Hermitian matrices and cohomology of Kähler varieties

We give some upper bounds on the dimension of the kernel of the cup product map $H^{1}(X,\mathbb{C}) \otimes H^{1}(X,\mathbb{C}) \to H^{2}(X,\mathbb{C})We give some upper bounds on the dimension of the kernel of the cup product map , where X is a compact K?hler variety without Albanese fibrations.     

Metamaterials and plasmonics: From nanoparticles to nanoantenna arrays,metasurfaces, and metamaterials

The rise of plasmonic metamaterials in recent years has unveiled the possibility of revolutionizing the entire field of optics and photonics, challenging well-established technological limitations and paving the way to innovations at an unprecedented level To capitalize the disruptive potential of this rising field of science and technology, it is important to be able to combine the richness of optical phenomena enabled by nanoplasmonics in order to realize metamaterial components, devices, and systems of increasing complexity. Here, we review a few recent research directions in the field of plasmonic metamaterials, which may foster further advancements in this research area. We will discuss the anomalous scattering features enabled by plasmonic nanoparticles and nanoclusters, and show how they may represent the fundamental building blocks of complex nanophotonic architectures. Building on these concepts, advanced components can be designed and operated, such as optical nanoantennas and nanoantenna arrays, which, in turn, may be at the basis of metasurface devices and complex systems. Following this path, from basic phenomena to advanced functionalities, the field of plasmonic metamaterials offers the promise of an important scientific and technological impact, with applications spanning from medical diagnostics to clean energy and information processing.     

Cortical disinhibition occurs in chronic neuropathic,but not in chronic nociceptive pain

Background  

The aim of this study was to examine the relationship between chronic neuropathic pain after incomplete peripheral nerve lesion, chronic nociceptive pain due to osteoarthritis, and the excitability of the motor cortex assessed by transcranial magnetic stimulation (TMS). Hence in 26 patients with neuropathic pain resulting from an isolated incomplete lesion of the median or ulnar nerve (neuralgia), 20 patients with painful osteoarthritis of the hand, and 14 healthy control subjects, the excitability of the motor cortex was tested using paired-pulse TMS to assess intracortical inhibition and facilitation. These excitability parameters were compared between groups, and the relationship between excitability parameters and clinical parameters was examined.     

On Pythagoras Theorem for Products of Spectral Triples

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes’ distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.     

Weakly precomplete computably enumerable equivalence relations

Using computable reducibility ? on equivalence relations, we investigate weakly precomplete ceers (a “ceer” is a computably enumerable equivalence relation on the natural numbers), and we compare their class with the more restricted class of precomplete ceers. We show that there are infinitely many isomorphism types of universal (in fact uniformly finitely precomplete) weakly precomplete ceers , that are not precomplete; and there are infinitely many isomorphism types of non‐universal weakly precomplete ceers. Whereas the Visser space of a precomplete ceer always contains an infinite effectively discrete subset, there exist weakly precomplete ceers whose Visser spaces do not contain infinite effectively discrete subsets. As a consequence, contrary to precomplete ceers which always yield partitions into effectively inseparable sets, we show that although weakly precomplete ceers always yield partitions into computably inseparable sets, nevertheless there are weakly precomplete ceers for which no equivalence class is creative. Finally, we show that the index set of the precomplete ceers is Σ₃‐complete, whereas the index set of the weakly precomplete ceers is Π₃‐complete. As a consequence of these results, we also show that the index sets of the uniformly precomplete ceers and of the e‐complete ceers are Σ₃‐complete.     

On coderivatives and Lipschitzian properties of the dual pair in optimization

In this paper, we apply the concept of coderivative and other tools from the generalized differentiation theory for set-valued mappings to study the stability of the feasible sets of both the primal and the dual problem in infinite-dimensional linear optimization with infinitely many explicit constraints and an additional conic constraint. After providing some specific duality results for our dual pair, we study the Lipschitz-like property of both mappings and also give bounds for the associated Lipschitz moduli. The situation for the dual shows much more involved than the case of the primal problem.     

A New Method for Measuring Scattering of Light from Optical Surfaces with Random Roughness

In this letter we report a new method for measuring light scattered from optically rough surfaces. By collecting scattered light in a given solid angle, the measurement system does not require a detection unit with an extremely large dynamic range. This in turn significantly simplifies the system configuration. Measurements of scattering close to specular reflection (the so-called small angle or near-specular scattering) also can be completed without any difficulty. Unlike in the common angle resolved scattering (ARS) measurement system, in this system a linear movement instead of rotation is adopted to scan scattered light. In this way, the angular resolution of scattering measurements is independent of the resolution of the translation stages and may be adjusted.     

Aromatic interactions impact ligand binding and function at serotonin 5-HT2C G protein-coupled receptors: receptor homology modelling,ligand docking,and molecular dynamics results validated by experimental studies

The serotonin (5-hydroxytryptamine, 5-HT) 5-HT₂ G protein-coupled receptor (GPCR) family consists of types 2A, 2B, and 2C that share ～75% transmembrane (TM) sequence identity. Agonists for 5-HT_2C receptors are under development for psychoses; whereas, at 5-HT_2A receptors, antipsychotic effects are associated with antagonists – in fact, 5-HT_2A agonists can cause hallucinations and 5-HT_2B agonists cause cardiotoxicity. It is known that 5-HT_2A TM6 residues W6.48, F6.51, and F6.52 impact ligand binding and function; however, ligand interactions with these residues at the 5-HT_2C receptor have not been reported. To predict and validate molecular determinants for 5-HT_2C-specific activation, results from receptor homology modelling, ligand docking, and molecular dynamics simulation studies were compared with experimental results for ligand binding and function at wild type and W6.48A, F6.51A, and F6.52A point-mutated 5-HT_2C receptors.     

Normal analytic polyhedra in ℂ2 with a noncompact automorphism group

Let P be a bounded analytic polyhedron in ℂ² whose boundary is smooth except for normal crossing singularities. We show that P is a holomorphic quotient of the bidisc, if its automorphism group is noncompact.     

Local branching

The availability of effective exact or heuristic solution methods for general Mixed-Integer Programs (MIPs) is of paramount importance for practical applications. In the present paper we investigate the use of a generic MIP solver as a black-box ``tactical' tool to explore effectively suitable solution subspaces defined and controlled at a ``strategic' level by a simple external branching framework. The procedure is in the spirit of well-known local search metaheuristics, but the neighborhoods are obtained through the introduction in the MIP model of completely general linear inequalities called local branching cuts. The new solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the MIP solver at hand. It alternates high-level strategic branchings to define the solution neighborhoods, and low-level tactical branchings to explore them. The result is a completely general scheme aimed at favoring early updatings of the incumbent solution, hence producing high-quality solutions at early stages of the computation. The method is analyzed computationally on a large class of very difficult MIP problems by using the state-of-the-art commercial software ILOG-Cplex 7.0 as the black-box tactical MIP solver. For these instances, most of which cannot be solved to proven optimality in a reasonable time, the new method exhibits consistently an improved heuristic performance: in 23 out of 29 cases, the MIP solver produced significantly better incumbent solutions when driven by the local branching paradigm. Mathematics Subject Classification (2000):90C06, 90C10, 90C11, 90C27, 90C59