**COMPUTER SCIENCE**

Computer science has a remarkable growth during the last decades. We may trace in its "ontogenesis" , the "philogenesis" of mathematical and other sciences. So we can see how, from bits only, (an analogue of the natural numbers) we can create, not only languages and algebraic structures of data bases, but also the real numbers and the "continuum" of the sounds ,images and visual animations (multi-media). The methods repeat the main bold ideas of Cartesian coordinates ,or definition of real numbers etc. The science of mathematics can gain also by elaborating and reformulating in a crystal-clear way , the older definitions. The infinite that was used in mathematics to derive the continuum from the discrete , is certainly a functional property and complexity relations in the procedures and phenomenology of software. Computer science has today , in addition, through the internet and mobiles, a profound influence in society and private life.

The next two
papers, were trying to explore the power and universality that the **concepts of tree
**has in logic and computer science. If a complicated circuit is like a
chaotic labyrinth , the tree on which it can be unfolded is a **free
order** in which all seem easier and more transparent.

**1) **
Application of Ω-algerbrae
, trees and rings in Hypertext.(1992)

** **

2) Universal covering entailment systems of Meseguers general Logics.

By
Dr. C.Kyritsis and Petros Stephaneas ,National Technical University of Athens.
Proceedings of the 3rd Barcelona Conference in Logic (1997).

*Comments and Interpretation:*

This paper develops applications of geometric
and topological concepts to computer Logic.

3) Petri-nets,trees and Topological Universal
Coverings.

By Dr. C.Kyritsis and P.Stephaneas (NTUA)
.Proceedings of the Conference HERMCA 98 at the University of Economics of
Athens (1997-1998).

*Comments and Interpretation:*

In this paper is proved that any flow-chart in computer programming can be obtained as a tangled (quotient) tree ,or tree-order. Thus any complex labyrinth of information flow is the result of a free (tree) order of information flow.

4) *The
Computer Programs as an algebra.* (1993)

In this paper we describe the programming language procedures as polynomials of a (non-commutative) ring -like algebra (the commands or elementary actions) with operators (as exponents) from a finite Boolean algebra (of elementary decisions of the user or the computer). The algebraic structure representing procedures that can be run over a finite set of data, in a computer, is a finite algebra

5) *A
general method to reduce the run-time complexity of algorithms from
non-polynomial complete to polynomial complete*.(2003)

In this paper we prove that by using a recursive sub-problem technique in solving a problem with an algorithm of non-polynomial complete run-time complexity we can reduce it to problem solvable with an algorithm of polynomial complete-run time complexity. To do so the problem solving algorithm must have some general particular properties

of decomposition. The technique resample, partly, some of the steps of the branch-and-bound algorithm in integer linear programming or the dynamic programming of Bellman.

**
Software
developed by the author:**

Α1) **
Market Scanner and Portfolio Trader
**(10,000 lines, 200 pages,140
procedures, 110 tables). Program for massive
scan of all instruments (securities, derivatives, commodities, currencies etc)
so as to select a short list of them according to specified investment criteria.
It makes use of Access, it is written in VBA,
4th generation RDBMS, SQL statements etc. It makes use as Graphical user
interface, the Microsoft Office.

A2) **
Portfolio Designer** (VB,
SQL server)

A program designed for optimal portfolio selection from commodities and securities and hedging with derivatives. It supports linear and non-linear (Markovitch theory) models of portfolio selection.

Α3)
**
Real Time Traffic Lights** (34,000
lines,
682 pages,
302 procedures).

Program with the same functionalities as the previous but designed to run at real time , responding to all intraday online changes of the prices of the instruments. In addition it has real-time forecasting, in its scan criteria. The program has the graphical user interface of Microsoft Excel, and also makes use of Outlook for e-mail, and mobile phones sms alerts, and queries.

A4)**Options
Simulator** (14,000
lines,287 pages, 194 procedures)**.**

A program that calculates the Greeks indicators of Options. In addition it supports historic and Monte Carlo simulation for options strategies and forecasting. It is also used in online real-time monitoring of options. The program is also linked with the data bases of the previous two for the needs of hedging.

A5) **
Quantitative Simulator
**(70,000 lines,1100 pages, 520
procedures, Interface: Excel)**. **

Program designed for the run of computer simulation experiments, so as to find and optimize algorithmic automated trading systems. It supports almost all types of stochastic models, in the academic research, and the most important technical analysis indicators. The program can also be used as a computer game, with user-interactive non-automated trading strategies, for educational and practice purposes.

**Front-Office,
Middle-Office, Back-Office and the previous programs:**

All the previous programs support functionalities of front-office, middle-office (risk management) and back-office (clearance and clearance statistics)

The next three PowerPoint presentation were Lectured at the University College of Engineering of the University of Southern Denmark at Odense during autumn of 2006 and spring 2008.

1. **
Unemployment and the
Internet in the new millennium.**

2.
**
S****uccessful
site functionalities and web-marketing **
**techniques****
**
**of **
** e-commerce****
in the 21****st**** century**

**3.
The effect of the abundance of
choices in the new internet marketing: The Long tail effect**