A new optimal estimate for the norm of time-frequency localization operators

In this paper we provide an optimal estimate for the operator norm of time-frequency localization operators with Gaussian window $L_{F,\varphi} : L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d)$, under the assumption that $F \in L^p(\mathbb{R}^{2d}) \cap L^q(\mathbb{R}^{2d})$ for some $p$ and $q$ in $(1,+\infty)$. We are also able to characterize optimal weight functions, whose shape turns out to depend on the ratio $\|F\|_q / \|F\|_p$. Roughly speaking, if this ratio is "sufficiently large" or "sufficiently small" optimal weight functions are certain Gaussians, while if it is in the intermediate regime the optimal functions are no longer Gaussians. As an application, we extend Lieb's uncertainty inequality to the space $L^p + L^q$.Comment: 18 pages, 1 figur

The quantitative isoperimetric inequality for the Hilbert-Schmidt norm of localization operators

In this paper we study the Hilbert-Schmidt norm of time-frequency localization operators $L_{\Omega} \colon L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d)$, with Gaussian window, associated with a subset $\Omega\subset\mathbb{R}^{2d}$ of finite measure. We prove, in particular, that the Hilbert-Schmidt norm of $L_\Omega$ is maximized, among all subsets $\Omega$ of a given finite measure, when $\Omega$ is a ball and that there are no other extremizers. Actually, the main result is a quantitative version of this estimate, with sharp exponent. A similar problem is addressed for wavelet localization operators, where rearrangements are understood in the hyperbolic setting.Comment: 24 pages, 3 figures. Added some observations, in particular Remark 5.3, about the Conjecture 5.

Nanoparticle-based receptors mimic protein-ligand recognition

The self-assembly of a monolayer of ligands on the surface of noble metal nanoparticles dictates the fundamental nanoparticle\u2019s behavior and its functionality. In this combined computational\u2013experimental study, we analyze the structure, organization, and dynamics of functionalized coating thiols in monolayer-protected gold nanoparticles (AuNPs). We explain how functionalized coating thiols self-organize through a delicate and somehow counterintuitive balance of interactions within the monolayer itself and with the solvent. We further describe how the nature and plasticity of these interactions modulate nanoparticle-based chemosensing. Importantly, we found that self-organization of coating thiols can induce the formation of binding pockets in AuNPs. These transient cavities can accommodate small molecules, mimicking protein-ligand recognition, which may explain the selectivity and sensitivity observed for different organic analytes in NMR chemosensing experiments. Thus, our findings advocate for the rational design of tailored coating groups to form specific recognition binding sites on monolayer-protected AuNPs

Optimisation of ascent and descent trajectories for lifting body space access vehicles

One of the forerunners for future space access vehicles is the spaceplane, a lifting body vehicle capable of powered horizontal take-off and landing. Employing strategies from multidisciplinary design optimisation, this paper outlines the approaches and models used towards developing an integrated design platform to assess the preliminary design and performance of a spaceplane. The trajectory and control is optimised, based on different mission objectives and constraints, for the ascent and descent mission segments of a conceptual single stage to orbit vehicle, to a circular low Earth orbits from different take-off and landing sites. A modular approach is employed, dividing the mission into phases based on model discontinuities, changes in the operating environment or vehicle operation, mission objectives or constraints. The problem is reformulated by direct transcription using multiple shooting into a constrained NLP problem, and solved by a combination of genetic algorithms for a global search, and SQP plus interior point methods for local refinement with hard constraints

Jitter-Compensated VHT and Its Application to WSN Clock Synchronization

Accurate and energy-efficient clock synchronization is an enabler for many applications of Wireless Sensor Networks. A fine-grained synchronization is beneficial both at the system level, for example to favor deterministic radio protocols, and at the application level, when network-wide event timestamping is required. However, there is a tradeoff between the resolution of a WSN node's timekeeping device and its energy consumption. The Virtual High-resolution Timer (VHT) is an innovative solution, that was proposed to overcome this tradeoff. It combines a high-resolution oscillator to a low-power one, turning off the former when not needed. In this paper we improve VHT by first identifying the jitter of the low-power oscillator as the current limit to the technique, and then proposing an enhanced solution that synchronizes the fast and the slow clock, rejecting the said jitter. The improved VHT is also less demanding than the original technique in terms of hardware resources. Experimental results show the achieved advantages in terms of accuracy

Discovery of new diketopiperazines inhibiting Burkholderia cenocepacia quorum sensing in vitro and in vivo

Burkholderia cenocepacia, an opportunistic respiratory pathogen particularly relevant for cystic fibrosis patients, is difficult to eradicate due to its high level of resistance to most clinically relevant antimicrobials. Consequently, the discovery of new antimicrobials as well as molecules capable of inhibiting its virulence is mandatory. In this regard quorum sensing (QS) represents a good target for anti-virulence therapies, as it has been linked to biofilm formation and is important for the production of several virulence factors, including proteases and siderophores. Here, we report the discovery of new diketopiperazine inhibitors of the B. cenocepacia acyl homoserine lactone synthase CepI, and report their anti-virulence properties. Out of ten different compounds assayed against recombinant CepI, four were effective inhibitors, with IC50 values in the micromolar range. The best compounds interfered with protease and siderophore production, as well as with biofilm formation, and showed good in vivo activity in a Caenorhabditis elegans infection model. These molecules were also tested in human cells and showed very low toxicity. Therefore, they could be considered for in vivo combined treatments with established or novel antimicrobials, to improve the current therapeutic strategies against B. cenocepacia

Which benefit from subsequent chemotherapy lines beyond the second for women with metastatic breast cancer? Evidence from a single-center retrospective analysis of survivorship

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Benefit of continuing trastuzumab beyond progression in her2-positive metastatic breast cancer (mbc) is independent of the chemotherapy partner: message from a single-centre retrospective study

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A comprehensive overview on antibody-drug conjugates: from the conceptualization to cancer therapy

Antibody-Drug Conjugates (ADCs) represent an innovative class of potent anti-cancer compounds that are widely used in the treatment of hematologic malignancies and solid tumors. Unlike conventional chemotherapeutic drug-based therapies, that are mainly associated with modest specificity and therapeutic benefit, the three key components that form an ADC (a monoclonal antibody bound to a cytotoxic drug via a chemical linker moiety) achieve remarkable improvement in terms of targeted killing of cancer cells and, while sparing healthy tissues, a reduction in systemic side effects caused by off-tumor toxicity. Based on their beneficial mechanism of action, 15 ADCs have been approved to date by the market approval by the Food and Drug Administration (FDA), the European Medicines Agency (EMA) and/or other international governmental agencies for use in clinical oncology, and hundreds are undergoing evaluation in the preclinical and clinical phases. Here, our aim is to provide a comprehensive overview of the key features revolving around ADC therapeutic strategy including their structural and targeting properties, mechanism of action, the role of the tumor microenvironment and review the approved ADCs in clinical oncology, providing discussion regarding their toxicity profile, clinical manifestations and use in novel combination therapies. Finally, we briefly review ADCs in other pathological contexts and provide key information regarding ADC manufacturing and analytical characterization