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We investigate radial statistics of zeros of hyperbolic Gaussian Analytic Functions (GAF) of the form $\varphi (z) = \sum_{k\ge 0} c_k z^k$ given that $|\varphi (0)|^2=t$ and assuming coefficients $c_k$ to be independent standard complex normals. We obtain the full conditional distribution of $N_q$, the number of zeros of $\varphi (z)$ within a disk of radius $\sqrt{q}$ centred at the origin, and prove its asymptotic normality in the limit when $q\to 1^{-}$, the limit that captures the entire zero set of $\varphi (z)$. In the same limit we also develop precise estimates for conditional probabilities of moderate to large deviations from normality. Finally, we determine the asymptotic form of $P_k(t;q)=\mathrm{Prob} \{ N_q= k | |\varphi(0)|^2=t \}$ in the limit when $k$ is kept fixed whilst $q$ approaches 1. To leading order, the hole probability $P_0(t;q)$ does not depend on $t$ for $t>0$ but yet is different from that of $P_0(t=0;q)$ and coincides with the hole probability for unconditioned hyperbolic GAF of the form $\sum_{k\ge 0} \sqrt{k+1}\, c_k z^k$. We also find that asymptotically as $q \to 1^{-}$, $P_k(t;q)= e^t P_{k}(0;q)$ for every fixed $k \ge 1$ with $P_{k}(0;q)= \mathrm{Prob} \{ N_q =k-1 \}$., Comment: 48 pages, 8 figures

In this article, we introduce and analyse some statistical properties of a class of models of random landscapes of the form ${\cal H}({\bf x})=\frac{\mu}{2}{\bf x}^2+\sum_{l=1}^M \phi_l({\bf k}_l\cdot {\bf x}), \, \, {\bf x}\in \mathbb{R}^N,\,\, \mu>0 $ where both the functions $\phi_l(z)$ and vectors ${\bf k}_l$ are random. An important example of such landscape describes superposition of $M$ plane waves with random amplitudes, directions of the wavevectors, and phases, further confined by a parabolic potential of curvature $\mu$. Our main efforts are directed towards analysing the landscape features in the limit $N\to \infty, M\to \infty$ keeping $\alpha=M/N$ finite. In such a limit we find (i) the rates of asymptotic exponential growth with $N$ of the mean number of all critical points and of local minima known as the annealed complexities and (ii) the expression for the mean value of the deepest landscape minimum (the ground-state energy). In particular, for the latter we derive the Parisi-like optimisation functional and analyse conditions for the optimiser to reflect various phases for different values of $\mu$ and $\alpha$: replica-symmetric, one-step and full replica symmetry broken, as well as criteria for continuous, Gardner and random first order transitions between different phases., Comment: 42 pages, 0 figure

We study the mean diagonal overlap of left and right eigenvectors associated with complex eigenvalues in $N\times N$ non-Hermitian random Gaussian matrices. In well known works by Chalker and Mehlig the expectation of this (self-)overlap was computed for the complex Ginibre ensemble as $N\to \infty$. In the present work, we consider the same quantity in the real and complex elliptic Ginibre ensembles characterized by correlations between off-diagonal entries controlled by a parameter $\tau\in[0,1]$, with $\tau=1$ corresponding to the Hermitian limit. We derive exact expressions for the mean diagonal overlap in both ensembles at any finite $N$, for any eigenvalue off the real axis. We further investigate several scaling regimes as $N\rightarrow \infty$, both in the limit of strong non-Hermiticity keeping a fixed $\tau\in[0,1)$ and in the weak non-Hermiticity limit, with $\tau$ approaching unity in such a way that $N(1-\tau)$ remains finite., Comment: 29 pages, 6 figures

Celebrated fluctuation-dissipation theorem (FDT) linking the response function to time dependent correlations of observables measured in the reference unperturbed state is one of the central results in equilibrium statistical mechanics. In this letter we discuss an extension of the standard FDT to the case when multidimensional matrix representing transition probabilities is strictly non-normal. This feature dramatically modifies the dynamics, by incorporating the effect of eigenvector non-orthogonality via the associated overlap matrix of Chalker-Mehlig type. In particular, the rate of entropy production per unit time is strongly enhanced by that matrix. We suggest, that this mechanism has an impact on the studies of collective phenomena in neural matrix models, leading, via transient behavior, to such phenomena as synchronisation and emergence of the memory. We also expect, that the described mechanism generating the entropy production is generic for wide class of phenomena, where dynamics is driven by non-normal operators. For the case of driving by a large Ginibre matrix the entropy production rate is evaluated analytically, as well as for the Rajan-Abbott model for neural networks., Comment: 3 figures, 8 pages. Important references added, calculation of entropy production rates for Rajan-Abbott model of neural networks and for Ginibre ensemble completed, title changed

We study analytically the Chalker-Mehlig mean diagonal overlap $\mathcal{O}(z)$ between left and right eigenvectors associated with a complex eigenvalue $z$ of $N\times N$ matrices in the real Ginibre ensemble (GinOE). We first derive a general finite $N$ expression for the mean overlap and then investigate several scaling regimes in the limit $N\rightarrow \infty$. While in the generic spectral bulk and edge of the GinOE the limiting expressions for $\mathcal{O}(z)$ are found to coincide with the known results for the complex Ginibre ensemble (GinUE), in the region of eigenvalue depletion close to the real axis the asymptotic for the GinOE is considerably different. We also study numerically the distribution of diagonal overlaps and conjecture that it is the same in the bulk and at the edge of both the GinOE and GinUE, but essentially different in the depletion region of the GinOE., Comment: 23 pages, 7 figures

In an absorptive system the Wigner reaction $K-$matrix (directly related to the impedance matrix in acoustic or electromagnetic wave scattering) is non-selfadjoint, hence its eigenvalues are complex. The most interesting regime arises when the absorption, taken into account as an imaginary part of the spectral parameter, is of the order of the mean level spacing. I show how to derive the mean density of the complex eigenvalues for reflection problems in disordered or chaotic systems with broken time-reversal invariance. The computations are done in the framework of nonlinear $\sigma-$ model approach, assuming fixed $M$ and $N\to \infty$. Some explicit formulas are provided for zero-dimensional quantum chaotic system as well as for a semi-infinite quasi-1D system with fully operative Anderson localization., Comment: 22 pages, 2 figures

We derive, within the replica formalism, a generalisation of the Crisanti-Sommers formula to describe the large deviation function (LDF) ${\cal L}(e)$ for the speed-$N$ atypical fluctuations of the intensive ground-state energy $e$ of a generic spherical spin-glass in the presence of a random external magnetic field of variance $\Gamma$. We then analyse our exact formula for the LDF in much detail for the Replica symmetric, single step Replica Symmetry Breaking (1-RSB) and Full Replica Symmetry Breaking (FRSB) situations. Our main qualitative conclusion is that the level of RSB governing the LDF may be different from that for the typical ground state. We find that while the deepest ground-states are always controlled by a LDF of replica symmetric form, beyond a finite threshold $e\geq e_{t}$ a replica-symmetry breaking starts to be operative. These findings resolve the puzzling discrepancy between our earlier replica calculations for the $p=2$ spherical spin-glass and the rigorous results by Dembo and Zeitouni which we are able to reproduce invoking an 1-RSB pattern. Finally at an even larger critical energy $e_{c}\geq e_{t}$, acting as a "wall", the LDF diverges logarithmically, which we interpret as a change in the large deviation speed from $N$ to a faster growth. In addition, we show that in the limit $\Gamma \to 0$ the LDF takes non-trivial scaling forms (i) ${\cal L}(e) \sim G((e-e_c)/\Gamma)$ in the vicinity of the wall (ii) ${\cal L}(e) \sim \Gamma^{\eta \nu} F((e-e_{\rm typ})/\Gamma^{\nu})$ in the vicinity of the typical energy, characterised by two new exponents $\eta\geq 1$ and $\nu$ characterising universality classes. Via matching the latter allows us to formulate several conjectures concerning the regime of {\it typical fluctuations}, identified as $e-e_{\rm typ} \sim N^{-1/\eta}$ and $\Gamma \sim N^{-1/(\eta \nu)}$., Comment: 58 pages, 14 figures

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number $M$ of open channels the probability density ${\cal P}(I)$ for the single-point intensity $I$ decays as a power law for large intensities: ${\cal P}(I)\sim I^{-(M+2)}$, provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law ${\cal P}(I)\sim \exp(-I/\overline{I})$ which turns out to be valid only in the limit $M\to \infty$. We also find the joint probability density of intensities $I_1, \ldots, I_L$ in $L>1$ observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For $L\to \infty$ the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions., Comment: 17 pages + 3 figures

Using the framework of supersymmetric non-linear $\sigma$-model we develop a general non-perturbative characterisation of universal features of the density $\rho(\Gamma)$ of the imaginary parts (``width'') for $S$-matrix poles (``resonances'') describing waves incident and reflected from a disordered medium via $M$-channel waveguide/lead. Explicit expressions for $\rho(\Gamma)$ are derived for several instances of systems with broken time-reversal invariance, in particular for quasi-1D and 3D media. In the case of perfectly coupled lead with a few channels ($M\sim 1$) the most salient features are tails $\rho(\Gamma)\sim \Gamma^{-1}$ for narrow resonances reflecting exponential localization and $\rho(\Gamma)\sim \Gamma^{-2}$ for broad resonances reflecting states located in the vicinity of the attached wire. For multimode quasi 1D wires with $M\gg 1$, an intermediate asymptotics $\rho(\Gamma)\sim \Gamma^{-3/2}$ is shown to emerge reflecting diffusive nature of decay into wide enough contacts., Comment: The previous letter-style version is replaced by a full-length article

Complex eigenvalues of random matrices $J=\text{GUE }+ i\gamma \diag (1, 0, \ldots, 0)$ provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the limit of large matrix dimensions $N\gg 1$ the eigenvalue density of $J$ undergoes an abrupt restructuring at $\gamma = 1$, the critical threshold beyond which a single eigenvalue outlier (``broad resonance'') appears. We provide a detailed description of this restructuring transition, including the scaling with $N$ of the width of the critical region about the outlier threshold $\gamma=1$ and the associated scaling for the real parts (``resonance positions'') and imaginary parts (``resonance widths'') of the eigenvalues which are farthest away from the real axis. In the critical regime we determine the density of such extreme eigenvalues, and show how the outlier gradually separates itself from the rest of the extreme eigenvalues. Finally, we describe the fluctuations in the height of the eigenvalue outlier for large but finite $N$ in terms of the associated large deviation function., Comment: Revised version: Introduction is expanded to include more details and comparison of our results to the recent work of Dubach and Erdos; the discussion of universality of the exponent -1/3 in Section 2 clarifies how how this exponent is linked to the shape of the eigenvalue density of the undeformed matrix, several references and acknowledgements are added

This demo paper introduces the BLAB Reporter, a robot-journalist covering the Brazilian Blue Amazon. The Reporter is based on a pipeline architecture for Natural Language Generation; it offers daily reports, news summaries and curious facts in Brazilian Portuguese. By collecting, storing and analysing structured data from publicly available sources, the robot-journalist uses domain knowledge to generate and publish texts in Twitter. Code and corpus are publicly available, Comment: Accepted at the 15th International Natural Language Generation Conference (INLG 2022)

The majority of NLG systems have been designed following either a template-based or a pipeline-based architecture. Recent neural models for data-to-text generation have been proposed with an end-to-end deep learning flavor, which handles non-linguistic input in natural language without explicit intermediary representations. This study compares the most often employed methods for generating Brazilian Portuguese texts from structured data. Results suggest that explicit intermediate steps in the generation process produce better texts than the ones generated by neural end-to-end architectures, avoiding data hallucination while better generalizing to unseen inputs. Code and corpus are publicly available., Comment: Accepted at the 19th National Meeting on Artificial and Computational Intelligence (ENIAC 2022)

We review recent developments on the characterization of random landscapes in high-dimension. We focus in particular on the problem of characterizing the landscape topology and geometry, discussing techniques to count and classify its stationary points and stressing connections with the statistical physics of disordered systems and with random matrix theory., Comment: Contribution to the book Spin Glass Theory and Far Beyond: Replica Symmetry Breaking after 40 Years

We describe the first steps in the development of an artificial agent focused on the Brazilian maritime territory, a large region within the South Atlantic also known as the Blue Amazon. The "BLue Amazon Brain" (BLAB) integrates a number of services aimed at disseminating information about this region and its importance, functioning as a tool for environmental awareness. The main service provided by BLAB is a conversational facility that deals with complex questions about the Blue Amazon, called BLAB-Chat; its central component is a controller that manages several task-oriented natural language processing modules (e.g., question answering and summarizer systems). These modules have access to an internal data lake as well as to third-party databases. A news reporter (BLAB-Reporter) and a purposely-developed wiki (BLAB-Wiki) are also part of the BLAB service architecture. In this paper, we describe our current version of BLAB's architecture (interface, backend, web services, NLP modules, and resources) and comment on the challenges we have faced so far, such as the lack of training data and the scattered state of domain information. Solving these issues presents a considerable challenge in the development of artificial intelligence for technical domains.

We compute analytically the probability distribution and moments of the sum and product of the non-zero eigenvalues and singular values of random matrices with (i) non-negative entries, (ii) fixed rank, and (iii) prescribed sums of the entries in each row. Applications of such matrices are discussed in the context of Markov chains, economics and social networks to name a few. All results are valid at finite matrix size and are given in terms of the statistics of vectors of general Dirichlet random variables. Analytical results are corroborated by numerical simulations throughout with excellent agreement., Comment: 43 pages, 5 figures

Motivated by current interest in understanding statistical properties of random landscapes in high-dimensional spaces, we consider a model of the landscape in $\mathbb{R}^N$ obtained by superimposing $M>N$ plane waves of random wavevectors and amplitudes. For this landscape we show how to compute the "annealed complexity" controlling the asymptotic growth rate of the mean number of stationary points as $N\to \infty$ at fixed ratio $\alpha=M/N>1$. The framework of this computation requires us to study spectral properties of $N\times N$ matrices $W=KTK^T$, where $T$ is diagonal with $M$ mean zero i.i.d. real normally distributed entries, and all $MN$ entries of $K$ are also i.i.d. real normal random variables. We suggest to call the latter Gaussian Marchenko-Pastur Ensemble, as such matrices appeared in the seminal 1967 paper by those authors. We compute the associated mean spectral density and evaluate some moments and correlation functions involving products of characteristic polynomials for such and related matrices., Comment: 40 pages, 6 figures

We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete system of $M>N$ linear equations $({\bf a}_k,{\bf x})=b_k, \, k=1,\ldots,M$ on the $N-$sphere ${\bf x}^2=N$. We treat both the $N-$component vectors ${\bf a}_k$ and parameters $b_k$ as independent mean zero real Gaussian random variables. First, we derive the exact expressions for the mean number of stationary points of the least-square loss function in the framework of the Kac-Rice approach combined with the Random Matrix Theory for Wishart Ensemble, and then perform its asymptotic analysis as $N\to \infty$ at a fixed $\alpha=M/N>1$ in various regimes. In particular, this analysis allows to extract the Large Deviation Function for the density of the smallest Lagrange multiplier $\lambda_{min}$ associated with the problem, and in this way to find its most probable value. This can be further used to predict the asymptotic minimal value ${\cal E}_{min}$ of the loss function as $N\to \infty$. Finally, we develop an alternative approach based on the replica trick to conjecture the form of the Large Deviation function for the density of ${\cal E}_{min}$ at $N\gg 1$. As a by-product, we find the value of the {\it compatibility threshold} $\alpha_c$ which is the minimal value of the asymptotic ratio $M/N$ such that the random linear system on the $N-$sphere is typically compatible., Comment: 38 pages, 4 figures

We consider a nonlinear autonomous random dynamical system of $N$ degrees of freedom coupled by Gaussian random interactions and characterized by a continuous spectrum $n_{\mu}(\lambda)$ of real positive relaxation rates. Using Kac-Rice formalism, the computation of annealed complexities (both of stable equilibria and of all types of equilibria) is reduced to evaluating the averages involving the modulus of the determinant of the random Jacobian matrix. In the limit of large system $N\gg 1$ we derive exact analytical results for the complexities for short-range correlated coupling fields, extending results previously obtained for the "homogeneous" relaxation spectrum characterised by a single relaxation rate. We show the emergence of a "topology trivialisation" transition from a complex phase with exponentially many equilibria to a simple phase with a single equilibrium as the magnitude of the random field is decreased. Within the complex phase the complexity of stable equilibria undergoes an additional transition from a phase with exponentially small probability to find a single equilibrium to a phase with exponentially many stable equilibria as the fraction of gradient component of the field is increased. The behaviour of the complexity at the transition is found only to depend on the small $\lambda$ behaviour of the spectrum of relaxation rates $n_{\mu}(\lambda)$ and thus conjectured to be universal. We also provide some insights into a counting problem motivated by a paper by B. Spivak and A. Zyuzin of 2004 about wave scattering in a disordered nonlinear medium., Comment: 43 pages, 3 figures. J. Phys. A: Math. Theor. 2022

We study the statistical properties of the complex generalization of Wigner time delay $\tau_\text{W}$ for sub-unitary wave chaotic scattering systems. We first demonstrate theoretically that the mean value of the $\text{Re}[\tau_\text{W}]$ distribution function for a system with uniform absorption strength $\eta$ is equal to the fraction of scattering matrix poles with imaginary parts exceeding $\eta$. The theory is tested experimentally with an ensemble of microwave graphs with either one or two scattering channels, and showing broken time-reversal invariance and variable uniform attenuation. The experimental results are in excellent agreement with the developed theory. The tails of the distributions of both real and imaginary time delay are measured and are also found to agree with theory. The results are applicable to any practical realization of a wave chaotic scattering system in the short-wavelength limit., Comment: 8 pages, 3 figures. Supplementary material added

Motivated by the phenomenon of Coherent Perfect Absorption, we study the shape of the deepest minima in the frequency-dependent single-channel reflection of waves from a cavity with spatially uniform losses. We show that it is largely determined by non-orthogonality factors $O_{nn}$ of the eigenmodes associated with the non-selfadjoint effective Hamiltonian. For cavities supporting chaotic ray dynamics we then use random matrix theory to derive, fully non-perturbatively, the explicit probability density ${\cal P}(O_{nn})$ of the non-orthogonality factors for systems with both broken and preserved time reversal symmetry. The results imply that $O_{nn}$ are heavy-tail distributed, with the universal tail ${\cal P}(O_{nn}\gg 1)\sim O_{nn}^{-3}$.

Small cations such as guanidinium and cesium can act as templating cations to form low dimensional phases (2D, 1D, 0D) in the case of excess of organic halides. However, such phases with the widely used formamidinium (FA+) cation have not been reported so far. In this study, we discovered two novel low dimensional phases with a composition of FA2PbBr4 and investigated the prerequisites of their formation upon crystallization of FABr-excessive solutions of FAPbBr3. We found that both phases have the structure of (110) layered perovskite but are represented by two different polymorphs with eclipsed and staggered arrangement of adjacent layers. It was shown that FA2PbBr4 phases usually exist in a labile equilibrium with FAPbBr3 3D perovskite and can form composites with it. The optical properties of both polymorphs were comprehensively studied by means of absorption spectroscopy, diffuse reflection spectroscopy and photoluminescence spectroscopy. DFT calculations were applied to investigate the band structure of the FA2PbBr4 and to corroborate the conclusions on their optoelectronic properties. As a result, we found that FA2PbBr4 phases irradiated by UV can exhibit effective green photoluminescence due to a transfer of excitation energy to defective states or 3D perovskite inclusions., Comment: 24 pages, 19 figures

We introduce a complex generalization of Wigner time delay $\tau$ for sub-unitary scattering systems. Theoretical expressions for complex time delay as a function of excitation energy, uniform and non-uniform loss, and coupling, are given. We find very good agreement between theory and experimental data taken on microwave graphs containing an electronically variable lumped-loss element. We find that time delay and the determinant of the scattering matrix share a common feature in that the resonant behavior in $\text{Re}[\tau]$ and $\text{Im}[\tau]$ serves as a reliable indicator of the condition for Coherent Perfect Absorption (CPA). This work opens a new window on time delay in lossy systems and provides a means to identify the poles and zeros of the scattering matrix from experimental data. The results also enable a new approach to achieving CPA at an arbitrary energy/frequency in complex scattering systems., Comment: 8 pages, 2 figures. Supplementary material added