38,046 research outputs found
Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably?
Classical interpretations of Goedel's formal reasoning imply that the truth
of some arithmetical propositions of any formal mathematical language, under
any interpretation, is essentially unverifiable. However, a language of
general, scientific, discourse cannot allow its mathematical propositions to be
interpreted ambiguously. Such a language must, therefore, define mathematical
truth verifiably. We consider a constructive interpretation of classical,
Tarskian, truth, and of Goedel's reasoning, under which any formal system of
Peano Arithmetic is verifiably complete. We show how some paradoxical concepts
of Quantum mechanics can be expressed, and interpreted, naturally under a
constructive definition of mathematical truth.Comment: 73 pages; this is an updated version of the NQ essay; an HTML version
is available at http://alixcomsi.com/Do_Goedel_incompleteness_theorems.ht
Learning by Seeing by Doing: Arithmetic Word Problems
Learning by doing in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children\u27s ability to see significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children\u27s ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children\u27s own word problems; play with dynamically linked representations with attention to children\u27s prior connections; and systematic problem variation based on empirically determined level of difficulty
Digital waveguide modeling for wind instruments: building a state-space representation based on the Webster-Lokshin model
This paper deals with digital waveguide modeling of wind instruments. It presents the application of state-space representations for the refined acoustic model of Webster-Lokshin. This acoustic model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross-section, visco-thermal losses at the walls, and without assuming planar or spherical waves. Moreover, three types of discontinuities of the shape can be taken into account (radius, slope and curvature).
The purpose of this work is to build low-cost digital simulations in the time domain based on the Webster-Lokshin model. First, decomposing a resonator into independent elementary parts and isolating delay operators lead to a Kelly-Lochbaum network of input/output systems and delays. Second, for a systematic assembling of elements, their state-space representations are derived in discrete time. Then, standard tools of automatic control are used to reduce the complexity of digital simulations in the time domain. The method is applied to a real trombone, and results of simulations are presented and compared with measurements. This method seems to be a promising approach in term of modularity, complexity of calculation and accuracy, for any acoustic resonators based on tubes
Cross-domain priming from mathematics to relative-clause attachment: a visual-world study in French
Human language processing must rely on a certain degree of abstraction, as we can produce and understand sentences that we have never produced or heard before. One way to establish syntactic abstraction is by investigating structural priming. Structural priming has been shown to be effective within a cognitive domain, in the present case, the linguistic domain. But does priming also work across different domains? In line with previous experiments, we investigated cross-domain structural priming from mathematical expressions to linguistic structures with respect to relative clause attachment in French (e.g., la fille du professeur qui habitait Ă Paris/the daughter of the teacher who lived in Paris). Testing priming in French is particularly interesting because it will extend earlier results established for English to a language where the baseline for relative clause attachment preferences is different form English: in English, relative clauses (RCs) tend to be attached to the local noun phrase (low attachment) while in French there is a preference for high attachment of relative clauses to the first noun phrase (NP). Moreover, in contrast to earlier studies, we applied an online-technique (visual world eye-tracking). Our results confirm cross-domain priming from mathematics to linguistic structures in French. Most interestingly, different from less mathematically adept participants, we found that in mathematically skilled participants, the effect emerged very early on (at the beginning of the relative clause in the speech stream) and is also present later (at the end of the relative clause). In line with previous findings, our experiment suggests that mathematics and language share aspects of syntactic structure at a very high-level of abstraction
Network Representation and Passivity of Delayed Teleoperation Systems
The paper proposes a general network based
analysis and design guidelines for teleoperation systems. The
electrical domain is appealing because it enjoys proficient analysis
and design tools and allows a one step higher abstraction
element, the network. Thus, in order to analyze the system by
means of network elements the mechanical system must be first
modeled as an electric circuit. Only then power ports become
apparent and networks can be defined. This kind of analysis
has been previously performed in systems with well defined
causalities, specially in the communication channel. Indeed,
a communication channel exchanging flow-like and effort-like
signals, as for instance velocity and computed force, has a
well defined causality and can thus be directly mapped as a
two-port electrical network. However, this is only one of the
many possible system architectures. This paper investigates how
other architectures, including those with ambiguous causalities,
can be modeled by means of networks, even in the lack of
flow or effort being transmitted, and how they can be made
passive for any communication channel characteristic (delay,
package-loss and jitter). The methods are exposed in the form
of design guidelines sustained with an example and validated
with experimental results
Optimizing construction of scheduled data flow graph for on-line testability
The objective of this work is to develop a new methodology for behavioural synthesis using a flow of synthesis, better suited to the scheduling of independent calculations and non-concurrent online testing. The traditional behavioural synthesis process can be defined as the compilation of an algorithmic specification into an architecture composed of a data path and a controller. This stream of synthesis generally involves scheduling, resource allocation, generation of the data path and controller synthesis. Experiments showed that optimization started at the high level synthesis improves the performance of the result, yet the current tools do not offer synthesis optimizations that from the RTL level. This justifies the development of an optimization methodology which takes effect from the behavioural specification and accompanying the synthesis process in its various stages. In this paper we propose the use of algebraic properties (commutativity, associativity and distributivity) to transform readable mathematical formulas of algorithmic specifications into mathematical formulas evaluated efficiently. This will effectively reduce the execution time of scheduling calculations and increase the possibilities of testability
- âŠ