In Singularities at the Threshold: The Ontology of Unrest, Bruno Gullì calls into question the concept of the independent and sovereign individual of the liberal (and neoliberal) tradition from the standpoint of the ontology of singularity, that is, the plural constitution of what appears to be an individual. Singularity is not the result of a process of individuation, but the process itself. He argues that the process of individuation—whereby at each stage everything appears to be individuated as such, to be an individual thing—is in reality always already plural, a process of transindividuation, or better, trans-dividuation. Gullì further examines why singularity is usually confused with individuality; what comes after the sovereign and independent individual, after the subject; and what the role of subversive and liberated singularities is in bringing about a new ethos and a better world.

This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.

Biological engineering is a field of engineering in which the emphasis is on life and life-sustaining systems. Biological engineering is an emerging discipline that encompasses engineering theory and practice connected to and derived from the science of biology. The most important trend in biological engineering is the dynamic range of scales at which biotechnology is now able to integrate with biological processes. An explosion in micro/nanoscale technology is allowing the manufacture of nanoparticles for drug delivery into cells, miniaturized implantable microsensors for medical diagnostics, and micro-engineered robots for on-board tissue repairs. This book aims to provide an updated overview of the recent developments in biological engineering from diverse aspects and various applications in clinical and experimental research.

Local electromagnetic field fluctuations and related enhancement of nonlinear phenomena in metal-dielectric composites near the percolation threshold (percolation composites) have recently become an area of active study, because of the many fundamental problems involved and the high potential for various applications. It has been recognized recently that local field fluctuations can be especially large in the optical and infrared spectral ranges due to the surface plasmon resonance in metallic granules and their clusters. The strong fluctuations of the local electric and magnetic fields result in the enhancement of various optical effects: anomalous absorption, Rayleigh and Raman scattering, generation of the higher harmonic, Kerr nonlinearity, etc. Nonlinear percolation composites are potentially of great practical importance as media with intensity-dependent dielectric functions and, in particular, as nonlinear filters and optical bistable elements. The optical response of nonlinear composites can be tuned, for example, by controlling the volume fraction and morphology of constituents. This book presents a new theory of electromagnetic field distribution and nonlinear optical processes in metal-dielectric composites. The new approach is based on a percolation theory and the fact that the problem of optical excitations in percolation composites mathematically maps the Anderson transition problem in quantum mechanics. The theory predicts localization of the excitations (surface plasmons) in percolation composites and describes in detail the localization pattern that allows one to obtain relatively simple expressions for the enhancement of linear and nonlinear optical responses. Thistheory is supported by recent near-field experiments where the surface plasmon localization has been directly observed in the percolating composites in optical and microwave bands.

It has been said that the future of Life is about Artificial Intelligence (AI) and that as AI advances a point will be reached, the Singularity, when humans will no longer have a clue as to what is going on nor why. Essentially as a species, humans will at this point have been marginalized by a global, singular intelligence, whose capabilities far outstrip human intelligence. On the contrary, this book will make the case that the future of Life is enabled by the pre-existent complexity that exists in every iota of it and that there have already been a series of light-based epiphanies by virtue of which Life in its continuing complexities has emerged as partial-singularities, and further, will culminate in a Second Singularity as more of our species consciously opens to the fullness of Light. The power and capabilities of the Second Singularity will far outstrip any AI-based singularity. This pre-existent complexity derives from the fact that Light exists in multiple states simultaneously. Hence, there is a fundamental and single light-based edifice that informs our universe, and it is by virtue of this light-based edifice that all matter, all life, all mind, and all emergences beyond the level of mind will surface. The future of life, hence, cannot be due to AI. At best, AI, can create a process by which many tasks that usually require utilization of the fundamental light-derived capacity of intelligence in order to be completed, can be completed by an exhaustively repetitive running of algorithms driven by massive computing power, hence giving the illusion of intelligence. Projected forward, the exhaustively repetitive running of algorithms driven by massive computing power, endow a practically ubiquitous digitally-enabled strata to control many tasks, and this may create the phenomenon of a “singularity” – in which humankind effectively cannot even fathom how things are happening anymore and is seemingly outpaced and outthought at every step in every direction by an ‘intelligence’ that appears to be all-knowing, all-present, and all-powerful. But this kind of singularity is fundamentally separated from the light-based edifice behind all things, and from which all things rise. It is hence not a true singularity in the sense of a finite function assuming infinite value, but is fundamentally limited in its scope by virtue of its disconnection from the founts of Life. This does not preclude an AI-based singularity from having massive practical power that can have an enormous destructive or constructive effect on humankind and material life. What it does mean though is that there is another singularity, a human-founded singularity, the Second Singularity, which can exceed the limits of any AI-based singularity due to its fundamental union with the light-based edifice that is behind and informs all of Life. The possible human-founded singularity, it will be discovered, is one in a long series of naturally occurring though partial-singularities that derive their existence from a fundamental union with the light-based edifice behind all things. Such partial-singularities are characterized by having all the power of the light-edifice behind them, though the emergences in such partial-singularities are not necessarily aware of their oneness with the light-based edifice. In the Second Singularity humans become aware of such oneness, becoming conscious projections animated by a single intelligence, love, and power of which they are a part. It is hence no more the human-level capacity that drives such humans, but the infinite capacities of the one light-based edifice that drives. This book focuses on the mathematics of emergence of these naturally occurring partial-singularities, leading up to the possible human-founded singularity that will endow humankind with the potential for extraordinary capacities.

This book provides a modern perspective on the analytic structure of scattering amplitudes in quantum field theory, with the goal of understanding and exploiting consequences of unitarity, causality, and locality. It focuses on the question: Can the S-matrix be complexified in a way consistent with causality? The affirmative answer has been well understood since the 1960s, in the case of 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε-like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties of the physical amplitude. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. We illustrate all the points on explicit examples, both symbolically and numerically, in addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view. To help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points. This book is well suited for anyone with knowledge of quantum field theory at a graduate level who wants to become familiar with the complex-analytic structure of Feynman integrals.

The book provides a step by step construction of the framework of relativistic quantum field theory, starting from a minimal set of basic foundational postulates. The emphasis is on a careful and detailed description of the conceptual subtleties of modern field theory, many of which are glossed over in other texts.