A Subsampling Line-Search Method with Second-Order Results

In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic algorithms that sample problem data, which can jeopardize the guarantees obtained through classical globalization techniques in optimization such as a trust region or a line search. Using subsampled function values is particularly challenging for the latter strategy, which relies upon multiple evaluations. On top of that all, there has been an increasing interest for nonconvex formulations of data-related problems, such as training deep learning models. For such instances, one aims at developing methods that converge to second-order stationary points quickly, i.e., escape saddle points efficiently. This is particularly delicate to ensure when one only accesses subsampled approximations of the objective and its derivatives. In this paper, we describe a stochastic algorithm based on negative curvature and Newton-type directions that are computed for a subsampling model of the objective. A line-search technique is used to enforce suitable decrease for this model, and for a sufficiently large sample, a similar amount of reduction holds for the true objective. By using probabilistic reasoning, we can then obtain worst-case complexity guarantees for our framework, leading us to discuss appropriate notions of stationarity in a subsampling context. Our analysis encompasses the deterministic regime, and allows us to identify sampling requirements for second-order line-search paradigms. As we illustrate through real data experiments, these worst-case estimates need not be satisfied for our method to be competitive with first-order strategies in practice

Dye‑doped silica nanoparticles: synthesis, surface chemistry and bioapplications

Background: Fluorescent silica nanoparticles have been extensively utilised in a broad range of biological applications and are facilitated by their predictable, wellunderstood, flexible chemistry and apparent biocompatibility. The ability to couple various siloxane precursors with fluorescent dyes and to be subsequently incorporated into silica nanoparticles has made it possible to engineer these fluorophores-doped nanomaterials to specific optical requirements in biological experimentation. Consequently, this class of nanomaterial has been used in applications across immunodiagnostics, drug delivery and human-trial bioimaging in cancer research. Main body: This review summarises the state-of-the-art of the use of dye-doped silica nanoparticles in bioapplications and firstly accounts for the common nanoparticle synthesis methods, surface modification approaches and different bioconjugation strategies employed to generate biomolecule-coated nanoparticles. The use of dye-doped silica nanoparticles in immunoassays/biosensing, bioimaging and drug delivery is then provided and possible future directions in the field are highlighted. Other non-cancerrelated applications involving silica nanoparticles are also briefly discussed. Importantly, the impact of how the protein corona has changed our understanding of NP interactions with biological systems is described, as well as demonstrations of its capacity to be favourably manipulated. Conclusions: Dye-doped silica nanoparticles have found success in the immunodiagnostics domain and have also shown promise as bioimaging agents in human clinical trials. Their use in cancer delivery has been restricted to murine models, as has been the case for the vast majority of nanomaterials intended for cancer therapy. This is hampered by the need for more human-like disease models and the lack of standardisation towards assessing nanoparticle toxicity. However, developments in the manipulation of the protein corona have improved the understanding of fundamental bio–nano interactions, and will undoubtedly assist in the translation of silica nanoparticles for disease treatment to the clinic

‘Overloading’ fluorescent silica nanoparticles with dyes to improve biosensor performance

Using dye-doped silica nanoparticles (DSNP) as reporter probes, we describe a simple method of enhancing fluorescent signal and the extension of the detectable target concentration range in a proof-of-concept ‘dissolution immunoassay’. DSNPs were intentionally ‘overloaded’ with 3% (w/w) FITC such that the high concentration of dye inside the NP core induced self-quenching. Despite exhibiting reduced brightness, the ‘overloaded’ DSNPs were then functionalized with anti-human IgG and were subsequently used to detect human IgG, a model biomarker, in whole serum. Following human IgG recognition, the ‘overloaded’ DSNPs were dissolved using pH10.6, 0.1M sodium carbonate-bicarbonate buffer. The large quantity of FITC inside the NP core was consequently released into solution, thus liberating the dyes from self-quenching, and led to a large increase in fluorecein emission intensity. This effect was further enhanced when coupled with FITC’s increased quantum yield in basic conditions. The overall result was a 12-fold enhancement in fluorescent signal intensity and an 11-fold improvement in signal-to-noise ratio after a dissolution time of 60 mins. In the assay setup presented, the net signal-to-noise ratio for ‘overloaded’ DSNPs was up to 9 times greater following degradation compared to traditionally used 1% (w/w) ‘optimal’ dye-loaded DSNPs. Crucially, this ‘dissolution assay’ strategy using ‘overloaded’ DSNPs could confidently detect human IgG at a 10-fold lower concentration than traditionally used ‘optimal’ DSNPs

Stabilizing silica nanoparticles in hydrogels: impact on storage and polydispersity

For successful nanomedicine, it is important that the unique, size-dependent physico-chemical properties of the nanomaterial remain predictably constant during both the storage and the manipulation of the material. Here a novel approach to preserve the colloidal stability and degradation of NPs is described. The concept is simple: (a) a solution of monodisperse particles is formulated into a responsive water- or PBS-based hydrogel; (b) the gel can be reversibly turned into a solution after long term storage by shaking it by hand; (c) the NP can be diluted and used in any desired application without the need for excessive manipulation. The differences between the physico-chemical properties of NPs stored in solution and in gel are compared. Two types of NPs were involved in this study: silica NPs of similar100 nm and Au-NPs of 30 and 80 nm in diameter. The key findings are: the fibrous matrix of the hydrogel limits the NP mobility{,} significantly reduces NP aggregation and conserves the NP morphology; both the hydrogelator and the NPs show negligible toxicity towards the model U937 human hematopoietic cell line; undesired leaching of cargo material loaded inside the particles is reduced{,} which could be an important feature for drug delivery systems

Dye‑doped silica nanoparticles: synthesis, surface chemistry and bioapplications

Fluorescent silica nanoparticles have been extensively utilised in a broad range of biological applications and are facilitated by their predictable, well-understood, flexible chemistry and apparent biocompatibility. The ability to couple various siloxane precursors with fluorescent dyes and to be subsequently incorporated into silica nanoparticles has made it possible to engineer these fluorophores-doped nanomaterials to specific optical requirements in biological experimentation. Consequently, this class of nanomaterial has been used in applications across immunodiagnostics, drug delivery and human-trial bioimaging in cancer research. </p

Stabilizing silica nanoparticles in hydrogels: impact on storage and polydispersity

For successful nanomedicine, it is important that the unique, size-dependent physico-chemical properties of the nanomaterial remain predictably constant during both the storage and the manipulation of the material. Here a novel approach to preserve the colloidal stability and degradation of NPs is described. The concept is simple: (a) a solution of monodisperse particles is formulated into a responsive water- or PBS-based hydrogel; (b) the gel can be reversibly turned into a solution after long term storage by shaking it by hand; (c) the NP can be diluted and used in any desired application without the need for excessive manipulation. The differences between the physico-chemical properties of NPs stored in solution and in gel are compared. Two types of NPs were involved in this study: silica NPs of ∼100 nm and Au-NPs of 30 and 80 nm in diameter. The key findings are: the fibrous matrix of the hydrogel limits the NP mobility, significantly reduces NP aggregation and conserves the NP morphology; both the hydrogelator and the NPs show negligible toxicity towards the model U937 human hematopoietic cell line; undesired leaching of cargo material loaded inside the particles is reduced, which could be an important feature for drug delivery systems

Vivat academia : 25/50 : Piano Extravaganza (Katarina Krpan (klavir), Vladimir Krpan (klavir) i gosti, 26.5.2021.)

Snimka koncerta iz ciklusa Vivat academia održanog na Muzičkoj akademiji u Koncertnoj dvorani "Blagoje Bersa" 26.5.2021. Koncert Katarine Krpan, Vladimira Krpana te njihovih bivših i sadašnjih studenata, u povodu 25 godina rada Katarine Krpan i 50 godina rada Vladimira Krpana. Izvođači: Katarina Krpan (klavir), Vladimir Krpan (klavir), Maria Babić (klavir), Mihael Plantak (klavir), Taša Šinkovec (klavir), Katarina Nera Biondić (klavir), Andrej Vesel (klavir), Ante Sladoljev (klavir), Elizabeta Skobe (klavir), Katarina Makević (klavir), Danijel Oto (klavir), Ena Hadžihasanović (klavir), Sara Jurišić (klavir), Lucija Majstorović (klavir), Ivona Konjetić (klavir), Jadranka Garin (klavir), Bože Cigić (klavir), Marko Šantek (klavir), Andrea Furlan (klavir), Mirna Alfirević (klavir), Petra Gilming (klavir), Ana Lucić (klavir), Borut Vidošević (klavir), Petra Filimonović (klavir), Dora Grizelj (klavir), Petra Akrap (klavir), Tamara Jurkić Sviben (klavir), Zrinka Ivančić Cikojević (klavir), Ljubomir Gašparović (klavir), Srđan Filip Čaldarović (klavir). Program: 1. Johannes Brahms: 16 valcera za klavir četveroručno, op. 39 (Valcer u B-duru, br. 1 – Valcer u E-duru, br. 2 – Valcer u gis-molu, br. 3 – Valcer u e-molu, br. 4) (izvođači: Katarina Krpan, Vladimir Krpan); 2. Johannes Brahms: Akademska svečana uvertira u c-molu op. 80, za 4 klavira (izvođači: Maria Babić, Mihael Plantak, Taša Šinkovec, Katarina Nera Biondić); 3. Antonín Dvořák: Slavenski ples op. 48 br. 8, u g-molu (izvođači: Andrej Vesel, Ante Sladoljev); 4. Božidar Kunc: Hurdy-Gurdy valcer, za dva klavira (izvođači: Elizabeta Skobe, Katarina Makević); 5. Edward Elgar: Salut d’Amour (Liebesgruß), op. 12, za klavir četveroručno (izvođači: Katarina Krpan, Danijel Oto); 6. George Gershwin: Summertime, za klavir četveroručno (izvođači: Ena Hadžihasanović, Sara Jurišić); 7. Claude Debussy: Petite suite, L 65, za klavir četveroručno (En bateau – Cortège – Menuet – Ballet) (izvođači: Lucija Majstorović, Andrej Vesel); 8. Albert Lavignac: Galop Marche, za 8 ruku (izvođači: Ivona Konjetić, Jadranka Garin, Bože Cigić, Marko Šantek); 9. Astor Piazzolla: Libertango 2+2 (izvođači: Katarina Nera Biondić, Ante Sladoljev, Andrej Vesel, Katarina Krpan); 10. Sergej Rahmanjinov: Romance, za klavir šesteroručno (izvođači: Andrea Furlan, Maria Babić, Mirna Alfirević); 11. Sergej Rahmanjinov: Valse, za klavir šesteroručno (izvođači: Petra Gilming, Ana Lucić, Borut Vidošević); 12. Bruno Vlahek: Varijacije na hrvatsku temu, za klavir četveroručno (izvođači: Petra Filimonović, Danijel Oto); 13. Witold Lutosławski: Varijacije na Paganinijevu temu, za dva klavira (izvođači: Dora Grizelj, Petra Akrap); 13. Gabriel Fauré: Berceuse iz Dolly Suite, op. 56, za klavir četveroručno (izvođači: Tamara Jurkić Sviben, Zrinka Ivančić Cikojević); 14. Johannes Brahms: Mađarski plesovi WoO 1, za klavir četveroručno (Mađarski ples br. 1 (izvođači: Katarina Krpan, Vladimir Krpan) – Mađarski ples br. 2 (izvođači: Petra Gilming, Vladimir Krpan) – Mađarski ples br. 3 (izvođači: Bože Cigić, Vladimir Krpan) – Mađarski ples br. 4 (izvođači: Ljubomir Gašparović, Vladimir Krpan) – Mađarski ples br. 5 (izvođači: Srđan Čaldarović, Vladimir Krpan)

Vivat academia : 25/50 : Piano Extravaganza (Katarina Krpan (klavir), Vladimir Krpan (klavir) i gosti, 26.5.2021.)

Snimka koncerta iz ciklusa Vivat academia održanog na Muzičkoj akademiji u Koncertnoj dvorani "Blagoje Bersa" 26.5.2021. Koncert Katarine Krpan, Vladimira Krpana te njihovih bivših i sadašnjih studenata, u povodu 25 godina rada Katarine Krpan i 50 godina rada Vladimira Krpana. Izvođači: Katarina Krpan (klavir), Vladimir Krpan (klavir), Maria Babić (klavir), Mihael Plantak (klavir), Taša Šinkovec (klavir), Katarina Nera Biondić (klavir), Andrej Vesel (klavir), Ante Sladoljev (klavir), Elizabeta Skobe (klavir), Katarina Makević (klavir), Danijel Oto (klavir), Ena Hadžihasanović (klavir), Sara Jurišić (klavir), Lucija Majstorović (klavir), Ivona Konjetić (klavir), Jadranka Garin (klavir), Bože Cigić (klavir), Marko Šantek (klavir), Andrea Furlan (klavir), Mirna Alfirević (klavir), Petra Gilming (klavir), Ana Lucić (klavir), Borut Vidošević (klavir), Petra Filimonović (klavir), Dora Grizelj (klavir), Petra Akrap (klavir), Tamara Jurkić Sviben (klavir), Zrinka Ivančić Cikojević (klavir), Ljubomir Gašparović (klavir), Srđan Filip Čaldarović (klavir). Program: 1. Johannes Brahms: 16 valcera za klavir četveroručno, op. 39 (Valcer u B-duru, br. 1 – Valcer u E-duru, br. 2 – Valcer u gis-molu, br. 3 – Valcer u e-molu, br. 4) (izvođači: Katarina Krpan, Vladimir Krpan); 2. Johannes Brahms: Akademska svečana uvertira u c-molu op. 80, za 4 klavira (izvođači: Maria Babić, Mihael Plantak, Taša Šinkovec, Katarina Nera Biondić); 3. Antonín Dvořák: Slavenski ples op. 48 br. 8, u g-molu (izvođači: Andrej Vesel, Ante Sladoljev); 4. Božidar Kunc: Hurdy-Gurdy valcer, za dva klavira (izvođači: Elizabeta Skobe, Katarina Makević); 5. Edward Elgar: Salut d’Amour (Liebesgruß), op. 12, za klavir četveroručno (izvođači: Katarina Krpan, Danijel Oto); 6. George Gershwin: Summertime, za klavir četveroručno (izvođači: Ena Hadžihasanović, Sara Jurišić); 7. Claude Debussy: Petite suite, L 65, za klavir četveroručno (En bateau – Cortège – Menuet – Ballet) (izvođači: Lucija Majstorović, Andrej Vesel); 8. Albert Lavignac: Galop Marche, za 8 ruku (izvođači: Ivona Konjetić, Jadranka Garin, Bože Cigić, Marko Šantek); 9. Astor Piazzolla: Libertango 2+2 (izvođači: Katarina Nera Biondić, Ante Sladoljev, Andrej Vesel, Katarina Krpan); 10. Sergej Rahmanjinov: Romance, za klavir šesteroručno (izvođači: Andrea Furlan, Maria Babić, Mirna Alfirević); 11. Sergej Rahmanjinov: Valse, za klavir šesteroručno (izvođači: Petra Gilming, Ana Lucić, Borut Vidošević); 12. Bruno Vlahek: Varijacije na hrvatsku temu, za klavir četveroručno (izvođači: Petra Filimonović, Danijel Oto); 13. Witold Lutosławski: Varijacije na Paganinijevu temu, za dva klavira (izvođači: Dora Grizelj, Petra Akrap); 13. Gabriel Fauré: Berceuse iz Dolly Suite, op. 56, za klavir četveroručno (izvođači: Tamara Jurkić Sviben, Zrinka Ivančić Cikojević); 14. Johannes Brahms: Mađarski plesovi WoO 1, za klavir četveroručno (Mađarski ples br. 1 (izvođači: Katarina Krpan, Vladimir Krpan) – Mađarski ples br. 2 (izvođači: Petra Gilming, Vladimir Krpan) – Mađarski ples br. 3 (izvođači: Bože Cigić, Vladimir Krpan) – Mađarski ples br. 4 (izvođači: Ljubomir Gašparović, Vladimir Krpan) – Mađarski ples br. 5 (izvođači: Srđan Čaldarović, Vladimir Krpan)