Videos by Lorenzo Carlucci
Estratto della cerimonia di premiazione del Premio Geiger per la traduzione poetica 2021. Per la ... more Estratto della cerimonia di premiazione del Premio Geiger per la traduzione poetica 2021. Per la sezione Opera Prima/Giovane traduttore è stato premiato il nostro Architrenius (Carocci 2019). 12 views
Papers by Lorenzo Carlucci
Discret. Math., 2021
We give upper bounds for a positional game — in the sense of Beck — based on the Paris-Harrington... more We give upper bounds for a positional game — in the sense of Beck — based on the Paris-Harrington principle for bi-colorings of graphs and uniform hypergraphs of arbitrary dimension. The bounds show a striking difference with respect to the bounds of the combinatorial principle itself. Our results confirm a phenomenon already observed by Beck and others: the upper bounds for the game version of a combinatorial principle are drastically smaller than the upper bounds for the principle itself. In the case of Paris-Harrington games the difference is qualitatively very striking. For example, the bounds for the game on 3uniform hypergraphs are a fixed stack of exponentials while the bounds on the corresponding combinatorial principle are known to be Ackermannian! For higher dimensions, the combinatorial Paris-Harrington numbers are known to be cofinal in the Schwichtenberg-Wainer Hiearchy of fast-growing functions up to ε0, while we show that the game Paris-Harrington numbers are fixed st...
Order
Recent results of Hindman, Leader and Strauss and of Fernández-Bretón and Rinot showed that natur... more Recent results of Hindman, Leader and Strauss and of Fernández-Bretón and Rinot showed that natural versions of Hindman's Theorem fail for all uncontable cardinals. On the other hand, Komjáth proved a result in the positive direction, showing that there are arbitrarily large abelian groups satisfying some Hindman-type property. In this note we show how a family of natural Hindman-type theorems for uncountable cardinals can be obtained by adapting some recent results of the author from their original countable setting. We also show how lower bounds for some of the variants considered can be obtained.
Archive for Mathematical Logic
Hirst investigated a slight variant of Hindman's Finite Sums Theorem-called Hilbert's Theorem-and... more Hirst investigated a slight variant of Hindman's Finite Sums Theorem-called Hilbert's Theorem-and proved it equivalent over RCA 0 to the Infinite Pigeonhole Principle for all colors. This gave the first example of a natural restriction of Hindman's Theorem provably much weaker than Hindman's Theorem itself. We here introduce another natural variant of Hindman's Theorem-which we name the Adjacent Hindman's Theorem-and prove it to be provable from Ramsey's Theorem for pairs and strictly stronger than Hirst's Hilbert's Theorem. The lower bound is obtained by a direct combinatorial implication from the Adjacent Hindman's Theorem to the Increasing Polarized Ramsey's Theorem for pairs introduced by Dzhafarov and Hirst. In the Adjacent Hindman's Theorem homogeneity is required only for finite sums of adjacent elements.
We classify the sharp phase transition threshold from provability to unprovability in fragments o... more We classify the sharp phase transition threshold from provability to unprovability in fragments of Peano Arithmetic for the Kanamori-McAloon principle for fixed dimension. For a non negative integer d let IΣ d be the fragment of Peano arithmetic where the induction is restricted to formulas of alternating quantifier depths d (bounded quantifiers are not counted). We prove that the threshold for IΣ d-unprovable totality of f-regressive Ramsey numbers lies above all functions n → g −1 (n) q log d−1 (n) where g −1 is the functional inverse of an increasing function g which is primitive recursive in some fast growing function Fα from the Schwichtenberg-Wainer-hierarchy for some α < ω d. Moreover we show that the threshold for IΣ d-provable totality of f-regressive Ramsey numbers lies below the function n → F −1 ω d (n) q log d−1 (n).
We classify the sharp phase transition threshold from provability to unprovability in fragments o... more We classify the sharp phase transition threshold from provability to unprovability in fragments of Peano Arithmetic for a combinatorial principle going back to Kanamori-McAloon (9). For a non negative integer d let Id be the fragment of Peano arithmetic where the induction is restricted to formulas of alternating quantifier depth d (bounded quantifiers are not counted). We prove that the
Lecture Notes in Computer Science, 2012
ABSTRACT We give a new treatment of the relations between Ramsey’s Theorem, ACA 0 and ACA 0 &... more ABSTRACT We give a new treatment of the relations between Ramsey’s Theorem, ACA 0 and ACA 0 &#39; . First we combine a result by Girard with a colouring used by Loebl and Nešetril for the analysis of the Paris-Harrington principle to obtain a short combinatorial proof of ACA 0 from Ramsey Theorem for triples. We then extend this approach to ACA 0 &#39; using a characterization of this system in terms of preservation of well-orderings due to Marcone and Montalbán. We finally discuss how to apply this method to ACA 0 + using an extension of Ramsey’s Theorem for colouring relatively large sets due to Pudlàk and Rödl and independently to Farmaki.
Journal of Computer and System Sciences, 2012
A bounded example memory learner operates incrementally and maintains a memory of finitely many d... more A bounded example memory learner operates incrementally and maintains a memory of finitely many data items. The paradigm is well-studied and known to coincide with setdriven learning. A hierarchy of stronger and stronger learning criteria had earlier been obtained when one considers, for each k ∈ N, iterative learners that can maintain a memory of at most k previously processed data items. We investigate an extension of the paradigm into the constructive transfinite. For this purpose we use Kleene's universal ordinal notation system O. To each ordinal notation in O one can associate a learning criterion in which the number of times a learner can extend its example memory is bounded by an algorithmic countdown from the notation. We prove a general hierarchy result: if b is larger than a in Kleene's system, then learners that extend their example memory "at most b times" can learn strictly more than learners that can extend their example memory "at most a times". For notations for ordinals below ω 2 the result only depends on the ordinals and is notation-independent. For higher ordinals it is notation-dependent. In the setting of learners with ordinal-bounded memory, we also study the impact of requiring that a learner cannot discard an element from memory without replacing it with a new one. A learner satisfying this condition is called cumulative.
Electronic Colloquium on Computational Complexity, 2010
We introduce a new quantum adversary method to prove lower bounds on the query complexity of the ... more We introduce a new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem. This problem encompasses both, the computation of partial or total functions and the preparation of target quantum states. There has been hope for quite some time that quantum state generation might be a route to tackle the Graph Isomorphism problem. We show that for the related problem of Index Erasure our method leads to a lower bound of Ω(√ N) which matches an upper bound obtained via reduction to quantum search on N elements. This closes an open problem first raised by Shi [FOCS'02]. Our approach is based on two ideas: (i) on the one hand we generalize the known additive and multiplicative adversary methods to the case of quantum state generation, (ii) on the other hand we show how the symmetries of the underlying problem can be leveraged for the design of optimal adversary matrices and dramatically simplify the computation of adversary bounds. Taken together, these two ideas give the new result for Index Erasure by using the representation theory of the symmetric group. Also, the method can lead to lower bounds even for small success probability, contrary to the standard adversary method. Furthermore, we answer an open question due toŠpalek [CCC'08] by showing that the multiplicative version of the adversary method is stronger than the additive one for any problem. Finally, we prove that the multiplicative bound satisfies a strong direct product theorem, extending a result by Spalek to quantum state generation problems.
Rvista di Cultura Classica e Medioevale, 2021
Accounts of the fortune of Pliny’s Natural History in the Middle Ages focus on its impact on the ... more Accounts of the fortune of Pliny’s Natural History in the Middle Ages focus on its impact on the resurgent interest in the natural sciences and on the partially related mirabilia tradition. Knowledge of the strongly pessimistic anthropology and of the related ‘stepmother Nature dilemma’ that Pliny sketches at the beginning of Book 7 of his Natural History very rarely surfaces in medieval literature and invariably under the sign of doctrinal correction. The Twelfth-Century Latin poem Architrenius by Johannes of Hauvilla, whose protagonist roams the world in order to quarrel with Nature about the misery of the human condition, might be a significant exception. We analyze the impact on the Architrenius of the pessimistic description of the human condition in Plin., nat., 7, 1-5, arguing that its use in Johannes’ poem represents a unicum in Twelfth-Century culture.
Dianoia 28 (2019), 2019
We present a reading of the poem Architrenius by Johannes de Hauvilla in the context of the twelf... more We present a reading of the poem Architrenius by Johannes de Hauvilla in the context of the twelfth-century debate on dualist heresy. We argue that the dialogue between man and Nature in Johannes' poem can be read as a quaestio de providentia between a potential dualist heretic and Christian orthodoxy. In particular we claim that the basic tenets expressed by the main character are typical of what contemporary anti-heretical writers called “Manichaeism”. On the other hand the views expressed by Nature match anti-dualistic arguments common in twelfth-century anti-heretical literarure.
Testo a Fronte n. 59, 2019
Conduciamo una comparazione tra il Dialogo della Natura e di un Islandese di Giacomo Leopardi e i... more Conduciamo una comparazione tra il Dialogo della Natura e di un Islandese di Giacomo Leopardi e il poema latino medievale Architrenius di Giovanni di Altavilla. Evidenziamo una serie di strette corrispondenze tematiche, strutturali e linguistiche tra le due opere. Esse ci inducono a ritenere il poema latino una importante fonte diretta, se non un prototipo, dell'operetta di Leopardi. Le corrispondenze rilevate tra i due testi testimoniano una conoscenza approfondita e forse una lunga consuetudine del poeta marchigiano con il poema medievale. Tale ipotesi risulta coerente con le notizie biografiche su Leopardi. Proponiamo di inserire il dialogo leopardiano e il poema medievale nell'ambito della disputa classica sulla Divina Provvidenza. Argomentiamo inoltre che le tesi dei protagonisti di entrambe le opere sono tipiche del Manicheismo. Suggeriamo pertanto che l'interesse di Leopardi per il poema latino debba leggersi come segno di un più profondo interesse specifico verso l'eresia manichea negli anni di gestazione e composizione delle Operette Morali. Abstract.
We present a comparative analysis of Giacomo Leopardi's Dialogo della Natura e di un Islandese and the medieval latin poem Architrenius by Johannes of Hauvilla. We highlight a conspicuous series of strict thematical, structural and textual correspondences. We argue that the latin poem has to be considered an important direct source and a prototype of Leopardi's operetta. The correspondences between the two texts suggest a deep knowledge and possibly a long frequentation of Leopardi and the medieval poem. This hypothesis is coherent with the biographical evidence on Leopardi. We propose to read Leopardi's dialogue and the medieval poem in the context of the classical dispute on Divine Providence. We furthermore suggest that in both works the ideological posture of the main character is that of a Manichaean. We argue that Leopardi's interest in the latin poem has to be read as an indication of a wider specific interest of the poet for the manichaean heresy in the years of ideation and writing of the Operette Morali.
Rivista di Studi Italiani, 2015
Anno XXXIII, n. 2 BIBLIOTECA DI RIVISTA DI STUDI ITALIANI Dicembre 2015 9 CONTRIBUTI NOTE SU MATE... more Anno XXXIII, n. 2 BIBLIOTECA DI RIVISTA DI STUDI ITALIANI Dicembre 2015 9 CONTRIBUTI NOTE SU MATEMATICA E POESIA E SUI LORO RAPPORTI: DUALITÀ E ISOMORFISMI PARZIALI LORENZO CARLUCCI Università di Roma 1 "La Sapienza"
Topics in Cognitive Science, Jan 2013
A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good per... more A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good performance followed by bad performance followed by good performance once again. U-shaped curves have been observed in a wide variety of cognitive-developmental and learning contexts. Ushaped learning seems to contradict the idea that learning is a monotonic, cumulative process and thus constitutes a challenge for competing theories of cognitive development and learning. U-shaped behaviour in language learning (in particular in learning English past tense) has become a central topic in the Cognitive Science debate about learning models. Antagonist models (e.g., connectionism vs. nativism) are often judged on their ability of modeling or accounting for U-shaped behaviour. The prior literature is mostly occupied with explaining how U-shaped behaviour occurs. Instead, we are interested in the necessity of this kind of apparently inefficient strategy. We present and discuss a body of results in the abstract mathematical setting of (extensions of) Gold-style computational learning theory addressing a mathematically precise version of the following question: Are there learning tasks that require U-shaped behaviour? All notions considered are learning in the limit from positive data. We present results about the necessity of U-shaped learning in classical models of learning as well as in models with bounds on the memory of the learner. The pattern emerges that, for parameterized, cognitively relevant learning criteria, beyond very few initial parameter values, U-shapes are necessary for full learning power! We discuss the possible relevance of the above results for the Cognitive Science debate about learning models as well as directions for future research.
Relazione scritta per l'incontro “Identità concettuale e dilatazione dell’istante”, Tokyo Univers... more Relazione scritta per l'incontro “Identità concettuale e dilatazione dell’istante”, Tokyo University of Foreign Studies, Tokyo, 4 Ottobre 2010, organizzato da Marco Mazzi.
In Marco Mazzi (Ed.) "Relational Syntax. Aesthetic awareness and ideological experience in post-industrial society", Oct 2012
Journal of Symbolic Logic, Apr 5, 2014
We characterize the computational content and the proof-theoretic strength of a Ramseytype theore... more We characterize the computational content and the proof-theoretic strength of a Ramseytype theorem for bi-colorings of so-called exactly large sets. An exactly large set is a set X ⊂ N such that card(X) = min(X) + 1. The theorem we analyze is as follows. For every infinite subset M of N, for every coloring C of the exactly large subsets of M in two colors, there exists and infinite subset L of M such that C is constant on all exactly large subsets of L. This theorem is essentially due to Pudlàk and Rödl and independently to Farmaki. We prove that -over Computable Mathematics -this theorem is equivalent to closure under the ω Turing jump (i.e., under arithmetical truth). Natural combinatorial theorems at this level of complexity are rare. Our results give a complete characterization of the theorem from the point of view of Computable Mathematics and of the Proof Theory of Arithmetic. This nicely extends the current knowledge about the strength of Ramsey Theorem. We also show that analogous results hold for a related principle based on the Regressive Ramsey Theorem. In addition we give a further characterization in terms of truth predicates over Peano Arithmetic. We conjecture that analogous results hold for larger ordinals.
Proceedings of The London Mathematical Society, 2010
We construct long sequences of braids that are descending with respect to the standard order of b... more We construct long sequences of braids that are descending with respect to the standard order of braids ("Dehornoy order"), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements involving the braid order are true, but not provable in the subsystems IΣ IΣ IΣ 1 or IΣ IΣ IΣ 2 of the standard Peano system. 1991 Mathematics Subject Classification. 03B30, 03F35, 20F36, 91A50. 1 2 LORENZO CARLUCCI, PATRICK DEHORNOY, AND ANDREAS WEIERMANN state in the context of B + 3
Uploads
Videos by Lorenzo Carlucci
Papers by Lorenzo Carlucci
We present a comparative analysis of Giacomo Leopardi's Dialogo della Natura e di un Islandese and the medieval latin poem Architrenius by Johannes of Hauvilla. We highlight a conspicuous series of strict thematical, structural and textual correspondences. We argue that the latin poem has to be considered an important direct source and a prototype of Leopardi's operetta. The correspondences between the two texts suggest a deep knowledge and possibly a long frequentation of Leopardi and the medieval poem. This hypothesis is coherent with the biographical evidence on Leopardi. We propose to read Leopardi's dialogue and the medieval poem in the context of the classical dispute on Divine Providence. We furthermore suggest that in both works the ideological posture of the main character is that of a Manichaean. We argue that Leopardi's interest in the latin poem has to be read as an indication of a wider specific interest of the poet for the manichaean heresy in the years of ideation and writing of the Operette Morali.
We present a comparative analysis of Giacomo Leopardi's Dialogo della Natura e di un Islandese and the medieval latin poem Architrenius by Johannes of Hauvilla. We highlight a conspicuous series of strict thematical, structural and textual correspondences. We argue that the latin poem has to be considered an important direct source and a prototype of Leopardi's operetta. The correspondences between the two texts suggest a deep knowledge and possibly a long frequentation of Leopardi and the medieval poem. This hypothesis is coherent with the biographical evidence on Leopardi. We propose to read Leopardi's dialogue and the medieval poem in the context of the classical dispute on Divine Providence. We furthermore suggest that in both works the ideological posture of the main character is that of a Manichaean. We argue that Leopardi's interest in the latin poem has to be read as an indication of a wider specific interest of the poet for the manichaean heresy in the years of ideation and writing of the Operette Morali.
di un Islandese di Giacomo Leopardi sembrano possedere alcune somiglianze macroscopiche: mossi dalla considerazione della miseria della condizione umana, i protagonisti delle due opere vanno pellegrini per
il mondo, incontrano una personificazione femminile della Natura e ingaggiano con essa un intenso dialogo, accusandola di nutrire sentimenti
di odio per l’umanità. Una approfondita indagine comparativa dei dati
interni ed esterni alle due opere ci ha permesso di dare corpo e coerenza
all’ipotesi che il poema medievale sia da considerarsi una fonte della celebre operetta leopardiana, aggiungendo una significativa componente
medievale al novero delle fonti antiche e moderne già note. La comparazione testuale evidenzia una ricca serie di corrispondenze tali da non potersi ritenere casuali. L’analisi dei dati esterni permette di isolare un
buon numero di opere da cui Leopardi può avere tratto notizia dell’Architrenius e dimostra la possibilità di un accesso diretto di Leopardi al testo medievale durante il soggiorno di studi filologici a Roma (1822-
1823). Cosa giustifica l’interesse di Leopardi per l’Architrenius? Nell’aspra
disputa tra il protagonista e la Natura si ha una problematizzazione
delle tesi classiche del provvidenzialismo che sembra prefigurare temi
cari all’Illuminismo e a Leopardi. Si tratta più verosimilmente di una eco
del dibattito medievale sul dualismo “manicheo”, della quale troviamo
ampia traccia nell’Architrenius. Suggeriamo di leggere l’interesse di Leopardi per l’Architrenius come la spia di un interesse specifico del poeta
per l’eresia manichea.
probably continued to be read in Northern Europe (first of all, France and England) long after the Carolingian Age, at least up to the beginning of the 13th century. This study aims at offering crucial confirmation to this thesis, by detecting and analyzing some previously unnoticed Lucretian echoes in poems Anticlaudianus by Alan of Lille and Alexandreis by Walter of Châtillon, both written in Northern France at the end of the twelfth
century. These echoes are placed in key positions within the hexameter (mostly verse-end, involving at least two words) and seem to be part of an intertextual dialogue with the De rerum natura. Significantly, there is no clear intermediary source between Lucretius’ poem and these texts, therefore indirect transmission can be ruled out and it is possible to assume a direct dependence from the De rerum natura.
of a Lucretian tradition in the Middle Ages. The idea of a connection between the Architrenius and the De rerum natura can be, interestingly, traced back to the Renaissance, in particular to the work of Giovan Battista Pio, who authored the first humanist com mentary on the De rerum natura.