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We consider the orientational diffusion controlled by the hyperspherical Laplacian, $\nabla^2_D$, on the surface of the $D$--dimensional hypersphere in the limit $D \to \infty$. We find that for stretched paths with lengths relatively short compared to the hypersphere's radius, the finite-size corrections in orientational correlations are controlled by the Kardar-Parisi-Zhang (KPZ) scaling exponent, $\gamma = 1/3$. In addition, we speculate about the topology of the orientational target space representing the surface of the hypersphere., Comment: 11 pages, 3 figures

Despite the recent advancements in information retrieval (IR), zero-shot IR remains a significant challenge, especially when dealing with new domains, languages, and newly-released use cases that lack historical query traffic from existing users. For such cases, it is common to use query augmentations followed by fine-tuning pre-trained models on the document data paired with synthetic queries. In this work, we propose a novel Universal Document Linking (UDL) algorithm, which links similar documents to enhance synthetic query generation across multiple datasets with different characteristics. UDL leverages entropy for the choice of similarity models and named entity recognition (NER) for the link decision of documents using similarity scores. Our empirical studies demonstrate the effectiveness and universality of the UDL across diverse datasets and IR models, surpassing state-of-the-art methods in zero-shot cases. The developed code for reproducibility is included in https://github.com/eoduself/UDL, Comment: Accepted for publication at EMNLP 2024 Main Conference

Pathology, the microscopic examination of diseased tissue, is critical for diagnosing various medical conditions, particularly cancers. Traditional methods are labor-intensive and prone to human error. Digital pathology, which converts glass slides into high-resolution digital images for analysis by computer algorithms, revolutionizes the field by enhancing diagnostic accuracy, consistency, and efficiency through automated image analysis and large-scale data processing. Foundational transformer pretraining is crucial for developing robust, generalizable models as it enables learning from vast amounts of unannotated data. This paper introduces the Hibou family of foundational vision transformers for pathology, leveraging the DINOv2 framework to pretrain two model variants, Hibou-B and Hibou-L, on a proprietary dataset of over 1 million whole slide images (WSIs) representing diverse tissue types and staining techniques. Our pretrained models demonstrate superior performance on both patch-level and slide-level benchmarks, surpassing existing state-of-the-art methods. Notably, Hibou-L achieves the highest average accuracy across multiple benchmark datasets. To support further research and application in the field, we have open-sourced the Hibou models, which can be accessed at https://github.com/HistAI/hibou.

Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis. We focus on the Heisenberg time scale, which approximately corresponds to the ramp--plateau transition for the Krylov complexity in systems with a large but finite number degrees of freedom. Two frameworks are under consideration: i) the system with growing Lanczos coefficients and an artificial cut-off, and ii) the system with the finite Hilbert space. In both cases via numerical analysis, we observe the transition from Gaussian to KPZ-like scaling at the critical Euclidean time $t_{E}^*=c_{cr}K$, for the Krylov chain of finite length $K$, and $c_{cr}=O(1)$. In particular, we find a scaling $\sim K^{1/3}$ for fluctuations in the one-point correlation function and a dynamical scaling $\sim K^{-2/3}$ associated with the return probability (Loschmidt echo) corresponding to autocorrelators in physical space. In the first case, the transition is of the 3rd order and can be considered as an example of dynamical quantum phase transition (DQPT), while in the second, it is a crossover. For case ii), utilizing the relationship between the spectrum of tridiagonal matrices at the spectral edge and the spectrum of the stochastic Airy operator, we demonstrate analytically the origin of the KPZ scaling for the particular Krylov chain using the results of the probability theory. We argue that there is some outcome of our study for the double scaling limit of matrix models. For the case of topological gravity, the white noise $O(\frac{1}{N})$ term is identified, which should be taken into account in the controversial issue of ensemble averaging in 2D/1D holography., Comment: 32 pages, 15 figures

In our daily lives, we encounter numerous independent events, each occurring with varying probabilities over time. This letter delves into the scientific background behind the inhomogeneous distribution of these events over time, often resulting in what we refer to as ``black days'', where multiple events seem to converge at once. In the first part of the work we performed an analysis involving $D$ independent periodic and random sequences of events. Using the Uniform Manifold Approximation and Projection (UMAP) technique, we observed a clustering of event sequences on a two-dimensional manifold ${\cal M}$ at a certain large $D$. We interpret this clustering as a signature of ``black days'', which bears a clear resemblance to traffic jams in vehicle flow. In the second part of the work we examined in detail clustering patterns of independently distributed $N$ points within the corners of a $D$-dimensional cube when $1\ll N

In this study, we explore the fundamental principles behind the architecture of the human brain's structural connectome, from the perspective of spectral analysis of Laplacian and adjacency matrices. Building on the idea that the brain strikes a balance between efficient information processing and minimizing wiring costs, we aim to understand the impact of the metric properties of the connectome and how they relate to the existence of an inherent scale. We demonstrate that a simple generative model, combining nonlinear preferential attachment with an exponential penalty for spatial distance between nodes, can effectively reproduce several key characteristics of the human connectome, including spectral density, edge length distribution, eigenmode localization and local clustering properties. We also delve into the finer spectral properties of the human structural connectomes by evaluating the inverse participation ratios ($\text{IPR}_q$) across various parts of the spectrum. Our analysis reveals that the level statistics in the soft cluster region of the Laplacian spectrum deviate from a purely Poisson distribution due to interactions between clusters. Additionally, we identified scar-like localized modes with large IPR values in the continuum spectrum. We identify multiple fractal eigenmodes distributed across different parts of the spectrum, evaluate their fractal dimensions and find a power-law relationship in the return probability, which is a hallmark of critical behavior. We discuss the conjectures that a brain operates in the Griffiths or multifractal phases.

Currently, the development of Foreign Accent Conversion (FAC) models utilizes deep neural network architectures, as well as ensembles of neural networks for speech recognition and speech generation. The use of these models is limited by architectural features, which does not allow flexible changes in the timbre of the generated speech and requires the accumulation of context, leading to increased delays in generation and makes these systems unsuitable for use in real-time multi-user communication scenarios. We have developed the non-autoregressive model for real-time accent conversion with voice cloning. The model generates native-sounding L1 speech with minimal latency based on input L2 accented speech. The model consists of interconnected modules for extracting accent, gender, and speaker embeddings, converting speech, generating spectrograms, and decoding the resulting spectrogram into an audio signal. The model has the ability to save, clone and change the timbre, gender and accent of the speaker's voice in real time. The results of the objective assessment show that the model improves speech quality, leading to enhanced recognition performance in existing ASR systems. The results of subjective tests show that the proposed accent and gender encoder improves the generation quality. The developed model demonstrates high-quality low-latency accent conversion, voice cloning, and speech enhancement capabilities, making it suitable for real-time multi-user communication scenarios., Comment: 8 pages, 6 figures, 3 tables

We carry out particle-in-cell simulations of complex current sheets of the family of analytically found Vlasov--Maxwell equilibria that model a collisionless magnetopause and allow for arbitrary energy distributions and countercurrents of various particle component. We find that, depending on the parameters, i)~a weak small-scale bending-type instability is always present at the sharp low-density plasma boundary of such a magnetopause, and ii)~the development of a small-scale Weibel-type instability inside a magnetopause is either excluded or possible. Both cases are studied and compared for two variants of the particle energy distribution~ -- Maxwellian and Kappa. The long-term stability of the whole current sheet is observed either without or with saturated Weibel-type turbulence, which can be generated in a low-magnetized region between neighboring countercurrents. We point out the applicability of the developed model of distributed current sheets and the results of analysis of their small-scale instability for the description of physical phenomena in the magnetopauses of planets and late-type stars., Comment: 26 pages, 9 figs

We outline transient quasi-magnetostatic phenomena associated with Weibel-type instabilities, mainly, the formation and decay of the current sheets and filaments. We consider a collisionless anisotropic plasma cloud with hot electrons expanding into an inhomogeneous background plasma taking into account an external magnetic field in different geometries entailing (i) a hot-electron spot of a circular or cylindrical form within an initial-value problem or a finite-time injection of electrons from a target surface, (ii) inhomogeneous layers of cold background plasma of different densities and spatial scales, (iii) an external magnetic field with three orientations: perpendicular to the target or along it, directed either across or parallel to a long axis of the hot-electron spot. We heed typical laser-plasma experiments. We outline development of the principle current structures linked with distinct forms of the anisotropic electron velocity distribution using particle-in-cell modeling of the instability process for diverse sets of the attributes (i)--(iii). Applications to the analysis of laboratory and space plasma problems involving an explosive development of the small-scale filamentation of the electric current and self-consistent magnetic turbulence are discussed., Comment: 102 pages, 30 figures, submitted to Review of Modern Plasma Physics

We discuss the generalization of a classical problem involving an $N$-step ideal polymer adsorption at a sticky boundary (potential well of depth $U$). It is known that as $N$ approaches infinity, the path undergoes a 2nd-order localization transition at a certain value of $U_{\text{tr}}$. By considering the random walk on a half-line with a sticky boundary (Model I), we demonstrate that the order of the phase transition can be altered by adjusting the scaling of the first return probability to the boundary. Additionally, we present a model of a random path on a discrete 1D lattice with non-uniform local hopping amplitudes and a potential well at the boundary (Model II). We illustrate that one can tailor such amplitudes so that the polymer undergoes a 3rd-order phase transition., Comment: 10 pages, 5 figures

We discuss a two-parameter renormalization group (RG) consideration of a phyllotaxis model in the framework of the ``energetic approach'' proposed by L. Levitov in 1991. Following L. Levitov, we consider an equilibrium distribution of strongly repulsive particles on the surface of a finite cylinder and study the redistribution of these particles when the cylinder is squeezed along its axis. We construct explicitly the $\beta$-function of a given system in terms of the modular Dedekind $\eta$-function. On basis of this $\beta$-function we derive the equations describing the RG flow in the vicinity of the bifurcation points between different lattices. Analyzing the structure of RG equations, we claim emergence of Berezinskii-Kosterlitz-Thouless (BKT) transitions at strong compression of the cylinder., Comment: 13 pages, 5 figures; On the basis of the talk delivered by one of authors (S.N.) at the workshop "Statistical mechanics and its applications'', Dilijan, Armenia (October 2022). arXiv admin note: substantial text overlap with arXiv:2304.07640

We explore numerically the impact of additive Gaussian noise on the spatio-temporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the Henon map. 2D distributions of the probability of observing chimera states are constructed in terms of the coupling strength and the noise intensity and for several choices of the local dynamics parameters. It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance., Comment: 15 pages, 14 figures; typos corrected, references added

We investigate the statistics of the largest eigenvalue, $\lambda_{\rm max}$, in an ensemble of $N\times N$ large ($N\gg 1$) sparse adjacency matrices, $A_N$. The most attention is paid to the distribution and typical fluctuations of $\lambda_{\rm max}$ in the vicinity of the percolation threshold, $p_c=\frac{1}{N}$. The overwhelming majority of subgraphs representing $A_N$ near $p_c$ are exponentially distributed linear subchains, for which the statistics of the normalized largest eigenvalue can be analytically connected with the Gumbel distribution. For the ensemble of {\rm all} subgraphs near $p_c$ we suggest that under an appropriate modification of the normalization constant the Gumbel distribution provides a reasonably good approximation. Using numerical simulations we demonstrate that the proposed transformation of $\lambda_{\rm max}$ is indeed Gumbel-distributed and the leading finite-size corrections in the vicinity of $p_c$ scale with $N$ as $\sim \ln^{-2}N$. All together, our results reveal a previously unknown universality in eigenvalue statistics of sparse matrices close to the percolation threshold., Comment: 18 pages, 8 figures

We discuss a two-parameter renormalization group (RG) flow when parameters are organized in a single complex variable, $\tau$, with modular properties. Throughout the work we consider a special limit when the imaginary part of $\tau$ characterizing the disorder strength tends to zero. We argue that generalized Riemann-Thomae (gRT) function and the corresponding generalized Devil's staircase emerge naturally in a variety of physical models providing a universal behavior. In 1D we study the Anderson-like probe hopping in a weakly disordered lattice, recognize the origin of the gRT function in the spectral density of the probe and formulate specific RG procedure which gets mapped onto the discrete flow in the fundamental domain of the modular group $SL(2,Z)$. In 2D we consider the generalization of the phyllotaxis crystal model proposed by L. Levitov and suggest the explicit form of the effective potential for the probe particle propagating in the symmetric and asymmetric 2D lattice of defects. Analyzing the structure of RG flow equations in the vicinity of saddle points we claim emergence of BKT-like transitions at ${\rm Im}\,\tau\to 0$. We show that the RG-like dynamics in the fundamental domain of $SL(2,Z)$ for asymmetric lattices asymptotically approaches the "Silver ratio". For a Hubbard model of particles on a ring interacting via long-ranged potentials we investigate the dependence of the ground state energy on the potential and demonstrate by combining numerical and analytical tools the emergence of the generalized Devil's staircase. Also we conjecture a bridge between a Hubbard model and a phyllotaxis., Comment: bugs fixed and figures corrected (49 pages and 18 figures), to apear in Nucl Phys. B (accepted)

We discuss the eigenvalue detachment transition in terms of scaling of fluctuations in ensembles of paths located near convex boundaries of various physical nature. We consider numerically the BBP-like (Baik-Ben Arous-P\'ech\'e) transition from the Gaussian to the Tracy-Widom scaling of fluctuations in several statistical systems for both canonical and microcanonical ensembles and identify the corresponding control parameter in each case. In particular, for fixed path length (microcanonical) ensemble of paths located in the vicinity of a partially permeable semicircle, the transition occurs at the critical value of a permeability. The Tracy-Widom regime and the BBP-like transition for fluctuations are discussed in terms of the Jakiw-Teitelbom (JT) gravity with a radial cutoff which, in turn, has an interpretation as a ensemble of fixed length world-line geometrically constrained trajectories of a charged particle in an effective transversal magnetic field., Comment: 24 pages, 6 figures