Direct and inverse problems for degenerate differential equations

We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on \((-\infty ,\infty )\). Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too.     

Healing DNA Self-Assemblies Using Punctures

In self-assembly, individual components (commonly referred to as tiles) have sufficient infor mation to build templates for structures such as lat tices for two-dimensional scaffolds. Tile sets that can heal (fully or partially) an erroneous DNA assembly have been proposed. Healing requires growth to be restarted such that erroneous tiles can be removed and the correct tiles can bind to the aggregate. Punctures have been proposed for this purpose; in this paper, a puncture is intentionally induced in the self-assembly to restart the growth process. The goal of this paper is to characterize an intentionally induced puncture (and its relevant properties) on an erroneous tile site in the grown crystal as part of a healing process. This allows to propagate any newly generated error away from the source of growth (i.e. the seed tile), such that self-assembly can continue along specific directions. Different types of puncture are considered with respect to healing and related features, such as growth direction, error and aggregate types. Punctures are analyzed using a new characterization and metric; different tile sets are investigated in detail for healing of a DNA self-assembly.

Objective bayesian analysis of the Yule–Simon distribution with applications

The Yule–Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, has ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule–Simon distribution. In particular, we discuss the Jeffreys prior and a loss-based prior, which has recently appeared in the literature. We illustrate the performance of the derived priors through a simulation study and the analysis of real datasets.     

Design of a Composite Membrane with Patches

This paper is concerned with minimization and maximization problems of eigenvalues. The principal eigenvalue of a differential operator is minimized or maximized over a set which is formed by intersecting a rearrangement class with an affine subspace of finite co-dimension. A solution represents an optimal design of a 2-dimensional composite membrane Ω, fixed at the boundary, built out of two different materials, where certain prescribed regions (patches) in Ω are occupied by both materials. We prove existence results, and present some features of optimal solutions. The special case of one patch is treated in detail.     

Multivariate Hierarchical Copulas with Shocks

A transformation to obtain new multivariate hierarchical copulas, starting with an arbitrary copula, is introduced. In addition to the hierarchical structure, the presented construction principle explicitly supports singular components. These may be interpreted as the effect of local or global shocks to the underlying random variables. A large spectrum of dependence patterns can be achieved by the presented transformation, which seems promising for practical applications. Moreover, copulas arising from this construction are similarly admissible with respect to analytical tractability and sampling routines as the original copula. Finally, several well-known families of copulas may be interpreted as special cases.     

Financial contagion: extending the exposures network of the Mexican financial system

Direct contagion has been widely studied in recent years and little evidence has been found to be relevant to the study of systemic risk. However, we argue that this limited contagion effect might be associated with a lack of relevant data. A common assumption for the estimation of the matrices of exposures is to apply the maximum entropy principle to deal with data gaps; such an assumption might lead to an underestimation of contagion risk. In this paper, there are no data gaps and the information set is extended from interbank exposures alone to exposures among most of the financial intermediaries in the Mexican financial system (we even include exposures to some international foreign banks). Naturally, the contagion risk of an extended network of exposures changes with respect to the interbank exposures network, as there are many more institutions which can be the source of contagion and there are more institutions which can fail due to contagion. The most important contribution of this paper is that it provides evidence on financial contagion with an extended exposures network under stressful conditions. The results presented here support the international efforts by the Bank for International Settlements, the International Monetary Fund and the Financial Stability Board to increase the amount of information available which can be used to assess systemic risk and contagion based on exposures and funding data.     

Phytochemical Constituents,Antioxidant Activity,and Toxicity Assessment of the Aerial Part Extracts from the Infraspecific Taxa of Matthiola fruticulosa (Brassicaceae) Endemic to Sicily

In a project designed to investigate the specific and infraspecific taxa of Matthiola endemic to Sicily (Italy) as new potential sources of bioactive compounds in this work, the infraspecific taxa of Matthiola fruticulosa were studied, namely, subsp. fruticulosa and subsp. coronopifolia. HPLC–PDA/ESI–MS and SPME–GC/MS analyses of hydroalcoholic extracts obtained from the aerial parts of the two subspecies led to the detection of 51 phenolics and 61 volatile components, highlighting a quite different qualitative–quantitative profile. The antioxidant properties of the extracts were explored through in vitro methods: 1,1-diphenyl-2-picrylhydrazyl (DPPH), reducing power and Fe²⁺ chelating activity assays. The results of the antioxidant tests showed that the extracts possess a different antioxidant ability: particularly, the extract of M. fruticulosa subsp. fruticulosa exhibited higher radical scavenging activity than that of subsp. coronopifolia (IC₅₀ = 1.25 ± 0.02 mg/mL and 2.86 ± 0.05 mg/mL), which in turn displayed better chelating properties (IC₅₀ = 1.49 ± 0.01 mg/mL and 0.63 ± 0.01 mg/mL). Lastly, Artemia salina lethality bioassay was performed for toxicity assessment. The results of the bioassay showed lack of toxicity against brine shrimp larvae for both extracts. The data presented indicate the infraspecific taxa of M. fruticulosa as new and safe sources of antioxidant compounds.     

CMOS-Compatible Room-Temperature Rectifier Toward Terahertz Radiation Detection

In this paper, we present a new rectifying device, compatible with the technology of CMOS image sensors, suitable for implementing a direct-conversion detector operating at room temperature for operation at up to terahertz frequencies. The rectifying device can be obtained by introducing some simple modifications of the charge-storage well in conventional CMOS integrated circuits, making the proposed solution easy to integrate with the existing imaging systems. The rectifying device is combined with the different elements of the detector, composed of a 3D high-performance antenna and a charge-storage well. In particular, its position just below the edge of the 3D antenna takes maximum advantage of the high electric field concentrated by the antenna itself. In addition, the proposed structure ensures the integrity of the charge-storage well of the detector. In the structure, it is not necessary to use very scaled and costly technological nodes, since the CMOS transistor only provides the necessary integrated readout electronics. On-wafer measurements of RF characteristics of the designed junction are reported and discussed. The overall performances of the entire detector in terms of noise equivalent power (NEP) are evaluated by combining low-frequency measurements of the rectifier with numerical simulations of the 3D antenna and the semiconductor structure at 1 THz, allowing prediction of the achievable NEP.