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Improvements in diffusion models have boosted the quality of image generation, which has led researchers, companies, and creators to focus on improving watermarking algorithms. This provision would make it possible to clearly identify the creators of generative art. The main challenges that modern watermarking algorithms face have to do with their ability to withstand attacks and encrypt many unique messages, such as user IDs. In this paper, we present METR: Message Enhanced Tree-Ring, which is an approach that aims to address these challenges. METR is built on the Tree-Ring watermarking algorithm, a technique that makes it possible to encode multiple distinct messages without compromising attack resilience or image quality. This ensures the suitability of this watermarking algorithm for any Diffusion Model. In order to surpass the limitations on the quantity of encoded messages, we propose METR++, an enhanced version of METR. This approach, while limited to the Latent Diffusion Model architecture, is designed to inject a virtually unlimited number of unique messages. We demonstrate its robustness to attacks and ability to encrypt many unique messages while preserving image quality, which makes METR and METR++ hold great potential for practical applications in real-world settings. Our code is available at https://github.com/deepvk/metr, Comment: 14 pages, 9 figures, code is available at https://github.com/deepvk/metr

The Seebeck effect consists in the induction of a voltage drop due to the temperature difference in a conductor. In the middle of XIXth century, Lord Kelvin has proposed a relation between the Seebeck coefficient and the derivative of the chemical potential over temperature in the broken circuit regime. This relation appears to be nearly universal as it equally well applies to metals, semimetals and semiconductors. We show that it may fail, however, in graphene, due to the non-locality effects in the ballistic electronic transport regime. The correction to the Kelvin's formula emerges due to the coexistence of counter-propagating non-dissipative currents of cold and hot electrons. The external magnetic field normal to the graphene sample allows separating hot and cold currents in real space. The developed formalism may help interpreting the recent experimental data on ballistic edge currents in graphene bi-layers in the quantum Hall regime [1]., Comment: 6 pages, 3 figures. Any comments are welcome

We consider nonreciprocal supercurrent effects in Josephson junctions based on multiband superconductors with a pairing structure that can break time-reversal symmetry. We demonstrate that a nonreciprocal supercurrent can be generally achieved by the cooperation of interband superconducting phase mismatch and interband scattering as well as by multiband phase frustration. The effect of interband impurity scattering indicates that the amplitude and sign of the nonreciprocal supercurrent are sensitive to the interband phase relation. For the case of a three-band superconductor, due to phase frustration, we show that the profile of the supercurrent rectification is marked by a hexagonal pattern of nodal lines with vanishing amplitude. Remarkably, around the nodal lines, the supercurrent rectification amplitude exhibits three-fold structures with an alternating sign. We show that the hexagonal pattern and the three-fold structure in the interband phase space turn out to be dependent on the tunneling amplitude of each band. These findings provide hallmarks of the supercurrent rectification which can be potentially employed to unveil the occurrence of spin-singlet multiband superconductivity with time-reversal symmetry breaking., Comment: 9 pages with 4 figures

Online network crawling tasks require a lot of efforts for the researchers to collect the data. One of them is identification of important nodes, which has many applications starting from viral marketing to the prevention of disease spread. Various crawling algorithms has been suggested but their efficiency is not studied well. In this paper we compared six known crawlers on the task of collecting the fraction of the most influential nodes of graph. We analyzed crawlers behavior for four measures of node influence: node degree, k-coreness, betweenness centrality, and eccentricity. The experiments confirmed that greedy methods perform the best in many settings, but the cases exist when they are very inefficient.

Well-known Mott's formula links the thermoelectric power characterised by Seebeck coefficient to conductivity. We calculate analytically the thermoelectric current and Seebeck coefficient in one-dimensional systems and show that, while the prediction of Mott's formula is valid for Dirac fermions, it is misleading for the carriers having a parabolic dispersion. We apply the developed formalism to metallic single wall carbon nanotubes and obtain a non-trivial non-monotonic dependence of the Seebeck coefficient on the chemical potential. We emphasize that, in contrast to Mott's formula, the classical Kelvin's formula that links thermoelectric power to the temperature derivative of the chemical potential is perfectly valid in carbon nanotubes in the ballistic regime. Interestingly, however, the Kelvin's formula fails in two- and three-dimensional systems in the ballistic regime., Comment: Accepted version

The concept of the energy gap is a fundamental characteristic of the band structure of a material and it determines its physical properties. Formally the energy gap appears in the dispersion relation $E_k$, where the vector $k$ is determined on the whole momentum space. However, today the {\it gapped momentum materials} are in the focus of research in which the so-called {\it momentum or $k$-gap} can emerge, i.e. some lacunae of momentum space are excluded from the domain of the function $E_k$. One of such examples present the non-Hermitian systems. Within the random phase approximation we study the dielectric properties of the momentum gapped materials in one, two and three dimensions for both cases of zero and finite temperatures. We find the corresponding plasmon modes and determine the unusual behavior of the appropriate dispersion relations for each dimensionality. Based on these findings we evaluate the absorption coefficient of gapped momentum media and provide some numerical estimations of its value for the practical applications., Comment: 11 pages, 13 figures

Why do we need to pour less water in an egg steamer to prepare more eggs to the same degree of doneness? We discuss the physical processes at work in the electric egg steamer and resolve this seeming paradox. We demonstrate that the main heat transfer mechanism from steam to egg is due to latent heat through condensation. This not only explains the paradox, but also allows us to estimate the amount of water reduction. Comparing the preparation time to the one for traditional boiling, we estimate the eggshell temperature during steaming. We also describe the device design and provide further theoretical estimates and experimental kitchen measurement data for this appealing kitchen experiment that can be easily accomplished at home., Comment: 8 pages, 2 figures

Recently it was demonstrated that the long-known transition between the gap and gapless superconducting states in the Abrikosov-Gor'kov theory of superconducting alloy with paramagnetic impurities is of the Lifshitz's type, i.e. at zero temperature this is the $2\frac12$ order phase transition. Since transitions of this kind in a normal metal are always associated to certain topological changes, then below we clarify the topological nature of the transition under consideration. Namely, we demonstrate that the topological invariant which in process of the transition undergoes the change is nothing but the Euler characteristic. Alternatively, in terms of the theory of catastrophes one can relate this transition to appearance of the cuspidal edge at the corresponding surface of the density of states as the function of energy and superconducting order parameter. The concept of experiments for the confirmation of $2\frac12$ order topological phase transition is proposed. Obtained theoretical results can be applied for the explanation of recent experiments with lightwave-induced gapless superconductivity, for the interpretation of the disorder induced transition $s_{\pm}$-$s_{++}$ states via gapless phase in two-band superconductors, and the emergence of gapless color superconductivity in quantum chromodynamics., Comment: 6 pages, 2 figures

We consider a structure of the $\mathbb{K}$-Hilbert space, where $\mathbb{K}\simeq\mathbb{R}$ is a field of real numbers, $\mathbb{K}\simeq\mathbb{C}$ is a field of complex numbers, $\mathbb{K}\simeq\mathbb{H}$ is a quaternion algebra, within the framework of division rings of Clifford algebras. The $\mathbb{K}$-Hilbert space is generated by the Gelfand-Naimark-Segal construction, while the generating $C^\ast$-algebra consists of the energy operator $H$ and the generators of the group $SU(2,2)$ attached to $H$. The cyclic vectors of the $\mathbb{K}$-Hilbert space corresponding to the tensor products of quaternionic algebras define the pure separable states of the operator algebra. Depending on the division ring $\mathbb{K}$, all states of the operator algebra are divided into three classes: 1) charged states with $\mathbb{K}\simeq\mathbb{C}$; 2) neutral states with $\mathbb{K}\simeq\mathbb{H}$; 3) truly neutral states with $\mathbb{K}\simeq\mathbb{R}$. For pure separable states that define the fermionic and bosonic states of the energy spectrum, the fusion, doubling (complexification) and annihilation operations are determined., Comment: 29 pages

Exploiting the theory of solitons in a nonlinear elastic medium we predict a novel phenomenon called a phononic tsunami, which is characterized by the dramatic increase of the local amplitude of phonon modes. To elucidate the possible experimental detection of this phenomenon we propose to use a wedge-shaped sample in which a sharp edge serves for the emulation of the shoaling effect and such a local enhancement can be observed. Together with eigenfrequencies of transverse and longitudinal phonon modes of a system we find the characteristic dispersion relations that can be considered as a hallmark of a phononic tsunami. We justify our predictions by means of analytical calculations and numerical simulations showing a possible realization of this nonlinear effect in such a geometry. Our results provide the framework for the implementation of new kind experiments aimed at realizing and investigating a phononic tsunami phenomenon in relevant materials., Comment: 14 pages, 8 figures