We investigate the effective potential and scattering length of ultracold polar molecules under different shielding techniques. First, we derive the effective potential for two polar molecules in the presence of an elliptical polarization field, combined elliptical and linear polarization fields, and combined elliptical polarization and static fields. The effective potential is then expressed as a sum of a zero-range contact interaction and a long-range dipole-dipole interaction under the Born approximation. We find that the first two shielding methods only partially suppress attractive interactions, while the second method allows for the construction of bound states with different polarization shapes. The last shielding method can achieve complete cancellation of residual attractive forces, which is particularly significant for maintaining quantum degeneracy in ultracold dipolar systems. Our results provide a comprehensive understanding of the effective potential and scattering length of shielding polar molecules, which is crucial for studying many-body physics in ultracold dipolar systems.

Chemical reactions in a statistical ensemble are conventionally regarded as incoherent processes driven by thermodynamics. In the quantum degenerate regime, where atoms and molecules form coherent matter waves, reactions are theoretically described by nonlinear mixing of matter-wave fields. In this scenario, we expect phase matching between reactants and products, analogous to the mixing of photonic fields in nonlinear optics. Here we report on the observation of phase coherent reaction dynamics of Bose-condensed atoms and molecules near a Feshbach resonance. Using matter-wave diffraction with optical lattices, we verify spatial coherence of both atoms and molecules and observe phase doubling when atomic waves combine into molecular waves, the matter-wave analogue of optical frequency doubling. The diffraction patterns further reveal two-atom entanglement generated during the reaction. Our observations establish phase coherence and entanglement generation as two essential features of "quantum many-body chemistry". Moreover, our work opens a pathway to control of reaction dynamics by manipulation of matter-wave phases.

Various imaging techniques have significantly enhanced our ability to visualize objects embedded within complex media such as biological tissues, fog, atmosphere, or various turbid media. Optical imaging, in particular, offers multiple advantages, including non-invasive capabilities, absence of ionizing radiation, and high contrast for many biological tissues. However, optical imaging through substantially thick scattering media remains challenging due to extensive photon diffusion, significantly restricting reconstruction quality and achievable resolution. To address these limitations, we introduce Diffuse Optical Ptychography (DOP), a novel imaging method inspired by ptychography technique, which exploits additional spatial information gained from multiple overlapping illumination patterns. The primary technical innovation of DOP lies in its effective use of overlapping yet minimally correlated illuminations, significantly enhancing reconstruction accuracy and image quality. Compared to existing optical imaging methods through thick diffusive media, DOP achieves superior resolution (down to 1 mm) and reliably reconstructs both binary and grayscale objects embedded within media thicker than 100 transport mean free paths. Importantly, DOP demonstrates robust reconstruction performance both with accurately calibrated diffusion properties and even without prior calibration. Furthermore, the experimental setup for DOP remains straightforward, utilizing only a conventional camera and scanning illumination spots. Our demonstrations underscore the broad potential impact of DOP in applications ranging from medical diagnostics to non-destructive testing, thus opening promising avenues for high-resolution imaging in highly scattering environments.

In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random fields is expected to prohibit any finite temperature ordering. Here, we prove that this is not necessarily true, and show rigorously that for physically relevant systems in $\mathbb{Z}^d$ with $d\ge 3$, disorder can induce ordering that is \textit{infinitely stable}, in the sense that (1) there exists ordering at arbitrarily large disorder strength and (2) the transition temperature is asymptotically nonzero in the limit of infinite disorder. Analogous results can hold in 2 dimensions provided that the underlying graph is non-planar (e.g., $\mathbb{Z}^2$ sites with nearest and next-nearest neighbor interactions).

We prove that Grothendieck-Witt spaces of Poincaré categories are, in many cases, group completions of certain moduli spaces of hermitian forms. This, in particular, identifies Karoubi's classical hermitian and quadratic K-groups with the genuine Grothendieck-Witt groups from our joint work with Calmès, Dotto, Harpaz, Land, Moi, Nardin and Nikolaus, and thereby completes our solution of several conjectures in hermitian K-theory. The method of proof is abstracted from work of Galatius and Randal-Williams on cobordism categories of manifolds using the identification of the Grothendieck-Witt space of a Poincaré category as the homotopy type of the associated cobordism category.

We investigate the dressed bound states (DBS) in an open cavity with a whispering-gallery-mode microring coupled to a two-level atom and a waveguide with a mirror at the right end. We demonstrate that the non-Hermiticity of an open cavity facilitates the formation of the DBS, which consists of the vacancy-like DBS and Friedrich-Wintgen DBS. By deriving analytical conditions for these DBS, we show that when a two-level atom couples to the standing-wave mode that corresponds to a node of the photonic wave function the vacancy-like DBS occur, which are characterized by null spectral density at cavity resonance. Conversely, Friedrich-Wintgen DBS can be realized by continuously adjusting system parameters and indicated by the disappearance of the Rabi peak in the emission spectrum, which is a distinctive feature in the strong-coupling regime. Moreover, we extend our analysis to the non-Markovian regime and find that our results are consistent with those obtained under the Markovian approximation in the wideband limit. In the non-Markovian regime, we analyze DBS for both zero and non-zero accumulated phase factors. For zero accumulated phase factors, the non-Markovian regime exhibits higher peak values and longer relaxation times for vacancy-like DBS compared to the Markovian regime, where the Friedrich-Wintgen DBS are absent in the non-Markovian case. Finally, we establish the correspondence between the energy spectrum and bound state conditions for non-zero accumulated phase factors and analyze the influence of various parameters on non-Markovian bound states. Our work exhibits bound state manipulations through non-Markovian open quantum system, which holds great potential for building high-performance quantum devices for applications such as sensing, photon storage, and nonclassical light generation.

We introduce a systematic procedure based on optimal control theory to address the full counting statistics of particle transport in a stochastic system. Our approach enhances the performance of a Thouless pump in the non-adiabatic regime by simultaneously optimizing the average pumping rate while minimizing noise. We demonstrate our optimization procedure on a paradigmatic model for the electronic transport through a quantum dot, both in the limit of vanishing Coulomb interaction and in the interacting regime. Our method enables independent control of the moments associated with charge and spin transfer, allowing for the enhancement of spin current with minimal charge current or the independent tuning of spin and charge fluctuations. These results underscore the versatility of our approach, which can be applied to a broad class of stochastic systems.

Fix a prime number $p$. Let $\mathbb{F}_q$ be a finite field of characteristic coprime to 2, 3, and $p$, which also contains the primitive $p$-th root of unity $μ_p$. Based on the works by Swinnerton-Dyer and Klagsbrun, Mazur, and Rubin, we prove that the probability distribution of the sizes of prime Selmer groups over a family of cyclic prime twists of non-isotrivial elliptic curves over $\mathbb{F}_q(t)$ satisfying a number of mild constraints conforms to the distribution conjectured by Bhargava, Kane, Lenstra, Poonen, and Rains with explicit error bounds. The key tools used in proving these results are the Riemann hypothesis over global function fields, the Erdös-Kac theorem, and the geometric ergodicity of Markov chains.

Spinors are mathematical objects susceptible to the spacetime characteristics upon which they are defined. Not all spacetimes admit spinor structure; when it does, it may have more than one spinor structure, depending on topological properties. When more than one nonequivalent spinor structure is allowed in a given spacetime, the spinors resulting from the extra structures are called exotic. In this review, we revisit the topological conditions driving the discussion about the spacetime characteristics leading to the existence and (non)uniqueness of spinor structures in a relatively comprehensive manner, accounting for step-to-step demonstrations. In the sequel, we delve into the topologically corrected Dirac operator, explicitly obtaining it and exploring the physical consequences encoded in the exotic spinor dynamics. Finally, we overview early and recent achievements in the area, pointing out possible directions within this research program.

The E. coli chemosensory lattice, consisting of receptors, kinases, and adaptor proteins, is an important test case for biochemical signal processing. Kinase output is characterized by precise adaptation to a wide range of background ligand levels and large gain in response to small relative changes in concentration. Existing models of this lattice achieve their gain through allosteric interactions between either receptors or core units of receptors and kinases. Here we introduce a model which operates through an entirely different mechanism in which receptors gate inherently far from equilibrium enzymatic reactions between neighboring kinases. Our lattice model achieves gain through a mechanism more closely related to zero-order ultrasensitivity than to allostery. Thus, we call it lattice ultrasensitivity (LU). Unlike other lattice critical models, the LU model can achieve arbitrarily high gain through time-scale separation, rather than through fine-tuning. The model also captures qualitative experimental results which are difficult to reconcile with existing models. We discuss possible implementations in the lattice's baseplate where long flexible linkers could potentially mediate interactions between neighboring core units.

Flagellar motors enable bacteria to navigate their environments by switching rotation direction in response to external cues with high sensitivity. Previous work suggested that ultrasensitivity of the flagellar motor originates from conformational spread, in which subunits of the switching complex are strongly coupled to their neighbors as in an equilibrium Ising model. However, dynamic single-motor measurements indicated that rotation switching is driven out of equilibrium, and the mechanism for this dissipative driving remains unknown. Here, based on recent cryo-EM structures, we propose that local mechanical torques on motor subunits can affect their conformation dynamics. This gives rise to a tug of war between stator-associated subunits, which produces cooperative, non-equilibrium switching responses without requiring nearest-neighbor interactions. Since subunits are effectively coupled at a distance, we call this mechanism ``Global Mechanical Coupling." Our model makes a qualitatively new prediction that the motor response cooperativity grows with the number of stators driving rotation. Re-analyzing published motor dose-response curves in varying load conditions, we find tentative experimental evidence for this prediction. Finally, we show that operating out of equilibrium enables motors to achieve high cooperativity with faster responses compared to equilibrium motors. Our results suggest a general role for mechanics in sensitive chemical regulation.

We analyze the task of estimating a multi-parameter unitary belonging to the $SU(2)$ or $SU(1,1)$ groups, in a two-bosonic-mode scenario and investigate the scaling of the precision in terms of the total particle number. For the $SU(2)$ case, the total particle number is conserved by the evolution and we discuss optimal states in fixed-$n$ subspaces, identifying eigenstates of $J_z^2$ as useful resources, even allowing simultaneous Heisenberg precision scaling for all three parameters. In the $SU(1,1)$ case instead, the conserved quantity is the particle number difference between the two modes, and we identify useful probe states in the sector with an equal number of particles in the two modes. These states are analogous to the $SU(2)$ case and would also allow simultaneous Heisenberg precision scaling for all three parameters. We then consider the more pragmatic scenario of an estimation via expectation values of time-evolved observables, which we restrict to be the first two moments of the generators. We analyze the maximal precision achievable in this setting and we find that the twin-Fock state emerges in both the $SU(2)$ and the $SU(1,1)$ cases as the only one potentially allowing Heisenberg scaling for the estimation of two out of the three parameters. As a complement, we also consider other probe states with fluctuating number of particles, with measurements restricted to quadratic expressions in the mode operators. In this scenario, simultaneous Heisenberg scaling in multiple parameters seems mostly forbidden, with the only exception being an input two-mode squeezed state for the estimation of a two-parameter $SU(2)$. This extends to the multiparameter scenario the well-established intuition that the performance of a $SU(2)$ interferometer can be enhanced by a prior $SU(1,1)$ operation.

Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a constant entropy-loss rate across scales in a renormalization-group coarse-graining setting. This framework enables us to differentiate between scale-free and scale-invariant networks, revealing distinct characteristics within each class. Furthermore, we offer a comprehensive inventory of genuinely scale-invariant networks, both natural and artificially constructed, demonstrating, e.g., that the human connectome exhibits notable features of scale invariance. Our findings open new avenues for exploring the scale-invariant structural properties crucial in biological and socio-technological systems.

We introduce an alternative route to quasiparticle self-consistent $GW$ calculations ($\mathrm{qs}GW$) on the basis of a Joint Approximate Diagonalization of the one-body $GW$ Green's functions $G(\varepsilon_n^{QP})$ taken at the input quasiparticle energies. Such an approach allows working with the full dynamical self-energy, without approximating the latter by a symmetrized static form as in the standard $\mathrm{qs}GW$ scheme. Calculations on the $GW$100 molecular test set lead nevertheless to a good agreement, at the 65 meV mean-absolute-error accuracy on the ionization potential, with respect to the conventional $\mathrm{qs}GW$ approach. We show further that constructing the density matrix from the full Green's function as in the fully self-consistent $\mathrm{sc}GW$ scheme, and not from the occupied quasiparticle one-body orbitals, allows obtaining a scheme intermediate between $\mathrm{qs}GW$ and $\mathrm{sc}GW$ approaches, closer to CCSD(T) reference values.

We introduce and analyze a natural game formulated as follows. In this one-person game, the player is given a random permutation $A=(a_1,\dots, a_n)$ of a multiset $M$ of $n$ reals that sum up to $0$, where each of the $n!$ permutation sequences is equally likely. The player only knows the value of $n$ beforehand. The elements of the sequence are revealed one by one and the player can stop the game at any time. Once the process stops, say, after the $i$th element is revealed, the player collects the amount $\sum_{j=i+1}^{n} a_j$ as his/her payoff and the game is over (the payoff corresponds to the unrevealed part of the sequence). Three online algorithms are given for maximizing the expected payoff in the binary case when $M$ contains only $1$'s and $-1$'s. $\texttt{Algorithm 1}$ is slightly suboptimal, but is easier to analyze. Moreover, it can also be used when $n$ is only known with some approximation. $\texttt{Algorithm 2}$ is exactly optimal but not so easy to analyze on its own. $\texttt{Algorithm 3}$ is the simplest of all three. It turns out that the expected payoffs of the player are $Θ(\sqrt{n})$ for all three algorithms. In the end, we address the general problem and deal with an arbitrary zero-sum multiset, for which we show that our $\texttt{Algorithm 3}$ returns a payoff proportional to $\sqrt{n}$, which is worst case-optimal.

FLASH radiotherapy (FLASH-RT) is a new modality of radiotherapy by delivering doses with ultra-high dose rates. FLASH-RT has the ability to suppress tumor growth while sparing normal tissues, known as the FLASH effect. Although FLASH effect has proved valid in various models by different ionizing radiations, the exact underlying mechanism is still unclear. This article summarizes mainstream hypotheses of FLASH effect at physicochemical and biological levels, including oxygen depletion and free radical reactions, nuclear and mitochondria damage, as well as immune response. These hypotheses contribute reasonable explanations to the FLASH effect, and are interconnected according to the chronological order of the organism's response to ionizing radiation. By collating the existing consensus, evidence, and hypotheses, this article provides a comprehensive overview of potential mechanisms of FLASH effect and practical guidance for future investigation in the field of FLASH-RT.

The wall cycle in wall-bounded turbulent flows is a complex turbulence regeneration mechanism that remains not fully understood. This study explores the potential of deep reinforcement learning (DRL) for managing the wall regeneration cycle to achieve desired flow dynamics. We integrate the StableBaselines3 DRL libraries with the open-source DNS solver CaNS to create a robust platform for dynamic flow control. The DRL agent interacts with the DNS environment, learning policies that modify wall boundary conditions to optimize objectives such as the reduction of the skin-friction coefficient or the enhancement of certain coherent structures features. Initial experiments demonstrate the capability of DRL to achieve drag-reduction rates comparable with those achieved via traditional methods, though limited to short time periods. We also propose a strategy to enhance the coherence of velocity streaks, assuming that maintaining straight streaks can inhibit instability and further reduce skin friction. The implementation makes use of the message-passing-interface (MPI) wrappers for efficient communication between the Python-based DRL agent and the DNS solver, ensuring scalability on high-performance computing architectures. Our results highlight the promise of DRL in flow control applications and underscore the need for more advanced control laws and objective functions. Future work will focus on optimizing actuation periods and exploring new computational architectures to extend the applicability and the efficiency of DRL in turbulent flow management.

We define a new class of rings parameterized by binary forms of a certain type, and give an effective lower bound for the number of such rings whose discriminant is less than a bound $X$. We also obtain a lower bound for the number of number fields whose ring of integers lies in the above class and whose discriminant is less than a bound $X$. Our results improve an estimate of Bhargava-Shankar-Wang in \cite{bhargava2022squarefree}. In particular we show the following: $\bullet$ When $n\ge 4,$ the number of rings of rank $n$ over $\mathbb{Z}$ with discriminant less than or equal to $X$ is $$\gg_n X^{\frac{1}{2}+\frac{1}{n-\frac{4}{3}}}.$$ $\bullet$ When $n\ge 6,$ the number of number fields of degree $n$ with discriminant less than $X$ is $$\gg_{n,ε} X^{\frac{1}{2} +\frac{1}{n-1} + \frac{(n-3)r_n}{(n-2)(n-1)}-ε}$$ where $r_n=\frac{η_n}{n^2-4n+3-2η_n (n+\frac{2}{n-2})}$ and where $η_n$ is $\frac{1}{5n}$ if $n$ is odd and is $\frac{1}{88n^6}$ when $n$ is even.

We identify the wave maps type nonlinearities of incompressible Hookean elastodynamics equations in Lagerangian coordinates, and iterate them in the adapted $U^2$-type spaces to prove the small data global well-posedness in the critical Besov space $\dot{B}^{\frac{n}{2}+1}_{2,1}(\mathbb{R}^n)\times \dot{B}^{\frac{n}{2}}_{2,1}(\mathbb{R}^n)\ (n\ge 2)$.

The demand of the Internet of Things (IoT) has witnessed exponential growth. These progresses are made possible by the technological advancements in artificial intelligence, cloud computing, and edge computing. However, these advancements exhibit multiple challenges, including cyber threats, security and privacy concerns, and the risk of potential financial losses. For this reason, this study developed a computationally inexpensive one-dimensional convolutional neural network (1DCNN) algorithm for cyber-attack classification. The proposed study achieved an accuracy of 99.90% to classify nine cyber-attacks. Multiple other performance metrices have been evaluated to validate the efficacy of the proposed scheme. In addition, comparison has been done with existing state-of-the-art schemes. The findings of the proposed study can significantly contribute to the development of secure intrusion detection for IIoT systems.

The stellar-mass--halo-mass (SMHM) relation is central to our understanding of galaxy formation and the nature of dark matter. However, its normalisation, slope, and scatter are highly uncertain at dwarf galaxy scales. In this paper, we present DarkLight, a new semi-empirical dwarf galaxy formation model designed to robustly predict the SMHM relation for the smallest galaxies. DarkLight harnesses a correlation between the mean star formation rate of dwarfs and their peak rotation speed -- the $\langle$SFR$\rangle$-$v_{\rm max}$ relation -- that we derive from simulations and observations. Given the sparsity of data for isolated dwarfs with $v_{\rm max} \lesssim 20$ km/s, we fit the $\langle$SFR$\rangle$-$v_{\rm max}$ relation to observational data for dwarfs above this velocity scale and to the high-resolution EDGE cosmological simulations below. Reionisation quenching is implemented via distinct $\langle$SFR$\rangle$-$v_{\rm max}$ relations before and after reionisation. We find that the SMHM scatter is small at reionisation, $\sim$0.2 dex, but rises to $\sim$0.5 dex ($1σ$) at a halo mass of $\sim$10$^9$ M$_\odot$ as star formation is quenched by reionisation but dark matter halo masses continue to grow. While we do not find a significant break in the slope of the SMHM relation, one can be introduced if reionisation occurs early ($z_{\rm quench} \gtrsim 5$). Finally, we find that dwarfs can be star forming today down to a halo mass of $\sim$2 $\times 10^9$ M$_\odot$. We predict that the lowest mass star forming dwarf irregulars in the nearby universe are the tip of the iceberg of a much larger population of quiescent isolated dwarfs.

We study an analog of the anisotropic Calderón problem for fractional Schrödinger operators $(-Δ_g)^α+ V$ with $α\in (0,1)$ on closed Riemannian manifolds of dimensions two and higher. We prove that the knowledge of a Cauchy data set of solutions of the fractional Schrödinger equation, given on an open nonempty a priori known subset of the manifold determines both the Riemannian manifold up to an isometry and the potential up to the corresponding gauge transformation, under certain geometric assumptions on the manifold as well as the observation set. Our method of proof is based on: (i) studying a new variant of the Gel'fand inverse spectral problem without the normalization assumption on the energy of eigenfunctions, and (ii) the discovery of an entanglement principle for nonlocal equations involving two or more compactly supported functions. Our solution to (i) makes connections to antipodal sets as well as local control for eigenfunctions and quantum chaos, while (ii) requires sharp interpolation results for holomorphic functions. We believe that both of these results can find applications in other areas of inverse problems.

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the $AdS/CFT$ correspondence by solving the Einstein-Abelian-Higgs model in an $AdS_4$ black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter.

In this paper, we propose a novel multiscale model reduction strategy tailored to address the Poisson equation within heterogeneous perforated domains. The numerical simulation of this intricate problem is impeded by its multiscale characteristics, necessitating an exceptionally fine mesh to adequately capture all relevant details. To overcome the challenges inherent in the multiscale nature of the perforations, we introduce a coarse space constructed using the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). This involves constructing basis functions through a sequence of local energy minimization problems over eigenspaces containing localized information pertaining to the heterogeneities. Through our analysis, we demonstrate that the oversampling layers depend on the local eigenvalues, thereby implicating the local geometry as well. Additionally, we provide numerical examples to illustrate the efficacy of the proposed scheme.

We study bacterial diffusion in disordered porous media. Interactions with obstacles, at unknown locations, make this problem challenging. We approach it by abstracting the environment to cell states with memoryless transitions. With this, we derive an effective diffusivity that agrees well with simulations in explicit geometries. The diffusivity is non-monotonic, and we solve the optimal run length. We also find a rescaling that causes all of the theory and simulations to collapse. Our results indicate that a small set of microscopic features captures bacterial diffusion in disordered media.

The derived algebra of a symmetrizible Kac-Moody algebra $\lie g$ is generated (as a Lie algebra) by its root spaces corresponding to real roots. In this paper, we address the natural reverse question: given any subset of real root vectors, is the Lie subalgebra of $\lie g$ generated by these again the derived algebra of a Kac-Moody algebra? We call such Lie subalgebras root generated, give an affirmative answer to the above question and show that there is a one-to-one correspondence between them, real closed subroot systems and $π$-systems contained in the positive system of $\lie g$. Finally, we apply these identifications to all untwised affine types in order to classify symmetric regular subalgebras first introduced by Dynkin in the finite-dimensional setting. We show that any root generated subalgebra associated to a maximal real closed subroot system can be embedded into a unique maximal symmetric regular subalgebra.

A positive integer $k$ is called a magic constant if there is a graph $G$ along with a bijective function $f$ from $V(G)$ to first $|V(G)|$ natural numbers such that the weight of the vertex $w(v) = \sum_{uv \in E}f(v) =k$ for all $v \in V$. It is known that all odd positive integers greater equal $3$ and the integer powers of $2$, $2^{t}$, $t \ge 6$ are magic constants. In this paper we characterise all positive integers which are magic constants.

Given a complex balanced manifold $X$ and a compact complex manifold $S$ equipped with a positive volume form $dV>0$ and satisfying an extra condition such that $\mbox{dim}\,S\geq\mbox{dim}\,X -1$, we construct a moment map for the action of the Lie group of biholomorphisms of $S$ that preserve $dV$ onto the space of holomorphic maps $f:S\longrightarrow X$ that satisfy a certain condition with respect to the Bott-Chern cohomology class of the balanced metric of $X$. The purpose is twofold: to study such maps as a possible addition to some very recent hyperbolicity notions involving holomorphic maps with a certain type of growth from some $\C^p$, rather than $S$, to $X$; and to lay the groundwork for a possible future construction of balanced quotients as an analogue of the classical symplectic quotients.

We further develop the abstract representation theory of affine Hecke algebras with arbitrary positive parameters. We establish analogues of several results that are known for reductive p-adic groups. These include: the relation between parabolic induction/restriction and Hermitian duals, Bernstein's second adjointness and generalizations of the Langlands classification. We check that, in the known cases of equivalences between module categories of affine Hecke algebras and Bernstein blocks for reductive p-adic groups, such equivalences preserve Hermitian duality. We also initiate the study of generic representation of affine Hecke algebras. Based on an analysis of the Hecke algebras associated to generic Bernstein blocks for quasi-split reductive p-adic groups, we propose a fitting definition of genericity for modules over affine Hecke algebras. With that notion we prove special cases of the generalized injectivity conjecture, about generic subquotients of standard modules for affine Hecke algebras.

Context. The game industry is increasingly growing in recent years. Every day, millions of people play video games, not only as a hobby, but also for professional competitions (e.g., e-sports or speed-running) or for making business by entertaining others (e.g., streamers). The latter daily produce a large amount of gameplay videos in which they also comment live what they experience. But no software and, thus, no video game is perfect: Streamers may encounter several problems (such as bugs, glitches, or performance issues) while they play. Also, it is unlikely that they explicitly report such issues to developers. The identified problems may negatively impact the user's gaming experience and, in turn, can harm the reputation of the game and of the producer. Objective. In this paper, we propose and empirically evaluate GELID, an approach for automatically extracting relevant information from gameplay videos by (i) identifying video segments in which streamers experienced anomalies; (ii) categorizing them based on their type (e.g., logic or presentation); clustering them based on (iii) the context in which appear (e.g., level or game area) and (iv) on the specific issue type (e.g., game crashes). Method. We manually defined a training set for step 2 of GELID (categorization) and a test set for validating in isolation the four components of GELID. In total, we manually segmented, labeled, and clustered 170 videos related to 3 video games, defining a dataset containing 604 segments. Results. While in steps 1 (segmentation) and 4 (specific issue clustering) GELID achieves satisfactory results, it shows limitations on step 3 (game context clustering) and, above all, step 2 (categorization).