The mathematical structure underlying a sentence is made of two independent processing units in series. The conditional probability density function of sentence length (measured in words) recordable in the extended short–term memory (E–STM) buffer made of CF cells is Gaussian. The number of sentences that authors of Italian and English Literatures have written is compared to that theoretically available to them. The multiplicity factor α describes this comparison. α>1 is more likely than α<1 and often α≫1, therefore the same sentence pattern is reused many times. These texts are easier to read. Very few novels show α<1. In these cases, there are enough diverse sentence patters to convey meaning, but most of them are not used. Texts are more difficult to read, as measured by a universal readability index GU. A mismatch index IM synthetically describes the process. α, GU. and IM increase with year of publication. Future work will concern other literatures – including ancient ones as Greek and Latin – to confirm what, in our opinion, is general feature of human mind.

We propose that the short−term memory (STM), when processing a sentence, uses two uncorrelated processing units in series. The clues for conjecturing this model emerge from studying many novels of the Italian and English Literatures. This simple model, referring to the surface of language, seems to describe mathematically the input-output characteristics of a complex mental process involved in a reading/writing a sentence. We show that there are no significant mathematical/statistical differences between the two literary corpora by considering deep-language variables and linguistic communication channels, therefore, the surface mathematical structure of alphabetical languages is very deeply rooted in human mind, independently of the language used. The first processing unit is linked to the number of words between two contiguous interpunctions, variable Ip, approximately ranging in Miller’s 7±2 range; the second unit is linked to the number of Ip’s contained in a sentence, variable MF, ranging approximately from 1 to 6. The overall capacity required to process fully of a sentence ranges from 8.3 to 61.23 words, values that can be converted into time by assuming a reading speed, giving the range 2.64~19.54 seconds for fast-reading and 5.3~30.1 seconds for average reader. Since a sentence conveys meaning, the surface features we have found might be the starting point to arrive at an Information Theory that includes meaning.

We study two fundamental linguistic channels ‒ the Sentences and the Interpunctions channels ‒ and show they can reveal deeper connections between texts. The theory applied does not follow the actual paradigm of linguistic studies. As study‒case, we consider the Greek New Testament, with the purpose of determining mathematical connections between its texts and possible differences in writing style (mathematically defined) of writers, and in reading skill required to their readers. The analysis is based on deep‒language parameters and communication/information theory. To set the New Testament texts in the larger Greek Classical Literature, we consider texts written by Aesop, Polybius, Flavius Josephus and Plutarch. The results largely confirm what scholars have found about the New Testament texts giving, therefore, credibility to the theory. The gospel according to John is very similar to Fables written by Aesop. Surprisingly, the Epistle to the Hebrews and Apocalypse, are each other “photocopy” in the two linguistic channels, and not linked to all other texts. These two texts deserve further study by historians of the early Christian Church Literature at the level of meaning, readers and possible Old Testament texts which might have influenced them. The theory can guide scholars to study any literary corpus.

We study the short−term memory capacity of ancient readers of the original New Testament written in Greek, of its translations to Latin and modern languages. To model the short–term capacity, we have considered the number of words per interpunctions, the “word interval” , because this parameter can model how the human mind memorizes “chunks” of information. Since can be calculated for any alphabetical text, we can perform experiments − otherwise impossible − with ancient readers by studying the literary works they used to read. The “experiments” compare the of texts of a language/translation to those of another language/translation by measuring the minimum average probability of finding joint readers (those who can read both texts because of their similar short–-term memory capacity) and by defining an “overlap index”. We also define a population of universal readers who can read any the New Testament written in alphabetical language. More than 50% of the readers of specific languages overlap with the universal readers with probability . Future work is vast, with many research tracks, because alphabetical literatures are very large and allow many experiments, such as comparing authors, translations or even texts written by artificial intelligence tools.

Statistics of languages are calculated by counting characters, words, sentences, word rankings. Some of these random variables are also the main “ingredients” of classical readability formulae. Revisiting the readability formula of Italian, known as GULPEASE, shows that of the two terms that determine the readability index G – the semantic index G_C, proportional to the number of characters per word, and the syntactic index G_F, proportional to the reciprocal of the number of words per sentence −, G_F is dominant because G_C is, in practice, constant for any author throughout seven centuries of Italian Literature. Each author can modulate the length of sentences more freely than he can do with the length of words, and in different ways from author to author. For any author, any couple of text variables can be modelled by a linear relationship y=mx, but with different slope m from author to author, except for the relationship between characters and words, which is unique for all. The most important relationship found in the paper is, in author’s opinion, that between the short−term memory capacity, described by Miller’s “7∓2 law”, and the word interval, a new random variable defined as the average number of words between two successive punctuation marks. The word interval can be converted into a time interval through the average reading speed. The word interval is spread in the same of Miller’s law, and the time interval is spread in the same range of short−term memory response times. The connection between the word interval (and time interval) and short−term memory appears, at least empirically, justified and natural, and should further investigated. Technical and scientific writings (papers, essays etc.) ask more to their readers. A preliminary investigation of these texts shows clear differences: words are on the average longer, the readability index G is lower, word and time intervals are longer. Future work done on ancient languages, such as Greek or Latin, could bring us a flavor of the short term−memory features of these ancient readers.

We have studied the stochastic processes A and B concerning fade durations due to rain, by simulating attenuation time series A(t) (dB) in the zenith paths of GeoSurf satellite constellations, at sites located in different climatic regions, with the Synthetic Storm Technique. Process B gives the statistics of outages (occurrences), process A gives the statistics of outage duration (fraction of time), for the same rain attenuation threshold A(t)>S. The two processes are not independent, therefore, we have studied the relationship between their probabilities and defined a uniformity index 0<U(S)≤1. U(S) is useful for comparing real cases – fade durations fragmented in many different intervals, with changing S and site – and the limiting case of all fades lasting the same time. As S increases, U(S) increases, approaching 1 at very large thresholds. These results should guide the designers of future GeoSurf satellite constellations to consider the impact of A(t) on the diverse communications services. Process B (occurrences) impacts on non–real time services, such as data delivery, more disturbed by the number of outages rather than by their duration. Process A (fraction of time) impacts on real–time services such as television, video conference etc., more disturbed by the duration of the outage.

We have studied the very large amount of literary works written by the Italian mystic Maria Valtorta to assess similarities and differences in her writings because she claims that most of them are due to mystical visions. We have used mathematical and statistical tools developed for specifically studying deep linguistic aspects of texts. The general trend indicates that the literary works explicitly attributable to Maria Valtorta differ significantly from her other literary works, that she claims are attributable to the alleged characters Jesus and Mary. Mathematically, they seem to have been written by different authors. The comparison with the Italian literature is very striking. A single author, namely Maria Valtorta, seems to be able to write texts so diverse to cover the entire mathematical range (suitable defined) of the Italian literature of seven centuries.

Keywords: Baseband, GeoSurf Constellation, Interference, Linear Distortions, Passband, Time Delay, Rain attenuation, Synthetic Storm Technique, ultra–wideband.

The traditional approach of considering the probability distribution of rain attenuation leads to overdesign the power margin of data channels. We have first recalled a method, proposed in 2016, which with a small power margin, bandwidth expansion and variable symbol rate avoids overdesign and can transfer the same data volume as if the link were in clear–sky conditions. It is charaterized only by the link mean efficiency 0≤η≤1, suitably defined. It is usefull only if: (a) data must be downloaded also when it is raining; (b) real–time communication is not strictly required. We have applied it to the links of GeoSurf satellite constellations by simulating rain attenuation time series at 80 GHz (mm–wave) with the Synthetic Storm Technique, from rain-rate time series recorded on–site, at sites located in different climatic regions. The power margin to be implemented ranges from 2.0 dB to 7.4 dB – well within the current technology – regardless the instantaneous rain attenuation. The clear–sky bandwidth is expanded 1.75 to 2.80 times, not large per se, but it may challenge current technology if the clear–sky bandwidth is already large.

The purpose of our study is to research Peter’s memory ad catacumbas. According to the Depositio Martyrum ‒ a document of the late Emperor Constantine ‒, there was no memory of the first St Peter’s Basilica on the Vatican Hill. We start with a critical analysis on the Roman Basilicae attributed to Emperor Constantine in the Liber Pontificalis, then we deepen the search of Peter’s memory in the catacombs of the SS Marcellino and Pietro (ad Duos Lauros), also known as Tor Pignattara. Indeed, the Basilica and Mausoleum built in this cemeterial area are the only buildings attributable, with certainty, to Emperor Constantine, who wished to be buried in the Mausoleum, close to an apostle. Besides some striking archeological finds on Peter’s memory already discovered near a particular cubicle in these catacombs, a geometrical and mathematical study of the unusual architectonic characteristics of the Basilica and Mausoleum of Tor Pignattara shows that the buildings were part of a single architectonic plan, very likely designed for coding data useful to locate Peter’s burial site unambiguously, in the area of the cubicle mentioned.