Ribbon graphs and bialgebra of Lagrangian subspaces

To each ribbon graph we assign a so-called L-space, which is a Lagrangian subspace in an even-dimensional vector space with the standard symplectic form. This invariant generalizes the notion of the intersection matrix of a chord diagram. Moreover, the actions of Morse perestroikas (or taking a partial dual) and Vassiliev moves on ribbon graphs are reinterpreted nicely in the language of L-spaces, becoming changes of bases in this vector space. Finally, we define a bialgebra structure on the span of L-spaces, which is analogous to the 4-bialgebra structure on chord diagrams.Comment: 21 pages, 13 figures. v2: major revision, Sec 2 and 3 completely rewritten; v3: minor corrections. Final version, to appear in Journal of Knot Theory and its Ramification

Quality-Aware Prototype Memory for Face Representation Learning

Prototype Memory is a powerful model for face representation learning. It enables the training of face recognition models using datasets of any size, with on-the-fly generation of prototypes (classifier weights) and efficient ways of their utilization. Prototype Memory demonstrated strong results in many face recognition benchmarks. However, the algorithm of prototype generation, used in it, is prone to the problems of imperfectly calculated prototypes in case of low-quality or poorly recognizable faces in the images, selected for the prototype creation. All images of the same person, presented in the mini-batch, used with equal weights, and the resulting averaged prototype could be contaminated with imperfect embeddings of such face images. It can lead to misdirected training signals and impair the performance of the trained face recognition models. In this paper, we propose a simple and effective way to improve Prototype Memory with quality-aware prototype generation. Quality-Aware Prototype Memory uses different weights for images of different quality in the process of prototype generation. With this improvement, prototypes get more valuable information from high-quality images and less hurt by low-quality ones. We propose and compare several methods of quality estimation and usage, perform extensive experiments on the different face recognition benchmarks and demonstrate the advantages of the proposed model compared to the basic version of Prototype Memory.Comment: Preprin

Pipe dreams for Schubert polynomials of the classical groups

Schubert polynomials for the classical groups were defined by S.Billey and M.Haiman in 1995; they are polynomial representatives of Schubert classes in a full flag variety of a classical group. We provide a combinatorial description for these polynomials, as well as their double versions, by introducing analogues of pipe dreams, or RC-graphs, for the Weyl groups of the classical types.Comment: 36 pages, 10 figures. v2: appendix adde

Improving Electro-Weak Fits with TeV-scale Sterile Neutrinos

We study the impact of TeV-scale sterile neutrinos on electro-weak precision observables and lepton number and flavour violating decays in the framework of a type-I see-saw extension of the Standard Model. At tree level sterile neutrinos manifest themselves via non-unitarity of the PMNS matrix and at one-loop level they modify the oblique radiative corrections. We derive explicit formulae for the S,T,U parameters in terms of the neutrino masses and mixings and perform a numerical fit to the electro-weak observables. We find regions of parameter space with a sizable active-sterile mixing which provide a better over-all fit compared to the case where the mixing is negligible. Specifically we find improvements of the invisible Z-decay width, the charged-to-neutral-current ratio for neutrino scattering experiments and of the deviation of the W boson mass from the theoretical expectation.Comment: 16 pages, 17 figures, Journal accepted versio

Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets

Spatial separation of the wave packets (WPs) of neutrino mass eigenstates leads to decoherence and damping of neutrino oscillations. Damping can also be caused by finite energy resolution of neutrino detectors or, in the case of experiments with radioactive neutrino sources, by finite width of the emitted neutrino line. We study in detail these two types of damping effects using reactor neutrino experiments and experiments with radioactive $^{51}$Cr source as examples. We demonstrate that the effects of decoherence by WP separation can always be incorporated into a modification of the energy resolution function of the detector and so are intimately entangled with it. We estimate for the first time the lengths $\sigma_x$ of WPs of reactor neutrinos and neutrinos from a radioactive $^{51}$Cr source. The obtained values, $\sigma_x = (2\times 10^{-5} - 1.4\times 10^{-4})$ cm, are at least six orders of magnitude larger than the currently available experimental lower bounds. We conclude that effects of decoherence by WP separation cannot be probed in reactor and radioactive source experiments.Comment: LaTeX 21 pages, 1 figure. v2: typos fixed; minor textual changes; results and conclusions unchange

Reply to "Comment on "Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets""

In arXiv:2209.00561 our treatment arXiv:2208.03736 of effects of particles emitted together with neutrinos on neutrino wave packets is criticized on several grounds. We show here that this criticism is based on misinterpretation of our results and is invalid. Our conclusions and, in particular, the conclusion that neutrino wave packet separation effects are unobservable in reactor and neutrino source experiments, remain unchanged.Comment: 3 pages, 1 figur

Ideas of Newton-Okounkov bodies

In this snapshot, we will consider the problem of finding the number of solutions to a given system of polynomial equations. This question leads to the theory of Newton polytopes and Newton-Okounkov bodies of which we will give a basic notion

Assemblies of gold nanoparticles at liquid-liquid interfaces:from liquid optics to electrocatalysis

The interface between two immiscible liquids, i.e. oil and water, is an extremely attractive scaffold to self-assemble nanoparticles (NP) in arranged films. The liquid-liquid interfaces (LLIs) are defect-free and pristine by the nature, they are transparent and self-healing as well as mechanically flexible. Therefore, the present thesis is devoted to self-assembly of gold NPs into nanofilms at various LLIs and further investigation of their optical, mechanical and electrochemical properties. The thesis consists of two large parts: (i) self-assembly of gold nanoparticles into Metal Liquid-Like Droplets (MeLLDs) and (ii) electrocatalytic capability of nanoparticles placed at the interface. In the first part we showed that the irreversible adsorption of AuNPs at LLIs was achieved by charging nanoparticles with a lipophilic electron donor, tetrathiafulvalene (TTF). The established role of TTF was to charge directly the gold core of citrate stabilized AuNPs, reducing the Coulombic repulsion between separate NPs, as well as to "glue"€ nanoparticles together, providing the mechanical stability of the film. The present process was facile and required only vigorous shaking of organic phase with TTF and aqueous phase with AuNPs. Detailed study of optical properties demonstrated that MeLLDs could be used as liquid mirrors and filters with tuned optical response by varying NPs size, concentration and the solvent’s nature. This study opens a new way to understand requirements for voltage-induced self-assembly of NPs at the interface of two immiscible electrolyte solutions (ITIES). Further, we investigated ion and electron transfer properties of nanoparticle assemblies. A new method was developed to prepare nanofilm in four-electrode electrochemical cell. It consisted in precise microinjection of pre-concentrated solution of AuNPs in methanol directly at the ITIES. Primary achievement of this technique was prevention pollution of aqueous and organic phases. The nanofilm occupied roughly 30% of available surface area and did not interfere with the ion transfer across the ITIES. However, these films showed a capability to be charge by electron donors in organic phase with subsequent formation of the corresponding ions. In the second part we focused on electron transfer (ET) reactions at ITIES between redox couple in adjunct phases and interfacial redox electrocatalysis phenomenon at AuNPs film modified ITIES. Firstly, the difference between pure heterogeneous ET (HET) reactions and ET-IT mechanism was distinguished by numerical simulations. In the latter case, homogeneous ET reaction is followed by ion-transfer (IT). The model system consisted of ferrocene (Fc) in organic phase and ferry/ferro-cyanide (Fe(CN)6) in aqueous phase illustrated co-existence of HET and ET-IT mechanisms, but the main contribution to the overall observed current belonged to the IT across ITIES. Secondly, we developed a concept of Fermi level equilibration to describe observed interfacial ET for the model system with and without AuNPs at ITIES. Functionalization of the interface with AuNPs significantly improved kinetics of the interfacial reaction by changing reaction mechanism to a bipolar pathway, where NP provided electrical conductance between two phases. Therefore, we highlighted the interfacial redox electrocatalitic property of nanofilms towards HET from the viewpoint the developed theory

How do people experience innocent suffering?

IntroductionThe paper examines the psychological facet of innocent suffering. One can find a description of this phenomenon in social psychology as a factor that affects the belief in a just world, but there is a lack of qualitative scientific data about related psychological features, processes, copings, and consequences on the personality level.MethodsTo study innocent suffering, semi-structured in-depth interview was conducted (31 respondents, ~223 minutes per respondent, 6,924 min in total) aimed to gather data about the experiences of innocent sufferings happened to participants. For the analysis of texts, a narrative and content analysis are used within the framework of grounded theory. The reliability of the results is based on expert assessment.Results and discussionAs a result, six essential properties of innocent sufferings were identified: complexity, stability, distress, injustice, casual incoherence, and breaks of integrity of a life story. The most “popular” life domains, in which participants reported about innocent sufferings, are violence, abuse (physical and psychological), and quitting romantic relationships. It is proposed a scientific definition of innocent suffering and the prototype of the phenomenon