How much Mathematics does Economy Need? ...Or... Some Brief Epistemological Excursions into the Mathematics located on the border with Social Sciences

In our paper we try to answer to the epistemological question how much mathematics does economy need.economics, economy, mathematics, epistemology

Econophysics: A new discipline

This paper debates the contribution of Econophysics to the economic or financial domains. Since the traditional approach performed by Economics or Finance has revealed to be insufficient in fully characterizing and explaining the correspondingly phenomena, we discuss whether Econophysics can provide a new insight onto these matters. Thus, an assessment is presented in order to weight its potential opportunities and limitations. This is particularly relevant as it is widely recognized that during its yet short existence Econophysics has experienced a growing interest not only by physicists but also by economists in searching for new approaches that could help explaining existing questions. In fact, many papers have been submitted, some books have been released, new journals have been published, several conferences have been held, a site is maintained -- http://www.unifr.ch/econophysics where news, events, book reviews, papers and a blog are exhibited; a 3-year licentiate studies (University of Silesia [1]) and a B.Sc. course (University of Wroclaw [2]) have been created and also some Ph.D. thesis have been written. Therefore, a fundamental question arises: Is this just a fad or is it something much more consistent that will prevail? This is what this paper addresses

The Complexity of Finding Reset Words in Finite Automata

We study several problems related to finding reset words in deterministic finite automata. In particular, we establish that the problem of deciding whether a shortest reset word has length k is complete for the complexity class DP. This result answers a question posed by Volkov. For the search problems of finding a shortest reset word and the length of a shortest reset word, we establish membership in the complexity classes FP^NP and FP^NP[log], respectively. Moreover, we show that both these problems are hard for FP^NP[log]. Finally, we observe that computing a reset word of a given length is FNP-complete.Comment: 16 pages, revised versio

Generalised exponential families and associated entropy functions

A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential families. The well-known result that the inequality of Cramer and Rao becomes an equality in the case of an exponential family can be generalised. However, this requires the introduction of escort probabilities.Comment: 20 page

Duality and interval analysis over idempotent semirings

In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose of this paper is to consider a dual product, denoted $\odot$, and the dual residuation of matrices, in order to solve the following inequality $A \otimes X \preceq X \preceq B \odot X$. Sufficient conditions ensuring the existence of a non-linear projector in the solution set are proposed. The results are extended to semirings of intervals