FROM LINGUISTIC REPRESENTATION TO FUZZY MATHEMATICS IN GROWN UP PEOPLE

The aim of this note is to give some critical examples where even the use of the same clustering rules lead to fuzziness. It starts from poor numerical systems and compares them with the expanded Sergeyev model, where the grossone is used, as an infinite terminal element. It can be compared with terminal elements of the ancient languages, such as the Greek myriad and the Chinese wan. On them some propositions that hold in the arithmetic of the grossone are similar, while they are not meaningful for the countable system of infinity. The note shows that both the upward and downward trend are actually present in human language and in conceptual arrangements. The note then goes on to sketch the model of evolution of Bak-Sneppen, showing two significant applications: the case of the evolution and  study of foreign languages and, according to the model of Lloyd, the territorial analysis. In both cases it is highlighted how the Bak-Sneppen model becomes more stable when the universe is segmented, as already proven by the authors in previous works. The third part examines some cases of false probabilistic intuition due to incomplete perception  of the phenomena, what could therefore be defined as hidden conditional probability. Interesting is the classic application of the theory of games to lotteries and ternary games, such as Chinese morra

Partitioned Frames in Bak Sneppen Models

In the first section we recall Bak Sneppen model and its evolutions. In this paper we wish to present some simplified cases in which explicit computations via Markov chains are possible, hence reaching a better understanding of some rather hidden phenomena of the general case: in particular “avalanches” can be read in terms of average return times and in terms of transitions between structures. A short comparison of the behaviour of different model of graphs of interaction is contained in section 2. The simple models allow us to introduce new frames that do not seem to have been considered in the previous literature, namely the case of partitioned Bak-Sneppen frames, that appear more realistic from the point of view of speed of evolution and do not present a unique criticality level, but a staircase tending towards a final equilibrium level. This is the object of section 3, while section 4 shows how this model clearly explains the overtaking of competitors with respect to species that seem to be well assessed and recalls some of our experimental data

Endogenous control in a ternary lotka-volterra model and its applications

This paper aims at highlighting the role of endogenous controls in Lotka-Volterra predator-prey models. Unlike other studies in which the core lies in expanding the number of con\ub0icting species, here the stress is laid upon a control variable that does not need to be of the same nature as the species involved in the con\ub0ict. As in the case of the logistic equation Lotka-Volterra models have proved highly fruitful also outside the pure biological frame, clarifying many socio-economical and psychological evolution phenomena. A main problem lies in the change of the structural parameters, that can alter the evolution. Rather than an exterior action a model is most satisfactory in pres- ence of an endogenous change, that should happen without any external intervention. The critical model is described in Section 2 under the name of tripartite antagonist model, where there are three actors, and three predator-prey equations involving, two at each time, the actors. The structure is that each actor once is predator and once prey in a circular scheme. In some natural cases the three variables are all biological, but in most meaningful cases the control has a di\uaeerent nature, usually social or behavioral. The paper highlights the particular case where the initial existence of a control, albeit at a very low level, is essential to allow the development towards equilibrium, while its absence leads to the destruction of the prey. A similar case arises when predator and prey are in temporary equilibrium, but a hidden control variable operates until a sudden change of equilibrium bursts out. Section 1 is devoted to recall some preliminary know-ledge of system theory and of Lotka.Volterra classical equations. Section 3 is devoted to illustrate some actual cases where tripartite antagonist system can explain social, psychological, economic developments, even with reference to the academic world. The long lasting competition between Stoicism and Epicurism, between hedonism and Aristotle's eudaimonia fully enters in this scheme

PARTITIONED FRAMES IN DISCRETE BAK SNEPPEN MODELS

In this paper, we wish to present some simpli¯ed cases of discrete Bak- Sneppen models in which explicit computations via Markov chains are possible, hence reaching a better understanding of some rather hidden phenomena of the general case: in particular "avalanches" can be read in terms of mean waiting times and in terms of transitions between structures. The simple models allow us to introduce new frames that do not seem to have been considered in the previous literature, namely the case of partitioned Bak-Sneppen frames, that appear more realistic from the point of view of speed of evolution and do not present a unique criticality level, but a staircase tending towards a ¯nal equilibrium level, cadenced by an increasing sequence of footholds. The introduction summarizes Bak-Sneppen models, starting from the central model due to Bak and Sneppen, and recalls their use in applied sciences. The ¯rst section gives the ge- neral frame of models where locality and globality coexist, the second section shows the simplest case of a matching between locality and globality, that will become exemplar in the most complex frames of Bak-Sneppen processes. The main quantitative theorems are stated and proved in the third section and ¯nally the fourth section presents exam- ples that illustrate the more sophisticated points of our paper and the use (and limits) of experimental results, while the ¯fth section considers real world situations where Bak Sneppen partitioned schemes can be tailored to represent the core of their evolution

Minimal models of self-organized criticality

The paper deals with an evaluation of the behavior of non equilibrium systems displaying self- organized criticality, according to the concept of Bak-Tang-Wiesenfeld ([3]). One of the fundamental characteristics of a system in a self-organized state is to exhibit a stationary state with a long-range power law of decay of both spatial and temporal correlations

THE RECOVERY OF COMPREHENSIBLE MATHEMATICS

The main objective is to get over the gap that exists between mathematics and common people, especially grown up people. Apart mathematical details, the problem lies in a good choice of notices (curiosity) and nice problems (play). Some historical notes about great mathematicians are presented and discussed, with explicit reference to the cases when the boundary between Nobel prize and mathematics was broken. Favourable fields are probability and operations research. Since probability tends to an excess of theory, operations research seemed to be a good choice. The Fields Medal, a kind of Nobel prize for Mathematics, was also considered, since in 2018 it was achieved by the Italian mathematician Figalli, former student of Scuola Normale Superiore di Pisa. He started from an important field in the frame of Operations Research, namely Optimal Transport. This sector allows to summarize a very nice procedure for its solution, non at all obvious to be trasferred to the computer. Since mathematics is forgotten in the course of life, except for those few parts of current use, to bring the adult back into the interest of mathematics, topics related to everyday life should be presented. Operations research, and especially network optimization, provide significant but pleasing problems.

Structured knowledge in the frame of Bak-Sneppen models

Instruction aims at the acquisition of a structured or procedural knowledge and was always torn between a frame of imitation of examples (more or less exhaustive) and a frame of theoretical or conceptual knowledge, exposed more or less systematically. Mathematics has the longest history at the level of its phylogeny, since it built in time many alternating systems of consistent relations, even if they clashed when they had to be mixed and glued together. The mathematical evolution of the individual (ontogeny) is subject to sudden jumps unlike the softer evolution of less structured disciplines. The moments of confrontation between di\uc6erent structures or innovation sparks need time to a\uc6ect the existing structures, both in philogeny and in ontogeny. Bak-Sneppen models of evolution help to understand many social phenomena, especially when voluntary or random competition may hinder the search of optimal individual paths, but at the same time forces development. In mathematics, because of its high developed structure, knowledge waves can hinder comprehension both of pupils and of scholars. The paper discusses some paradoxes where a greater knowledge has proved to diminish e\ub1ciency and capability

Forensic Radiology: An Update

Forensic radiology is a specialized area of medical imaging using radiological techniques to assist physicians and pathologists in matters related to the law. The forensic application of diagnostic medical radiology can be applied in many fields; the prime target of evaluation is the osseous skeleton, but soft tissues and abdominal and thoracic viscera may offer key findings. The technological progress in clinical radiology provides a lot of potential tools to forensic radiology, allowing wider fields of applications in this matter

Clinical characteristics of a large cohort of patients with narcolepsy candidate for pitolisant: a cross-sectional study from the Italian PASS Wakix® Cohort

Introduction Narcolepsy is a chronic and rare hypersomnia of central origin characterized by excessive daytime sleepiness and a complex array of symptoms as well as by several medical comorbidities. With growing pharmacological options, polytherapy may increase the possibility of a patient-centered management of narcolepsy symptoms. The aims of our study are to describe a large cohort of Italian patients with narcolepsy who were candidates for pitolisant treatment and to compare patients' subgroups based on current drug prescription (drug-naive patients in whom pitolisant was the first-choice treatment, switching to pitolisant from other monotherapy treatments, and adding on in polytherapy). Methods We conducted a cross-sectional survey based on Italian data from the inclusion visits of the Post Authorization Safety Study of pitolisant, a 5-year observational, multicenter, international study. Results One hundred ninety-one patients were enrolled (76.4% with narcolepsy type 1 and 23.6% with narcolepsy type 2). Most patients (63.4%) presented at least one comorbidity, mainly cardiovascular and psychiatric. Pitolisant was prescribed as an add-on treatment in 120/191 patients (62.8%), as switch from other therapies in 42/191 (22.0%), and as a first-line treatment in 29/191 (15.2%). Drug-naive patients presented more severe sleepiness, lower functional status, and a higher incidence of depressive symptoms. Conclusion Our study presents the picture of a large cohort of Italian patients with narcolepsy who were prescribed with pitolisant, suggesting that polytherapy is highly frequent to tailor a patient-centered approach

SARS-CoV-2 susceptibility and COVID-19 disease severity are associated with genetic variants affecting gene expression in a variety of tissues

Variability in SARS-CoV-2 susceptibility and COVID-19 disease severity between individuals is partly due to genetic factors. Here, we identify 4 genomic loci with suggestive associations for SARS-CoV-2 susceptibility and 19 for COVID-19 disease severity. Four of these 23 loci likely have an ethnicity-specific component. Genome-wide association study (GWAS) signals in 11 loci colocalize with expression quantitative trait loci (eQTLs) associated with the expression of 20 genes in 62 tissues/cell types (range: 1:43 tissues/gene), including lung, brain, heart, muscle, and skin as well as the digestive system and immune system. We perform genetic fine mapping to compute 99% credible SNP sets, which identify 10 GWAS loci that have eight or fewer SNPs in the credible set, including three loci with one single likely causal SNP. Our study suggests that the diverse symptoms and disease severity of COVID-19 observed between individuals is associated with variants across the genome, affecting gene expression levels in a wide variety of tissue types