5. Observable algebras of two one-dimensional fermionic quasi-Hermitian chains are explicitly constructed. Notably, there can be spatial subsystems with no nontrivial observables. Despite devising a new framework for local quantum theory, I show that expectation values of local quasi-Hermitian observables can be equivalently computed as expectation values of Hermitian observables. Thus, quasi-Hermitian theories do not increase the values of nonlocal games set by Hermitian theories. Furthermore, Bell's inequality violations in quasi-Hermitian theories never exceed the Tsirelson bound of Hermitian quantum theory. A perturbative feature present in pseudo-Hermitian curves which has no Hermitian counterpart is the exceptional point, a branch point in the set of eigenvalues. An original finding presented in section 2.6.3 is a correspondence between cusp singularities of algebraic curves and higher-order exceptional points. Eigensystems of one-dimensional lattice models admit closed-form expressions that can be used to explore the new features of non-Hermitian physics. One-dimensional lattice models with a pair of non Hermitian defect potentials with balanced gain and loss, Δ±iγ, are investigated in chapter 3. Conserved quantities and positive-definite metric operators are examined. When the defects are nearest neighbour, the entire spectrum simultaneously becomes complex when γ increases beyond a second-order exceptional point. When the defects are at the edges of the chain and the hopping amplitudes are 2-periodic, as in the Su-Schrieffer-Heeger chain, the PT-phase transition is dictated by the topological phase of the system. In the thermodynamic limit, PT-symmetry spontaneously breaks in the topologically non-trivial phase due to the presence of edge states. Chiral symmetry and representation theory are utilized in chapter 4 to derive large classes of pseudo-Hermitian operators with closed-form intertwining operators. These intertwining operators include positive-definite metric operators in the quasi-Hermitian case. The PT-phase transition is explicitly determined in a special case

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Automatic machine learning:methods, systems, challenges

This open access book presents the first comprehensive overview of general methods in Automatic Machine Learning (AutoML), collects descriptions of existing systems based on these methods, and discusses the first international challenge of AutoML systems. The book serves as a point of entry into this quickly-developing field for researchers and advanced students alike, as well as providing a reference for practitioners aiming to use AutoML in their work. The recent success of commercial ML applications and the rapid growth of the field has created a high demand for off-the-shelf ML methods that can be used easily and without expert knowledge. Many of the recent machine learning successes crucially rely on human experts, who select appropriate ML architectures (deep learning architectures or more traditional ML workflows) and their hyperparameters; however the field of AutoML targets a progressive automation of machine learning, based on principles from optimization and machine learning itself

Scientific Opinion on the risks to public health related to the presence of bisphenol A (BPA) in foodstuffs : Executive summary

Adopted 11 December 2014 Panel members: Claudia Bolognesi, Laurence Castle, Jean-Pierre Cravedi, Karl-Heinz Engel, Paul Fowler, Roland Franz, Konrad Grob, Rainer Gürtler, Trine Husøy, Wim Mennes, Maria Rosaria Milana, André Penninks, Franz Roland, Vittorio Silano, Andrew Smith, Maria de Fátima Tavares Poças, Christina Tlustos, Fidel Toldrá, Detlef Wölfle and Holger Zorn. Acknowledgement: The Panel wishes to thank the members of the Working Groups on BPA Exposure and Toxicology: Claire Beausoleil, Diane Benford, Emma Bradley, Anne Lise Brantsaeter, Gemma Calamandrei, Daniel Doerge, Paul Fowler, Peter Greaves (until July 2012), Ursula Gundert-Remy, Andrew David Hart, Edel Holene, Trine Husøy, Catherine Leclercq (until July 2013), Inger Therese Laugsand Lillegaard, Wim Mennes, Ralph Pirow, Maria de Fátima Tavares Poças, Iona Pratt (deceased in February 2014), Josef Rudolf Schlatter, Catherine Simoneau, Wout Slob, Jacqueline Van Engelen, Henk Van Loveren, Natalie Von Götz, Detlef Wölfle and Rudolf Antonius Woutersen for the preparatory work on this scientific opinion and the hearing experts: Jan Alexander, Pasquale Mosesso and Alfonso Siani, and EFSA staff: Davide Arcella, Anna F. Castoldi, Cristina Croera and Anne Theobald for the support provided to this scientific opinion. Suggested citation: EFSA CEF Panel (EFSA Panel on Food Contact Materials, Enzymes, Flavourings and Processing Aids), 2015. Scientific Opinion on the risks to public health related to the presence of bisphenol A (BPA) in foodstuffs: Executive summary. EFSA Journal 2015;13(1):3978, 22 pp. doi:10.2903/j.efsa.2015.3978Publisher PD