Publications

In the reservoir computing literature, the information processing capacity is frequently used to characterize the computing capabilities of a reservoir. However, it remains unclear how the information processing capacity connects to the performance on specific tasks. We demonstrate on a set of standard benchmark tasks that the total information processing capacity correlates poorly with task specific performance. Further, we derive an expression for the normalized mean square error of a task as a weighted function of the individual information processing capacities. Mathematically, the derivation requires the task to have the same input distribution as used to calculate the information processing capacities. We test our method on a range of tasks that violate this requirement and find good qualitative agreement between the predicted and the actual errors as long as the task input sequences do not have long autocorrelation times. Our method offers deeper insight into the principles governing reservoir computing performance. It also increases the utility of the evaluation of information processing capacities, which are typically defined on i.i.d. input, even if specific tasks deliver inputs stemming from different distributions. Moreover, it offers the possibility of reducing the experimental cost of optimizing physical reservoirs, such as those implemented in photonic systems.

Muscle fatigue as a defense body mechanism against overload is a result of the products of incomplete oxygen oxidation such as reactive oxygen species. Hence, C60 fullerene as a powerful nanoantioxidant can be used to speed up the muscle recovery process after fatigue. Here, the residual effect of C60 fullerene on the biomechanical and biochemical markers of the development of muscle soleus fatigue in rats for 2 days after 5 days of its application was studied. The known antioxidant N-acetylcysteine (NAC) was used as a comparison drug. The atomic force microscopy to determine the size distribution of C60 fullerenes in an aqueous solution, the tensiometry of skeletal muscles, and the biochemical analysis of their tissues and rat blood were used in this study. It was found that after the cessation of NAC injections, the value of the integrated muscle power is already slightly different from the control (5%-7%) on the first day, and on the second day, it does not significantly differ from the control. At the same time, after the cessation of C60 fullerene injections, its residual effect was 45%-50% on the first day, and 17%-23% of the control on the second one. A significant difference (more than 25%) between the pro- and antioxidant balance in the studied muscles and blood of rats after the application of C60 fullerene and NAС plays a key role in the long-term residual effect of C60 fullerene. This indicates prolonged kinetics of C60 fullerenes elimination from the body, which contributes to their long-term (at least 2 days) compensatory activation of the endogenous antioxidant system in response to muscle stimulation, which should be considered when developing new therapeutic agents based on these nanoparticles.

A classical result by Rado characterises the so-called partition-regular matrices A, i.e. those matrices A for which any finite colouring of the positive integers yields a monochromatic solution to the equation Ax=0. We study the asymmetric random Rado problem for the (binomial) random set [n]p in which one seeks to determine the threshold for the property that any r-colouring, r≥2, of the random set has a colour i∈[r] admitting a solution for the matrical equation Aix=0, where A1,…,Ar are predetermined partition-regular matrices pre-assigned to the colours involved. We prove a 1-statement for the asymmetric random Rado property. In the symmetric setting our result retrieves the 1-statement of the symmetric random Rado theorem established in a combination of results by Rödl and Ruciânski [34] and by Friedgut, Rödl and Schacht [11]. We conjecture that our 1-statement in fact unveils the threshold for the asymmetric random Rado property, yielding a counterpart to the so-called Kohayakawa-Kreuter conjecture concerning the threshold for the asymmetric random Ramsey problem in graphs. We deduce the aforementioned 1-statement for the asymmetric random Rado property after establishing a broader result generalising the main theorem of Friedgut, Rödl and Schacht from [11]. The latter then serves as a combinatorial framework through which 1-statements for Ramsey-type problems in random sets and (hyper)graphs alike can be established in the asymmetric setting following a relatively short combinatorial examination of certain hypergraphs. To establish this framework we utilise a recent approach put forth by Mousset, Nenadov and Samotij [26] for the Kohayakawa-Kreuter conjecture.

Set-valued optimization using the set approach is a research topic of high interest due to its practical relevance and numerous interdependencies to other fields of optimization. However, it is a very difficult task to solve these optimization problems even for specific cases. In this paper, we study set-valued optimization problems and develop a multiobjective optimization problem that is strongly related to it. We prove that the set of weakly minimal solutions of this subproblem is closely related to the set of weakly minimal elements of the set-valued optimization problem and that these sets can get arbitrarily close in a certain sense. Subsequently, we introduce a concept of approximations of the solution set of the set-valued optimization problem. We define a quality measure in the image space that can be used to compare finite approximations of this kind and outline a procedure to enhance a given approximation. We conclude the paper with some numerical examples.

The pentasaccharide Fondaparinux, a synthetic selective factor Xa inhibitor, is one of the safest anticoagulants in the heparin family that is recommended as an alternative drug for patients with hypersensitivity to other drugs such as heparin-induced thrombocytopenia (HIT). However, some observations of Fondaparinux-induced thrombocytopenia (FIT) have been reported while others claimed that FIT does not occur in patients with fondaparinux therapy, indicating that the mechanism of FIT remains controversial. Here, we utilized different methodologies including dynamic light scattering, immunosorbent and platelet aggregation assays, confocal laser scanning microscopy, and flow cytometry to gain insights into FIT. We found that at a certain concentration, Fondaparinux formed sufficient large and stable complexes with PF4 that facilitated binding of the HIT-like monoclonal KKO antibody and enhanced platelet aggregation and activation. We proposed a model to describe the role of Fondaparinux concentration in the formation of complexes with platelet factor 4 and how it promotes the binding of KKO. Our results clarify controversial observations of FIT in patients as each contains a dissimilar PF4:Fondaparinux concentration ratio.