Cohomology of D-complex manifolds

In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups made up of the classes admitting invariant, respectively anti-invariant, representatives with respect to the almost D-complex structure, miming the theory introduced by Li and Zhang (2009) in [20] for almost complex manifolds. In particular, we prove that, on a 4-dimensional D-complex nilmanifold, such subgroups provide a decomposition at the level of the real second de Rham cohomology group. Moreover, we study deformations of D-complex structures, showing in particular that admitting D-Kähler structures is not a stable property under small deformations

On a parabolic Hamilton-Jacobi-Bellman equation degenerating at the boundary

We derive the long time asymptotic of solutions to an evolutive Hamilton-Jacobi-Bellman equation in a bounded smooth domain, in connection with ergodic problems recently studied in \cite{bcr}. Our main assumption is an appropriate degeneracy condition on the operator at the boundary. This condition is related to the characteristic boundary points for linear operators as well as to the irrelevant points for the generalized Dirichlet problem, and implies in particular that no boundary datum has to be imposed. We prove that there exists a constant $c$ such that the solutions of the evolutive problem converge uniformly, in the reference frame moving with constant velocity $c$, to a unique steady state solving a suitable ergodic problem.Comment: 12p

Degree of non-K\"ahlerianity for 6-dimensional nilmanifolds

We use Bott-Chern cohomology to measure the non-K\"ahlerianity of 6-dimensional nilmanifolds endowed with the invariant complex structures in M. Ceballos, A. Otal, L. Ugarte, and R. Villacampa's classification, [Invariant Complex Structures on 6-Nilmanifolds: Classification, Fr\"olicher Spectral Sequence and Special Hermitian Metrics, J. Geom. Anal. (2014)]. We investigate the existence of pluriclosed metric in connection with such a classification

Removal of electrostatic artifacts in magnetic force microscopy by controlled magnetization of the tip: application to superparamagnetic nanoparticles

Magnetic force microscopy (MFM) has been demonstrated as valuable technique for the characterization of magnetic nanomaterials. To be analyzed by MFM techniques, nanomaterials are generally deposited on flat substrates, resulting in an additional contrast in MFM images due to unavoidable heterogeneous electrostatic tip-sample interactions, which cannot be easily distinguished from the magnetic one. In order to correctly interpret MFM data, a method to remove the electrostatic contributions from MFM images is needed. In this work, we propose a new MFM technique, called controlled magnetization MFM (CM-MFM), based on the in situ control of the probe magnetization state, which allows the evaluation and the elimination of electrostatic contribution in MFM images. The effectiveness of the technique is demonstrated through a challenging case study, i.e., the analysis of superparamagnetic nanoparticles in absence of applied external magnetic field. Our CM-MFM technique allowed us to acquire magnetic images depurated of the electrostatic contributions, which revealed that the magnetic field generated by the tip is sufficient to completely orient the superparamagnetic nanoparticles and that the magnetic tip-sample interaction is describable through simple models once the electrostatic artifacts are removed

Multipartite entanglement detection for hypergraph states

We study the entanglement properties of quantum hypergraph states of $n$ qubits, focusing on multipartite entanglement. We compute multipartite entanglement for hypergraph states with a single hyperedge of maximum cardinality, for hypergraph states endowed with all possible hyperedges of cardinality equal to $n-1$ and for those hypergraph states with all possible hyperedges of cardinality greater than or equal to $n-1$. We then find a lower bound to the multipartite entanglement of a generic quantum hypergraph state. We finally apply the multipartite entanglement results to the construction of entanglement witness operators, able to detect genuine multipartite entanglement in the neighbourhood of a given hypergraph state. We first build entanglement witnesses of the projective type, then propose a class of witnesses based on the stabilizer formalism, hence called stabilizer witnesses, able to reduce the experimental effort from an exponential to a linear growth in the number of local measurement settings with the number of qubits

Gamma-Ray Bursts and Afterglow Polarisation

Polarimetry of Gamma-Ray Burst (GRB) afterglows in the last few years has been considered one of the most effective tool to probe the geometry, energetic, dynamics and the environment of GRBs. We report some of the most recent results and discuss their implications and future perspectives.Comment: 6 pages, 4 figures. Proceeding for the "Interacting Binaries: Accretion, Evolution and Outcome" worshop held in Cefalu' (Italy) in July 200

Hardware Trojan Detection on a PCB Through Differential Power Monitoring

There is a general consensus that contemporary electronics are at risk of cyber-attacks or malicious modifications, such as Hardware Trojans (HT). This makes it crucial to develop reliable countermeasures at both Integrated Circuit (IC) and Printed Circuit Board (PCB) levels. While HT detection at IC level has been widely studied in the past several years, there is still very limited research carried out to tackle HTs on PCBs. We propose a power analysis method for detecting HT components implanted on PCBs. An experimental setup, using a hardware prototype, is built and tested for verification of the methodology, taking process and temperature variations into account. The results confirm the ability to detect alien components on a PCB and provide directions for further research. The performance degradation of the original PCB due to the implementation of the proposed approach is negligible. The area overhead of the proposed method is small, related to the original PCB design, and consists of Sub Power Monitors of individual ICs on the PCB and Main Power Monitor for the overall power measurement of the PCB. To the best of our knowledge this research is the first to develop a PCB HT detection methodology using power analysis

Revision of failed osteochondritis dissecans surgical treatment: case report

Background: Osteochondritis dissecans (OD) is one of the most common cartilage lesions of the knee. Conservative treatment is recommended if the lesions are stable with no loose bodies or there are open physes. Surgical intervention is recommended as the primary treatment in symptomatic adults with unstable chondral lesions or with concomitant loose bodies. Methods: We describe a case of a patient suffering from OD with a bone lesion in the weight-bearing area of medial femoral condyle. Arthroscopy was performed and an osteochondral fragment from the medial femoral condyle was observed and two articular loose bodies were removed. After months, the patient returned with pain and a locked knee. magnetic resonance imaging (MRI) presented a new unstable chondral flap at the posterior border of the previous lesion. Surgery was performed again, and at open examination, the previous OD lesions were covered by regenerative tissue, with a lesion of 3 cm2 at the inferior medial part of the chondral flap. The peripheral margins were cleaned, and a subchondral crater was curetted. The subchondral lesion was debrided, and the flap was fixed with pins and a central bioresorbable screws. Results: Revision surgery with fixation of the chondral flap using bioresorbable pins and screws led to satisfactory results. Conclusion: Open revision surgery allowed us a more accurate assessment of the OD area to provide an effective fixation of the chondral flap and in this circumstance, this should have been done after seeing the first MRI.Hintergrund Die Osteochondritis dissecans (OD) ist eine der häufigsten Knorpelläsionen des Knies. Eine konservative Behandlung wird empfohlen, wenn die Läsionen stabil sind und keine Wackelkörper vorhanden sind oder es sich um offene Stellen handelt. Bei symptomatischen Erwachsenen mit instabilen chondralen Läsionen oder gleichzeitigen lockeren Körpern wird als erste Maßnahme ein chirurgischer Eingriff empfohlen. Methoden Wir beschreiben den Fall eines Patienten, der an einer OD mit einer Knochenläsion im lasttragenden Bereich des medialen Femurkondylus litt. Es wurde eine Arthroskopie durchgeführt, bei der ein osteochondrales Fragment des medialen Femurkondylus festgestellt und 2 Gelenklockerungskörper entfernt wurden. Nach Monaten kehrte der Patient mit Schmerzen und blockiertem Knie zurück. Die MRT zeigte einen neuen instabilen Knorpellappen am hinteren Rand der früheren Läsion. Der Patient wurde operiert, und bei der offenen Untersuchung wurde die frühere OD-Läsion durch regeneratives Gewebe mit einer 3 cm2 großen Läsion im unteren medialen Teil des Knorpellappens bedeckt. Die peripheren Ränder wurden gesäubert und der subchondrale Krater wurde kürettiert. Die subchondrale Läsion wurde debridiert, und der Lappen wurde mit Stiften und einem zentralen bioresorbierbaren Skalpell fixiert. Ergebnisse Die Revisionsoperation mit Fixierung des chondralen Lappens mit bioresorbierbaren Stiften und Schrauben führte zu zufriedenstellenden Ergebnissen. Schlussfolgerung Die offene Revisionsoperation ermöglichte uns eine genauere Beurteilung des OD-Bereichs, um eine wirksame Fixierung des Knorpellappens vorzunehmen, was in diesem Fall nach der ersten MRT-Untersuchung hätte erfolgen sollen