117,759 research outputs found
Towards the Formal Specification and Verification of Maple Programs
In this paper, we present our ongoing work and initial results on the formal
specification and verification of MiniMaple (a substantial subset of Maple with
slight extensions) programs. The main goal of our work is to find behavioral
errors in such programs w.r.t. their specifications by static analysis. This
task is more complex for widely used computer algebra languages like Maple as
these are fundamentally different from classical languages: they support
non-standard types of objects such as symbols, unevaluated expressions and
polynomials and require abstract computer algebraic concepts and objects such
as rings and orderings etc. As a starting point we have defined and formalized
a syntax, semantics, type system and specification language for MiniMaple
Origin of the Scaling Law in Human Mobility: Hierarchical Organization of Traffic Systems
Uncovering the mechanism leading to the scaling law in human trajectories is
of fundamental importance in understanding many spatiotemporal phenomena. We
propose a hierarchical geographical model to mimic the real traffic system,
upon which a random walker will generate a power-law travel displacement
distribution with exponent -2. When considering the inhomogeneities of cities'
locations and attractions, this model reproduces a power-law displacement
distribution with an exponential cutoff, as well as a scaling behavior in the
probability density of having traveled a certain distance at a certain time.
Our results agree very well with the empirical observations reported in [D.
Brockmann et al., Nature 439, 462 (2006)].Comment: 6 figures, 4 page
Magnetic Phase Transitions in One-dimensional Strongly Attractive Three-Component Ultracold Fermions
We investigate the nature of trions, pairing and quantum phase transitions in
one-dimensional strongly attractive three-component ultracold fermions in
external fields. Exact results for the groundstate energy, critical fields,
magnetization and phase diagrams are obtained analytically from the Bethe
ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of
trions, bound pairs, a normal Fermi liquid and four mixtures of these states.
Particularly, a smooth phase transition from a trionic phase into a pairing
phase occurs as the highest hyperfine level separates from the two lower energy
levels. In contrast, there is a smooth phase transition from the trionic phase
into a normal Fermi liquid as the lowest level separates from the two higher
levels.Comment: 4 pages, 3 figures, minor revisions to text, replacement figure, refs
added and update
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