Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

Interpretative e-Learning Personalization: Methodology, Formal Aspects and generic Scenarios of Individual/Group Dynamics. A case of a course in art history.

International audienceMost of today’s e-learning development focus on knowledge formats and production, supposing perhaps that reception can be seen as the symmetric case of production in a courseware. In other words, that the point of view of the teacher may be transposed towards the learner. Nevertheless, understanding is an interpretation-dependent process, lying mainly on reading Strategies adopted by the learner. We may thus wonder whether it is yet possible to conceive systems whose architecture is driven by hermeneutical principles (i.e. where the interpretational activity is considered as a priority, and the role of the receptor of the course in the very constitution of the course is at least as important as this of the teacher) inherited from [3]. A reading strategy may be represented as a knowledge path built up from information put at disposal in the framework of a course. The aim of our work is to furnish some modeling issues in such a direction, using as case study academic course in art history. In collaboration with the Art Diagnosis Centre of Ormylia (Greece), some of us contributed, in the framework of various projects, to the setting up of a fine art ontology (over 30 000 concepts) able to cover the knowledge of large range iconographic corpora (see, for instance, [1])

Completely reducible hypersurfaces in a pencil

We study completely reducible fibers of pencils of hypersurfaces on $\mathbb P^n$ and associated codimension one foliations of $\mathbb P^n$. Using methods from theory of foliations we obtain certain upper bounds for the number of these fibers as functions only of $n$. Equivalently this gives upper bounds for the dimensions of resonance varieties of hyperplane arrangements. We obtain similar bounds for the dimensions of the characteristic varieties of the arrangement complements.Comment: 15 pages, 2 figure

Incremental View Maintenance For Collection Programming

In the context of incremental view maintenance (IVM), delta query derivation is an essential technique for speeding up the processing of large, dynamic datasets. The goal is to generate delta queries that, given a small change in the input, can update the materialized view more efficiently than via recomputation. In this work we propose the first solution for the efficient incrementalization of positive nested relational calculus (NRC+) on bags (with integer multiplicities). More precisely, we model the cost of NRC+ operators and classify queries as efficiently incrementalizable if their delta has a strictly lower cost than full re-evaluation. Then, we identify IncNRC+; a large fragment of NRC+ that is efficiently incrementalizable and we provide a semantics-preserving translation that takes any NRC+ query to a collection of IncNRC+ queries. Furthermore, we prove that incremental maintenance for NRC+ is within the complexity class NC0 and we showcase how recursive IVM, a technique that has provided significant speedups over traditional IVM in the case of flat queries [25], can also be applied to IncNRC+.Comment: 24 pages (12 pages plus appendix

Quantum communication networks with optical vortices

Quantum communications bring a paradigm change in internet security by using quantum resources to establish secure keys between parties. Present-day quantum communications networks are mainly point-to-point and use trusted nodes and key management systems to relay the keys. Future quantum networks, including the quantum internet, will have complex topologies in which groups of users are connected and communicate with each-other. Here we investigate several architectures for quantum communication networks. We show that photonic orbital angular momentum (OAM) can be used to route quantum information between different nodes. Starting from a simple, point-to-point network, we will gradually develop more complex architectures: point-to-multipoint, fully-connected and entanglement-distribution networks. As a particularly important result, we show that an $n$-node, fully-connected network can be constructed with a single OAM sorter and $n-1$ OAM values. Our results pave the way to construct complex quantum communication networks with minimal resources.Comment: 10 pages, 9 figure

Comparative animal study of the antinociceptive efficacy of lamotrigine and gabapentin for the management of pain

Pain relief using drugs with high efficacy provides significant improvement in the patients’ lives. Drugs like lamotrigine (LTG) and gabapentin (GBP) have the ability to overcome the symptoms of neuropathic pain. Aim: The present study offers a comparative analysis of LTG and GBP efficacy in a rat model of nociceptive pain after single administration. Method: Sixty-three Wistar-Bratislava rats randomized into 7 groups were included: a control group treated with saline solution and 6 groups treated with different doses of LTG and GBP. Nociceptive responses to thermal and mechanical stimulations were evaluated before and after drug administration, at different time intervals, using paw pressure and hot plate tests. The obtained data were statistically analyzed, with significance at p value < 0.05. Results: LTG 100 mg/kg and 50 mg/kg presented a significant analgesic effect in both mechanical and thermal tests, 1 and 2 hours after administration. GBP 100 mg/kg increased latency time in hot plate test. The effect of both anticonvulsant drugs occurred rapidly after administration, but had a short duration. Conclusions: LTG and GBP had an analgesic effect in a single dose administration. The effect of LTG was more evident since it was observed in both tests. Their effect was dose dependent

Chamber basis of the Orlik-Solomon algebra and Aomoto complex

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.Comment: 16 page

Telocytes in pleura: two- and three-dimensional imaging by transmission electron microscopy

Information about the ultrastructure of connective (interstitial) cells supporting the pleural mesothelium is scarce. Our aim has been to examine whether telocytes (TCs) are present in pleura, as in epicardium and mesentery. TCs are a distinct type of cell, characterized by specific prolongations named telopodes (Tp). We have used transmission electron microscopy (TEM) and electron tomography (ET) to determine whether ultrastructural diagnostic criteria accepted for TCs are fulfilled by any of the cell subpopulations existing in the sub-mesothelial layer in mouse and human pleura. TCs have been identified with TEM by their characteristic prolongations. Tp appear long and moniliform, because of the alternation of podomeres (thin segments of less than 0.2 μm) and podoms (small dilations accommodating caveolae, mitochondria, and endoplasmic reticulum). Tp ramifications follow a dichotomic pattern and establish specialized cell-to-cell junctional complexes. TCs, via their Tp, seem to form an interstitial network beneath the mesothelium, covering about two-thirds of the abluminal mesothelial layer. ET has revealed complex junctional structures and tight junctions connecting pleural TCs, and small vesicles at this level in Tp. Thus, pleural TCs share significant similarities with TCs described in other serosae. Whether TCs are a (major) player in mesothelial-cell-induced tissue repair remains to be established. Nevertheless, the extremely long thin Tp and complex junctional structures that they form and the release of vesicles (or exosomes) indicate the participation of TCs in long-distance homo- or heterocellular communication