Stratifications of Newton polygon strata and Traverso's conjectures for p-divisible groups

The isomorphism number (resp. isogeny cutoff) of a p-divisible group D over an algebraically closed field is the least positive integer m such that D[p^m] determines D up to isomorphism (resp. up to isogeny). We show that these invariants are lower semicontinuous in families of p-divisible groups of constant Newton polygon. Thus they allow refinements of Newton polygon strata. In each isogeny class of p-divisible groups, we determine the maximal value of isogeny cutoffs and give an upper bound for isomorphism numbers, which is shown to be optimal in the isoclinic case. In particular, the latter disproves a conjecture of Traverso. As an application, we answer a question of Zink on the liftability of an endomorphism of D[p^m] to D.Comment: 50 pages, to appear in Annals of Mathematic

Level m stratifications of versal deformations of p-divisible groups

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $c,d,m$ be positive integers. Let $D$ be a $p$-divisible group of codimension $c$ and dimension $d$ over $k$. Let \scrD be a versal deformation of $D$ over a smooth $k$-scheme \scrA which is equidimensional of dimension $cd$. We show that there exists a reduced, locally closed subscheme \grs_D(m) of \scrA that has the following property: a point y\in\scrA(k) belongs to \grs_D(m)(k) if and only if y^*(\scrD)[p^m] is isomorphic to $D[p^m]$. We prove that \grs_D(m) is {\it regular and equidimensional} of {\it dimension} $cd-\dim(\pmb{\text{Aut}}(D[p^m]))$. We give a proof of {\it Traverso's formula} which for $m>>0$ computes the codimension of \grs_D(m) in \scrA (i.e., $\dim(\pmb{\text{Aut}}(D[p^m]))$) in terms of the Newton polygon of $D$. We also provide a criterion of when \grs_D(m) satisfies the {\it purity property} (i.e., it is an affine \scrA-scheme). Similar results are proved for {\it quasi Shimura $p$-varieties of Hodge type} that generalize the special fibres of good integral models of Shimura varieties of Hodge type in unramified mixed characteristic $(0,p)$.Comment: 35 pages. Accepted (in final form) for publication in J. Alg. Geo

Enabling Distributed Knowledge Management: Managerial and Technological Implications

In this paper we show that the typical architecture of current KM systems re.ects an objectivistic epistemology and a traditional managerial control paradigm. We argue that such an objectivistic epistemology is inconsistent with many theories on the nature of knowledge, in which subjectivity and sociality are taken as essential features of knowledge creation and sharing. We show that adopting such a new epistemological view has dramatic consequences at an architectural, managerial and technological level

Graph- versus Vector-Based Analysis of a Consensus Protocol

The Paxos distributed consensus algorithm is a challenging case-study for standard, vector-based model checking techniques. Due to asynchronous communication, exhaustive analysis may generate very large state spaces already for small model instances. In this paper, we show the advantages of graph transformation as an alternative modelling technique. We model Paxos in a rich declarative transformation language, featuring (among other things) nested quantifiers, and we validate our model using the GROOVE model checker, a graph-based tool that exploits isomorphism as a natural way to prune the state space via symmetry reductions. We compare the results with those obtained by the standard model checker Spin on the basis of a vector-based encoding of the algorithm.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767

Modeling and Evaluation of Multisource Streaming Strategies in P2P VoD Systems

In recent years, multimedia content distribution has largely been moved to the Internet, inducing broadcasters, operators and service providers to upgrade with large expenses their infrastructures. In this context, streaming solutions that rely on user devices such as set-top boxes (STBs) to offload dedicated streaming servers are particularly appropriate. In these systems, contents are usually replicated and scattered over the network established by STBs placed at users' home, and the video-on-demand (VoD) service is provisioned through streaming sessions established among neighboring STBs following a Peer-to-Peer fashion. Up to now the majority of research works have focused on the design and optimization of content replicas mechanisms to minimize server costs. The optimization of replicas mechanisms has been typically performed either considering very crude system performance indicators or analyzing asymptotic behavior. In this work, instead, we propose an analytical model that complements previous works providing fairly accurate predictions of system performance (i.e., blocking probability). Our model turns out to be a highly scalable, flexible, and extensible tool that may be helpful both for designers and developers to efficiently predict the effect of system design choices in large scale STB-VoD system

The chiral anomaly in real space

The chiral anomaly is based on a non-conserved chiral charge and can happen in Dirac fermion systems under the influence of external electromagnetic fields. In this case, the spectral flow leads to a transfer of right- to left-moving excitations or vice versa. The corresponding transfer of chiral particles happens in momentum space. We here describe an intriguing way to introduce the chiral anomaly into real space. Our system consists of two quantum dots that are formed at the helical edge of a quantum spin Hall insulator on the basis of three magnetic impurities. Such a setup gives rise to fractional charges which we show to be sharp quantum numbers for large barrier strength. Interestingly, it is possible to map the system onto a quantum spin Hall ring in the presence of a flux pierced through the ring where the relative angle between the magnetization directions of the impurities takes the role of the flux. The chiral anomaly in this system is then directly related to the excess occupation of particles in the two quantum dots. This analogy allows us to predict an observable consequence of the chiral anomaly in real space.Comment: 7 pages, 5 figure

Model Checking Paxos in Spin

We present a formal model of a distributed consensus algorithm in the executable specification language Promela extended with a new type of guards, called counting guards, needed to implement transitions that depend on majority voting. Our formalization exploits abstractions that follow from reduction theorems applied to the specific case-study. We apply the model checker Spin to automatically validate finite instances of the model and to extract preconditions on the size of quorums used in the election phases of the protocol.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Probing Wigner correlations in a suspended carbon nanotube

The influence of the electron-vibron coupling on the transport properties of a strongly interacting quantum dot built in a suspended carbon nanotube is analyzed. The latter is probed by a charged AFM tip scanned along the axis of the CNT which induces oscillations of the chemical potential and of the linear conductance. These oscillations are due to the competition between finite-size effects and the formation of a Wigner molecule for strong interactions. Such oscillations are shown to be suppressed by the electron-vibron coupling. The suppression is more pronounced in the regime of weak Coulomb interactions, which ensures that probing Wigner correlations in such a system is in principle possible