Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design

Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GP-UCB, an intuitive upper-confidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many commonly used covariance functions. In some important cases, our bounds have surprisingly weak dependence on the dimensionality. In our experiments on real sensor data, GP-UCB compares favorably with other heuristical GP optimization approaches

Abrasive Water Jet Cutting: A Risk-Free Technology for Machining Mg-Based Materials

Mg-based materials are considered to be the most machinable of all materials due to their good machinability. Though conventional machining of Mg-based materials is a topic that has been widely discussed, they are associated with ignition issues. Ignition risk in conventional machining of Mg-based materials thus cannot be denied and should be avoided. Literature has witnessed ignition risk when machining temperature reaches above 450°C during turning and milling processes, and some cases are reported with fire hazard. In order to obtain the safest machining atmosphere, abrasive water jet machining, a most desired machining technology for machining Mg-based materials, is discussed in the present chapter. The text covers ignition risk in conventional machining of Mg-based materials, an overview of non-traditional methods for machining Mg-based materials, advantages of abrasive water jet machining over other methods, abrasive water jet linear cutting of Mg alloys and composites, and drilling of Mg alloys. Experimental investigations are carried out to know the effect of abrasive water jet process parameters on machining Mg alloys and Mg nanocomposites. Surface topography of cut surfaces is analyzed. Suitability of abrasive water jet in drilling Mg alloys is justified by comparing results with holes drilled by conventional drilling and jig boring

Efficient size estimation and impossibility of termination in uniform dense population protocols

We study uniform population protocols: networks of anonymous agents whose pairwise interactions are chosen at random, where each agent uses an identical transition algorithm that does not depend on the population size $n$. Many existing polylog$(n)$ time protocols for leader election and majority computation are nonuniform: to operate correctly, they require all agents to be initialized with an approximate estimate of $n$ (specifically, the exact value $\lfloor \log n \rfloor$). Our first main result is a uniform protocol for calculating $\log(n) \pm O(1)$ with high probability in $O(\log^2 n)$ time and $O(\log^4 n)$ states ($O(\log \log n)$ bits of memory). The protocol is converging but not terminating: it does not signal when the estimate is close to the true value of $\log n$. If it could be made terminating, this would allow composition with protocols, such as those for leader election or majority, that require a size estimate initially, to make them uniform (though with a small probability of failure). We do show how our main protocol can be indirectly composed with others in a simple and elegant way, based on the leaderless phase clock, demonstrating that those protocols can in fact be made uniform. However, our second main result implies that the protocol cannot be made terminating, a consequence of a much stronger result: a uniform protocol for any task requiring more than constant time cannot be terminating even with probability bounded above 0, if infinitely many initial configurations are dense: any state present initially occupies $\Omega(n)$ agents. (In particular, no leader is allowed.) Crucially, the result holds no matter the memory or time permitted. Finally, we show that with an initial leader, our size-estimation protocol can be made terminating with high probability, with the same asymptotic time and space bounds.Comment: Using leaderless phase cloc

Newly proposed classification of celiac artery variations based on embryology and correlation with computed tomography angiography

Purpose: We studied the prevalence of celiac trunk and its anatomical variations on diagnostic computed tomography angiography (CTA) studies and have proposed a new classification to define the celiac artery (CA) variations based on embryology. Material and methods: We retrospectively assessed the celiac trunk variations in 1113 patients who came to our department for diagnostic CTA for liver and renal donor workup. The patient data were acquired from the Picture Archiving and Communication System of our institutions. We analysed the celiac trunk’s origin and branching pattern, including the superior mesenteric artery (SMA) and inferior phrenic artery (IPA). Results: We evaluated the CTA studies of 1050 patients. A normal trifurcation pattern, the most common type, was observed in 39% of cases. Variation with CA + left IPA was the most common subtype. Other variations noted in the study and their incidences are listed in the table below. We attempted to propose a new classification based on embryology, which comprises 6 main types and their subtypes. We also analysed previous studies from the literature, including cadaveric, post-mortem, CTA, and digital subtraction angiography studies and compared them with the present study. Conclusions: Because variations of CA classifications reported to date do not encompass all CA branching pattern variants, we have proposed a new classification that incorporates most of the variants. We reiterate the clinical importance of anatomical variants of CA, IPA, and SMA in surgical and interventional radiology procedures

Enzyme-Free Nucleic Acid Dynamical Systems

An important goal of synthetic biology is to create biochemical control systems with the desired characteristics from scratch. Srinivas et al. describe the creation of a biochemical oscillator that requires no enzymes or evolved components, but rather is implemented through DNA molecules designed to function in strand displacement cascades. Furthermore, they created a compiler that could translate a formal chemical reaction network into the necessary DNA sequences that could function together to provide a specified dynamic behavior

On the biophysics and kinetics of toehold-mediated DNA strand displacement

Dynamic DNA nanotechnology often uses toehold-mediated strand displacement for controlling reaction kinetics. Although the dependence of strand displacement kinetics on toehold length has been experimentally characterized and phenomenologically modeled, detailed biophysical understanding has remained elusive. Here, we study strand displacement at multiple levels of detail, using an intuitive model of a random walk on a 1D energy landscape, a secondary structure kinetics model with single base-pair steps and a coarse-grained molecular model that incorporates 3D geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Two factors explain the dependence of strand displacement kinetics on toehold length: (i) the physical process by which a single step of branch migration occurs is significantly slower than the fraying of a single base pair and (ii) initiating branch migration incurs a thermodynamic penalty, not captured by state-of-the-art nearest neighbor models of DNA, due to the additional overhang it engenders at the junction. Our findings are consistent with previously measured or inferred rates for hybridization, fraying and branch migration, and they provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems

Towards Practical Lipschitz Bandits

Stochastic Lipschitz bandit algorithms balance exploration and exploitation, and have been used for a variety of important task domains. In this paper, we present a framework for Lipschitz bandit methods that adaptively learns partitions of context- and arm-space. Due to this flexibility, the algorithm is able to efficiently optimize rewards and minimize regret, by focusing on the portions of the space that are most relevant. In our analysis, we link tree-based methods to Gaussian processes. In light of our analysis, we design a novel hierarchical Bayesian model for Lipschitz bandit problems. Our experiments show that our algorithms can achieve state-of-the-art performance in challenging real-world tasks such as neural network hyperparameter tuning

Programmable chemical controllers made from DNA

Biological organisms use complex molecular networks to navigate their environment and regulate their internal state. The development of synthetic systems with similar capabilities could lead to applications such as smart therapeutics or fabrication methods based on self-organization. To achieve this, molecular control circuits need to be engineered to perform integrated sensing, computation and actuation. Here we report a DNA-based technology for implementing the computational core of such controllers. We use the formalism of chemical reaction networks as a 'programming language' and our DNA architecture can, in principle, implement any behaviour that can be mathematically expressed as such. Unlike logic circuits, our formulation naturally allows complex signal processing of intrinsically analogue biological and chemical inputs. Controller components can be derived from biologically synthesized (plasmid) DNA, which reduces errors associated with chemically synthesized DNA. We implement several building-block reaction types and then combine them into a network that realizes, at the molecular level, an algorithm used in distributed control systems for achieving consensus between multiple agents