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Nonmagnetic metal LuB$_{12}$ is known to exhibit considerable transport anisotropy, which was explained in literature by different mechanisms including possible formation of dynamic charge stripes below the point $\sim$ 150K. Here we study transport properties of solid solutions based on LuB$_{12}$ host compound with general formula $R$$_x$Lu$_{1-x}$B$_{12}$ ($R$$-$Dy, Er, Tm, Yb, Lu) and with $x$ $\leq$ 0.03. The experiment has been performed on single crystals of high quality in the temperature range 1.8 $-$ 300K in magnetic fields up to 82kOe. The application of several models to the analysis of zero-field resistivity is discussed. A phenomenological description of large positive quadratic component of transverse magnetoresistance $\Delta$$\rho$/$\rho$($H$) = $\mu_D^2$$H^2$, which dominates for all compounds under investigation, allows to estimate drift mobility exponential changes $\mu_D$ $\sim$ $T^{-\alpha}$ with the index $\alpha$ $\approx$ 0.95 $-$ 1.46. In order to check the existence of additional channel of scattering, caused by probable presence of dynamic charge stripes, we performed the study of the anisotropy of magnetoresistance in Dy$_{0.01}$Lu$_{0.99}$B$_{12}$ and Tm$_{0.03}$Lu$_{0.97}$B$_{12}$ compositions including the measurements of the field scans with different current and field geometries. The data obtained allow us to confirm the fulfillment of semi-empirical Kohler's rule in a wide interval of temperatures 30 $-$ 240K regardless of the orientation of current and magnetic field. This result was attributed as a proof of the absence of additional channel of scattering caused by stripes. We argue, that charge-transport anisotropy is originated in $R$$_x$Lu$_{1-x}$B$_{12}$ due to the anisotropy of electron-phonon scattering on the one hand and the effects of Fermi surface (FS) topology (at low temperatures) on the other.

The presented studies of resistivity (R), thermal conductivity (k) and specific heat (C) at low temperature 1.8-7 K in magnetic field up to 90 kOe made it possible to detect for the first time the exponential field dependences R(H), 1/k(H), $C(H) \sim \exp(-{\mu}_{\rm eff}H/kBT)$ of the charge transport and thermal characteristics in the so-called antiferroquadrupole (AFQ) phase of the archetypal heavy-fermion CeB$_6$ hexaboride. From magnetoresistance measurements it is shown that in the AFQ state the effective magnetic moment varies in the range ${\mu}_{\rm eff}(T) = 1.4$-1.9$\mu$B, and its value is very close to ${\mu}_{\rm eff}(\tau)(T) = 2{\mu}$B, derived from the field dependence of the relaxation time $|tau(H)$ observed in the heat capacity and thermal conductivity experiments. The phenomenological model proposed here allowed us to attribute the magnetic moments to spin droplets (ferrons), that appear in the bulk AFQ phase of CeB$_6$ crystals. The relevant electron phase separation at the nanoscale, manifested by dynamic charge stripes, that leads to the formation of ferrons, was revealed from the analysis of low-temperature X-ray diffraction experiments using the maximum entropy method. We argue that the Jahn-Teller collective mode of B$_6$ clusters is responsible for the charge stripe formation, which subsequently induces transverse quasi-local vibrations of Ce ions in the form of pairs and triples. These lead to 4f-5d spin fluctuations providing spin-polarons (ferrons) in the CeB$_6$ matrix., Comment: 25 pages, 9 figires and 2 tables

Text-to-image diffusion models have emerged as a powerful framework for high-quality image generation given textual prompts. Their success has driven the rapid development of production-grade diffusion models that consistently increase in size and already contain billions of parameters. As a result, state-of-the-art text-to-image models are becoming less accessible in practice, especially in resource-limited environments. Post-training quantization (PTQ) tackles this issue by compressing the pretrained model weights into lower-bit representations. Recent diffusion quantization techniques primarily rely on uniform scalar quantization, providing decent performance for the models compressed to 4 bits. This work demonstrates that more versatile vector quantization (VQ) may achieve higher compression rates for large-scale text-to-image diffusion models. Specifically, we tailor vector-based PTQ methods to recent billion-scale text-to-image models (SDXL and SDXL-Turbo), and show that the diffusion models of 2B+ parameters compressed to around 3 bits using VQ exhibit the similar image quality and textual alignment as previous 4-bit compression techniques., Comment: project page: https://yandex-research.github.io/vqdm

In previous work, we introduced Mysterious Triality, extending the Mysterious Duality of Iqbal, Neitzke, and Vafa between physics and algebraic geometry to include algebraic topology in the form of rational homotopy theory. Starting with the rational Sullivan minimal model of the 4-sphere $S^4$, capturing the dynamics of M-theory via Hypothesis H, this progresses to the dimensional reduction of M-theory on torus $T^k$, $k \ge 1$, with its dynamics described via the iterated cyclic loop space $\mathcal{L}_c^k S^4$ of the 4-sphere. From this, we also extracted data corresponding to the maximal torus/Cartan subalgebra and the Weyl group of the exceptional Lie group/algebra of type $E_k$. In this paper, we discover much richer symmetry by extending the data of the Cartan subalgebra to a maximal parabolic subalgebra $\mathfrak{p}_k^{k(k)}$ of the split real form $\mathfrak{e}_{k(k)}$ of the exceptional Lie algebra of type $E_k$ by exhibiting an action, in rational homotopy category, of $\mathfrak{p}_k^{k(k)}$ on the slightly more symmetric than $\mathcal{L}_c^k S^4$ toroidification $\mathcal{T}^k S^4$. This action universally represents symmetries of the equations of motion of supergravity in the reduction of M-theory to $11-k$ dimensions. Along the way, we identify the minimal model of the toroidification $\mathcal{T}^k S^4$, generalizing the results of Vigu\'{e}-Poirrier, Sullivan, and Burghelea, and establish an algebraic toroidification/totalization adjunction., Comment: 29 pages

The use of self-assembled monolayers (SAMs) with anchoring groups was considered as an effective approach for interface engineering in perovskite solar cells with metal oxide charge transporting layers. However, the coating of SAM layers in PSMs by means of a slot-die is a challenging process due to the low viscosity of the solutions and the low wettability of the films. In this study, we integrate a triphenylamine-based polymer, pTPA-TDP, blended with SAM based on 5-[4-[4-(diphenylamino) phenyl] thiophene-2-carboxylic acid (TPATC), to address the challenges of uniform slot-die coating and interface passivation in large-area modules. We fabricated p-i-n oriented PSMs on 50x50 mm2 substrates (12-sub-cells) with NiO hole transport layer (HTL) and organic interlayers for surface modification. Wetting angle mapping demonstrated that ununiform regions of the slot-die coated SAM have hydrophobicity with contact angle values up to 90{\deg}, causing fluctuations in absorber thickness and the presence of macro-defects at buried interfaces. The incorporation of the blended interlayer to NiO/perovskite junction homogenized the surface wettability (contact angle=40{\deg}) and mitigated lattice strain in the absorber. This enabled the effective use of SAM properties on a large-area surface, improving energy level alignment and enhancing the power conversion efficiency (PCE) of the modules from 13.98% to 15.83% and stability (ISOS-L-2, T80 period) from 500-1000 hours to 1630 hours. Investigation of PSMs upon cooling till -5 {\deg}C showed that the PCE increased by +0.19%/{\deg}C for samples with NiO HTL, while using SAM and blended interlayers raised the coefficient to ~0.40%/{\deg}C due to changes in activation energy and trap contributions to device performance across a wide temperature range.

This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership., Comment: 19 pages, submitted as a chapter in Encyclopedia of Mathematical Physics, 2nd edition

We present a complete computation of superstring scattering amplitudes at tree level, for the case of Neveu-Schwarz insertions. Mathematically, this is to say that we determine explicitly the superstring measure on the moduli space $\mathcal{M}_{0,n,0}$ of super Riemann surfaces of genus zero with $n \ge 3$ Neveu-Schwarz punctures. While, of course, an expression for the measure was previously known, we do this from first principles, using the canonically defined super Mumford isomorphism. We thus determine the scattering amplitudes, explicitly in the global coordinates on $\mathcal{M}_{0,n,0}$, without the need for picture changing operators or ghosts, and are also able to determine canonically the value of the coupling constant. Our computation should be viewed as a step towards performing similar analysis on $\mathcal{M}_{0,0,n}$, to derive explicit tree-level scattering amplitudes with Ramond insertions., Comment: 25 pages

As a by-product of our work on super Pl\"{u}cker embedding, we came to the notion of a weighted projective superspace $P_{+1,-1}(V\oplus W)$ with weights $+1,-1$. The construction is not in itself super and makes sense in ordinary (purely even) framework. Unlike the familiar weighted projective spaces with positive weights, the (super)space $P_{+1,-1}(V\oplus W)$ is a smooth (super)manifold. We describe its structure and show that it possesses an analog of the Fubini--Study form.

Quantum magnonics investigates the quantum-mechanical properties of magnons such as quantum coherence or entanglement for solid-state quantum information technologies at the nanoscale. The most promising material for quantum magnonics is the ferrimagnetic yttrium iron garnet (YIG), which hosts magnons with the longest lifetimes. YIG films of the highest quality are grown on a paramagnetic gadolinium gallium garnet (GGG) substrate. The literature has reported that ferromagnetic resonance (FMR) frequencies of YIG/GGG decrease at temperatures below 50 K despite the increase in YIG magnetization. We investigated a 97 nm-thick YIG film grown on 500 $\mathrm{\mu}$m-thick GGG substrate through a series of experiments conducted at temperatures as low as 30 mK, and using both analytical and numerical methods. Our findings suggest that the primary factor contributing to the FMR frequency shift is the stray magnetic field created by the partially magnetized GGG substrate. This stray field is antiparallel to the applied external field and is highly inhomogeneous, reaching up to 40 mT in the center of the sample. At temperatures below 500 mK, the GGG field exhibits a saturation that cannot be described by the standard Brillouin function for a paramagnet. Including the calculated GGG field in the analysis of the FMR frequency versus temperature dependence allowed the determination of the cubic and uniaxial anisotropies. We find that the total anisotropy increases more than three times with the decrease in temperature down to 2 K. Our findings enable accurate predictions of the YIG/GGG magnetic systems behavior at low and ultra-low millikelvin temperatures, crucial for developing quantum magnonic devices.

We present Raman spectroscopy of the polycrystalline Si and Ge films deposited by molecular beam deposition on a dielectric substrate. The Raman study has been made using lasers with different wavelengths. Structural properties of the poly-films have been studied by XRD and TEM. The Raman spectra are characterized by appearance of the additional wide peaks around 500 cm$^{-1}$ and 290 cm$^{-1}$ in the main vibrational bands of TO(c-Si) and TO(c-Ge) phonons, respectively. It is shown that these peaks correspond to scattering in grain boundary area. For the poly-Si films, both a downward shift and an asymmetrical broadening of the vibrational band of TO(c-Si) near 520 cm$^{-1}$ are observed, whereas there is only a symmetric broadening in the spectra of poly-Ge. The Raman line shape has been modeled within the framework of the phonon confinement theory taking into account the sizes of coherent scattering domains obtained using XRD. The model includes a symmetrical band broadening observed in polycrystalline films. It is shown that confinement of phonon propagation might be in the poly-Si films. The phonon dispersion and the density of phonon states have been simulated using density functional theory. It has been found that phonon confinement relates to grain boundaries rather than other extended defects such as twins (multiple twins, twin boundaries), the appearance of which does not lead to significant changes in phonon dispersion and density of phonon states., Comment: 46 pages, 23 figures, 1 table

We consider the problem of partitioning a two-dimensional flat torus $T^2$ into $m$ sets in order to minimize the maximal diameter of a part. For $m \leqslant 25$ we give numerical estimates for the maximal diameter $d_m(T^2)$ at which the partition exists. Several approaches are proposed to obtain such estimates. In particular, we use the search for mesh partitions via the SAT solver, the global optimization approach for polygonal partitions, and the optimization of periodic hexagonal tilings. For $m=3$, the exact estimate is proved using elementary topological reasoning., Comment: 18 pages, 8 figures

Large language models demonstrate a remarkable capability for learning to solve new tasks from a few examples. The prompt template, or the way the input examples are formatted to obtain the prompt, is an important yet often overlooked aspect of in-context learning. In this work, we conduct a comprehensive study of the template format's influence on the in-context learning performance. We evaluate the impact of the prompt template across 21 models (from 770M to 70B parameters) and 4 standard classification datasets. We show that a poor choice of the template can reduce the performance of the strongest models and inference methods to a random guess level. More importantly, the best templates do not transfer between different setups and even between models of the same family. Our findings show that the currently prevalent approach to evaluation, which ignores template selection, may give misleading results due to different templates in different works. As a first step towards mitigating this issue, we propose Template Ensembles that aggregate model predictions across several templates. This simple test-time augmentation boosts average performance while being robust to the choice of random set of templates., Comment: Accepted to Findings of ACL 2024. 24 pages, 10 figures. Code: https://github.com/yandex-research/mind-your-format

We study the role of size effects on atomic collapse of charged impurity in the flat band system. The tight-binding simulations are made for the dice lattice with circular quantum dot shapes. It is shown that the mixing of in-gap edge states with bound states in impurity potential leads to increasing the critical charge value. This effect, together with enhancement of gap due to spatial quantization, makes it more difficult to observe the dive-into-continuum phenomenon in small quantum dots. At the same time, we show that if in-gap states are filled, the resonant tunneling to bound state in the impurity potential might occur at much smaller charge, which demonstrates non-monotonous dependence with the size of sample lattice. In addition, we study the possibility of creating supercritical localized potential well on different sublattices, and show that it is possible only on rim sites, but not on hub site. The predicted effects are expected to naturally occur in artificial flat band lattices., Comment: 7 pages, 6 figures

The work is devoted to one of the variations of the Hadwiger--Nelson problem on the chromatic number of the plane. In this formulation one needs to find for arbitrarily small $\varepsilon$ the least possible number of colors needed to color a Euclidean plane in such a way that any two points, the distance between which belongs to the interval $[1-\varepsilon, 1+\varepsilon]$, are colored differently. The conjecture proposed by G. Exoo in 2004, states that for arbitrary positive $\varepsilon$ at least 7 colors are required. Also, with a sufficiently small $\varepsilon$ the number of colors is exactly 7. The main result of the present paper is that the conjecture is true for the Euclidean plane as well as for any Minkowski plane., Comment: 13 pages, 6 figures. Added details concerning the generalization of the result to an arbitrary norm. The bibliography has been expanded, and a discussion of some related results has been added. Corrected some inaccuracies

Text-to-image generation models represent the next step of evolution in image synthesis, offering a natural way to achieve flexible yet fine-grained control over the result. One emerging area of research is the fast adaptation of large text-to-image models to smaller datasets or new visual concepts. However, many efficient methods of adaptation have a long training time, which limits their practical applications, slows down experiments, and spends excessive GPU resources. In this work, we study the training dynamics of popular text-to-image personalization methods (such as Textual Inversion or DreamBooth), aiming to speed them up. We observe that most concepts are learned at early stages and do not improve in quality later, but standard training convergence metrics fail to indicate that. Instead, we propose a simple drop-in early stopping criterion that only requires computing the regular training objective on a fixed set of inputs for all training iterations. Our experiments on Stable Diffusion for 48 different concepts and three personalization methods demonstrate the competitive performance of our approach, which makes adaptation up to 8 times faster with no significant drops in quality., Comment: Accepted to Conference on Neural Information Processing Systems (NeurIPS) 2023. 20 pages, 15 figures. Code: https://github.com/yandex-research/DVAR

In a previous paper, we introduced Mysterious Triality as an extension, via algebraic topology in the form of rational homotopy theory, of Mysterious Duality by Iqbal, Neitzke, and Vafa, which provides connections between physics, in the form of dimensional reduction of M-theory, and algebraic geometry, in the form of intersection theory on del Pezzo surfaces. The starting point for that connection to rational homotopy theory is the description of M-theory dynamics using the 4-sphere, via Hypothesis H. This progresses to dimensional reduction of M-theory on tori $T^k$ with its dynamics described via cyclic loop spaces of the 4-sphere $\mathcal{L}_c^k S^4$, producing a series of data analogous to that given by the del Pezzo surfaces $\mathbb{B}_k$, for $k=0, \dots, 8$. With the mathematical constructions established in the previous paper, in this companion physics paper we present novel connections to M-theory that enhance the triality, including those strengthening the duality. This uncovers interesting ties between algebraic geometry, algebraic topology, and M-theory and provides tantalizing links. We further expand on the extension of the duality and triality to the Kac-Moody setting., Comment: 69 pages. This is an updated version, which takes into account corrections and improvements of the final version of the mathematical companion paper arXiv:2111.14810 [hep-th]

Performing propagating spin-wave spectroscopy of thin films at millikelvin temperatures is the next step towards the realisation of large-scale integrated magnonic circuits for quantum applications. Here we demonstrate spin-wave propagation in a $100\,\mathrm{nm}$-thick yttrium-iron-garnet film at the temperatures down to $45 \,\mathrm{mK}$, using stripline nanoantennas deposited on YIG surface for the electrical excitation and detection. The clear transmission characteristics over the distance of $10\,\mu \mathrm{m}$ are measured and the subtracted spin-wave group velocity and the YIG saturation magnetisation agree well with the theoretical values. We show that the gadolinium-gallium-garnet substrate influences the spin-wave propagation characteristics only for the applied magnetic fields beyond $75\,\mathrm{mT}$, originating from a GGG magnetisation up to $47 \,\mathrm{kA/m}$ at $45 \,\mathrm{mK}$. Our results show that the developed fabrication and measurement methodologies enable the realisation of integrated magnonic quantum nanotechnologies at millikelvin temperatures., Comment: 6 pages, 5 figures

In this paper, we report on the method of nondestructive quality control that can be used in fabrication of GaAs high-speed electronics. The method relies on the surface potential mapping and enables rigid in vivo analysis of transport properties of an active electronic device incorporated into a complex integrated circuit. The study is inspired by our ongoing development of a millimeter wave intelligent reflective surface for 6G communications. To provide desired beamforming capabilities, such a surface should utilize hundreds of identical microscale GaAs diode switches with series resistance of a few ohms. Thus, we develop a ladder-like layered ohmic contact to heavily Si-doped GaAs and cross-study it via transmission line method and Kelvin probe force microscopy. The contact resistivity as low as 0.15~$\mu \Omega \,$cm$^2$ is measured resulting in only a 0.6~$\Omega$ of resistance for the contact area of 3$\times$3~$\mu$m$^2$. Moreover, the tendencies observed suggest that one can rigidly analyze the evolution of contact resistance and the profile of resistivity under contact in response to rapid thermal annealing, once the surface potential map across the ``ladder'' is known.

The adoption of pre-trained language models to generate action plans for embodied agents is a promising research strategy. However, execution of instructions in real or simulated environments requires verification of the feasibility of actions as well as their relevance to the completion of a goal. We propose a new method that combines a language model and reinforcement learning for the task of building objects in a Minecraft-like environment according to the natural language instructions. Our method first generates a set of consistently achievable sub-goals from the instructions and then completes associated sub-tasks with a pre-trained RL policy. The proposed method formed the RL baseline at the IGLU 2022 competition., Comment: 6 pages, 3 figures

Quantitative estimates related to the classical Borsuk problem of splitting set in Euclidean space into subsets of smaller diameter are considered. For a given $k$ there is a minimal diameter of subsets at which there exists a covering with $k$ subsets of any planar set of unit diameter. In order to find an upper estimate of the minimal diameter we propose an algorithm for finding sub-optimal partitions. In the cases $10 \leqslant k \leqslant 17$ some upper and lower estimates of the minimal diameter are improved. Another result is that any set $M \subset \mathbb{R}^3$ of a unit diameter can be partitioned into four subsets of a diameter not greater than $0.966$., Comment: 19 pages, 17 figures