# Renaud Di FrancescoThe Institution of Engineering and Technology | IET · Electrical Engineering

Renaud Di Francesco

PhD

## About

111

Publications

53,161

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99

Citations

Introduction

Al and loT,
Edge Computing,
Agent Based Models,
Real-time Data,
Information Theory,
Future Networks,
Matrices of sets and generalised spectral analysis,
Adjacency sets for Graphs,
Behavioural Economics, Commons Management,
Intertemporal choice and utility,
Set valued maps,
Subjective probability,
Accessibility,
AAL,
Privacy Protection,
NPI and loT (non pharmaceutical interventions) for Health Policy implementation,
Animal Vision and machine emulation in VLSI,
Pedestrian-level smart cities

Additional affiliations

Education

January 2002 - July 2003

September 1987 - July 1990

September 1985 - August 1987

## Publications

Publications (111)

We have developed a framework of Matrices of Sets and Vectors of Sets [1], where matrix terms and vector coordinates are sets, instead of numbers in the classical case of matrices of numbers and vectors in countable dimensional spaces. In this framework, a practical example of interest includes Vectors of Intervals, when the sets used are intervals...

A mathematical approach for matrices of sets (Matrices M with terms M(i,j) which are sets at row i and column j), with minimum illustration at the end
Reference are given to more detailed approaches of some of the opportunities arising.
Here you will find the framework, just “what it does”

This research is a component of the FLUSYNCHRO initiative and is focused on constructing a decision support tool for comparing multimodal transport routes from one point to another based on several factors, including distance, time, and environmental considerations. The study employs the innovative theoretical framework of matrices of sets to model...

This patent is about a method to assess the credit of a requester before granting the requester access to service

Covid-19 has caught the world unprepared, partly because the lessons learnt from the 1918-1919 Influenza Global Pandemic had been long forgotten or ignored by Public Health Policy decision makers [Stephen S. Morse, 2007] [Martin C. J. Bootsma et al, 2007]. There are now less excuses for not building a robust approach ahead of future viral pandemics...

The analysis of similarities and differences between ports at the global level can help the Maritime ecosystem for different purposes, including business planning, operation, and regulation. Our methodology is demonstrated in a particular case of interest as the "short sea shipping" traffic through a harbour. However, no structural limit to the sco...

Covid-19 has caught the world unprepared, partly because the lessons learnt from the 1918-1919 Influenza Global Pandemic had been long forgotten or ignored by Public Health Policy decision makers [Stephen S. Morse, 2007] [Martin C. J. Bootsma et al, 2007]. There are now less excuses for not building a robust approach ahead of future viral pandemics...

The sum Sp (n) of the power p of the first n integers, is well-known for p=1 to be n(n+1)/2, and for p=2 as n(n+1)(2n+1)/6. A general formula has been established by Faulhaber (see Wikipedia). Our approach is to step away from a pure number-based approach for the proof, and to show an alternate minimalistic proof which uses elementary geometry. The...

This is a tutorial on the recently developed framework of Matrices of Sets, with latest results. The presentation contains the foundation of Matrices of Sets, an extensive section on its properties, and a consolidation of first results obtained in different application use cases

In line with previous industrial revolutions, standardisation must
accompany the deployment of artificial intelligence systems that
promise to revolutionise the way we live (home automation,
autonomous vehicles, EdTech, etc.) and work (collaborative
industrial robots, agricultural robots, inspection and maintenance
robots, LegalTech, FinTech, etc.)...

Artificial Intelligence (AI) is experiencing growing interest as the society and the economy is accelerating its digitisation. To harness the potential of AI, already illustrated by proprietary developments from multiple leading Internet Platforms, while giving it a trusted and secure framework for users from Europe to be able to confidently benefi...

The present disclosure relates to a method of generating pictographic representations. The method comprises receiving input content comprising textual information and a video item, the textual information being associated with the video item and aligned to a video playback timeline associated with the video item, obtaining summarisation information...

During Covid-19, prevention through lockdown belongs to the portfolio of Non-Pharmaceutical Intervention (NPI). The implementation of a lockdown mesure comes with a health care benefit, however with an economic and human cost: people are constrained to stay in their homes. Households hence have to live together in what we call “zero-space”, which m...

Patent application for vehicle equipped with sensors, with a view to detecting risk taken (insurance and other purpose)

Cities are observed and compared using their monthly temperature intervals [Tmin, Tmax]. The methodology is structured by the use of Matrices of sets: a city i (line index) and a month m (among the twelve months of the year, column index) are associated to the set T(i,m) which is the temperature interval observed. The Jaccard index, which is the ca...

Patent application on collision mitigation (based on detection)

Overview This article summarises the already established framework of Matrices of Sets, with a published corpus of properties developed initially as a complement with engineering purpose to the concise notion of edge/adjacency matrix in graph theory, then generalised with a Matrix multiplication for Matrixes of Sets, "x", suitable for representing...

Real-Time Detection of the glottal closure from the speech signal, based on convexity disruptions of accumulated signal.

Speech signal carefully processed for extracting glottal closure time

This presentation is a tutorial approach to Matrices of Sets (and L-sets), which are tables, in which the position at line i and column j is allocated to a set (resp.L-set) M(i,j), instead of a number m(i,j) in classical matrices.
We start with a short reminder of the parallel timeline of development of matrices and set theory, by leading mathemat...

Digital technologies are already used
ubiquitously in maritime transport, and in the
protection of the oceanic ecosystems, as well
as the sustainable exploitation of its
resources for instance where fishing is duly
regulated.
The potential of digital technologies for the
sea, and for those humans living from it is
within reach. A major step has bee...

In the Covid19 pandemic, behavioural economics analysis and "nudging" know-how was put to serve the general interest of the public. A more detailed nanoeconomic angle has been the behaviour of households in lockdown, sharing tasks, and jointly managing time allocation and priorities to keep the household running with daily chores added to child sup...

This document presents an operational framework for using generalised sets, along the lines introduced by D. Loeb with another application purpose [1].
Two categories of generalised sets are considered and combined: classical sets allowing for multiple occurrence of elements, as sets of actual locally available elements, and sets formed of missing...

Inversion of Matrices of Sets

British Computer Society seminar on the new framework of Matrices of Sets, which builds on set versatility and matrix computational efficiency, in the dynamic of large data set collection and processing, through data science

The British Computer Society has invited this presentation on Matrices of Sets, in its Interest Group on Formal Aspects of Computing Science (BCS/FACS).
Outline:
* short reminder of the parallel timeline of development of matrices and set theory, by leading mathematicians as Cayley, Sylvester, Jordan, Hilbert for matrices, and mainly Cantor for se...

Matrices of Sets offer a convenient way to organise and operationalise algebraically Data, as a tiling of Datasets. We illustrate the use of such algebraical organisation of data, in the context of Economics, and for Logistics Optimisation.
We present a generational model using matrices of sets, and discuss its reduction using summaries at discret...

The world is experiencing a global pandemic with Covid19, for which few measures
have proven efficiency. Prevention through lockdown belongs to the portfolio of NonPharmaceutical Intervention (NPI), with re-acquisition of forgotten learnings from the 1918
Global Influenza [1] [2] [3] and of Great Plagues [4][5]. The implementation of a lockdown
com...

Revised and improved Tutorial on Matrices of Sets
Adding examples, applications, and considerations on implementation

This presentation addresses:
-The datasets generated/consumed in Cognitive Manufacturing
-Ownership of data: rights granted to access/use, roles in data value chain
-Value of data: why pricing is needed, and how to do it

Extended Abstract Containerised transport is central to global commerce as shown by the recent traffic halt in the Suez Canal in March 2021, and the consequent threat to global freight transport, which our economies are used to rely upon. The new framework of Matrices of Sets considers matrices where each term at line i and column j is a set, inste...

Extended Abstract The recently developed framework of Matrices of sets, where matrix term at line i and column j is a set M(i,j) (instead of a number m(i,j) in classical matrices) is used to re-visit key notions used by Maritime Economics:-(1) Economically efficient routing of goods on water and land, including their delivery to points of retail.-(...

Once upon a time in India, and later in Arabic language literature, a strong and deep legend developed with scientific impact:
-a chess player (or the inventor of the chess game, depending on version) pleased so much a ruler/lord/prince that he/she was offered to chose a reward of his/her choice
-he or she (it's an old story, difficult to know fo...

This presentation is a tutorial approach to Matrices of Sets, which are tables in which the position at line i and column j is occupied by a set, instead of a number in classical matrices.
We start with a short reminder of the parallel timeline of development of matrices and set theory, by leading mathematicians as Cayley, Sylvester, Jordan, Hilber...

Containers are a convenient way for organising international goods transport, in multimodal form, by road, rail, sea.
Containers are similar to mathematical sets: they contain objects (physical elements).
Therefore, for harbour logistics and container based transport, it seems natural to consider Matrices of Set, as this presentation shows.
Feedbac...

This article considers matrices of sets, where in matrix table M, the term M(i,j) at line i and column j is a set instead of an element of the set of real numbers, complex numbers or of a similar group G. In previous publications 1 a framework for multiplication, symmetric difference, eigenvalue/eigenvector analysis and polynomials has been establi...

This presentation is an introduction to Matrices of Sets, i.e. tables in which the position at line i and column j is occupied by a set M(i,j), instead of a number m(i,j) in classical matrices.
Outline:
-short reminder of the parallel timeline of development of matrices and set theory, by leading mathematicians as Cayley, Sylvester, Jordan, Hilbert...

Matrices, developed by Cayley, Sylvester, Jordan and other leading mathematicians from the mid XIXth century into the XXth century have proven their efficiency, especially in the programmable computing age, up to this day of layered algorithms for Artificial Intelligence applications. The reader is referred to any undergraduate course on linear alg...

Matrices, developed by Cayley, Sylvester, Jordan and other leading mathematicians from the mid XIXth century into the XXth century have proven their efficiency, especially in the programmable computing age, up to this day of layered algorithms for Artificial Intelligence applications. The reader is referred to any undergraduate course on linear alg...

Matrices, developed by Cayley, Sylvester, Jordan and other leading mathematicians from the mid XIXth century into the XXth century have proven their efficiency, especially in the programmable computing age, up to this day of layered algorithms for Artificial Intelligence applications. The reader is referred to any undergraduate course on linear alg...

The framework is set for matrices where m(i,j) is not a value, number, or a matrix as in the classical matrix theory, but a SET.
Efficient operations on sets are sketched, and direction for future work are suggested.

Graph Theory is now in the classical toolbox of any Computer Scientist, Engineer, and Applied Mathematician, even of any scientist... It is very powerful, but to get to this degree of power, the Graph Theory imposes a simplification, which we want to revisit. Classical graphs have vertices and edges linking some of the vertices. Graph edges are usu...

Graph Theory is now in the classical toolbox of any Computer Scientist, Engineer, and Applied Mathematician, even of any scientist... It is very powerful, but to get to this degree of power, the Graph Theory imposes a simplification, which we want to revisit. Classical graphs have vertices and edges linking some of the vertices. Graph edges are usu...

Graph Theory is now in the classical toolbox of any Computer Scientist, Engineer, and Applied Mathematician, even of any scientist...
It is very powerful, but to get to this degree of power, the graph imposes a simplification, which we want to revisit. Classical graphs have vertices and edges linking some of the vertices. The edges are usually repr...

Integrating Artificial Intelligence, Edge Computing, and evolving SCADA concepts and methods for Advanced Manufacturing

Over the past few years, street furniture, and in
particular, traffic lights have been intelligently controlled
to monitor and ensure the flow of traffic around an urban
environment such as a city centre. This has meant a significant investment has been made in infrastructure allowing data to flow around these pieces of street furniture.With the ad...

The world is experiencing a global pandemic with Covid19, for which few measures have proven efficiency. Prevention through lockdown belongs to the portfolio of Non-Pharmaceutical Intervention (NPI), with re-acquisition of forgotten learnings from the 1918 Global Influenza [1] [2] [3] and of Great Plagues [4][5]. The implementation of a lockdown co...

Whereas the scientific area of Covid 19 transmission and propagation models has been dominated by top-down models, typically considering a whole country or geographical area, we consider as a starting point the context of interaction between people who bear a random attribute of healthy or infectious. Limiting ourselves to this two-state model heal...

The classical audio and video coding domain was centered on human perception.
With the advent of AI and Automation embedding AI, world input is acquired, "sensorially perceived", analysed, decisions are made, and action feeds back to the real world.
The sensorial information acquired needs to be optimised for correct analysis and decision making, w...

We develop a simple computable model for infection propagation, based on vicinity and interaction time conditions, between healthy and infectious persons. This simple and robust model can be adapted for realistic simulations. The three use cases studied in detail are: 1) an elderly care home where contamination at joint meals is considered, 2) a ho...

A very interesting article has been published recently as a pre-print on Researchgate.net by Gabriele Ciminelli and Sílvia Garcia-Mandicó, which shows for the case of Italy of how variable the fate of the elderly persons in nursing homes versus those living at home may have been in the past months of the pandemic of Covid19.
We will explore here if...

A very interesting article has been published recently as a pre-print on Researchgate.net by Gabriele Ciminelli and Sílvia Garcia-Mandicó, which shows for the case of Italy of how variable the fate of the elderly persons in nursing homes versus those living at home may have been in the past months of the pandemic of Covid19.
This article brings for...

We develop a simple computable model, which can be adapted for realistic simulations. The three use cases considered are: 1) a household in lockdown, “stay at home”, with contamination at joint meals considered, and 2) large venue event with lots of interaction between participants and crowd effects.
Readers interested by the specific case of Elder...

We develop a simple computable model, which can be adapted for realistic simulations. The three
use cases considered are: 1) an elderly care home where contamination at joint meals is
considered, 2) a household in lockdown, “stay at home”, with contamination at joint meals
considered, and 3) large venue event with lots of interaction between partic...

Emotion icons, also known by the portmanteau emoticons, have existed for several decades.
These are typically entirely text and character based, often using letters, punctuation marks and
numbers, and include a vast number of variations. This vary by region, with Western style
emoticons typically being written at a rotation of 90° anticlockwise to...

A method of transmitting data from a mobile terminal over a wireless network. The method includes: applying a different priority level to different types of data transmission; determining quantity of data remaining before expiry of the data connection between the mobile terminal and the wireless network; and transmitting the different types of data...

User equipment comprising communication circuitry configured to communicate data with infrastructure equipment and controller circuitry configured to : operate in a first mode using a first communication protocol and operate in a second mode using a second communication protocol , wherein the first communication protocol has a higher bandwidth than...

IoT and data, privacy and security

I am happy to announce the IoT event jointly hosted by AFNOR Standards Institute and Telecom Paris Tech in Paris, on 25 October 2018.
https://www.linkedin.com/feed/update/urn:li:activity:6460072243794845697

Standards for the industrial Internet

This chapter assumes a commonly adopted framework of use for mobile connectivity in the 5G era. It reviews the standardization path, and the expected objectives and characteristics in the 5G phase, learning from best practice and bottlenecks alike, in the development of mobile standards in previous and current generations: 2G, 3G, and 4G (LTE). The...

In the context of the General Data Protection Regulation entering into force in Europe in Mau 2018, Privacy needs a lot of attention, including from a technological perspective (active privacy protection technologies)

The roles for the economy revolving around data are defined, and principles are proposed to make data rights tradeable as any other good

A relay device operable to relay emergency information to a plurality of mobile terminals. The device includes: a receiver configured in use to receive a broadcast signal, the broadcast signal being in a first format and containing the emergency information; a transmitter configured in use to connect to the plurality of mobile terminals using a com...

A method of obfuscating information communicated between a first apparatus and a second apparatus, comprising: in the first apparatus, obtaining genuine information to be communicated to the second apparatus; obtaining decoy information to be communicated to the second apparatus; indicating the decoy information to be communicated to the second app...

A method of transmitting data from a mobile terminal over a wireless network is disclosed. The method comprises the steps of: applying a different priority level to different types of data transmission; determining the quantity of data remaining before expiry of the data connection between the mobile terminal and the wireless network; and transmitt...

The impact of trust/mistrust towards a source leads humans to decide along, somewhat along, or somewhat against to fully against what the source recommends. We have used this observation for building a fully computable agent model, to simulate such trust/mistrust and its impact

A particular point of interest in the Cumulated Perspective Theory and the resulting of Behavioural Economics pioneered by Kahneman & Tversky, is that humans, faced with input information of a probability distribution p, tend to process and transform this input into an output they will use, call it subjective probability distribution q. q is a non-...

How to address immunity to unwanted intervention in robotic/AI/IoT systems

Roles and mechanisms around data
Criteria for fairness, recognition of ownership on data, use in respect of rights of owner
Privacy aspects

With the Internet of Things, the question of protecting the privacy of people by technical means gets more acute. The current emphasis by organisations on protecting their infrastructure, assets, and services with cybersecurity methods and techniques, is faced by a mainly legal protection for individuals users of services. Legal protection is a pos...

A relay device operable to relay emergency information to a plurality of mobile terminals. The device includes: a receiver configured in use to receive a broadcast signal, the broadcast signal being in a first format and containing the emergency information; a transmitter configured in use to connect to the plurality of mobile terminals using a com...

Part I: Right to be forgotten
Part II: Asymmetry in Digital Revolution -phase 1: Moore's Law; -phase2: « the age of data »
Part III: unpaid data ?

There is described a device for providing a media content item to a user, the device comprising: a media content item receiver operable to receive the media content item as a data stream, the data stream comprising identifying data which identifies the media content item; a memory operable to store user profile information associated with the user...

http://www.amazon.co.uk/Microeconomics-big-data-Commodities-Society-ebook/dp/B014N7I4SU/

Ceux qu'on appelle les utilisateurs, c'est-à-dire nous tous les individus vus comme citoyens ou consommateurs, ou simplement des personnes, sont maintenant de nano-producteurs de données.
La relation entre nano-producteurs, en milliards de personnes (utilisateurs de téléphones mobiles par exemple) et les quelques grandes marques de l'Internet, très...

Les big data reposent sur trois piliers: les logiciels ("analytics"), les réseaux ("Cloud", etc), et les données elles-mêmes. Pourtant, si la valeur (et le prix) des réseaux, et des logiciels sontreconnus, il n'en va pas systématiquement de même pour les données.
Nous nous intéressons ici aux données en tant que telles. Quels sont les mécanismes éc...

Big Data is seen today as an Information Technology opportunity. It can change Society and the Economy. However, the fuel of big data, which is the source data itself, has received little specific attention from the economists. Beyond the information technology project by project cost analysis, we address here the data itself and all economic quest...

This book addresses the economics of Big Data, beyond a project by project cost analysis.
The fuel or input of any Big Data system is source data. In many cases of current use of Big Data, excepting Open Data, the data is obtained for one single purpose, and used by a single organisation, because of the likely absence of an open and transparent mar...

This book addresses the economics of Big Data, beyond a project by project cost analysis.
The fuel or input of any Big Data system is source data. In many cases of current use of Big Data, excepting Open Data, the data is obtained for one single purpose, and used by a single organisation, because of the likely absence of an open and transparent ma...

BOOK:
https://www.amazon.co.uk/gp/product/B00JTKGM2C/ref=dbs_a_def_rwt_bibl_vppi_i2
ASIN : B00JTKGM2C
Big Data driving decisions with direct impact on the real-world: this is the deep transformation ahead of us.
With billions of humans connected through mobile and fixed networks, the challenge is now shifting to connecting things in a meaningful w...

Big Data driving decisions with direct impact on the real-world: this is the deep transformation ahead of us.
With billions of humans connected through mobile and fixed networks, the challenge is now shifting to connecting things in a meaningful way. This is what Big Data, enabled by Machine to Machine connectivity, is all about:
-making sense of...

Big Data driving decisions with direct impact on the real-world: this is the deep transformation ahead of us.
With billions of humans connected through mobile and fixed networks, the challenge is now shifting to connecting things in a meaningful way. This is what Big Data, enabled by Machine to Machine connectivity, is all about:
-making sense of...

A method for data exchange between a vehicle and a server, the vehicle including a battery and a first communication unit, the server including a second communication unit. The method connects the first communication unit and the second communication unit via a connection line wherein the connection line is adapted for charging the battery via a po...

In a session on education for standards developers, present some key aspects of use to anyone wanting to run a serious game between teams, simulating standards development

## Questions

Questions (86)

**The Covid shock**

Covid19 caught us by surprise. The previous comparable event had happened 100 years earlier and it had been named the Spanish flu, and it probably killed more people than World War I. The 1919 lessons learnt by health policy makers such as the US cities and European governments had been long forgotten.

**Now we have learnt something**

This time, it's 2023, and the Covid years, which are not over, have left a clear memory. We have no excuse, not to go prepared.

What about behavioural economists, looking at the exchange of value, time, tasks, anything, in human groups?

What can they tell us, of practical and explanatory interest for the next wave of Covid, or ahead of a similar event?

**Behavioural economics scenarios and the pandemic**

Can I suggest to look back at the micro-problem replicated a large number of times worldwide, where each household had to self-manage meals, schooling the children, etc. Trade-offs happened at high frequency between the members of the household, seen as agents in a behavioral nano-economy of the house...

**The behavioual economist and a vademecum for the next wave?**

What do you consider worthwhile for planning the next wave each household likely to have to isolate for while, at least now and then?

Let me share the assessment and model developed for the case of Covid19 "household lockdown":

REF

[1]

**Agent Based Model for Covid 19 Transmission: -field approach based on context of interaction**, July 2020,R. Di Francesco, DOI: 10.13140/RG.2.2.24583.83364[2] "

**Nanoeconomics of Households in Lockdown Using Agent Models during COVID-19**," Sustainability, by Javier Cifuentes-Faura & Renaud Di Francesco, 2022, vol. 14(4), pages 1, February.[3]

**Microeconomics of intertemporal choice in zero-space during Covid-19: a behavioral economics perspective**. by Cifuentes-Faura, J., Di Francesco, R.,*J Health Econ***23**, 559–563 (2022). https://doi.org/10.1007/s10198-021-01403-z**Challenge faced worldwide: a new spread of Covid**

We all have lived through Covid19, across the world. Prior to the availability of vaccines, Non-Pharmaceutic Interventions by health-aware governments were implemented, with significant success, well into a stage of lockdown, where residents of a country were asked and then required to stay at home, with stringent conditions to get out of their homes. The logistics of food supply was usually well managed, even if there were cases of people remaining isolated from food supply at times.

**Anticipating the risk through propagation models**

The key to not letting Covid-19 take its toll, and it actually did take its toll, especially among elderly residents of care homes, in Italy, France, the UK, etc, was to model in an anticipatory manner the spread of the disease and assess its risk realistically.

**Macro-models available (statistics), but what about micro-level (few humans)?**

Modelling was mostly at macro-level: cities, regions, countries. However the different context of human interaction in daily life received much less attention, although large data sets and use cases build on a number of elementary interactions, and smaller numbers of humans involved in each.

**Elementary interactions of few humans**

Our endeavour, which could not afford the ambition of health statisticians in larger teams, to model the spread of the disease at country level, focused instead then, in the years 2019-2020, onto elementary use cases of interaction, with few humans involved (few starting from 2). Such use cases covered elderly patients of care homes, and their interactions during joint meals in the care home meal area, with tables shared, it also covered households in close (and closed) interaction during lockdown. It also tried to make sense of large events, where many humans interact during a limited time (football game, women's day celebration, etc).

The typology of likely propagation in such use cases was modeled, and parameters of a simple but robust model were tuned to known data, and in turn simulations could be run, and such simulation could be assessed on other known outcomes (such as the observation of virus propagation among the citizen team running a polling center during elections in France).

**Next steps: anticipating the wave coming, with micro-models?**

Can we ask the researchgate community if anyone is interested to undertake similar micro-level models of elementary human interaction leading to a likely spread of the virus?

Could we consider building a federated collaborative project, with data fed by anyone having access to these (literature, publications, etc)?

What approach do you recommend? Have you published on the topic?

**REF**

*Here is a reference to the model mentioned above, with associated training/verification data:*

*[1]*

**Agent Based Model for Covid 19 Transmission**: -field approach based on context of interaction, July 2020, R. Di Francesco, DOI:*10.13140/RG.2.2.24583.83364*

I have looked at data base management and applications, data-sets and their use in different contexts. I have looked at digital in general, and I have noticed that there seems to be a single split:

-binary computers, performing number crunching (basically), and behind this you find the Machine Learning, ML, DL, RL, etc at the root fo the current AI

-quantum computing, still with numbers as key objects, with added probability distributions, randomisation, etc. This deviates from deterministic binary computing but only to a certain extent.

Then, WHAT ABOUT computing "DIRECTLY ON SETS", instead of "speaking of sets" and actually only "extracting vectors of numbers from them"? We can program and operate with non-numerical objects, old languages like LISP and LELISP, where the basic objects are lists of characters of any length and shape have done just that decades ago.

So, to every desktop user of spreadsheets (the degree-zero of data-set analytics) I am saying: you work with matrices, the mathematical name of tables of numbers, you know about data-sets, and about analytics. Why would not YOU put the two together: sets are flexible. Sets are sometimes are incorrectly named "bags" because it sounds fashionable (but bags have holes, they may be of plastic, not reusable, sets are more sustainable, math is clean -joking). It's cool to speak of "bags of words", I don't do that. Sets, why? Sets handle heterogeineity, and they can be formed with anything you need them to contain, in the same way a vehicle can carry people, dogs, potatoes, water, diamonds, paper, sand, computers. Matrices? Matrices nicely "vector-multiply", and are efficient in any area of work, from engineering to accounting to any science or humanities domain. They can be simplified in many cases (eigenvector, eigenvalue, along some geometric directions operations get simple, sometimes the change of reference vectors gives a diagonal matrix with zeros everywhere except on the diagonal, by a simple change of coordinates (geometric transformation).

HOW DO WE DO THAT IN PRACTICE? Compute on SETS NOT ON NUMBERS? One can imagine the huge efficiencies gained in some domains, potentially (new: yet to be explored, maybe BY YOU? IN YOUR AREA). Here is the math, simple, it combines knowledge of 11 years old (basic set theory) and knowledge of 15 years old (basic matrix theory). SEE FOR YOURSELF ,and please POST YOUR VIEW on where and how to apply...

Is Leg-tec providing a solution?

How do you train legal workers and civil servants to using digital technology and remove errors by accessing the right text/version of the Law of interest, applicable at a certain date?

Any experience of multiple versions of the same law pulled out by different people on the same case?

How do you explain Management inertia to recognise legal errors in Legal Processes (three versions, at least two of them are false/fake law)?

See attached real story of official documents quoting incompatible text for the same article of Law. Unexpected but TRUE!

I have put together a geometric method to compute the sum of the power p of the first n integers. Do you know of previous articles? A more general framework? Suggestions of applications?

I carve an hypercube into shells of thickness 1, and I repeat until nothing remains. See here https://www.researchgate.net/publication/363484666_A_Geometric_approach_to_Sums_of_Powers_of_Integers_-Faulhaber's_formula_from_Partitions_of_Squares_Cubes_Hypercubes#fullTextFileContent

**1. The current world challenge: efficiency increase as a must**

The world context has been facing over the last few month a new energy challenge. Therefore it is advisable to revisit how we address data-based problem solving, encompassing what Internet Platform call data science.

**2. How to improve energy/data efficiency?**

Data gathering, data search and processing ("machine learning", deep or not), using AI in many cases, should not be repeated blindly again and again, instead of keeping records of first results, modeling structural relations from within the datasets, and sharing preliminary analysis results.

**3. A candidate encapsulation of data relations and expanded set-based modeling**

The Framework of Matrices of Set, enhancing and generalising the matrices of numbers halps keep data until final computation on numbers is required.

An example of application is Collaborative filtering, observing users facing products, and formulating comments.

Below some references with details:

**REF1: Matrices of sets**Presentation Matrices of Sets: -Properties, Applications

**REF2: Logical propositions and relations formulated as Matrices of Sets**

**REF3: Considering applications (see slides 46 to 52 below)**Preprint Matrices of Sets and L-Sets

*REF4: sets and L-sets (negative sets of what is missing, versus sets of what is presents as multi-sets)*

Preprint Matrices of L-sets -Meaning and use