Type Inference for Variant Object Types

Existing type systems for object calculi are based on invariant subtyping. Subtyping invariance is required for soundness of static typing in the presence of method overrides, but it is often in the way of the expressive power of the type system. Flexibility of static typing can be recovered in different ways: in first-order systems, by the adoption of object types with variance annotations, in second-order systems by resorting to Self types. Type inference is known to be P-complete for first-order systems of finite and recursive object types, and NP-complete for a restricted version of Self types. The complexity of type inference for systems with variance annotations is yet unknown. This paper presents a new object type system based on the notion of Split types, a form of object types where every method is assigned two types, namely, an update type and a select type. The subtyping relation that arises for Split types is variant and, as a result, subtyping can be performed both in width and in depth. The new type system generalizes all the existing first-order type systems for objects, including systems based on variance annotations. Interestingly, the additional expressive power does not affect the complexity of the type inference problem, as we show by presenting an O(n^3) inference algorithm.

EXPERIMENTAL INVESTIGATION OF LINEAR BUBBLE DYNAMICS IN A VISCOELASTIC XANTHAN GEL

Oceanic bubble plumes caused by ship wakes or breaking waves disrupt sonar communi- cation because of the dramatic change in sound speed and attenuation in the bubbly fluid. Experiments in bubbly fluids have suffered from the inability to quantitatively characterize the fluid because of continuous air bubble motion. Conversely, single bubble experiments, where the bubble is trapped by a pressure field or stabilizing object, are limited in usable frequency range, apparatus complexity, or the invasive nature of the stabilizing object (wire, plate, etc.). Suspension of a bubble in a viscoelastic Xanthan gel allows acoustically forced oscilla- tions with negligible translation over a broad frequency band. Assuming only linear, radial motion, laser scattering from a bubble oscillating below, through, and above its resonance is measured. As the bubble dissolves in the gel, different bubble sizes are measured in the range 240 – 470 μm radius, corresponding to the frequency range 6 – 14 kHz. Equalization of the cell response in the raw data isolates the frequency response of the bubble. Compari- son to theory for a bubble in water shows good agreement between the predicted resonance frequency and damping, such that the bubble behaves as if it were oscillating in water.

Statistical Properties of Single and Competing Non-Linear Fast-Slow Oscillators in Noise

Statistical properties offast-slow Ellias-Grossberg oscillators are studied in response to deterministic and noisy inputs. Oscillatory responses remain stable in noise due to the slow inhibitory variable, which establishes an adaptation level that centers the oscillatory responses of the fast excitatory variable to deterministic and noisy inputs. Competitive interactions between oscillators improve the stability in noise. Although individual oscillation amplitudes decrease with input amplitude, the average to'tal activity increases with input amplitude, thereby suggesting that oscillator output is evaluated by a slow process at downstream network sites.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.