Parametrized spaces model locally constant homotopy sheaves

We prove that the homotopy theory of parametrized spaces embeds fully and faithfully in the homotopy theory of simplicial presheaves, and that its essential image consists of the locally homotopically constant objects. This gives a homotopy-theoretic version of the classical identification of covering spaces with locally constant sheaves. We also prove a new version of the classical result that spaces parametrized over X are equivalent to spaces with an action of the loop space of X. This gives a homotopy-theoretic version of the correspondence between covering spaces over X and sets with an action of the fundamental group of X. We then use these two equivalences to study base change functors for parametrized spaces.Comment: 26 pages; exposition improve

Cap Products in String Topology

Chas and Sullivan showed that the homology of the free loop space LM of an oriented closed smooth finite dimensional manifold M admits the structure of a Batalin-Vilkovisky (BV) algebra equipped with an associative product called the loop product and a Lie bracket called the loop bracket. We show that the cap product is compatible with the above two products in the loop homology. Namely, the cap product with cohomology classes coming from M via the circle action acts as derivations on loop products as well as on loop brackets. We show that Poisson identities and Jacobi identities hold for the cap product action, extending the BV structure in the loop homology to the one including the cohomology of M. Finally, we describe the cap product in terms of the BV algebra structure in the loop homology.Comment: 19 pages. Revised version 2 with added references, improved exposition, and simplified sign

Early Life Stress, Drug Abuse, Exercise Effects on BDNF and Sex-influenced Excercise Differences

In 2011, the U.S. reported 3 million child maltreatment cases, an uncomfortably high but recurring figure each year. Research shows exposure to early life stress (ELS) increases an individual’s susceptibility to substance abuse, specifically of nicotine, alcohol, and cocaine. Increased susceptibility may result from dysregulation of the HPA axis sustaining activation into adulthood after ELS. Hyperactivation of the HPA axis significantly reduces hippocampal BDNF, a neurotrophin involved in neuronal growth and plasticity. Reduced hippocampal BDNF may be a factor in substance abuse vulnerability. Additionally, research shows exercise protects hippocampal BDNF from stress induced down-regulation. To explore these relationships, this study used maternal separation (MS) to model ELS in rats. Following MS, rats voluntarily exercised for three weeks, or were sedentary, followed by cocaine conditioned place preference. We quantified hippocampal BDNF from these groups and predicted MS would down-regulate BDNF and exercise would ameliorate this effect. Finally, we predicted BDNF levels would correlate with total running activity. We found no significant effect of MS or exercise, and total running activity weakly correlated with BDNF expression. Our results parallel the behavioral results of this experiment, in which there also were no significant effects of exercise on sensitivity to the locomotor or rewarding effects of cocaine. Thus, although no significance was found in this study, it may provide further insight into the relationships between ELS, exercise, and substance abuse and provide footing for improvement in the development of designs exploring them

Student Experience: Megan Dold, MSc Development Management 2011/12

After completing the Development Management programme in August 2012, I started a full-time job as a communications officer at the Thomson Reuters Foundation in London

Geodesic flow for CAT(0)-groups

We associate to a CAT(0)-space a flow space that can be used as the replacement for the geodesic flow on the sphere tangent bundle of a Riemannian manifold. We use this flow space to prove that CAT(0)-group are transfer reducible over the family of virtually cyclic groups. This result is an important ingredient in our proof of the Farrell-Jones Conjecture for these groups

Harnessing function from form: towards bio-inspired artificial intelligence in neuronal substrates

Despite the recent success of deep learning, the mammalian brain is still unrivaled when it comes to interpreting complex, high-dimensional data streams like visual, auditory and somatosensory stimuli. However, the underlying computational principles allowing the brain to deal with unreliable, high-dimensional and often incomplete data while having a power consumption on the order of a few watt are still mostly unknown. In this work, we investigate how specific functionalities emerge from simple structures observed in the mammalian cortex, and how these might be utilized in non-von Neumann devices like “neuromorphic hardware”. Firstly, we show that an ensemble of deterministic, spiking neural networks can be shaped by a simple, local learning rule to perform sampling-based Bayesian inference. This suggests a coding scheme where spikes (or “action potentials”) represent samples of a posterior distribution, constrained by sensory input, without the need for any source of stochasticity. Secondly, we introduce a top-down framework where neuronal and synaptic dynamics are derived using a least action principle and gradient-based minimization. Combined, neurosynaptic dynamics approximate real-time error backpropagation, mappable to mechanistic components of cortical networks, whose dynamics can again be described within the proposed framework. The presented models narrow the gap between well-defined, functional algorithms and their biophysical implementation, improving our understanding of the computational principles the brain might employ. Furthermore, such models are naturally translated to hardware mimicking the vastly parallel neural structure of the brain, promising a strongly accelerated and energy-efficient implementation of powerful learning and inference algorithms, which we demonstrate for the physical model system “BrainScaleS–1”

Global dynamics of asymptotically locally AdS spacetimes with negative mass

The Einstein vacuum equations in five dimensions with negative cosmological constant are studied in biaxial Bianchi IX symmetry. We show that if initial data of Eguchi-Hanson type, modelled after the four-dimensional Riemannian Eguchi-Hanson space, have negative mass, the future maximal development does not contain horizons, i. e. the complement of the causal past of null infinity is empty. In particular, perturbations of Eguchi-Hanson-AdS spacetimes within the biaxial Bianchi IX symmetry class cannot form horizons, suggesting that such spacetimes are potential candidates for a naked singularity to form. The proof relies on an extension principle proven for this system and a priori estimates following from the monotonicity of the Hawking mass