1,772 research outputs found

    Classical and quantum algorithms for scaling problems

    Get PDF
    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers

    Full text link
    We develop three new methods to implement any Linear Combination of Unitaries (LCU), a powerful quantum algorithmic tool with diverse applications. While the standard LCU procedure requires several ancilla qubits and sophisticated multi-qubit controlled operations, our methods consume significantly fewer quantum resources. The first method (Single-Ancilla LCU) estimates expectation values of observables with respect to any quantum state prepared by an LCU procedure while requiring only a single ancilla qubit, and quantum circuits of shorter depths. The second approach (Analog LCU) is a simple, physically motivated, continuous-time analogue of LCU, tailored to hybrid qubit-qumode systems. The third method (Ancilla-free LCU) requires no ancilla qubit at all and is useful when we are interested in the projection of a quantum state (prepared by the LCU procedure) in some subspace of interest. We apply the first two techniques to develop new quantum algorithms for a wide range of practical problems, ranging from Hamiltonian simulation, ground state preparation and property estimation, and quantum linear systems. Remarkably, despite consuming fewer quantum resources they retain a provable quantum advantage. The third technique allows us to connect discrete and continuous-time quantum walks with their classical counterparts. It also unifies the recently developed optimal quantum spatial search algorithms in both these frameworks, and leads to the development of new ones. Additionally, using this method, we establish a relationship between discrete-time and continuous-time quantum walks, making inroads into a long-standing open problem.Comment: 72+16 pages, 3 Figure

    A Theistic Critique of Secular Moral Nonnaturalism

    Get PDF
    This dissertation is an exercise in Theistic moral apologetics. It will be developing both a critique of secular nonnaturalist moral theory (moral Platonism) at the level of metaethics, as well as a positive form of the moral argument for the existence of God that follows from this critique. The critique will focus on the work of five prominent metaethical theorists of secular moral non-naturalism: David Enoch, Eric Wielenberg, Russ Shafer-Landau, Michael Huemer, and Christopher Kulp. Each of these thinkers will be critically examined. Following this critique, the positive moral argument for the existence of God will be developed, combining a cumulative, abductive argument that follows from filling in the content of a succinct apagogic argument. The cumulative abductive argument and the apagogic argument together, with a transcendental and modal component, will be presented to make the case that Theism is the best explanation for the kind of moral, rational beings we are and the kind of universe in which we live, a rational intelligible universe

    To have done with theory? Baudrillard, or the literal confrontation with reality

    Get PDF
    Baudrillard, Eluding the temptation to reinterpret Jean Baudrillard once more, this work started from the ambition to consider his thought in its irreducibility, that is, in a radically literal way. Literalness is a recurring though overlooked term in Baudrillard’s oeuvre, and it is drawn from the direct concatenation of words in poetry or puns and other language games. It does not indicate a realist positivism but a principle that considers the metamorphoses and mutual alteration of things in their singularity without reducing them to a general equivalent (i.e. the meaning of words in a poem, which destroys its appearances). Reapplying the idea to Baudrillard and finding other singular routes through his “passwords” is a way to short-circuit its reductio ad realitatem and reaffirm its challenge to the hegemony of global integration. Even in the literature dedicated to it, this exercise has been rarer than the ‘hermeneutical’ one, where Baudrillard’s oeuvre was taken as a discourse to be interpreted and explained (finding an equivalent for its singularity). In plain polemic with any ideal of conformity between theory and reality (from which our present conformisms arguably derive, too), Baudrillard conceived thought not as something to be verified but as a series of hypotheses to be repeatedly radicalised – he often described it as a “spiral”, a form which challenges the codification of things, including its own. Coherent with this, the thesis does not consider Baudrillard’s work either a reflection or a prediction of reality but, instead, an out-and-out act, a precious singular object which, interrogated, ‘thinks’ us and our current events ‘back’. In the second part, Baudrillard’s hypotheses are taken further and measured in their capacity to challenge the reality of current events and phenomena. The thesis confronts the ‘hypocritical’ position of critical thinking, which accepts the present principle of reality. It questions the interminability of our condition, where death seems thinkable only as a senseless interruption of the apparatus. It also confronts the solidarity between orthodox and alternative realities of the COVID pandemic and the Ukrainian invasion, searching for what is irreducible to the perfect osmosis of “virtual and factual”. Drawing equally from the convulsions of globalisation and the psychopathologies of academics, from DeLillo’s fiction and Baudrillard’s lesser-studied influences, this study evaluates the irreversibility of our system against the increasingly silent challenges of radical thought. It looks for what an increasingly pessimistic late Baudrillard called ‘rogue singularities’: forms which, often outside the conventional realms one would expect to find them, constitute potential sources of the fragility of global power. ‘To have done with theory’ does not mean abandoning radical thought and, together with it, the singularity of humanity. It means, as the thesis concludes, the courage to leave conventional ideas of theory and listen to less audible voices which, at the heart of this “enormous conspiracy”, whisper — as a mysterious lady in Mariupol did to Putin — “It’s all not true! It’s all for show!”

    Sensing Collectives: Aesthetic and Political Practices Intertwined

    Get PDF
    Are aesthetics and politics really two different things? The book takes a new look at how they intertwine, by turning from theory to practice. Case studies trace how sensory experiences are created and how collective interests are shaped. They investigate how aesthetics and politics are entangled, both in building and disrupting collective orders, in governance and innovation. This ranges from populist rallies and artistic activism over alternative lifestyles and consumer culture to corporate PR and governmental policies. Authors are academics and artists. The result is a new mapping of the intermingling and co-constitution of aesthetics and politics in engagements with collective orders

    Epistemic Thought Experiments and Intuitions

    Get PDF
    This work investigates intuitions' nature, demonstrating how philosophers can best use them in epistemology. First, the author considers several paradigmatic thought experiments in epistemology that depict the appeal to intuition. He then argues that the nature of thought experiment-generated intuitions is not best explained by an a priori Platonism. Second, the book instead develops and argues for a thin conception of epistemic intuitions. The account maintains that intuition is neither a priori nor a posteriori but multi-dimensional. It is an intentional but non-propositional mental state that is also non-conceptual and non-phenomenal in nature. Moreover, this state is individuated by its progenitor, namely, the relevant thought experiment. Third, the author provides an argument for the evidential status of intuitions based on the correct account of the nature of epistemic intuition. The suggestion is the fitting-ness approach: intuition alone has no epistemic status. Rather, intuition has evidentiary value as long as it fits well with other pieces into a whole, namely, the pertinent thought experiment. Finally, the book addresses the key challenges raised by supporters of anti-centrality, according to which philosophers do not regard intuition as central evidence in philosophy. To that end, the author responds to them, showing that they fail to affect the account of intuition developed in this book. This text appeals to students and researchers working in epistemology

    Throwing therapy at the problem mental health and humanitarian intervention in Palabek refugee settlement, northern Uganda

    Get PDF
    This thesis examines the social, moral, and political lives of humanitarian mental health interventions in a refugee settlement in Uganda. It is written at the junction of two increasingly significant trends: the search for durable solutions for mass displacement, and the establishment of the field of global mental health as a key actor in the management of psychological suffering across the Global South. Through a scalar structure, it interrogates the intersections of psychological programmes with socio-economic conditions of chronic poverty and food insecurity, from policy discourses to refugees’ phenomenological experiences of suffering. In so doing, it critically examines the political significance and therapeutic potential of mental health interventions in extremely resource-poor contexts. Global mental health scholars and practitioners have developed approaches to refugee mental health based on three assumptions: that refugees’ emotional distress should be tackled by purely psychological interventions; that these programmes are clinically significant and politically neutral; and that the ‘contextual’ factors that should be considered in their implementation mostly concern ‘local’ interpretations of mental health and illness which diverge from Western biomedical frameworks. By ethnographically exploring experiences of psychological suffering among South Sudanese – and particularly Acholi – refugees in the settlement of Palabek, northern Uganda, this thesis disputes these contentions. Based on fourteen months of in-depth ethnographic fieldwork, this thesis puts forward a critique of global mental health and humanitarian interventions that takes seriously the role of poverty and power in shaping refugees’ afflictions. This thesis shows that forms of suffering experienced by refugees in Uganda are closely linked to the structural constraints of life in displacement. It shows how these interventions intersect with refugees’ phenomenological experiences of temporality and moral personhood. In so doing it argues that, when divorced from direct engagement with forms of structural injustice, current global mental health approaches actively ‘do harm’ by contributing to refugees’ psychological afflictions. Finally, this thesis proposes new directions for refugee and global mental health; it argues for a ‘temporal turn’ in refugee mental health which foregrounds refugees’ moral agency, and for the central role of livelihood interventions in generating therapeutic outcomes

    Bayesian computation in astronomy: novel methods for parallel and gradient-free inference

    Get PDF
    The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the author that aim to facilitate Bayesian data analysis for the next generation of astronomical observations and theoretical models. The first part of this thesis familiarises the reader with the notion of probability and its relevance for science through the prism of Bayesian reasoning, by introducing the key constituents of the theory and discussing its best practices. The second part includes a pedagogical introduction to the principles of Bayesian computation motivated by the geometric characteristics of probability distributions and followed by a detailed exposition of various methods including Markov chain Monte Carlo (MCMC), Sequential Monte Carlo (SMC) and Nested Sampling (NS). Finally, the third part presents two novel computational methods and their respective software implementations. The first such development is Ensemble Slice Sampling (ESS), a new class of MCMC algorithms that extend the applicability of the standard Slice Sampler by adaptively tuning its only hyperparameter and utilising an ensemble of parallel walkers in order to efficiently handle strong correlations between parameters. The parallel, black–box and gradient-free nature of the method renders it ideal for use in combination with computationally expensive and non–differentiable models often met in astronomy. ESS is implemented in Python in the well–tested and open-source software package called zeus that is specifically designed to tackle the computational challenges posed by modern astronomical and cosmological analyses. In particular, use of the code requires minimal, if any, hand–tuning of hyperparameters while its performance is insensitive to linear correlations and it can scale up to thousands of CPUs without any extra effort. The next contribution includes the introduction of Preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates effective sampling of probability distributions with non–trivial geometry. PMC utilises a Normalising Flow (NF) in order to decorrelate the parameters of the distribution and then proceeds by sampling from the preconditioned target distribution using an adaptive SMC scheme. PMC, through its Python implementation pocoMC, achieves excellent sampling performance, including accurate estimation of the model evidence, for highly correlated, non–Gaussian, and multimodal target distributions. Finally, the code is directly parallelisable, manifesting linear scaling up to thousands of CPUs

    Paul Natorp’s reformulation of the Kantian distinction between intuition and concept

    Get PDF
    The goal of our research is to analyze Natorp’s redefinition of the distinction between intuitions and concepts in relation to his conception of the method of philosophy. We will exhibit the connection between the way in which Natorp redefines the Kantian dichotomy and his conception of the method of philosophy. We will investigate how Natorp introduces his position in dialogue with Kant’s position and with contemporary approaches to the problem, psychologism and logicism. We will argue that the question of how a cognition may refer to the object requires rethinking the method of philosophy. It will be shown that the Kantian question of how thinking can have reference to objects was badly posed. The question is how the understanding can be the source of objectivity and not how it relates to the objects. We will study the arguments that led Natorp to argue that the object is the result of a construction of the understanding The hypothesis of this investigation is that Natorp’s redefinition of the distinction between intuitions and concepts is based on a new conception of the philosophical method. Consejo Nacional de Investigación Científica y Tenológica (CONICyT). Santiago de Chile, Chile.Philosophy of Knowledge and Cognitio
    • 

    corecore