We discuss results where the discrete spectrum (or partial information on the discrete spectrum) and partial information on the potential q of a one-dimensional Schrödinger operator H = − d2 dx2 + q determine the potential completely. Included are theorems for finite intervals and for the whole line. In particular, we pose and solve a new type of inverse spectral problem involving fractions of ...

The traditional technique for simulating physical systems modeled by partial differential equations is by means of time-stepping methodology where the state of the system is updated at regular discrete time intervals. This method has inherent inefficiencies. In contrast to this methodology, we have developed a new asynchronous type of simulation based on a discrete-event-driven (as opposed to t...

The traditional technique to simulate physical systems modeled by partial differential equations is by means of a time-stepped methodology where the state of the system is updated at regular discrete time intervals. This method has inherent inefficiencies. In contrast, we propose a new asynchronous type of simulation based on a discrete-event-driven (as opposed to time-driven) approach, where t...

In this paper we propose a component-based hybrid formalism, that represents physical phenomena by combining concurrent automata with continuous uncertain dynamic models. The formalism eases the modeling of complex physical systems, and adds concurrency to the supervision of hybrid systems. Uncertainties in the model are integrated as probabilities at the discrete level and intervals at the con...

Two experiments on categorical rhythm perception are reported, the object of which was to investigate how listeners perceive discrete rhythmic categories while listening to rhythms performed on a continuous time scale. This is studied by considering the space of all temporal patterns (all possible rhythms made up of three intervals) and how they, in perception, are partitioned into categories, ...

We discuss results where the discrete spectrum (or partial information on the discrete spectrum) and partial information on the potential q of a one-dimensional Schrr odinger operator H = ? d 2 dx 2 + q determine the potential completely. Included are theorems for nite intervals and for the whole line. In particular, we pose and solve a new type of inverse spectral problem involving fractions o...

Let a,b (b > a) be nonnegative integers. We define the discrete interval [a,b] = {a,a + 1, . . . ,b}. All other intervals will carry its standard meaning, for example, [0,∞) denotes the set of nonnegative real numbers. The symbol Δ denotes the forward difference operator with step size 1, that is, Δu(k) = u(k + 1)− u(k). Furthermore for a positive m, Δm is defined as Δmu(k)= Δm−1(Δu(k)). In thi...

Attractor networks are likely to underlie working memory and integrator circuits in the brain. It is unknown whether continuous quantities are stored in an analog manner or discretized and stored in a set of discrete attractors. In order to investigate the important issue of how to differentiate the two systems, here we compare the neuronal spiking activity that arises from a continuous (line) ...

The Borsuk-Ulam theorem of topology is applied to a problem in discrete mathematics. A bisection of a necklace with k colors of beads is a collection of intervals whose union captures half the beads of each color. Every necklace with fc colors has a bisection formed by at most k cuts. Higherdimensional generalizations are considered.

We consider classical and quantum propagators for two different time intervals. If these propagators follow one another in a Fibonacci sequence we get a discrete quasiperiodic system. A theorem due to Nielsen provides a novel conserved quantity for this system. For the quasiperiodically kicked oscillator we study this conserved quantity as a function of the system parameters.