This paper investigates a cylindrical nonlinear Schrödinger (cNLS) equation, which describes the cylindrically diverging quasi-plane envelope waves in a nonlinear medium. With the Hirota method and symbolic computation, bilinear form and N-soliton solutions in the form of an Nth-order polynomial in N exponentials are obtained for the cNLS equation. By means of the properties of double Wronskian...

Fugues alternate between instances of the subject and of other patterns, such as the counter-subject, and modulatory sections called episodes. The episodes play an important role in the overall design of a fugue: detecting them may help the analysis of the fugue, in complement to a subject and a counter-subject detection. We propose an algorithm to retrieve episodes in the fugues of the first b...

This report presents a novel family of linear-time algorithms for loop analysis based on the CR# (CR-sharp) algebra, which is a new nontrivial extension of the Chains of Recurrences (CR) algebra. Conventional compiler methods apply induction variable substitution and array recovery translations to construct closed forms for induction variables and pointers prior to dependence testing and loop o...

The lambda calculus is a formal symbolic term rewrite system that has been used for many years both as a mechanism for defining the semantics of programming languages, and as the basis for functional programming languages. In this paper, we describe a completely visual representation for lambda expressions, VEX, that has several advantages over traditional textual lambda calculus. Although VEX ...

The experiment consists in testing an hypothesizer that assembles, in different degrees of corruption of the input phonetic sequence, data on the processing time, on the complexity of those underlattices which develop "around" a single lexical hypothesis as well on performances, in numerical terms, of the separate hypotheses of the words present in the symbolic input sequence. An ltalian senten...

Achieving and understanding effective transfer of learning requires a careful analysis of the hidden knowledge and skills to be transferred. We present an experiment that tests a subtle prediction of such an analysis. It concluded that a critical difficulty in students’ learning to translate algebra story problems into symbolic expressions is in learning the grammar of such expressions. We hypo...

In this paper we present a proof-of-concept implementation of Neural Theorem Provers (NTPs), end-to-end differentiable counterparts of discrete theorem provers that perform first-order inference on vector representations of symbols using function-free, possibly parameterized, rules. As such, NTPs follow a long tradition of neural-symbolic approaches to automated knowledge base inference, but di...

In this paper we explore a new number system which uses a double base. The representation of the numbers has a very simple geometric interpretation, allowing potentially fast implementation of the basic arithmetic operations. The transformation of the integers into minimal form, however, leads to some problems associated with transcendental number theory, and we identify and open the discussion...

This paper proposes the enhancement in the design of adjustable pedals in automotive by incorporating gesture recognition methodologies. The design addresses the three primary controls: Accelerator, Brake and Clutch. Mechanical input of driver’s feet is deduced at location variant adjustable pedals in terms of feet gestures. Research work aims vision based technology for the feet gesture recogn...

Bugs in user input sanitation of software systems often lead to vulnerabilities. Among them many are caused by improper use of regular replacement. This paper presents a precise modeling of various semantics of regular substitution, such as the declarative, finite, greedy, and reluctant, using finite state transducers (FST). By projecting an FST to its input/output tapes, we are able to solve a...