On human dignity and State sovereignty: The Italian Constitutional Court's 238/2014 judgment on State immunity for international crimes

Judgment 238/2014 of the Italian Constitutional Court has flatly contravened the decision of the ICJ on Jurisdictional Immunity of States (Germany v. Italy: Greece intervening) of 2012, ruling that the customary norm on State immunity from civil suits before a foreign court as ascertained in the ICJ decision never entered the domestic legal order, because it is incompatible with core principles of the Italian Constitution. In execution of the Constitutional Court ruling, in 2015, some Italian tribunals have condemned Germany to pay damages to former Italian military internees victim of international crimes during World War II, thus integrating an international wrongful act on the part of Italy. The 238/2014 judgment has been criticised from many angles. Much criticism was addressed to its alleged dualist approach that seemed to insulate Italy. The paper argues that the 2014 judgment of the Italian court is rather a reasoned response to the ICJ decision, grounded on principles common to the Italian and the international law, and a call for a consistent application of State obligations concerning the effective implementation of human rights. From this perspective it constitutes a valuable contribution towards a principled and open-minded debate over the structure and function of international la

Products of ideals may not be Golod

We exhibit an example of a product of two proper monomial ideals such that the residue class ring is not Golod. We also discuss the strongly Golod property for rational powers of monomial ideals, and introduce some sufficient conditions for weak Golodness of monomial ideals. Along the way, we ask some related questions.Comment: 18 pages, minor changes from first versio

A counterexample to a conjecture of Ding

We give a counterexample to a conjecture posed by S. Ding regarding the index of a Gorenstein local ring by exhibiting several examples of one dimensional local complete intersections of embedding dimension three with index 5 and generalized L\"oewy length 6.Comment: 9 pages, a few changes from the first versio

Exploiting non-constant safe memory in resilient algorithms and data structures

We extend the Faulty RAM model by Finocchi and Italiano (2008) by adding a safe memory of arbitrary size $S$, and we then derive tradeoffs between the performance of resilient algorithmic techniques and the size of the safe memory. Let $\delta$ and $\alpha$ denote, respectively, the maximum amount of faults which can happen during the execution of an algorithm and the actual number of occurred faults, with $\alpha \leq \delta$. We propose a resilient algorithm for sorting $n$ entries which requires $O\left(n\log n+\alpha (\delta/S + \log S)\right)$ time and uses $\Theta(S)$ safe memory words. Our algorithm outperforms previous resilient sorting algorithms which do not exploit the available safe memory and require $O\left(n\log n+ \alpha\delta\right)$ time. Finally, we exploit our sorting algorithm for deriving a resilient priority queue. Our implementation uses $\Theta(S)$ safe memory words and $\Theta(n)$ faulty memory words for storing $n$ keys, and requires $O\left(\log n + \delta/S\right)$ amortized time for each insert and deletemin operation. Our resilient priority queue improves the $O\left(\log n + \delta\right)$ amortized time required by the state of the art.Comment: To appear in Theoretical Computer Science, 201

A sufficient condition for strong FF-regularity

Let $(R,\mathfrak{m},K)$ be an $F$-finite Noetherian local ring which has a canonical ideal $I \subsetneq R$. We prove that if $R$ is $S_2$ and $H^{d-1}_{\mathfrak{m}}(R/I)$ is a simple $R\{F\}$-module, then $R$ is a strongly $F$-regular ring. In particular, under these assumptions, $R$ is a Cohen-Macaulay normal domain.Comment: 9 pages, to appear in Proceedings of the American Mathematical Societ

Time indeterminacy and spatio-temporal building transformations: an approach for architectural heritage understanding

Nowadays most digital reconstructions in architecture and archeology describe buildings heritage as awhole of static and unchangeable entities. However, historical sites can have a rich and complex history, sometimes full of evolutions, sometimes only partially known by means of documentary sources. Various aspects condition the analysis and the interpretation of cultural heritage. First of all, buildings are not inexorably constant in time: creation, destruction, union, division, annexation, partial demolition and change of function are the transformations that buildings can undergo over time. Moreover, other factors sometimes contradictory can condition the knowledge about an historical site, such as historical sources and uncertainty. On one hand, historical documentation concerning past states can be heterogeneous, dubious, incomplete and even contradictory. On the other hand, uncertainty is prevalent in cultural heritage in various forms: sometimes it is impossible to define the dating period, sometimes the building original shape or yet its spatial position. This paper proposes amodeling approach of the geometrical representation of buildings, taking into account the kind of transformations and the notion of temporal indetermination

On the existence of FF-thresholds and related limits

The $F$-thresholds are important numerical invariants in prime characteristic, whose existence had been established only under certain assumptions. We show the existence of $F$-thresholds in full generality. We study properties of standard graded algebras over a field for which $F$-pure threshold and $F$-threshold at the irrelevant maximal ideal agree. We also exhibit explicit bounds for the $a$-invariants and Castelnuovo-Mumford regularity of Frobenius powers of ideals in terms of $F$-thresholds and $F$-pure thresholds, obtaining existence of related limits in certain cases.Comment: 21 page

An algorithm for constructing certain differential operators in positive characteristic

Given a non-zero polynomial $f$ in a polynomial ring $R$ with coefficients in a finite field of prime characteristic $p$, we present an algorithm to compute a differential operator $\delta$ which raises $1/f$ to its $p$th power. For some specific families of polynomials, we also study the level of such a differential operator $\delta$, i.e., the least integer $e$ such that $\delta$ is $R^{p^e}$-linear. In particular, we obtain a characterization of supersingular elliptic curves in terms of the level of the associated differential operator.Comment: 23 pages. Comments are welcom